![1.1 Electromechatronics
Electromechatronics, introduced in the 1980s by Professor Yuri P. Koskin of the
Department of Electromechanics and Electromechatronics of the Saint Petersburg
State Electrical Engineering University, Russia, corresponds to the integration of
electromechanical and electronic areas in a single technical/scientific field of
electrical engineering [1].
Electromechatronics, term formed by agglutination, according to the following
expression [1]
ELECTROMECHATRONICS ¼ ELECTROMECHANICS þ ELECTRONICS
(1.1)
brings together the areas of electrical machines, drives, and their associated power
electronics, namely, converters and capacitors.
1.2 Fault diagnosis
A fault may be defined as the condition of an equipment, material, or system,
characterized by the termination of the ability to fully perform the required
functions.
The following main categories of faults are distinguished [2]:
Catastrophic – Characterized by a sudden occurrence and involving the total
and immediate stoppage of the functions performed until then.
Evolutionary – Associated with a gradual development and affecting, at first
only partially, the performance of the functions.
Intentional – Deliberately caused and involving the interruption of the per-
formance of the functions, regardless of the registered condition.
Evolutionary faults are, therefore, the most appropriate to the application of early
diagnostic methods.
Similarly to the clinical diagnosis, the diagnosis of faults involves the char-
acterization of equipment state condition through the consideration of the symp-
toms it manifests. Thus, four intrinsic aspects to the diagnostic process are
distinguished, as shown in Figure 1.1.
The detection of faults is the primary objective of the monitoring of parameters
indicative of the fault occurrence. However, consideration of the remaining aspects
presented in Figure 1.1 is not possible through the exclusive use of monitoring.
Indeed, the detailed analysis of the information contained in the various indicators
of the occurrence of faults becomes crucial for the development of methods capable
of providing a complete and reliable diagnosis. Additionally, fault analysis, making
possible the understanding of the various phenomena associated to a fault occur-
rence, also becomes essential [2].
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![An exhaustive description of both signal-processing-based fault diagnostic algo-
rithms and model-based-fault diagnostic algorithms is provided, as well as com-
prehensive summary of the most relevant features and limitations of the algorithms
pertaining to each category. Next, the most relevant fault-tolerant architectures and
control strategies developed to overcome the negative effects of the occurrence of
faults in DC–DC converters are presented. Their applicability, main merits, and
drawbacks are addressed and a comparative analysis of their main features is also
provided.
Acknowledgment
This work was supported by the European Regional Development Fund (ERDF)
through the Operational Programme for Competitiveness and Internationalization
(COMPETE 2020), under Project POCI-01-0145-FEDER-029494, and by National
Funds through the FCT – Portuguese Foundation for Science and Technology,
under Projects PTDC/EEI-EEE/29494/2017 and UID/EEA/04131/2013.
References
[1] Koskin, Y. P.: ‘The electromechatronics as the scientifical background of
electromechanical converters and electronical components integration.’ Pro-
ceedings of the International Conference on Electrical Machines, Vigo,
Spain, 1996, Vol. III, pp. 513–518.
[2] Cardoso, A. J. M.: Fault Diagnosis in Three-Phase Induction Motors (in
Portuguese), Coimbra, Editora, 1991, pp. 34–35.
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![Chapter 2
Voltage-source inverter-fed drives
Jorge Oliveira Estima1
and Konstantinos N. Gyftakis1,2
2.1 Condition monitoring, fault diagnosis and prognosis
of electrical machines
2.1.1 Introduction
Electrical machines have infiltrated and supported our everyday modern life.
Electrical machines produce electric power working as generators or transform it
into mechanical power operating as motors. Electrical machines are operating
devices in power plants, wind farms, pumps, industry applications, cranes, con-
veyors, belts, mills, transportation and many other applications. So, it is to be
expected that electrical machines are related to huge financial variables as well as
safety and reliability.
Although electrical machines are robust devices, faults may appear and inter-
rupt their working life cycle in many ways. Faults can be classified in three cate-
gories: stator related, rotor related and mechanical.
Stator faults include electrical failures which means short-/open-circuits, as well
as inter-turn short-circuits which is a special case of short-circuits. Supply imbalance
belongs in this category also. Other stator faults are iron core related ones.
Similarly, rotor faults may be of electrical nature when the rotor has windings
and iron related ones. Other special faults are broken/cracked rotor bars/end-rings
for cage induction motors, permanent magnet cracks or demagnetisation for per-
manent magnet motors and commutator/slip rings/brushes failures for all machines
with rotor winding.
Mechanical faults mainly include bearing failures. However, in this category,
we can also include issues with the cooling fan as well as irregularities with the
connected mechanical load such as overloading and load oscillations.
Several surveys have been carried out in the past leading to percentages dis-
tributions of machine failures [1–3]. Representative results are shown in Figure 2.1.
It is interesting that three out of four failures in low voltage motors are bearings
related, while stator faults account for only 9% of total faults. The distribution is
1
CISE – Electromechatronic Systems Research Centre, Universidade da Beira Interior, Portugal
2
School of Computing, Electronics and Mathematics and the Research Institute for Future Transport and
Cities, Coventry University, UK](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-26-320.jpg)
![machines a fault will automatically create an asymmetry in the magnetic field. This
asymmetry will pass on to various electromagnetic variables like the currents,
voltages, magnetic flux, electric and mechanical power, torque and speed. So, the
diagnostics engineer needs to monitor and analyse some of the above variables
and detect any divergence from the expected healthy machine characteristics.
Figure 2.2 illustrates the most important characteristics of the diagnosis procedure.
2.1.3 Fault diagnosis of electrical machines
As there are many different machines, drives and applications, it is only natural that
there is also a plethora of electrical machines faults and diagnostic methods.
Amongst them the most favourable is the motor current signature analysis (MCSA)
which is the analysis of the stator current harmonic index [4,5]. Most define the
MCSA as the monitoring and spectral analysis of the stator current at steady state.
Despite the method’s origins, the name is very generic and should include the
analysis of the stator current spectra under transient operation also. Anyway, this
method has become favourable due to its unique characteristics such as remote
monitoring [6] (Figure 2.3), low implementation costs and equipment, and con-
tinuous and online monitoring capability. However, many other methods have been
proposed and they rely on the monitoring of other variables such as the magnetic
flux [7], torque [8], electric power [9], voltage [10], etc. As a priority, in this
chapter, all MCSA formulas will be given for most common faults. However, other
methods will be also discussed and analysed.
To facilitate reading and comprehension, this section will be organised in the
following strategy. First, faults that are common in both induction and permanent
magnet machines will be discussed and the different diagnostic strategies applied
for each machine will be properly analysed. Then faults uniquely existing in dif-
ferent machines will be discussed.
Diagnostic procedure
Speed of
diagnosis
Severity
estimation
Financial
cost
On/offline Intrusion
Monitoring
equipment
Decision
making
Manual
Automatic
No
Yes
Production
Interrupted? Level?
Electrical
machine
Prognosis
ability?
Service and
repair
Replacement
with new one
Complexity?
Permanently
installed
Portable
Is it possible?
Is it faster than
the evolution
of the fault?
Figure 2.2 Characteristics of the diagnostic procedure
Voltage-source inverter-fed drives 9](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-28-320.jpg)
![2.1.3.1 The eccentricity fault
Eccentricity is the condition where the rotor is abnormally positioned inside the
stator, and as a consequence, the air-gap around the rotor circumference is not
symmetrical [11]. There are mainly two types of eccentricity: static and dynamic.
In both eccentricity types, the geometrical centre of the rotor is different than
that of the stator. Moreover, in the case of the static eccentricity, the centre of rota-
tion is fixed in space and coincides with the rotor geometrical centre [Figure 2.4(a)].
However, in the case of the dynamic eccentricity, the centre of rotation does not
have a fixed location but constantly changing in space over time [Figure 2.4(b)].
A combination between the two above-mentioned conditions is called mixed
eccentricity. It is important to note that some inherent mixed eccentricity always
exists even in new electrical machines [12]. The maximum permitted level of
inherent eccentricity is 10%, although in most cases, manufacturers put an effort to
keep it significantly less than that.
The static eccentricity is a fault usually introduced during the manufacturing
stages of the motor. It can be caused by the ovality of the stator or by the mis-
placement of the rotor in the stator. On the other hand, the dynamic eccentricity is
usually related to bearing failures or bent motor shaft. If not detected at an early
stage, it will evolve and lead to the rubbing between rotor and stator, which will
cause irreparable damage and possible deformation of the electrical machine iron
core (Figure 2.5). Usually, deformation of an electrical machine’s iron core leads to
long service period and is expensive.
The eccentricity causes an asymmetry of the machine’s air-gap geometry,
which directly influences the air-gap permeance and will cause an asymmetry in
the machine’s rotating magnetic field. That asymmetry is expressed via enhanced
higher harmonics in the machine’s electromagnetic and mechanical operating
variables and characteristics.
Figure 2.3 Remote monitoring of motor currents. 2017–2018 IEEE. Reprinted,
with permission, from Reference [6]
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![Induction motors
For induction motors, the static or dynamic eccentricity fault can be detected
through the monitoring of signatures in the stator current located at frequencies
[14]:
fecc IM ¼ kR nd
ð Þ
1 s
p
n
fs (2.1)
where R is the rotor slot number, k is the integer, s is the slip, p is the pole pairs, n is
the stator harmonic ranks, fs is the supply frequency and nd is an integer which is
zero for static eccentricity and non-zero for dynamic eccentricity.
(a) (b)
Figure 2.5 Major mechanical damage to the stator due to rotor rubbing. Not
repairable unless (a) the core is dismantled and repaired and (b) the
core is restacked or replaced [13] (with permission from EASA)
OR OS OR OS OR OS OR OS
OR
OR
OS
OS
OS
OR
OR OS
(a)
(b)
Figure 2.4 Four different instances of the rotor rotation for (a) static and
(b) dynamic eccentricity
Voltage-source inverter-fed drives 11](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-30-320.jpg)
![Furthermore, the following formula [11] has also been proposed to detect the
mixed eccentricity fault in the low-frequency area of the stator current:
fecc IM2 ¼ fs fr (2.2)
where fr ¼ 1 s
ð Þ=p
½ fs, that is the mechanical rotation frequency.
It is important to note that formula (2.1) does not always offer reliable
results for the cases of only-dynamic or only-static eccentricity diagnosis [15].
Previous works have pointed out that diagnosis is possible only for certain com-
binations between the rotor slot and the pole pair numbers [16,17]. To be more
specific, if nd ¼ 0; k ¼ 1 then formula (2.1) transforms into:
fPSH ¼ R
1 s
p
n
fs (2.3)
Equation (2.3) corresponds to the location of the principle slot harmonics (PSH) in
the stator current frequency spectrum. Induction motors with a rotor slot number
multiple of the pole pair number produce such harmonics in the line current. For
those motors, the only-static and only-dynamic eccentricity faults cannot be
detected because the fault signatures are located at the same frequencies as the
normally existing PSH.
However, for non-PSH induction motors, if the rotor slot number is even, it is
possible to monitor the only-static and only-dynamic eccentricities at low or no-
load operation. Formula (2.1) is very reliable for non-PSH induction motors with
odd rotor slot numbers [15].
Figure 2.6 illustrates the application of MCSA to detect a mixed eccentricity
faulty condition in a four-pole cage induction motor with 28 rotor bars.
Permanent magnet machines
When there is eccentricity in permanent magnet (PM) machines, a portion of the
stator is closer to the PM of the rotor, thus generating a net attraction force acting
on the rotor [19]. As a result, an unbalanced magnetic force is generated between
the rotor and the stator. Unbalanced forces may be the most troubling problem
when brought by rotor eccentricity. That is because they may cause significant
levels of vibration and noise which accelerates the motor degradation [20].
Previous studies have shown that eccentricity affects interior PM (IPM) motors
differently than surface mounted PM (SPM) motors [21]. It has been shown that,
the eccentricity distorts the air-gap magnetic flux density more in the case of the
IPM motors. In the same work, authors came to the conclusion that the magnetic
unbalanced forces increase linearly due to relatively small eccentricity ratio in SPM
motors. However for the IPM motors, they increase significantly and non-linearly
due to severe magnetic saturation with the eccentricity level.
Furthermore, the eccentricity effects are different between symmetrical and
asymmetrical PM machines [20]. Rotor eccentricity has a minor impact on
asymmetric motors in terms of the magnitude of the radial force. Low detent
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![torque, the primary reason for using asymmetric motors, is magnified if rotor
eccentricity is involved, so the importance of manufacturing precision cannot
be overstressed.
One more important finding was reported in [22]. The results reveal that the
static eccentricity and the uneven magnetisation cause exactly the same harmonic
0
–50
–100
0
–50
–100
0 50
Fundamental
PSH
PSH
f[0.5(R–1)(1–s)–1]
f[0.5(R+1)(1–s)–1]
f[0.5(R+2)(1–S)–1]
f[0.5(R+3)(1–S)–1]
Fundamental
f+3fr
f+2fr
f+fr
4fr–f
3fr–f
f–fr
f–2fr
100 150
0 50
700
–120
–100
PSD
(dB)
PSD
(dB)
PSD
(dB)
–80
–60
–40
–120
–100
PSD
(dB)
–80
–60
–40
720 740 760 780 800 820 840 860
700 720 740 760 780
Frequency (Hz)
Frequency (Hz)
(a)
(b)
800 820 840 860
100 150
Figure 2.6 Simulated, normalised spectra of the line current of a four-pole
induction machine with 28 rotor slots under load (a) around the
fundamental and (b) around the PSH. Upper: healthy. Lower: with
mixed eccentricity (41.37% SE, 20.69% DE). 2017–2018 IEEE.
Reprinted, with permission, from Reference [18]
Voltage-source inverter-fed drives 13](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-32-320.jpg)
![index of the unbalanced magnetic force. However, in dynamic eccentricity condi-
tions, the amplitude of the DC component has been reported to rise significantly.
Regarding the diagnosis of eccentricity, formula (2.4) was initially proposed
for static eccentricity diagnosis via the stator current harmonic index [23]. Further
investigation led to the conclusion that the formula is also reliable for the cases of
dynamic and mixed eccentricity [24,25]. Results from the application of (2.4) can
be seen in Figure 2.7:
fecc PM ¼ 1
2k 1
ð Þ
p
fs (2.4)
where k is the integer, p is the pole pairs and fs is the supply frequency.
In a later work, the following formula was also proposed, the concept of which
is very similar to that of (2.2). That means examination of the sidebands around the
0
–20
–40
–60
PSD
(dB)
–80
–100
–120
0 20 40 60 80
Frequency (Hz)
Frequency (Hz) Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
100 120 140
0
–20
–40
–60
PSD
(dB)
–80
–100
–120
20 40 60 80 100 120 140
0
–20
–40
–60
0.25fs
1.25fs 2.25fs
0.25fs
1.25fs 2.25fs
0.25fs
1.25fs
2.25fs
0.25fs 1.25fs
2.25fs
0.25fs 1.25fs 2.25fs
PSD
(dB)
–80
–100
–120
20 40 60 80 100 120 140
0
–20
–40
–60
PSD
(dB)
–80
–100
–120
20 40 60 80 100 120 140
0
–20
–40
–60
PSD
(dB)
–80
–100
–120
20 40 60 80 100 120 140
0
–20
–40
–60
PSD
(dB)
–80
–100
–120
20 40 60 80 100 120 140
(a) (c)
(d)
(f)
(b)
(e)
Figure 2.7 Normalised line current spectra of an eight-pole, 50 Hz PM
synchronous motor where: (a) healthy, (b) with 30% SE, (c) with 40%
DE, (d) with 30% SE and 40% DE, (e) experimental result for 50% DE
and (f) experimental result for 50% SE. 2017–2018 IET. Reprinted,
with permission, from Reference [28]
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![fundamental stator current harmonic located at the mechanical rotation
frequency [26]:
fecc PM2 ¼ 1
1
p
fs (2.5)
A different later work though pointed out that (2.5) describes harmonics produced
not only by eccentricity but also demagnetisation and rotor and load imbalances
[27], which does not allow reliable discrimination and identification of the exact
fault condition.
2.1.3.2 The stator inter-turn fault
Stator electrical faults can be either short or open-circuit failures. Short-circuit
faulty conditions include phase-to-phase and phase-to-ground short-circuits. How-
ever, in both open and short-circuit conditions, the machine will suffer from high
currents and will be severely damaged, thus many protection methods exist the aim
of which is to trip the protection relays and disconnect the machine immediately
when the fault appears. So, the above-mentioned conditions are not to be discussed
any further in this section as they are not related to early fault stages where the
prompt diagnosis is meaningful. Instead, this section will focus on the stator inter-
turn faults.
Stator inter-turn faults happen between stator winding wires of the same phase
because of degradation of the insulation materials [29,30]. The stator inter-turn
fault is considered an early fault condition which will evolve into an actual short-
circuit and lead to machine damage. However, the term ‘‘early’’ can be misleading
because it has been shown that this fault evolves very fast (in seconds [31]) into
higher severity levels leading to an actual short-circuit condition and triggering the
protection relays to disconnect the machine. Different degradation mechanisms
might affect the end-winding portion or the slot portion [32]. In addition, it should
be noted that the time progression and extent of the damage depends on the location
of the fault and the original number of shorted turns [33].
In order to understand the motor winding configuration in the case of an inter-
turn fault, Figure 2.8 is presented, and one can see two neighbouring stator slots
where the winding turns go and then the two neighbouring stator slots where
the same winding turns return. Each slot’s conductors/wires are divided in
three groups. In the first and last slots, there are k turns, one single turn and j turns.
In the inner slots, there are m turns, a single turn and n turns. It is supposed that the
short-circuit happens between the points A and B. Then it is evident that, from left
to right, the four slots contain k þ 1, n, n þ 1 and k wires, respectively, which belong
to the healthy part of the winding. The other wires, which mean j, 1 þ m, m and j þ
1, form a closed loop where the short-circuit current will develop. It is to be noted
that when modelling this condition, a small resistance should be added between the
points A and B to account for the contact resistance between the shorted turns.
Typically, the contact resistance value is between 0.1 and 1 W. Figure 2.9 illustrates
a real case of an inter-turn fault which happened to an industrial induction motor.
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![double the supply frequency [34]. The consequent speed ripple induced harmonic
index back to the stator with frequency three times the fundamental one. Due to the
above, the stator current will experience an increase of the third harmonic [34–37].
This is clearly shown in Figure 2.10. Saturation plays an important role as it can
enhance the amplitude increase of the third harmonic in the stator current [37].
However, the third harmonic increase is also associated with other imbalances
[38] such as asymmetrical three-phase voltage supply, inherent asymmetry between
the three phase windings, high resistance connections which lead to unbalanced
phase currents, etc. Moreover, it was shown that the increase of the third harmonic
800Hz
(b)
(a)
0Hz
–95
dBVrms
–95
dBVrms
10
dB
/div
dB Mag
10
dB
/div
dB Mag
A: CH1 Lin Spec X:469 Hz Y:-72.1276 dBVrms
X:568 Hz Y:-69.8802 dBVrms
800Hz
0Hz
5
dBVrms
A: CH1 Lin Spec
5
dBVrms
Figure 2.10 Spectral content of the line current of a: (a) healthy motor and (b) motor
with stator inter-turn fault operating under s ¼ 0.028. 2017–2018
IEEE. Reprinted, with permission, from Reference [34]
Voltage-source inverter-fed drives 17](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-36-320.jpg)
![in the stator current does not have a monotonic relation to the fault level severity
[39]. So, the monitoring of the third harmonic is not deemed as very reliable for
very low severity levels of inter-turn short-circuits as it may lead to a false negative
alarm.
Practically, when there is a stator inter-turn fault, the created asymmetrical
rotating magnetic field will induce asymmetrical currents in the rotor. As a result,
rotor slot related harmonics will rise. So, past works [40] have proposed the fol-
lowing formula for the detection of stator inter-turn faults:
fsc IM ¼ kR
1 s
p
2nsa n
fs; k 2 N (2.6)
where R is the rotor slot number, k is the integer, s is the slip, p is the pole pairs,
n is the stator harmonic ranks, fs is the supply frequency and nsa is the rank of the
saturation harmonics.
An interesting method able to detect the fault existence as well as the faulty
phase with low computational time is the Park’s vector approach (PVA) [41]. The
method relies on the analysis of the Park’s vector components id; iq as follows:
id ¼
ffiffiffi
2
p
ffiffiffi
3
p ia
1
ffiffiffi
6
p ib
1
ffiffiffi
6
p ic (2.7)
iq ¼
1
ffiffiffi
2
p ib
1
ffiffiffi
2
p ic (2.8)
Under ideal conditions, the three phase currents in (where n ¼ a, b, c) lead to a
Park’s vector with the following components:
id ¼
ffiffiffi
6
p
2
iM sin wt (2.9)
iq ¼
ffiffiffi
6
p
2
iM sin wt
p
2
(2.10)
The corresponding representation is a circular locus centred at the origin of the
coordinates. Under abnormal conditions, (2.9) and (2.10) are no longer valid, and
consequently the observed picture differs from the reference pattern. This can be
seen in Figure 2.11 where id is on the x axis and iq on the y axis, respectively. The
displacement of the locus reveals the faulty phase.
However, the PVA on its own cannot offer an easy measure of determining the
fault level severity with accuracy. That is because the determination of the locus
angle shift is influenced by other parameters as well. This is why, the method
evolved into the extended PVA (EPVA) which relies on the monitoring of the
frequency spectra of the Park’s vector modulus [42]. It was found that, the stator
inter-turn fault gives rise to harmonics located at twice the supply frequency in the
Park’s vector modulus spectra (Figure 2.12).
18 Diagnosis and fault tolerance](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-37-320.jpg)
![Permanent magnet machines
PM machines are widely used in various special applications where high power
density and efficiency is required, while restrictions on the size of the motor apply,
such as electric vehicle propulsion, aerospace applications, etc. Due to their critical
role associated with safety, prompt and reliable diagnosis is required. This makes
the inter-turn short-circuits failure quite a timely and challenging issue because it is
the type of fault that progresses fast leading to undesired motor breakdown. It was
shown that the inter-turn fault may cause excessive heat that is proportional to the
square of the circulating current in the shorted turns [43].
This type of the PM machine plays an important role for the impact of the
inter-turn short-circuit faults. Past contributions have shown that the short-circuit
current is lower in IPM than SPM machines [44]. This is crucial for the evolution
time of the fault. The short-circuit current is relatively high and will generate heat.
This will lead not only to extension of the inter-turn fault including more and
more turns until the motor breakdown bus also demagnetisation of the PMs [45]
(Figure 2.13). However, the required motor toque is the same which leads to higher
(a) (b) (c)
Figure 2.11 Experimentally derived Park’s vector pattern for (a) healthy motor,
(b) motor with 18 shorted turns in Phase A and (c) motor with 18
shorted turns in Phase B. 2017–2018 IEEE. Reprinted, with
permission, from Reference [41]
0
3
2
1
Amplitude
(A)
Amplitude
(A)
Amplitude
(A)
3
2
1
3
2
1
20 40 60 80
Frequency (Hz) Frequency (Hz) Frequency (Hz)
(a) (b) (c)
100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120
Figure 2.12 EPVA signature corresponding to: (a) healthy motor, (b) motor with
12 shorted turns and (c) motor with 36 shorted turns. 2017–2018
IEEE. Reprinted, with permission, from Reference [42]
Voltage-source inverter-fed drives 19](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-38-320.jpg)
![1.0
[T]
0.8
0.6
0.4
0.2
0.0
14
mm
1
2
3
4
5
6
t
=
32.2
ms
t
=
35.6
ms
Front
Back
Rotating
direction
t
=
42
ms
t
=
46
ms
t
=
48.9
ms
Demagnetisation
part
Weak
point
Normal
1.0
0.5
0.0
0
7
14
PM
length
[mm]
Normal
0
7
14
PM
length
[mm]
t
=
32.2
ms
0
7
14
PM
length
[mm]
t
=
35.6
ms
0
7
14
PM
length
[mm]
Br
=
Residual
flux
density
of
PM
t
=
42
ms
(a)
(b)
0
7
14
PM
length
[mm]
t
=
46
ms
Br
of
PM
[T]
1.0
0.5
0.0
Br
of
PM
[T]
1.0
0.5
0.0
Br
of
PM
[T]
1.0
0.5
0.0
Br
of
PM
[T]
1.0
0.5
0.0
Br
of
PM
[T]
1.0
0.5
0.0
Br
of
PM
[T]
6
0
7
14
PM
length
[mm]
t
=
48.9
ms
1
6
5
4
3
2
Figure
2.13
(a)
Irreversible
demagnetisation
progress
of
six
PMs
while
the
BLDC
machine
operates
under
inter-turn
short-circuit
fault.
(b)
Residual
flux
density
of
the
sixth
PM
over
time.
2017–2018
IEEE.
Reprinted,
with
permission,
from
Reference
[45]](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-39-320.jpg)
![current to serve the load need. Higher current will lead to more heating accelerating
both demagnetisation and windings insulation degradation.
Similar to induction motors, the third line current harmonic as well as the other
odd triplet harmonics are expected to rise with the inter-turn fault due to the three
phase currents asymmetry, while absent in healthy motors [46]. This is shown in
Figure 2.14. At the same time, it can be seen that the negative third harmonic
frequency increases only in the case of inter-turn fault.
Furthermore, formula (2.11) has been proposed [44] for the detection of inter-
turn faults in PM machines through the spectral analysis of the stator current at
steady state. It is evident that for k ¼ 1, the formula depicts the fault related
80
40
0
–40
Line
current
(dB)
Line
current
(dB)
Line
current
(dB)
–80
80
40
0
–40
–80
80
40
0
–40
–80
–1.8
–9f –7f –5f –3f –f f 3f 5f 7f 9f
–9f –7f –5f –3f –f f 3f 5f 7f 9f
–9f –7f –5f –3f –f f 3f 5f 7f 9f
–1.2 –0.6 0.0
Frequency (kHz)
(a)
(b)
(c)
Frequency (kHz)
0.6 1.2 1.8
f = 175 Hz
f = 175 Hz
f = 175 Hz
–1.8 –1.2 –0.6 0.0 0.6 1.2 1.8
Frequency (kHz)
–1.8 –1.2 –0.6 0.0 0.6 1.2 1.8
Figure 2.14 Line current frequency spectra of a PM motor at a rated speed and
full load where: (a) healthy motor under balanced supply, (b) healthy
motor under imbalanced supply and (c) motor with inter-turn fault
under balanced supply. 2017–2018 IEEE. Reprinted, with
permission, from Reference [46]
Voltage-source inverter-fed drives 21](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-40-320.jpg)
![harmonics around the fundamental stator current harmonic. An example from the
application of the formula in a real PM motor is shown Figure 2.15:
fitsc PM ¼ k
2m þ 1
p
fs ; k; m 2 N (2.11)
2.1.3.3 Broken rotor bars or end-rings
There are two types of rotor squirrel cages of induction motors; fabricated and cast.
Usually, low voltage induction motor rotors are cast aluminium, and high voltage
ones are fabricated from copper. Medium voltage induction motor rotors can be of
0
–20
–40
–60
–80
PSD
of
stator
current
(dB)
PSD
(dB)
–100
–120
–140
0
–20
–40 (1–3/P)fs
(1–1/P)fs (1+1/P)fs
(1+3/P)fs
(1+5/P)fs
(1+7/P)fs
(1–3/P)fs (1–1/P)fs (1+1/P)fs
(1+3/P)fs (1+5/P)fs
(1+7/P)fs
–60
–80
–100
–120
–140
0 20 40 60 80
Frequency (Hz)
(a)
(b) Frequency (Hz)
100 120 140
0 20 40 60 80 100 120 140
Figure 2.15 Normalised line-current spectra of full-load PMSM in (a) healthy
and (b) motor with 1 short-circuited turn. 2017–2018 IEEE.
Reprinted, with permission, from Reference [44]
22 Diagnosis and fault tolerance](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-41-320.jpg)
![both types. Usually aluminium rotors have skewed bars, while in copper rotors, the
bars are usually parallel to the shaft. Another difference between them is that in
aluminium rotors, there is no insulation between the bars and the rotor iron core. On
the other hand, in copper rotors the bars are firstly insulated and then placed inside
the slots of the iron core. Those differences play an important role in the area of
diagnostics as it will be discussed below.
A crack or breakage in an aluminium cage usually originates from improper
casting which allows air bubbles inside the cage. This phenomenon is known as
porosity [47]. These air-bubbles result in local high-resistance areas that cause
hotspots and make the cage prone to local breakage [48].
On the other hand, copper rotors bars usually break due to thermal and
mechanical stresses. First, the thermal stress will cause thermal expansion of the
bars which might disconnect from the end-ring. Second, the mechanical stresses
such as vibrations and frequent start-ups may lead to the same result [49]. However,
the co-existence of both is probably the reason while the one mechanism enhances
the catastrophic effects of the other.
When there is a broken rotor bar, the adjacent bars are overcharged, thus
expected to break next [50,51]. This is shown in Figure 2.16. This is the usual case
in aluminium rotors; however, multiple cases of non-adjacent broken rotor bars
have been reported in large industrial induction motors [52]. Broken rotor bars do
not normally result in an immediate failure of the motor. If the fault goes unnoticed
and enough bars break then there is a chance that the motor will not be able to
develop enough starting torque to accelerate from stall. However, in the past, some
catastrophic failures have been reported like the one shown in Figure 2.17 where
the rotor bars bent and severely damaged the stator winding [53].
When there is a broken rotor bar fault, two counter rotating magnetic fields are
created with slip frequencies sf s and sf s. The first one does not interact with
the stator, while the second one induces components of frequency 2sf s back to
the stator windings. As a result, the broken rotor bar fault can be identified in the
stator current spectrum via the existence of harmonics at 1 2s
ð Þfs [55]. Further-
more, due to the speed ripple effect, a second broken bar fault harmonic appears to
the right of the fundamental frequency at frequency: 1 þ 2s
ð Þfs [56]. This interac-
tion between the mechanical and electromagnetic quantities continues, and as a
result multiple fault-related signatures are created at equal frequency distances 2sf s
from one another. As a result, the following formula has been proposed for the
identification of the broken rotor bar fault around the fundamental stator current
frequency:
fbb ¼ 1 2ks
ð Þfs; k 2 N (2.12)
The stator current is rich in harmonics due to the saturation and other interacting
phenomena. The result is that odd multiples of the supply frequency exist in the
stator current. Those higher harmonics create additional magnetic fields inside the
induction motor which are rotating with higher speeds due to their higher fre-
quencies. Those magnetic fields also interact with the broken rotor bar fault, and as
Voltage-source inverter-fed drives 23](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-42-320.jpg)
![a result more signatures are created. The following formula has been proposed to
include the broken bar fault sidebands at higher harmonics [57]:
fbb2 ¼
k
p
1 s
ð Þ s
fs;
k
p
2 N (2.13)
Figure 2.18 illustrates the application of (2.12) and (2.13) in order to detect a
broken rotor bar fault using the stator current frequency spectra. It is evident that
the fault creates specific fault-related harmonic sidebands around the odd multiples
of supply frequency.
0.0
10.0
8.0
6.0
4.0
2.0
–2.0
–4.0
–6.0
–8.0
–10.0
0.0
10.0
8.0
6.0
4.0
2.0
–2.0
–4.0
–6.0
–8.0
–10.0
0.0
20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0
Geometrical angle
200.0 220.0 240.0 260.0 280.0 300.0 320.0 340.0 360.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0
Geometrical angle
(a)
(b)
Current
density
(A/mm
2
)
Current
density
(A/mm
2
)
200.0 220.0 240.0 260.0 280.0 300.0 320.0 340.0 360.0
Broken bar
Figure 2.16 Spatial distribution of the amplitude of the current density of the
rotor bars along the rotor circumference for (a) healthy machine
and (b) machine model with one broken bar. 2017–2018 IEEE.
Reprinted, with permission, from Reference [54]
24 Diagnosis and fault tolerance](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-43-320.jpg)
![220
40
0
–100
(1 – 6s)fs
(1 – 4s)fs
–50
–150
Amplitude
(dB)
42 44 46 48 50 52 54 56 58 60
240
5fs – 6sfs 5fs – 4sfs 7fs – 8sfs 7fs – 6sfs
260 280 300 320 340 360
Frequency (Hz)
Frequency (Hz)
(a)
(b)
(1–2s)fs (1 + 2s)fs
(1 + 4s)fs
(1 + 6s)fs
Figure 2.18 Comparative frequency spectra of the healthy induction motor
(dashed) and one with a broken bar fault (solid) around (a) the
fundamental stator current harmonic and (b) the fifth (250 Hz)
and seventh (350 Hz) stator current harmonics (FEM result)
(a) (b)
Figure 2.17 Forced outage of 3.3-kV, 450-kW gasoline transfer pump induction
motor due to rotor bar damage. (a) Rotor bar detachment from end
ring and damage in rotor core due to arcing. (b) Damage in stator
end winding due to protrusion of rotor bar. 2017–2018 IEEE.
Reprinted, with permission, from Reference [53]
Voltage-source inverter-fed drives 25](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-44-320.jpg)
![Lately, a lot of work has been focused on broken rotor bar fault detection. One
of the reasons is that some phenomena exist, which can produce broken rotor bar
fault harmonics in the stator current spectra of healthy motors. The misdiagnosis
may lead to false positive alarms which may result in high costs for inspection and
service without need. Such cases are the following:
● Mechanical load oscillations [58]
● Magnetic anisotropy of the rotor iron core [59]
● Axial cooling rotor air ducts (Figure 2.19) [60]
● Fan blades number in pumping applications [61]
Furthermore, earlier in this section, it was mentioned that in large induction motors,
cases have been reported with multiple broken rotor bars (Figure 2.20). Moreover,
in some cases, the rotor bars might break in non-adjacent positions. It has been
reported that, the stator current analysis is not capable to provide information
regarding the health of the rotor cage via the proposed frequency component
1 2s
ð Þfs if the broken bars are located electrically p/2 rad away with respect to
each other [51,52].
Figure 2.20 Rotor of a 5-MW, 6-kV cage motor with multiple broken bars. 2017–
2018 IEEE. Reprinted, with permission, from Reference [52]
0
–20
–40
(a) (b)
–60
–80
I
s
spectrum
(dB)
–100
40 44
fd
k1 = 4
fd
k1 = 3
fd
k1 = 2
fd
k1 = 1
48 52 56 60
Frequency (Hz)
64 68 72 76 80
Figure 2.19 (a) A rotor with axial cooling air ducts. (b) Example of the stator
current spectrum of a healthy motor (kidney holes) with four magnetic
poles and equal axial air ducts operating under rated load conditions.
2017–2018 IEEE. Reprinted, with permission, from Reference [60]
26 Diagnosis and fault tolerance](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-45-320.jpg)
![Mainly due to such unreliability of the traditional diagnostic approach of the
fast Fourier transform application at steady state, to detect rotor-related faults,
a new trend has been developed. Special focus is now given to the monitoring and
analysis of the stator current during start-up. The proposed methods have defined a
new area called transient MCSA [62]. In this family, many methods have been
proposed so far: the short-time Fourier transform [63], the MUSIC [64] and the
Wavelet transform [62,65]. The main idea behind the application of such methods
is that the broken bar fault harmonics are slip dependent. As a result, in a time-
frequency decomposition, the trajectory of those harmonics frequency will vary
versus time. This is not the case for the stator-related harmonics. This allows for the
detection of the fault during transients. Another advantage of the stator current
monitoring at start-up is that the rotor current gets its maximum, and as a result,
rotor electrical faults are magnified during start-up with respect to the steady state.
Aiming to illustrate the application of such methods for the detection of broken
rotor bars, Figure 2.21(a) shows the application of the analytical wavelet transform
(AWT), whereas Figure 2.21(b) shows the application of the discrete wavelet
transform (DWT).
2.1.3.4 Demagnetisation of permanent magnets
Demagnetisation is the condition at which the PMs lose partially or fully their
ability to magnetise. Motor applications involving PM motors require high
power and torque density which cannot be usually supported by electrical machine
types applying only electromagnets. If the PMs are demagnetised, the magnetic
flux density drops, and with it the output torque and mechanical power. So, the PM
machine loses its main selection purpose. It is to be noted that the demagnetisation
effect could be irreversible, depending on the operating conditions. As a result, the
reliable detection of this fault is crucial for the safe and normal operation of the PM
machine.
Before discussing the diagnosis of the demagnetisation any further, it is
important to explain the phenomenon and its dependence on temperature. The
normal curve of a PM material is shown in Figure 2.22(a), following the line
described by the points Br; a; a0
; a00
; Hc. The curve can be assumed to be linear for
high magnetic flux density values followed by a sharp drop until the point of
coercive magnetic field strength Hc. The magnet operates at the intersection of the
demagnetisation curve and the load characteristic line. Normally, the intersection
point exists on the linear part of the curve (around the point a0
). However, an
increase in the load will drive the operation point below the knee of the curve
(around the point a00
). If that happens, the PM will not be able to fully recover its
former remanence magnetic flux density when the demagnetising effect disappears.
Instead it will be characterised by a new B0
r which is less than the original Br.
A similar approach is followed to explain the irreversible demagnetisation due
to the temperature increase. The impact of the temperature on the demagnetisation
curve of the PM is shown in Figure 2.22(b). An increase in temperature leads to a
new curve characterised by less coercive magnetic field strength as well as less
remanence magnetic flux density. As a result, the same load line, which for
Voltage-source inverter-fed drives 27](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-46-320.jpg)
![0
40
60
80
100
120
140
160
180
200
220
240
260
0.2
0.4
0.6
0.8
Time
(s)
Time
(s)
Frequency
(Hz)
(a)
(b)
40
60
80
100
120
140
160
180
200
220
240
260
Frequency
(Hz)
1
B2–
Bb
b5+
FC
P1–
P3+
P3–
WH5
B1+
1.2
1.4
1.6
0
d
8
(A)
d
9
(A)
a
9
(A)
I
(A)
–50
0
50
–50
0
50
–50
0
50
–2,000
2,000
0
1
2
3
4
5
6
7
8
9
Time
(s)
0
d
8
(A)
d
9
(A)
a
9
(A)
I
(A)
–50
0
50
–50
0
50
–50
0
50
–2,000
2,000
0
1
2
3
4
5
6
7
8
9
0
0.2
0.4
0.6
0.8
Time
(s)
EMT
+
BE
Induction
motor
with
one
broken
bar
Healthy
induction
motor
1
1.2
1.4
1.6
Figure
2.21
Application
of
the:
(a)
AWT
[62]
and
(b)
DWT
[65]
to
detect
a
broken
rotor
bar
during
an
induction
motor’s
start-up.
2017–2018
IEEE.
Reprinted,
with
permission,
from
References
[62,65]](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-47-320.jpg)
![temperature T1; intersected the demagnetisation curve at the linear part, now
intersects the curve for T2 T1 at point c0
which is below the knee of the shifted
demagnetisation curve. The result is that when the demagnetising effect dis-
appears, the new remanence magnetic flux density will be B00
r which is lower than
the original Br. Now if the temperature increases back to T1; the remanence
magnetic flux density will increase to B0
r with respect to B00
r ; however, it will be
less than the original one Br.
For applications where the load requirements are fixed, it is evident that
demagnetisation will evolve into increased fault levels. Due to demagnetisation, the
produced torque capability of the motor for a given current will decrease. So, in
order to serve the fixed load/torque requirements, the stator winding is forced to
draw more current, leading to increased Joule losses and elevation of temperature,
thus accelerating the demagnetisation of the PMs and leading to faster degradation
of the windings insulation materials [67].
It is to be noted that demagnetisation in electrical machines might be uniform
or partial. Uniform demagnetisation is more difficult to detect since its distorting
effect on the magnetic field distribution is minimum [68]. However, partial
demagnetisation leads to a strong asymmetry of the motor’s magnetic field which
will unavoidably lead to unbalanced magnetic pull (UMP) [69]. UMP will lead to
torque oscillations, vibrations and noise and could cause some level of eccentricity
[70]. A second level of fault evolution concerns the bearings which are overstressed
and degrade faster.
The PM demagnetisation effect gives rise to stator current frequencies
located at
fdm ¼ 1
k
p
fs; k 2 N (2.14)
The effect of partial demagnetisation on the magnetic flux density distribution and
stator current frequency spectra is presented in Figure 2.23 for a six-pole PM
synchronous machine (PMSM) operating at 6,000 rpm.
(a)
Demag.
effect of
current
Normal
load
Normal
load
Open
cct. load
Open
cct. load
B
Br
B′r
B
Br
B′r
B″r
H Hc
T1
T1T2
T2
H Hc
a″
a″
b′
a′ a′
c′
a a
b
(b)
Figure 2.22 PM operating point (demagnetisation curve and load line).
Irreversible demagnetisation due to (a) external demagnetising MMF.
(b) Operation at high temperature (SmCo- or NdFeB-based magnets).
2017–2018 IEEE. Reprinted, with permission, from Reference [66]
Voltage-source inverter-fed drives 29](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-48-320.jpg)
![2.1.3.5 Bearing faults
Bearings are the electrical machine components which guarantee and secure the
appropriate rotor positioning with respect to the stator while allowing rotation.
There are two types of bearings, namely rolling elements or ball and sleeve
(a)
(b)
0
–10
–20
–30
–40
–50
Amplitude
(dB)
–60
–70
–80
–90
0 1/3 2/3 1 4/3 5/3 2 7/3 8/3 3 10/3 11/3
Harmonic order (xfe)
4 13/3
Healthy motor
50%
magnetised
Flux density Tesla
352.30751E-6 / 138.14315E-3
138.14315E-3 / 275.9331E-3
275.9331E-3 / 413.72484E-3
413.72484E-3 / 551.51568E-3
551.51568E-3 / 689.30653E-3
689.30653E-3 / 827.09737E-3
827.09737E-3 / 964.88821E-3
964.88821E-3 / 1.10268
1.10268 / 1.24047
1.24047 / 1.37826
1.37826 / 1.51605
1.51605 / 1.65384
1.65384 / 1.79163
1.79163 / 1.92942
1.92942 / 2.06721
2.06721 / 2.20501
Demagnetised motor
14/3 5 16/317/318/3
Figure 2.23 (a) Spatial distribution of the magnetic flux density in a partially
demagnetised PMSM. (b) Simulated stator current harmonics in
a healthy and a partially demagnetised PMSM when running
at 6,000 rpm. 2017–2018 IEEE. Reprinted, with permission, from
Reference [71]
30 Diagnosis and fault tolerance](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-49-320.jpg)
![bearings (Figure 2.24). It was shown earlier in Figure 2.1 that bearing failures are
the main fault in low and medium voltage machines, while being of significantly
lesser importance in high voltage machines. This is due to the fact that high voltage
machines utilise sleeve bearings, while low and medium voltage machines utilise
rolling element bearings [3]. For this reason, this section will be focused on
the rolling element bearings fault detection.
It has been shown that, the location of the fault or in other words the faulty
component of the bearing produces a unique vibrating harmonic response. More
(a)
(b)
Vibration
accelerometer
Vibration
accelerometer
Shock pulse
transducer
Shaft rotation
Y-axis
proximeter
High pressure fluid
R Reaction
F Destabilising components
P Pressure
W Whirl force
Minimum
clearance point
Low pressure
fluid
W
F
P
R
Roller elements
Inner race
Housing
Shaft
Outer race
Cage
X-axis
proximeter
Figure 2.24 Bearing types and components: (a) rolling element bearing and
(b) forces acting upon a shaft in a sleeve bearing. 2017–2018 IET.
Reprinted, with permission, from Reference [2]
Voltage-source inverter-fed drives 31](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-50-320.jpg)
![specifically, the following formulas have been proposed to detect the origin of the
bearing fault [3,72]:
Outer race defect fo ¼
N
2
fr 1
Db
Dc
cos b
(2.15)
Inner race defect fi ¼
N
2
fr 1 þ
Db
Dc
cos b
(2.16)
Ball defect fb ¼
Dc
Db
fr 1
Db
Dc
cos b
2
#
(2.17)
where N is the number of balls, Db is the ball diameter, Dc is the bearing pitch
diameter and b is the contact angle of the balls on the races.
As a result, it is possible to monitor each individual defect via the stator current
frequency spectrum by applying the following formula [73]:
freb ¼ fs mf c; m 2 N (2.18)
where fc corresponds to the appropriate vibration frequency described by (2.15)–
(2.17).
An application of the above formulas can be seen in Figure 2.25 for inner and
outer race faults. However, past experience has shown that the use of the above
characteristic frequencies is not reliable when trying to detect general bearing
faults, such as contamination or degradation. It is to be noted that bearing failures
create some level of eccentricity, so there are numerous cases where the detection
of eccentricity has led to the detection of bearing failures indirectly.
2.1.4 Alternative diagnostic methods
It is to be expected that although the analysis of the stator current for diagnostic
purposes is indeed a powerful tool, it still has weaknesses in some applications or
specific problems. This is the reason for the existing rich literature where many
researchers propose alternative signals or methods to overcome the MCSA draw-
backs. Some of the most frequently met will be discussed in this section.
2.1.4.1 Electromagnetic/mechanical torque monitoring
The torque monitoring has drawn a lot of interest over the years, whether it is the
electromagnetic or the mechanical one. The electromagnetic is difficult to measure
directly, this is why methods exist to estimate it from current, voltage and/or flux
measurements [75,76]. The mechanical torque can be measured with a torque
transducer in the lab, however, has limited application in a real industrial envir-
onment. However, the signatures existing in the electromagnetic torque are prac-
tically the same in the mechanical torque, so multiple cases exist where researchers
do not differentiate between the two.
The motor’s torque comes as a result of Lenz law, so it is in some way the end
effect of the electromechanical energy conversion. Any fault or imbalance causing
32 Diagnosis and fault tolerance](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-51-320.jpg)
![an asymmetry in the magnetic field will express itself as torque oscillations. So, the
torque is just one signal originating from the synthesis of multiple electrical ones.
This is why the torque is considered a diagnostically valuable tool.
To enhance understanding, all faults described earlier produce specific side-
band harmonics to the fundamental in the stator current. The exact same sidebands
(a)
(b)
100
260 270 280 290 300
Frequency (Hz)
310 320 330
105
0
–5
–10
–15
–20
Amplitude
PSD
(dB)
Amplitude
PSD
(dB)
–25
–30
–35
–40
–45
–50
–15
–20
–25
–30
–35
–40
–45
110 115 120 125
2fi
5fs + fr
fs – fr + 2fi
|fs – 2*fo|
7fs – fr
fs + 2fi
130
Frequency (Hz)
135 140
Outer raceway defect
Healthy machine
Inner raceway defect
Healthy machine
145 150
Figure 2.25 Application of MCSA to detect bearing faults where (a) outer
raceway defect detection of loaded induction motor and (b) inner
raceway defect detection of unloaded induction motor. 2017–2018
IEEE. Reprinted, with permission, from Reference [74]
Voltage-source inverter-fed drives 33](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-52-320.jpg)
![(although of different amplitude) exist in the torque spectra around the DC com-
ponent. Similarly, higher harmonics also exist. Figure 2.26 illustrates the diagnosis
of a broken rotor bar fault located at 2sf s and at 6 2ks
ð Þfs in the mechanical
torque spectra of a four-pole, 400 V, 4 kW, 50 Hz cage induction motor.
2.1.4.2 Magnetic flux monitoring
The main idea of the diagnostic strategies is that a fault will cause an asymmetry in
the magnetic field. As a result, many works [35,77–80] have proposed the direct
monitoring of the magnetic flux using flux sensors. It is possible to monitor either
the radial or axial magnetic flux. The MCSA signatures exist also in the radial flux
spectra for radial flux electrical machines. However, the flux sensor is independent
from the motor geometry and more specifically does not depend on the number of
(a)
(b)
270
0 1 2 3 4 5 6 7 8
280 290
–50
–60
–70
–80
–90
–100
–110
–120
–130
–140
300
Frequency (Hz)
Frequency (Hz)
Amplitude
(dB)
Amplitude
(dB)
310 320 330
–60
–40
–20
0
–80
–100
–120
Figure 2.26 Comparative experimental spectra of the motors’ (healthy and
induction motor with a broken rotor bar) torque for s ¼ 0.027 (a) at the
low-frequency range and (b) at the frequency range close to 300 Hz.
2017–2018 IEEE. Reprinted, with permission, from Reference [54]
34 Diagnosis and fault tolerance](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-53-320.jpg)
![poles like the stator phase winding. As a result, the radial flux spectrum is richer in
harmonic index than the stator current.
The application of a search coil to detect partial demagnetisation of a PM
machine is shown in Figure 2.27 [81]. The distortion of the flux waveform is easily
noticed. However, in most real cases, the fault needs to be diagnosed at incipient
stages where it cannot be noticed by the flux waveform. As a result, spectral ana-
lysis is applied. Figure 2.28 illustrates the spectra of the radial flux derivative in an
induction motor under healthy condition as well as under broken bar fault [82].
2.1.4.3 Single-phase rotation test
The single-phase rotation test (SPRT) is a test applied offline and aiming to detect
rotor defects [83]. The rotor is manually rotated under fixed speed while only one
of the stator phases is supplied, thus producing a pulsating magnetic field. The aim
is to monitor the phase current and voltage, thus being able to calculate the phase
impedance. Variations of the impedance during rotation are strong indicators of
rotor asymmetries. The test belongs to the non-intrusive methods, so it does not
require the motor disassembly. The setup is shown in Figure 2.29(a). Furthermore,
the application of the test to detect different levels and types of eccentricity in an
induction machine is shown in Figure 2.29(b).
2.1.5 Fault prognosis of electrical machines
There are two end goals in the field of electrical machine prognosis. The first one is
to model the degradation mechanisms with accuracy. The second one is to estimate
the component or device RUL [84,85]. Degradation is the irreversible process
where a material, component or device loses its properties. Usually, the degradation
has a strong multi-scientific character, that means many different mechanisms act
together to produce the end effect which is the end of the subject’s life [86,87].
In electrical machines, the area of fault prognosis is meaningful and thus has met
significant interest and progress in the case of windings insulation materials. This is
t (20 ms/div)
Measured
voltage
of
the
search
coil
(V)
One mechanical round
–2
–1
0
1
2
Figure 2.27 Measured voltage of the search coil from the prototype machine
with partial demagnetisation
Voltage-source inverter-fed drives 35](https://image.slidesharecdn.com/18602635-250602205109-550ed244/85/Diagnosis-And-Fault-Tolerance-Of-Electrical-Machines-Power-Electronics-And-Drives-Energy-Engineering-Antonio-J-Marques-Cardoso-Editor-54-320.jpg)
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- 6. IET ENERGY ENGINEERING 126 Diagnosis and Fault Tolerance of Electrical Machines, Power Electronics and Drives
- 7. Other volumes in this series: Volume 1 Power Circuit Breaker Theory and Design C.H. Flurscheim (Editor) Volume 4 Industrial Microwave Heating A.C. Metaxas and R.J. Meredith Volume 7 Insulators for High Voltages J.S.T. Looms Volume 8 Variable Frequency AC Motor Drive Systems D. Finney Volume 10 SF6 Switchgear H.M. Ryan and G.R. Jones Volume 11 Conduction and Induction Heating E.J. Davies Volume 13 Statistical Techniques for High Voltage Engineering W. Hauschild and W. Mosch Volume 14 Uninterruptible Power Supplies J. Platts and J.D. St Aubyn (Editors) Volume 15 Digital Protection for Power Systems A.T. Johns and S.K. Salman Volume 16 Electricity Economics and Planning T.W. Berrie Volume 18 Vacuum Switchgear A. Greenwood Volume 19 Electrical Safety: A guide to causes and prevention of hazards J. Maxwell Adams Volume 21 Electricity Distribution Network Design, 2nd Edition E. Lakervi and E.J. Holmes Volume 22 Artificial Intelligence Techniques in Power Systems K. Warwick, A.O. Ekwue and R. Aggarwal (Editors) Volume 24 Power System Commissioning and Maintenance Practice K. Harker Volume 25 Engineers’ Handbook of Industrial Microwave Heating R.J. Meredith Volume 26 Small Electric Motors H. Moczala et al. Volume 27 AC–DC Power System Analysis J. Arrillaga and B.C. Smith Volume 29 High Voltage Direct Current Transmission, 2nd Edition J. Arrillaga Volume 30 Flexible AC Transmission Systems (FACTS) Y.-H. Song (Editor) Volume 31 Embedded Generation N. Jenkins et al. Volume 32 High Voltage Engineering and Testing, 2nd Edition H.M. Ryan (Editor) Volume 33 Overvoltage Protection of Low-Voltage Systems, Revised Edition P. Hasse Volume 36 Voltage Quality in Electrical Power Systems J. Schlabbach et al. Volume 37 Electrical Steels for Rotating Machines P. Beckley Volume 38 The Electric Car: Development and future of battery, hybrid and fuel-cell cars M. Westbrook Volume 39 Power Systems Electromagnetic Transients Simulation J. Arrillaga and N. Watson Volume 40 Advances in High Voltage Engineering M. Haddad and D. Warne Volume 41 Electrical Operation of Electrostatic Precipitators K. Parker Volume 43 Thermal Power Plant Simulation and Control D. Flynn Volume 44 Economic Evaluation of Projects in the Electricity Supply Industry H. Khatib Volume 45 Propulsion Systems for Hybrid Vehicles J. Miller Volume 46 Distribution Switchgear S. Stewart Volume 47 Protection of Electricity Distribution Networks, 2nd Edition J. Gers and E. Holmes Volume 48 Wood Pole Overhead Lines B. Wareing Volume 49 Electric Fuses, 3rd Edition A. Wright and G. Newbery Volume 50 Wind Power Integration: Connection and system operational aspects B. Fox et al. Volume 51 Short Circuit Currents J. Schlabbach Volume 52 Nuclear Power J. Wood Volume 53 Condition Assessment of High Voltage Insulation in Power System Equipment R.E. James and Q. Su Volume 55 Local Energy: Distributed generation of heat and power J. Wood Volume 56 Condition Monitoring of Rotating Electrical Machines P. Tavner, L. Ran, J. Penman and H. Sedding Volume 57 The Control Techniques Drives and Controls Handbook, 2nd Edition B. Drury Volume 58 Lightning Protection V. Cooray (Editor) Volume 59 Ultracapacitor Applications J.M. Miller Volume 62 Lightning Electromagnetics V. Cooray Volume 63 Energy Storage for Power Systems, 2nd Edition A. Ter-Gazarian Volume 65 Protection of Electricity Distribution Networks, 3rd Edition J. Gers Volume 66 High Voltage Engineering Testing, 3rd Edition H. Ryan (Editor) Volume 67 Multicore Simulation of Power System Transients F.M. Uriate Volume 68 Distribution System Analysis and Automation J. Gers Volume 69 The Lightening Flash, 2nd Edition V. Cooray (Editor) Volume 70 Economic Evaluation of Projects in the Electricity Supply Industry, 3rd Edition H. Khatib Volume 72 Control Circuits in Power Electronics: Practical issues in design and implementation M. 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- 8. Diagnosis and Fault Tolerance of Electrical Machines, Power Electronics and Drives Edited by Antonio J. Marques Cardoso The Institution of Engineering and Technology
- 9. Published by The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England & Wales (no. 211014) and Scotland (no. SC038698). † The Institution of Engineering and Technology 2019 First published 2018 This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publisher at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the authors and publisher believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the authors nor publisher assumes any liability to anyone for any loss or damage caused by any error or omission in the work, whether such an error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the authors to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. British Library Cataloguing in Publication Data A catalogue record for this product is available from the British Library ISBN 978-1-78561-531-3 (hardback) ISBN 978-1-78561-532-0 (PDF) Typeset in India by MPS Limited Printed in the UK by CPI Group (UK) Ltd, Croydon
- 10. Contents About the authors ix 1 Introduction 1 Antonio J. Marques Cardoso 1.1 Electromechatronics 2 1.2 Fault diagnosis 2 1.2.1 Diagnostic methods 3 1.3 Prognosis 4 1.4 Fault tolerance 4 1.5 Diagnosis and fault tolerance of electrical machines, power electronics, and drives 5 Acknowledgment 6 References 6 2 Voltage-source inverter-fed drives 7 Jorge Oliveira Estima and Konstantinos N. Gyftakis 2.1 Condition monitoring, fault diagnosis and prognosis of electrical machines 7 2.1.1 Introduction 7 2.1.2 Condition monitoring, fault diagnosis and prognosis 8 2.1.3 Fault diagnosis of electrical machines 9 2.1.4 Alternative diagnostic methods 32 2.1.5 Fault prognosis of electrical machines 35 2.2 Fault diagnostic techniques applied to voltage source inverter-fed drives 40 2.2.1 Introduction 40 2.2.2 Fault diagnostic approaches 41 2.3 Fault-tolerant techniques applied to VSI-fed drives 51 2.3.1 Introduction 51 2.3.2 Non-redundant topologies 52 2.3.3 Redundant topologies 55 Acknowledgement 58 References 58
- 11. 3 Switched reluctance machine drives 77 Davide S.B. Fonseca and Natália S. Gameiro 3.1 The switched reluctance motor 77 3.1.1 Performance analysis 81 3.2 Switched reluctance motor operation 84 3.2.1 Single pulse operation 85 3.2.2 Voltage chopping 86 3.3 Control of switched reluctance machine drives 88 3.4 Fault analysis in switched reluctance machine drives 89 3.4.1 Disconnected phase 90 3.4.2 Disconnected phase branch 91 3.4.3 Short-circuited pole 92 3.4.4 Short-circuit to ground 93 3.4.5 Phase-to-phase short-circuit 93 3.4.6 Inter-turn short-circuit 93 3.4.7 Power converter faults 94 3.4.8 Rotor-related faults 96 3.5 Fault diagnostic techniques applied to switched reluctance machine drives 97 3.5.1 Fault detection devices 98 3.5.2 Methods based on a single electric current 99 3.5.3 Methods based in all electric phase currents 102 3.5.4 Other methods 104 3.6 Fault-tolerant strategies 105 3.6.1 Fault-tolerant control 106 3.6.2 Fault-tolerant converters 109 Acknowledgement 115 References 115 4 High-power synchronous machine drives 121 Alberto Tessarolo and Adérito N. Alcaso 4.1 High-power synchronous motors 121 4.1.1 Permanent magnet motors 121 4.1.2 Wound-field synchronous motors 126 4.2 High-power converters 135 4.2.1 Voltage source inverters 135 4.2.2 Current source inverters 142 4.2.3 Cycloconverters 144 4.3 System-level fault-tolerant drive architectures 145 4.3.1 Redundant drive architectures 145 4.3.2 Multi-phase drive architectures 148 4.4 Fault-tolerant electric motor design 159 4.4.1 Fault-tolerant solutions in the stator design 160 4.4.2 Fault-tolerant solutions for the rotor design 162 vi Diagnosis and fault tolerance
- 12. 4.5 Fault-tolerant power converter design 165 4.5.1 Fault-tolerant VSIs 166 4.5.2 Fault-tolerant CSIs 169 4.6 Diagnostics 173 4.6.1 Diagnostics in medium-voltage converters 174 4.6.2 Diagnostics in large synchronous motors 175 Acknowledgment 189 References 189 5 Capacitors 195 Acácio M. R. Amaral and M. Sahraoui 5.1 Capacitor technologies 197 5.1.1 Electrolytic capacitors 199 5.1.2 Film capacitors 200 5.1.3 Ceramic capacitors 201 5.2 Aluminium electrolytic capacitors 203 5.2.1 Al-Caps equivalent circuit 205 5.2.2 Al-Caps failure modes 206 5.3 Metalized polypropylene film capacitors 209 5.3.1 MPPF-Caps equivalent circuit 210 5.3.2 MPPF-Caps failure modes 212 5.4 Fault diagnostic techniques 215 5.5 Off-line measurement techniques 217 5.5.1 Off-line measurement techniques based on the injection of a sinusoidal current 218 5.5.2 Off-line measurement techniques based on a charge–discharge circuit 223 5.5.3 Frequency and temperature multipliers 226 5.5.4 Off-line fault diagnostic techniques 229 5.6 On-line fault diagnostic techniques 234 5.6.1 On-line fault diagnostic techniques based on ESR estimation 235 5.6.2 On-line fault diagnostic techniques based on ESR and C estimation 251 5.6.3 On-line fault diagnostic techniques based on C estimation 265 5.7 Quasi-online fault diagnostic techniques 269 5.8 Summary 274 5.8.1 Off-line fault diagnosis techniques 275 5.8.2 On-line fault diagnosis techniques 275 5.8.3 Quasi-online fault diagnosis techniques 277 Acknowledgement 277 References 277 Contents vii
- 13. 6 DC–DC converters 287 Fernando Bento and Eunice Ribeiro Nomenclature 288 6.1 Fault diagnostic algorithms 288 6.1.1 Signal-processing-based algorithms 289 6.1.2 Model-based algorithms 323 6.2 Fault-tolerant strategies 332 6.2.1 Bypass of faulty module(s) 333 6.2.2 Phase-shift adjustment 336 6.2.3 Inclusion of additional components 337 6.2.4 Comparative analysis of the fault-tolerant strategies 343 6.3 Conclusions 344 Acknowledgement 345 References 345 Index 349 viii Diagnosis and fault tolerance
- 14. About the authors Adérito N. Alcaso was born in 1966. He received the diploma in Electrical and Computer Engineering from the Technical University of Lisbon, Lisbon, Portugal, in 1990. He received the MSc degree in Systems and Automation, and the PhD degree in Electrical Engineering from the University of Coimbra, Coimbra, Portugal, in 1995 and 2005, respectively. Since 1996 he is Adjunct Professor at the Polytechnic of Guarda, Guarda, Portugal, where he has been director of the Mechanical Engineering Department and member of the Pedagogical and Scientific Councils of the School of Technology and Management. He is also a Researcher of CISE – Electromechatronic Systems Research Centre. He has published several papers in technical journals and conference proceedings. His current research interests are focused in renewable energy systems, particularly of the co-generation type, and in electric mobility systems, exploring the application of low-cost microcontrollers and internet of things for monitoring and optimizing the operation of these systems. Acácio M. R. Amaral was born in Luso, Angola, in 1974. He received the Electrical Engineering Diploma, the MSc degree and the PhD degree from the University of Coimbra, Coimbra, Portugal in 1998, 2005 and 2010, respectively. Since 1998 he has been with the Polytechnic Institute of Coimbra, where he is currently an Adjunct Professor in the Department of Informatics and Systems. He is also a Researcher of CISE – Electromechatronic Systems Research Centre. He is the author of three books entitled: Circuit Analysis and Electronic Devices (Porto, Portugal, Publindustria, 2013, in Portuguese); Digital Systems: Principles, Analysis and Projects (Lisboa, Portugal, Edições Sı́labo, 2014, in Portuguese); and Analog Elec- tronics: Principles, Analysis and Projects (Lisboa, Portugal, Edições Sı́labo, 2017, in Portuguese). He has also published more than 40 papers in technical journals and conference proceedings. His research activities include fault diagnosis and design of linear and switch-mode power supplies, with emphasis on the consequences of aging of electrolytic and film capacitors, as well as the development of solutions to this problem.
- 15. Fernando Bento received both the BSc and MSc degrees in Electric and Computer Engineering from the University of Beira Interior, Covilhã, Portugal, in 2014 and 2016, respectively. Currently, he is a PhD student in Electric and Computer Engineering at the University of Beira Interior, and PhD student of CISE – Electro- mechatronic Systems Research Centre. His scientific research activities focus on energy efficiency analysis, fault diagnostic and fault tolerance in electronic power converters, namely DC-DC converters. Antonio J. Marques Cardoso received the Dipl. Eng., Dr. Eng., and Habilitation degrees from the University of Coimbra, Coimbra, Portugal, in 1985, 1995 and 2008, respectively, all in Electrical Engineering. From 1985 to 2011, he was with the University of Coimbra, Coimbra, Portugal, where he was the director of the Electrical Machines Laboratory. Since 2011 he has been with the University of Beira Interior (UBI), Covilhã, Portugal, where he is Full Professor at the Department of Electromechanical Engineering and director of CISE – Electromechatronic Systems Research Centre (http://cise.ubi.pt). He was Vice-Rector of UBI (2013–2014). His current research interests are in fault diagnosis and fault tolerance in electrical machines, power electronics and drives. He is the author of a book entitled Fault Diagnosis in Three-Phase Induction Motors (Coimbra, Portugal: Coimbra Editora, 1991), (in Portuguese) and he is also the author of around 500 papers published in technical journals and conference proceedings. He currently serves as an associate editor for the IEEE Transactions on Industry Applications, IEEE Transactions on Industrial Electronics, IEEE Transactions on Power Electronics, IEEE Journal of Emerging and Selected Topics in Power Electronics, and also for the Springer International Journal of Systems Assurance Engineering and Management. Jorge O. Estima was born in Aveiro, Portugal, in 1984. He received the Dipl. Eng. and the Dr. Eng. degree from the University of Coimbra, Coimbra, Portugal, in 2007 and 2012, respectively. From 2012 to 2016, he was a postdoctoral researcher at CISE – Electromechatronic Systems Research Centre (http://cise.ubi.pt), University of Beira Interior (UBI), Covilhã, Portugal. Since 2016 he has been with the UBI where he is an Invited Assistant Professor at the Department of Electromechanical Engineering and Researcher of CISE. He has also been with the company Enging where he is R&D Manager. His research interests are focused on condition monitoring and diagnostics of electric machines, power x Diagnosis and fault tolerance
- 16. electronics, fault-tolerant variable speed drives and energy efficiency in motor drive systems. Davide S. B. Fonseca was born in Castelo Branco, Portugal, on December 23, 1972. He received the Electrical Engineering Diploma in 1996 from the University of Coimbra, Coimbra, Portugal, and the PhD in electrical engineering from the University of Beira Interior, Covilhã, Portugal, in 2008. He has been with the University of Beira Interior since 1997, where he is currently an Assistant Professor in the Department of Electromechanical Engineering, and the Coordinator of the Electrical Machines and Power Electronics Laboratory. He is also Researcher of CISE – Electromechatronic Systems Research Centre. His research interests are focused on reluctance machines design and fault analysis. He has published more than 40 papers in technical journals and conference proceedings. Natália S. Gameiro received the Electrical Engi- neering Diploma, the MSc degree in Electrical Engi- neering, and the PhD degree in Electrical Engineering from the University of Coimbra, Coimbra, Portugal, in 1997, 2004 and 2014, respectively. Since 1997, she has been with the Polytechnic Institute of Leiria, Leiria, Portugal, where she is currently an Adjunct Professor with the Department of Electrical Engineering. She is also Researcher of CISE – Electromechatronic Sys- tems Research Centre. Her teaching interests cover electrical machines, control systems and basic electric network analysis, and her research interests also include electrical machines and drives, control of variable electric drives, fault diagnosis and fault-tolerant control. Currently, she is mainly focused on the analysis and development of fault-tolerant solutions, based on inverter and/or control reconfigurations applied to switched reluctance motor drives. Konstantinos N. Gyftakis was born in Patras, Greece, in May 1984. He received the Diploma in Electrical and Computer Engineering from the University of Patras, Patras, Greece, in 2010. He pursued a PhD in the same institution in the area of electrical machines condition monitoring and fault diagnosis (2010–2014). Then he worked as a Post- Doctoral Research Assistant in the Department of Engineering Science, University of Oxford, UK (2014–2015). In 2015, he was appointed Lecturer on Electrical and Electronic Engineering, School of About the authors xi
- 17. Computing, Electronics and Mathematics, Faculty of Engineering, Environment and Computing, Coventry University, UK. Moreover, he is a member of the Research Institute for Future Transport and Cities, Coventry University, UK. Additionally, he is a member of CISE – Electromechatronic Systems Research Centre, Portugal. Finally, he is an IEEE member as well as a member of the IEEE Industry Applications Society and IEEE Industrial Electronics Society. His research interests focus in the fault diagnosis, condition monitoring and degradation of electrical machines. He has authored/co-authored more than 60 papers in international scientific journals and conferences. Eunice Ribeiro holds a PhD degree in Electrical Engineering from the University of Coimbra (Portugal) awarded with ‘The Joseph J. Suozzi INTELEC Award Fellowship in Power Electronics’. As part of her studies and involvement in research projects, she has a considerable experience on power electronic con- verters covering a wide range of applications, such as energy management systems, electric vehicles, renewable energies power conditioning, hybrid energy storage solutions, fault diagnostic methods and fault tolerance strategies. She has published more than 20 scientific papers in peer-reviewed conferences and journals related to power electronic converters, renewable energies, energy storage and energy sys- tems. Previously, Eunice Ribeiro was H2020 National Contact Point, National Representative in H2020 Programme Committees and National Delegate for the European Strategic Energy Technology Plan (SET-Plan). Currently, she is the EU Programmes Manager at Ubiwhere and a Researcher at CISE – Electromechatronic Systems Research Centre. Mohamed Sahraoui was born in Biskra, Algeria, on May 26, 1978. He received the Engineer and Magister diploma and the PhD degree in Electrical Engineering from the University of Biskra, in 2001, 2004 and 2010, respectively. From 2005 to 2012, he was an Assistant Professor with the University of Constantine, Constantine, Algeria. Since 2012, he has been with the University of Biskra, Biskra, Algeria, where he is an Assistant Professor at the Department of Electrical Engineering and a member of the LGEB Laboratory. Dr Sahraoui is also a PhD Researcher of CISE – Electromechatronic Systems Research Centre (http://cise.ubi. pt). His research interests are related to condition monitoring and fault diagnosis in power electronics systems and AC machines. xii Diagnosis and fault tolerance
- 18. Alberto Tessarolo received the Laurea and PhD degrees in Electrical Engineering from the University of Trieste, Trieste, Italy, in 2000 and 2011, respec- tively. Before joining the University, he worked in the design and development of large innovative motors, generators and drives with NIDEC-ASI (formerly Ansaldo Sistemi Industriali). Since 2006, he has been with the Department of Engineering and Architecture, University of Trieste, where he teaches the course of Electric Machine Design. He holds the scientific responsibility for several funded research projects in coordination with leading companies and institutions. He has authored more than 150 international technical papers in the area of electrical machine and drive modelling and design. He serves as an editor for the IEEE Transactions on Energy Conversion and an associate editor for the IEEE Transactions on Industry Applications and IET Electric Power Applications. He received the Electric Machinery Committee 2012 Prize Paper Award of the IEEE Power and Energy Society and of various best paper awards for contributions presented at IEEE- sponsored or co-sponsored conferences. He is a senior member of the IEEE and a member of the Industry Applications, Power and Energy, Power Electronics, Industrial Electronics, and Magnetics and Reliability Societies of the IEEE. About the authors xiii
- 20. Chapter 1 Introduction Antonio J. Marques Cardoso1 Electrical machines, drives, and their associated power electronics, namely, con- verters and capacitors, play a key role in an ever increasingly technological society. Transportation electrification, renewable energies, and more efficient buildings are just some of the areas where the intensive application of these systems has been most noticed. This book will address, in the next five chapters, voltage source inverter (VSI)- fed drives, switched reluctance machine (SRM) drives, high-power synchronous machine drives, capacitors, and DC–DC converters. VSI-fed drives, SRM drives, and high-power synchronous machine drives are extensively used, namely, in the aforementioned areas of transportation elec- trification and renewable energies. Electrolytic capacitors and metallized polypropylene film capacitors are commonly found in the DC-link of the power converters of such drives. DC–DC converters are facing an exponential growth in the context of the ever increasing use of DC microgrids in the homes and businesses, driven by the fact that the vast majority of renewable energy sources, electrical appliances, and storage devices operate either in true DC mode or at least involve an intermediate DC-link bus. In all these applications, efficiency and reliability are of major concern. Reliability is a major challenge in these systems design, operation, and main- tenance. Unreliable systems are not only the cause of users frustration but they also drive up the cost, so diagnostics and fault tolerance become important to help maintain the systems and estimate their operational life. The scope of the book encompasses the issues related to fault analysis, fault detection and isolation, diagnostics, prognostics, condition monitoring, post-fault reconfiguration, remedial operation, robust control, and fault tolerance of electro- mechatronic systems. 1 CISE – Electromechatronic Systems Research Centre, Universidade da Beira Interior, Portugal
- 21. 1.1 Electromechatronics Electromechatronics, introduced in the 1980s by Professor Yuri P. Koskin of the Department of Electromechanics and Electromechatronics of the Saint Petersburg State Electrical Engineering University, Russia, corresponds to the integration of electromechanical and electronic areas in a single technical/scientific field of electrical engineering [1]. Electromechatronics, term formed by agglutination, according to the following expression [1] ELECTROMECHATRONICS ¼ ELECTROMECHANICS þ ELECTRONICS (1.1) brings together the areas of electrical machines, drives, and their associated power electronics, namely, converters and capacitors. 1.2 Fault diagnosis A fault may be defined as the condition of an equipment, material, or system, characterized by the termination of the ability to fully perform the required functions. The following main categories of faults are distinguished [2]: Catastrophic – Characterized by a sudden occurrence and involving the total and immediate stoppage of the functions performed until then. Evolutionary – Associated with a gradual development and affecting, at first only partially, the performance of the functions. Intentional – Deliberately caused and involving the interruption of the per- formance of the functions, regardless of the registered condition. Evolutionary faults are, therefore, the most appropriate to the application of early diagnostic methods. Similarly to the clinical diagnosis, the diagnosis of faults involves the char- acterization of equipment state condition through the consideration of the symp- toms it manifests. Thus, four intrinsic aspects to the diagnostic process are distinguished, as shown in Figure 1.1. The detection of faults is the primary objective of the monitoring of parameters indicative of the fault occurrence. However, consideration of the remaining aspects presented in Figure 1.1 is not possible through the exclusive use of monitoring. Indeed, the detailed analysis of the information contained in the various indicators of the occurrence of faults becomes crucial for the development of methods capable of providing a complete and reliable diagnosis. Additionally, fault analysis, making possible the understanding of the various phenomena associated to a fault occur- rence, also becomes essential [2]. 2 Diagnosis and fault tolerance
- 22. After fault detection, the identification or discrimination of faults is another important aspect to be considered in the diagnostics process. Depending on the particular type of fault identified, specific and more appropriate diagnostic approaches can be applied toward a complete and reliable diagnosis. Fault localization is particularly important when it comes to the application of subsequent repair actions. Knowledge about the position of the fault eliminates the need to completely dismantle the whole equipment, thus reducing the repair time and costs. Therefore, a complete and reliable diagnosis should also provide infor- mation regarding the fault localization. Fault severity assessment is another key aspect in the diagnostics process. Nowadays, risk analysis and decision support systems are widely recognized management tools that strongly rely on that piece of information. 1.2.1 Diagnostic methods In accordance with the way in which they are applied, diagnostic methods may be grouped into Off-line – Characterized by the need for the equipment to be out of service when they are applied, they even require, in most cases, that equipment should be disassembled, in order to make accessible some of its components. Online – Diagnosis can be achieved without the need to resort to interrupting the operation of the equipment. Obviously, online diagnostic methods are the most attractive. Among the online diagnostic methods, a further distinction can also be established between invasive and noninvasive methods. The former require that sensors have to be attached to the equipment structure or even inside, like accelerometers, search coils, thermis- tors, or thermocouples, while the latter are solely based on the information captured from sensors placed away from the equipment itself, like current probes or thermographic cameras. DETECTION IDENTIFICATION OR DISCRIMINATION FAULT DIAGNOSTICS LOCALIZATION SEVERITY ASSESSMENT Figure 1.1 Intrinsic aspects to the fault diagnostics process Introduction 3
- 23. 1.3 Prognosis Prognosis, or the anticipated knowledge, is the next step following diagnostics activities. It requires an accurate modeling of equipment-degradation mechanisms, and the manipulation of past and present condition related data, through suitable methods of analysis, in order to be able to predict equipment future con- dition, behavior, performance, or remaining useful life estimation. It is therefore a scientific area where a deep knowledge of the equipment under analysis is required, together with the application of statistical techniques, estima- tion and identification techniques, numerical analysis, risk analysis, etc. As far as electrical machines are concerned, prognosis has gained lately a focal research interest due to the importance of insulating materials’ prognosis for motors used in transportation electrification, where reliability and safety are of major concern. 1.4 Fault tolerance Similar to the fault diagnostics process, four aspects intrinsic to fault tolerance are also considered, as shown in Figure 1.2. Fault diagnostics is the first step to be considered. Only after this, it is possible to isolate the faulty component(s) and define the most appropriate hardware/soft- ware reconfigurations to be adopted. Time-to-diagnostics and isolation is a critical aspect. Indeed, post-fault remedial operating strategies have to be implemented before a complete shutdown may occur. For that, suitable hardware and/or software reconfiguration approaches have to be almost instantly considered, always aiming at minimizing any additional hardware requirements. Indeed, the basic principle behind the fault tolerance concept is the guarantee of a continuous operation, although under an acceptable degraded mode, at the cost of minimum changes. Otherwise, the use of full-duplicated components can always be considered, but that is redundancy – i.e., the most primary form of fault tolerance. FAULT DIAGNOSTICS ISOLATION HARDWARE / SOFTWARE RECONFIGURATION FAULT TOLERANCE REMEDIAL OPERATION Figure 1.2 Intrinsic aspects to fault tolerance 4 Diagnosis and fault tolerance
- 24. The challenge is therefore twofold: reaching the maximum functionality at the cost of minimum changes. 1.5 Diagnosis and fault tolerance of electrical machines, power electronics, and drives The next five chapters will address the issues related to diagnosis and fault toler- ance of electrical machines, power electronics, and drives. Chapter 2 focuses on VSI-fed drives. First, condition monitoring and fault diagnostics of electrical machines, particularly induction and permanent magnet machines, are considered. Eccentricity, inter-turn faults, broken rotor bars or end- rings, demagnetization of permanent magnets, and bearing faults are among the addressed types of machine faults. Fault prognosis is also considered. Second, fault diagnostic techniques applied to VSIs, particularly two-level VSIs, are addressed. Current-based fault diagnostic approaches and voltage-based fault diagnostic approaches are discussed. Fault-tolerant techniques applied to VSI-fed drives are also presented. Chapter 3 is dedicated to SRM drives. First, the overall characteristics related to the constitution, operation, and control of SRM drives are introduced, followed by a comprehensive description of SRM drives fault analysis. Secondly, fault diagnostic techniques and fault-tolerant strategies, applied to SRM drives, are presented. Chapter 4 addresses high-power synchronous machine drives. First of all, an overview is provided on the main technologies and design features which char- acterize large synchronous machines and the relevant supplying converters, also taking into account their field of application. Subsequently, the attention is focused on the major strategies intended to improve high-power synchronous machine drives fault tolerance, acting on the system-level drive architecture as well as on the design and operation of the individual components (electric motor, converter, control system). Finally, the main diagnostics and condition monitoring techniques for high-power synchronous machines drives is covered, describing the main methods to detect possible malfunctioning, anomalies, and faults in drive operation before they result in serious damages or hazards. Chapter 5 deals with capacitors, one of the most vulnerable components of electromechatronic systems. Capacitors main technologies (electrolytic capacitors, film capacitors, and ceramic capacitors) are presented firstly. Subsequently, a particular emphasis is given to aluminum electrolytic capacitors and metalized polypropylene film capacitors, currently the most commonly used capacitors in the DC-link of power electronic converters. Capacitors diagnostic techniques are then introduced. Off-line, online, and quasi-online techniques are described in detail. At the end, some key ideas are presented, which synthesize the advantages and disadvantages of the discussed fault diagnostic techniques, and some envisaged advancements in this domain are also addressed. Chapter 6 outlines the most important advances achieved in the development of fault diagnostic tools and fault-tolerant strategies aimed at DC–DC converters. Introduction 5
- 25. An exhaustive description of both signal-processing-based fault diagnostic algo- rithms and model-based-fault diagnostic algorithms is provided, as well as com- prehensive summary of the most relevant features and limitations of the algorithms pertaining to each category. Next, the most relevant fault-tolerant architectures and control strategies developed to overcome the negative effects of the occurrence of faults in DC–DC converters are presented. Their applicability, main merits, and drawbacks are addressed and a comparative analysis of their main features is also provided. Acknowledgment This work was supported by the European Regional Development Fund (ERDF) through the Operational Programme for Competitiveness and Internationalization (COMPETE 2020), under Project POCI-01-0145-FEDER-029494, and by National Funds through the FCT – Portuguese Foundation for Science and Technology, under Projects PTDC/EEI-EEE/29494/2017 and UID/EEA/04131/2013. References [1] Koskin, Y. P.: ‘The electromechatronics as the scientifical background of electromechanical converters and electronical components integration.’ Pro- ceedings of the International Conference on Electrical Machines, Vigo, Spain, 1996, Vol. III, pp. 513–518. [2] Cardoso, A. J. M.: Fault Diagnosis in Three-Phase Induction Motors (in Portuguese), Coimbra, Editora, 1991, pp. 34–35. 6 Diagnosis and fault tolerance
- 26. Chapter 2 Voltage-source inverter-fed drives Jorge Oliveira Estima1 and Konstantinos N. Gyftakis1,2 2.1 Condition monitoring, fault diagnosis and prognosis of electrical machines 2.1.1 Introduction Electrical machines have infiltrated and supported our everyday modern life. Electrical machines produce electric power working as generators or transform it into mechanical power operating as motors. Electrical machines are operating devices in power plants, wind farms, pumps, industry applications, cranes, con- veyors, belts, mills, transportation and many other applications. So, it is to be expected that electrical machines are related to huge financial variables as well as safety and reliability. Although electrical machines are robust devices, faults may appear and inter- rupt their working life cycle in many ways. Faults can be classified in three cate- gories: stator related, rotor related and mechanical. Stator faults include electrical failures which means short-/open-circuits, as well as inter-turn short-circuits which is a special case of short-circuits. Supply imbalance belongs in this category also. Other stator faults are iron core related ones. Similarly, rotor faults may be of electrical nature when the rotor has windings and iron related ones. Other special faults are broken/cracked rotor bars/end-rings for cage induction motors, permanent magnet cracks or demagnetisation for per- manent magnet motors and commutator/slip rings/brushes failures for all machines with rotor winding. Mechanical faults mainly include bearing failures. However, in this category, we can also include issues with the cooling fan as well as irregularities with the connected mechanical load such as overloading and load oscillations. Several surveys have been carried out in the past leading to percentages dis- tributions of machine failures [1–3]. Representative results are shown in Figure 2.1. It is interesting that three out of four failures in low voltage motors are bearings related, while stator faults account for only 9% of total faults. The distribution is 1 CISE – Electromechatronic Systems Research Centre, Universidade da Beira Interior, Portugal 2 School of Computing, Electronics and Mathematics and the Research Institute for Future Transport and Cities, Coventry University, UK
- 27. exactly opposite when looking at high voltage motors where two out of three failures are stator related, while bearing faults account for 13% of total failures. This is due to the fact that large machines have sleeve bearings degradation of which is significantly slower than ball bearings. In medium voltage, motors stator and bearing faults are more or less of equal severity. Finally, in all cases, the rotor faults account for about 10% of total motor failures. Due to the significance of the electrical machines uninterrupted operation and the negative impacts of failures, the area of electrical machines’ condition mon- itoring has flourished during the last 30 years and has known tremendous devel- opment and progress. However, the plethora of machine sizes, geometries, components and applications have been reported to create unique and special diagnostic cases where misdiagnosis may happen. Moreover, new applications constantly appear, where electrical machines and drives are the key components and as such, their reliable operation is of high importance. Typically new appli- cations require proper adjustment and reconfiguration of existing diagnostic pro- cedures or even completely new diagnostic approaches, and this is one more reason for continuous active research in this field. 2.1.2 Condition monitoring, fault diagnosis and prognosis Condition monitoring of electrical machines is a broad scientific area, the ultimate purpose of which is to ensure the safe, reliable and continuous operation of elec- trical machines. Condition monitoring can be divided into two sub-areas, namely fault prognosis and fault diagnosis. Prognosis (in Greek: ‘‘PrgnwsiV’’) is a complex Greek word from ‘‘pro’’ which means before and ‘‘gnosis’’ which means knowledge. Fault prognosis is the scientific area which aims to predict failures before they happen. The estimation of the remaining useful life (RUL) of a component or a device is the main goal of the fault prognosis area. For this reason, prognosis is strongly related to material sci- ence and degradation. On the other hand, diagnosis (in Greek: ‘‘Di agnwsiV’’) is also a complex Greek word from ‘‘dia’’ which is the term for division and ‘‘gnosis’’ for knowledge. So, the term diagnosis is related to penetrating into the problem to get knowledge. Fault diagnosis assumes that a fault has already happened in a device, while the final goal is to detect the fault with an appropriate diagnostic procedure. In electrical Low voltage machines 75% 10% 37% 12% 41% 10% 66% 8% 13% 13% 9% 6% Medium voltage machines High voltage machines Stator Rotor Bearings Other Figure 2.1 Distributions of electrical machine failures depending on the voltage supply level 8 Diagnosis and fault tolerance
- 28. machines a fault will automatically create an asymmetry in the magnetic field. This asymmetry will pass on to various electromagnetic variables like the currents, voltages, magnetic flux, electric and mechanical power, torque and speed. So, the diagnostics engineer needs to monitor and analyse some of the above variables and detect any divergence from the expected healthy machine characteristics. Figure 2.2 illustrates the most important characteristics of the diagnosis procedure. 2.1.3 Fault diagnosis of electrical machines As there are many different machines, drives and applications, it is only natural that there is also a plethora of electrical machines faults and diagnostic methods. Amongst them the most favourable is the motor current signature analysis (MCSA) which is the analysis of the stator current harmonic index [4,5]. Most define the MCSA as the monitoring and spectral analysis of the stator current at steady state. Despite the method’s origins, the name is very generic and should include the analysis of the stator current spectra under transient operation also. Anyway, this method has become favourable due to its unique characteristics such as remote monitoring [6] (Figure 2.3), low implementation costs and equipment, and con- tinuous and online monitoring capability. However, many other methods have been proposed and they rely on the monitoring of other variables such as the magnetic flux [7], torque [8], electric power [9], voltage [10], etc. As a priority, in this chapter, all MCSA formulas will be given for most common faults. However, other methods will be also discussed and analysed. To facilitate reading and comprehension, this section will be organised in the following strategy. First, faults that are common in both induction and permanent magnet machines will be discussed and the different diagnostic strategies applied for each machine will be properly analysed. Then faults uniquely existing in dif- ferent machines will be discussed. Diagnostic procedure Speed of diagnosis Severity estimation Financial cost On/offline Intrusion Monitoring equipment Decision making Manual Automatic No Yes Production Interrupted? Level? Electrical machine Prognosis ability? Service and repair Replacement with new one Complexity? Permanently installed Portable Is it possible? Is it faster than the evolution of the fault? Figure 2.2 Characteristics of the diagnostic procedure Voltage-source inverter-fed drives 9
- 29. 2.1.3.1 The eccentricity fault Eccentricity is the condition where the rotor is abnormally positioned inside the stator, and as a consequence, the air-gap around the rotor circumference is not symmetrical [11]. There are mainly two types of eccentricity: static and dynamic. In both eccentricity types, the geometrical centre of the rotor is different than that of the stator. Moreover, in the case of the static eccentricity, the centre of rota- tion is fixed in space and coincides with the rotor geometrical centre [Figure 2.4(a)]. However, in the case of the dynamic eccentricity, the centre of rotation does not have a fixed location but constantly changing in space over time [Figure 2.4(b)]. A combination between the two above-mentioned conditions is called mixed eccentricity. It is important to note that some inherent mixed eccentricity always exists even in new electrical machines [12]. The maximum permitted level of inherent eccentricity is 10%, although in most cases, manufacturers put an effort to keep it significantly less than that. The static eccentricity is a fault usually introduced during the manufacturing stages of the motor. It can be caused by the ovality of the stator or by the mis- placement of the rotor in the stator. On the other hand, the dynamic eccentricity is usually related to bearing failures or bent motor shaft. If not detected at an early stage, it will evolve and lead to the rubbing between rotor and stator, which will cause irreparable damage and possible deformation of the electrical machine iron core (Figure 2.5). Usually, deformation of an electrical machine’s iron core leads to long service period and is expensive. The eccentricity causes an asymmetry of the machine’s air-gap geometry, which directly influences the air-gap permeance and will cause an asymmetry in the machine’s rotating magnetic field. That asymmetry is expressed via enhanced higher harmonics in the machine’s electromagnetic and mechanical operating variables and characteristics. Figure 2.3 Remote monitoring of motor currents. 2017–2018 IEEE. Reprinted, with permission, from Reference [6] 10 Diagnosis and fault tolerance
- 30. Induction motors For induction motors, the static or dynamic eccentricity fault can be detected through the monitoring of signatures in the stator current located at frequencies [14]: fecc IM ¼ kR nd ð Þ 1 s p n fs (2.1) where R is the rotor slot number, k is the integer, s is the slip, p is the pole pairs, n is the stator harmonic ranks, fs is the supply frequency and nd is an integer which is zero for static eccentricity and non-zero for dynamic eccentricity. (a) (b) Figure 2.5 Major mechanical damage to the stator due to rotor rubbing. Not repairable unless (a) the core is dismantled and repaired and (b) the core is restacked or replaced [13] (with permission from EASA) OR OS OR OS OR OS OR OS OR OR OS OS OS OR OR OS (a) (b) Figure 2.4 Four different instances of the rotor rotation for (a) static and (b) dynamic eccentricity Voltage-source inverter-fed drives 11
- 31. Furthermore, the following formula [11] has also been proposed to detect the mixed eccentricity fault in the low-frequency area of the stator current: fecc IM2 ¼ fs fr (2.2) where fr ¼ 1 s ð Þ=p ½ fs, that is the mechanical rotation frequency. It is important to note that formula (2.1) does not always offer reliable results for the cases of only-dynamic or only-static eccentricity diagnosis [15]. Previous works have pointed out that diagnosis is possible only for certain com- binations between the rotor slot and the pole pair numbers [16,17]. To be more specific, if nd ¼ 0; k ¼ 1 then formula (2.1) transforms into: fPSH ¼ R 1 s p n fs (2.3) Equation (2.3) corresponds to the location of the principle slot harmonics (PSH) in the stator current frequency spectrum. Induction motors with a rotor slot number multiple of the pole pair number produce such harmonics in the line current. For those motors, the only-static and only-dynamic eccentricity faults cannot be detected because the fault signatures are located at the same frequencies as the normally existing PSH. However, for non-PSH induction motors, if the rotor slot number is even, it is possible to monitor the only-static and only-dynamic eccentricities at low or no- load operation. Formula (2.1) is very reliable for non-PSH induction motors with odd rotor slot numbers [15]. Figure 2.6 illustrates the application of MCSA to detect a mixed eccentricity faulty condition in a four-pole cage induction motor with 28 rotor bars. Permanent magnet machines When there is eccentricity in permanent magnet (PM) machines, a portion of the stator is closer to the PM of the rotor, thus generating a net attraction force acting on the rotor [19]. As a result, an unbalanced magnetic force is generated between the rotor and the stator. Unbalanced forces may be the most troubling problem when brought by rotor eccentricity. That is because they may cause significant levels of vibration and noise which accelerates the motor degradation [20]. Previous studies have shown that eccentricity affects interior PM (IPM) motors differently than surface mounted PM (SPM) motors [21]. It has been shown that, the eccentricity distorts the air-gap magnetic flux density more in the case of the IPM motors. In the same work, authors came to the conclusion that the magnetic unbalanced forces increase linearly due to relatively small eccentricity ratio in SPM motors. However for the IPM motors, they increase significantly and non-linearly due to severe magnetic saturation with the eccentricity level. Furthermore, the eccentricity effects are different between symmetrical and asymmetrical PM machines [20]. Rotor eccentricity has a minor impact on asymmetric motors in terms of the magnitude of the radial force. Low detent 12 Diagnosis and fault tolerance
- 32. torque, the primary reason for using asymmetric motors, is magnified if rotor eccentricity is involved, so the importance of manufacturing precision cannot be overstressed. One more important finding was reported in [22]. The results reveal that the static eccentricity and the uneven magnetisation cause exactly the same harmonic 0 –50 –100 0 –50 –100 0 50 Fundamental PSH PSH f[0.5(R–1)(1–s)–1] f[0.5(R+1)(1–s)–1] f[0.5(R+2)(1–S)–1] f[0.5(R+3)(1–S)–1] Fundamental f+3fr f+2fr f+fr 4fr–f 3fr–f f–fr f–2fr 100 150 0 50 700 –120 –100 PSD (dB) PSD (dB) PSD (dB) –80 –60 –40 –120 –100 PSD (dB) –80 –60 –40 720 740 760 780 800 820 840 860 700 720 740 760 780 Frequency (Hz) Frequency (Hz) (a) (b) 800 820 840 860 100 150 Figure 2.6 Simulated, normalised spectra of the line current of a four-pole induction machine with 28 rotor slots under load (a) around the fundamental and (b) around the PSH. Upper: healthy. Lower: with mixed eccentricity (41.37% SE, 20.69% DE). 2017–2018 IEEE. Reprinted, with permission, from Reference [18] Voltage-source inverter-fed drives 13
- 33. index of the unbalanced magnetic force. However, in dynamic eccentricity condi- tions, the amplitude of the DC component has been reported to rise significantly. Regarding the diagnosis of eccentricity, formula (2.4) was initially proposed for static eccentricity diagnosis via the stator current harmonic index [23]. Further investigation led to the conclusion that the formula is also reliable for the cases of dynamic and mixed eccentricity [24,25]. Results from the application of (2.4) can be seen in Figure 2.7: fecc PM ¼ 1 2k 1 ð Þ p fs (2.4) where k is the integer, p is the pole pairs and fs is the supply frequency. In a later work, the following formula was also proposed, the concept of which is very similar to that of (2.2). That means examination of the sidebands around the 0 –20 –40 –60 PSD (dB) –80 –100 –120 0 20 40 60 80 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) 100 120 140 0 –20 –40 –60 PSD (dB) –80 –100 –120 20 40 60 80 100 120 140 0 –20 –40 –60 0.25fs 1.25fs 2.25fs 0.25fs 1.25fs 2.25fs 0.25fs 1.25fs 2.25fs 0.25fs 1.25fs 2.25fs 0.25fs 1.25fs 2.25fs PSD (dB) –80 –100 –120 20 40 60 80 100 120 140 0 –20 –40 –60 PSD (dB) –80 –100 –120 20 40 60 80 100 120 140 0 –20 –40 –60 PSD (dB) –80 –100 –120 20 40 60 80 100 120 140 0 –20 –40 –60 PSD (dB) –80 –100 –120 20 40 60 80 100 120 140 (a) (c) (d) (f) (b) (e) Figure 2.7 Normalised line current spectra of an eight-pole, 50 Hz PM synchronous motor where: (a) healthy, (b) with 30% SE, (c) with 40% DE, (d) with 30% SE and 40% DE, (e) experimental result for 50% DE and (f) experimental result for 50% SE. 2017–2018 IET. Reprinted, with permission, from Reference [28] 14 Diagnosis and fault tolerance
- 34. fundamental stator current harmonic located at the mechanical rotation frequency [26]: fecc PM2 ¼ 1 1 p fs (2.5) A different later work though pointed out that (2.5) describes harmonics produced not only by eccentricity but also demagnetisation and rotor and load imbalances [27], which does not allow reliable discrimination and identification of the exact fault condition. 2.1.3.2 The stator inter-turn fault Stator electrical faults can be either short or open-circuit failures. Short-circuit faulty conditions include phase-to-phase and phase-to-ground short-circuits. How- ever, in both open and short-circuit conditions, the machine will suffer from high currents and will be severely damaged, thus many protection methods exist the aim of which is to trip the protection relays and disconnect the machine immediately when the fault appears. So, the above-mentioned conditions are not to be discussed any further in this section as they are not related to early fault stages where the prompt diagnosis is meaningful. Instead, this section will focus on the stator inter- turn faults. Stator inter-turn faults happen between stator winding wires of the same phase because of degradation of the insulation materials [29,30]. The stator inter-turn fault is considered an early fault condition which will evolve into an actual short- circuit and lead to machine damage. However, the term ‘‘early’’ can be misleading because it has been shown that this fault evolves very fast (in seconds [31]) into higher severity levels leading to an actual short-circuit condition and triggering the protection relays to disconnect the machine. Different degradation mechanisms might affect the end-winding portion or the slot portion [32]. In addition, it should be noted that the time progression and extent of the damage depends on the location of the fault and the original number of shorted turns [33]. In order to understand the motor winding configuration in the case of an inter- turn fault, Figure 2.8 is presented, and one can see two neighbouring stator slots where the winding turns go and then the two neighbouring stator slots where the same winding turns return. Each slot’s conductors/wires are divided in three groups. In the first and last slots, there are k turns, one single turn and j turns. In the inner slots, there are m turns, a single turn and n turns. It is supposed that the short-circuit happens between the points A and B. Then it is evident that, from left to right, the four slots contain k þ 1, n, n þ 1 and k wires, respectively, which belong to the healthy part of the winding. The other wires, which mean j, 1 þ m, m and j þ 1, form a closed loop where the short-circuit current will develop. It is to be noted that when modelling this condition, a small resistance should be added between the points A and B to account for the contact resistance between the shorted turns. Typically, the contact resistance value is between 0.1 and 1 W. Figure 2.9 illustrates a real case of an inter-turn fault which happened to an industrial induction motor. Voltage-source inverter-fed drives 15
- 35. Induction machines When there is an inter-turn short-circuit fault, the resistance of the faulted phase drops by a portion which depends on the fault level severity or in other words the resistive part of the phase which now belongs to the shorted loop. This means that when the machine is supplied by a symmetrical, three-phase, voltage source, the faulty phase will draw more current than the other two. As a result, there is an imbalance between the three phase currents which in principle means an asym- metrical rotating magnetic field. The negative sequence current interacts with the fundamental slip frequency current in the rotor to produce torque pulsation at A B k l j m l n n j l k l m Figure 2.8 Winding distribution in the case of an inter-turn short-circuit Figure 2.9 Burned out turns of an induction motor’s stator winding due to an inter-turn fault (courtesy of Mr M. Thumpy) 16 Diagnosis and fault tolerance
- 36. double the supply frequency [34]. The consequent speed ripple induced harmonic index back to the stator with frequency three times the fundamental one. Due to the above, the stator current will experience an increase of the third harmonic [34–37]. This is clearly shown in Figure 2.10. Saturation plays an important role as it can enhance the amplitude increase of the third harmonic in the stator current [37]. However, the third harmonic increase is also associated with other imbalances [38] such as asymmetrical three-phase voltage supply, inherent asymmetry between the three phase windings, high resistance connections which lead to unbalanced phase currents, etc. Moreover, it was shown that the increase of the third harmonic 800Hz (b) (a) 0Hz –95 dBVrms –95 dBVrms 10 dB /div dB Mag 10 dB /div dB Mag A: CH1 Lin Spec X:469 Hz Y:-72.1276 dBVrms X:568 Hz Y:-69.8802 dBVrms 800Hz 0Hz 5 dBVrms A: CH1 Lin Spec 5 dBVrms Figure 2.10 Spectral content of the line current of a: (a) healthy motor and (b) motor with stator inter-turn fault operating under s ¼ 0.028. 2017–2018 IEEE. Reprinted, with permission, from Reference [34] Voltage-source inverter-fed drives 17
- 37. in the stator current does not have a monotonic relation to the fault level severity [39]. So, the monitoring of the third harmonic is not deemed as very reliable for very low severity levels of inter-turn short-circuits as it may lead to a false negative alarm. Practically, when there is a stator inter-turn fault, the created asymmetrical rotating magnetic field will induce asymmetrical currents in the rotor. As a result, rotor slot related harmonics will rise. So, past works [40] have proposed the fol- lowing formula for the detection of stator inter-turn faults: fsc IM ¼ kR 1 s p 2nsa n fs; k 2 N (2.6) where R is the rotor slot number, k is the integer, s is the slip, p is the pole pairs, n is the stator harmonic ranks, fs is the supply frequency and nsa is the rank of the saturation harmonics. An interesting method able to detect the fault existence as well as the faulty phase with low computational time is the Park’s vector approach (PVA) [41]. The method relies on the analysis of the Park’s vector components id; iq as follows: id ¼ ffiffiffi 2 p ffiffiffi 3 p ia 1 ffiffiffi 6 p ib 1 ffiffiffi 6 p ic (2.7) iq ¼ 1 ffiffiffi 2 p ib 1 ffiffiffi 2 p ic (2.8) Under ideal conditions, the three phase currents in (where n ¼ a, b, c) lead to a Park’s vector with the following components: id ¼ ffiffiffi 6 p 2 iM sin wt (2.9) iq ¼ ffiffiffi 6 p 2 iM sin wt p 2 (2.10) The corresponding representation is a circular locus centred at the origin of the coordinates. Under abnormal conditions, (2.9) and (2.10) are no longer valid, and consequently the observed picture differs from the reference pattern. This can be seen in Figure 2.11 where id is on the x axis and iq on the y axis, respectively. The displacement of the locus reveals the faulty phase. However, the PVA on its own cannot offer an easy measure of determining the fault level severity with accuracy. That is because the determination of the locus angle shift is influenced by other parameters as well. This is why, the method evolved into the extended PVA (EPVA) which relies on the monitoring of the frequency spectra of the Park’s vector modulus [42]. It was found that, the stator inter-turn fault gives rise to harmonics located at twice the supply frequency in the Park’s vector modulus spectra (Figure 2.12). 18 Diagnosis and fault tolerance
- 38. Permanent magnet machines PM machines are widely used in various special applications where high power density and efficiency is required, while restrictions on the size of the motor apply, such as electric vehicle propulsion, aerospace applications, etc. Due to their critical role associated with safety, prompt and reliable diagnosis is required. This makes the inter-turn short-circuits failure quite a timely and challenging issue because it is the type of fault that progresses fast leading to undesired motor breakdown. It was shown that the inter-turn fault may cause excessive heat that is proportional to the square of the circulating current in the shorted turns [43]. This type of the PM machine plays an important role for the impact of the inter-turn short-circuit faults. Past contributions have shown that the short-circuit current is lower in IPM than SPM machines [44]. This is crucial for the evolution time of the fault. The short-circuit current is relatively high and will generate heat. This will lead not only to extension of the inter-turn fault including more and more turns until the motor breakdown bus also demagnetisation of the PMs [45] (Figure 2.13). However, the required motor toque is the same which leads to higher (a) (b) (c) Figure 2.11 Experimentally derived Park’s vector pattern for (a) healthy motor, (b) motor with 18 shorted turns in Phase A and (c) motor with 18 shorted turns in Phase B. 2017–2018 IEEE. Reprinted, with permission, from Reference [41] 0 3 2 1 Amplitude (A) Amplitude (A) Amplitude (A) 3 2 1 3 2 1 20 40 60 80 Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) (b) (c) 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Figure 2.12 EPVA signature corresponding to: (a) healthy motor, (b) motor with 12 shorted turns and (c) motor with 36 shorted turns. 2017–2018 IEEE. Reprinted, with permission, from Reference [42] Voltage-source inverter-fed drives 19
- 40. current to serve the load need. Higher current will lead to more heating accelerating both demagnetisation and windings insulation degradation. Similar to induction motors, the third line current harmonic as well as the other odd triplet harmonics are expected to rise with the inter-turn fault due to the three phase currents asymmetry, while absent in healthy motors [46]. This is shown in Figure 2.14. At the same time, it can be seen that the negative third harmonic frequency increases only in the case of inter-turn fault. Furthermore, formula (2.11) has been proposed [44] for the detection of inter- turn faults in PM machines through the spectral analysis of the stator current at steady state. It is evident that for k ¼ 1, the formula depicts the fault related 80 40 0 –40 Line current (dB) Line current (dB) Line current (dB) –80 80 40 0 –40 –80 80 40 0 –40 –80 –1.8 –9f –7f –5f –3f –f f 3f 5f 7f 9f –9f –7f –5f –3f –f f 3f 5f 7f 9f –9f –7f –5f –3f –f f 3f 5f 7f 9f –1.2 –0.6 0.0 Frequency (kHz) (a) (b) (c) Frequency (kHz) 0.6 1.2 1.8 f = 175 Hz f = 175 Hz f = 175 Hz –1.8 –1.2 –0.6 0.0 0.6 1.2 1.8 Frequency (kHz) –1.8 –1.2 –0.6 0.0 0.6 1.2 1.8 Figure 2.14 Line current frequency spectra of a PM motor at a rated speed and full load where: (a) healthy motor under balanced supply, (b) healthy motor under imbalanced supply and (c) motor with inter-turn fault under balanced supply. 2017–2018 IEEE. Reprinted, with permission, from Reference [46] Voltage-source inverter-fed drives 21
- 41. harmonics around the fundamental stator current harmonic. An example from the application of the formula in a real PM motor is shown Figure 2.15: fitsc PM ¼ k 2m þ 1 p fs ; k; m 2 N (2.11) 2.1.3.3 Broken rotor bars or end-rings There are two types of rotor squirrel cages of induction motors; fabricated and cast. Usually, low voltage induction motor rotors are cast aluminium, and high voltage ones are fabricated from copper. Medium voltage induction motor rotors can be of 0 –20 –40 –60 –80 PSD of stator current (dB) PSD (dB) –100 –120 –140 0 –20 –40 (1–3/P)fs (1–1/P)fs (1+1/P)fs (1+3/P)fs (1+5/P)fs (1+7/P)fs (1–3/P)fs (1–1/P)fs (1+1/P)fs (1+3/P)fs (1+5/P)fs (1+7/P)fs –60 –80 –100 –120 –140 0 20 40 60 80 Frequency (Hz) (a) (b) Frequency (Hz) 100 120 140 0 20 40 60 80 100 120 140 Figure 2.15 Normalised line-current spectra of full-load PMSM in (a) healthy and (b) motor with 1 short-circuited turn. 2017–2018 IEEE. Reprinted, with permission, from Reference [44] 22 Diagnosis and fault tolerance
- 42. both types. Usually aluminium rotors have skewed bars, while in copper rotors, the bars are usually parallel to the shaft. Another difference between them is that in aluminium rotors, there is no insulation between the bars and the rotor iron core. On the other hand, in copper rotors the bars are firstly insulated and then placed inside the slots of the iron core. Those differences play an important role in the area of diagnostics as it will be discussed below. A crack or breakage in an aluminium cage usually originates from improper casting which allows air bubbles inside the cage. This phenomenon is known as porosity [47]. These air-bubbles result in local high-resistance areas that cause hotspots and make the cage prone to local breakage [48]. On the other hand, copper rotors bars usually break due to thermal and mechanical stresses. First, the thermal stress will cause thermal expansion of the bars which might disconnect from the end-ring. Second, the mechanical stresses such as vibrations and frequent start-ups may lead to the same result [49]. However, the co-existence of both is probably the reason while the one mechanism enhances the catastrophic effects of the other. When there is a broken rotor bar, the adjacent bars are overcharged, thus expected to break next [50,51]. This is shown in Figure 2.16. This is the usual case in aluminium rotors; however, multiple cases of non-adjacent broken rotor bars have been reported in large industrial induction motors [52]. Broken rotor bars do not normally result in an immediate failure of the motor. If the fault goes unnoticed and enough bars break then there is a chance that the motor will not be able to develop enough starting torque to accelerate from stall. However, in the past, some catastrophic failures have been reported like the one shown in Figure 2.17 where the rotor bars bent and severely damaged the stator winding [53]. When there is a broken rotor bar fault, two counter rotating magnetic fields are created with slip frequencies sf s and sf s. The first one does not interact with the stator, while the second one induces components of frequency 2sf s back to the stator windings. As a result, the broken rotor bar fault can be identified in the stator current spectrum via the existence of harmonics at 1 2s ð Þfs [55]. Further- more, due to the speed ripple effect, a second broken bar fault harmonic appears to the right of the fundamental frequency at frequency: 1 þ 2s ð Þfs [56]. This interac- tion between the mechanical and electromagnetic quantities continues, and as a result multiple fault-related signatures are created at equal frequency distances 2sf s from one another. As a result, the following formula has been proposed for the identification of the broken rotor bar fault around the fundamental stator current frequency: fbb ¼ 1 2ks ð Þfs; k 2 N (2.12) The stator current is rich in harmonics due to the saturation and other interacting phenomena. The result is that odd multiples of the supply frequency exist in the stator current. Those higher harmonics create additional magnetic fields inside the induction motor which are rotating with higher speeds due to their higher fre- quencies. Those magnetic fields also interact with the broken rotor bar fault, and as Voltage-source inverter-fed drives 23
- 43. a result more signatures are created. The following formula has been proposed to include the broken bar fault sidebands at higher harmonics [57]: fbb2 ¼ k p 1 s ð Þ s fs; k p 2 N (2.13) Figure 2.18 illustrates the application of (2.12) and (2.13) in order to detect a broken rotor bar fault using the stator current frequency spectra. It is evident that the fault creates specific fault-related harmonic sidebands around the odd multiples of supply frequency. 0.0 10.0 8.0 6.0 4.0 2.0 –2.0 –4.0 –6.0 –8.0 –10.0 0.0 10.0 8.0 6.0 4.0 2.0 –2.0 –4.0 –6.0 –8.0 –10.0 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 Geometrical angle 200.0 220.0 240.0 260.0 280.0 300.0 320.0 340.0 360.0 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 Geometrical angle (a) (b) Current density (A/mm 2 ) Current density (A/mm 2 ) 200.0 220.0 240.0 260.0 280.0 300.0 320.0 340.0 360.0 Broken bar Figure 2.16 Spatial distribution of the amplitude of the current density of the rotor bars along the rotor circumference for (a) healthy machine and (b) machine model with one broken bar. 2017–2018 IEEE. Reprinted, with permission, from Reference [54] 24 Diagnosis and fault tolerance
- 44. 220 40 0 –100 (1 – 6s)fs (1 – 4s)fs –50 –150 Amplitude (dB) 42 44 46 48 50 52 54 56 58 60 240 5fs – 6sfs 5fs – 4sfs 7fs – 8sfs 7fs – 6sfs 260 280 300 320 340 360 Frequency (Hz) Frequency (Hz) (a) (b) (1–2s)fs (1 + 2s)fs (1 + 4s)fs (1 + 6s)fs Figure 2.18 Comparative frequency spectra of the healthy induction motor (dashed) and one with a broken bar fault (solid) around (a) the fundamental stator current harmonic and (b) the fifth (250 Hz) and seventh (350 Hz) stator current harmonics (FEM result) (a) (b) Figure 2.17 Forced outage of 3.3-kV, 450-kW gasoline transfer pump induction motor due to rotor bar damage. (a) Rotor bar detachment from end ring and damage in rotor core due to arcing. (b) Damage in stator end winding due to protrusion of rotor bar. 2017–2018 IEEE. Reprinted, with permission, from Reference [53] Voltage-source inverter-fed drives 25
- 45. Lately, a lot of work has been focused on broken rotor bar fault detection. One of the reasons is that some phenomena exist, which can produce broken rotor bar fault harmonics in the stator current spectra of healthy motors. The misdiagnosis may lead to false positive alarms which may result in high costs for inspection and service without need. Such cases are the following: ● Mechanical load oscillations [58] ● Magnetic anisotropy of the rotor iron core [59] ● Axial cooling rotor air ducts (Figure 2.19) [60] ● Fan blades number in pumping applications [61] Furthermore, earlier in this section, it was mentioned that in large induction motors, cases have been reported with multiple broken rotor bars (Figure 2.20). Moreover, in some cases, the rotor bars might break in non-adjacent positions. It has been reported that, the stator current analysis is not capable to provide information regarding the health of the rotor cage via the proposed frequency component 1 2s ð Þfs if the broken bars are located electrically p/2 rad away with respect to each other [51,52]. Figure 2.20 Rotor of a 5-MW, 6-kV cage motor with multiple broken bars. 2017– 2018 IEEE. Reprinted, with permission, from Reference [52] 0 –20 –40 (a) (b) –60 –80 I s spectrum (dB) –100 40 44 fd k1 = 4 fd k1 = 3 fd k1 = 2 fd k1 = 1 48 52 56 60 Frequency (Hz) 64 68 72 76 80 Figure 2.19 (a) A rotor with axial cooling air ducts. (b) Example of the stator current spectrum of a healthy motor (kidney holes) with four magnetic poles and equal axial air ducts operating under rated load conditions. 2017–2018 IEEE. Reprinted, with permission, from Reference [60] 26 Diagnosis and fault tolerance
- 46. Mainly due to such unreliability of the traditional diagnostic approach of the fast Fourier transform application at steady state, to detect rotor-related faults, a new trend has been developed. Special focus is now given to the monitoring and analysis of the stator current during start-up. The proposed methods have defined a new area called transient MCSA [62]. In this family, many methods have been proposed so far: the short-time Fourier transform [63], the MUSIC [64] and the Wavelet transform [62,65]. The main idea behind the application of such methods is that the broken bar fault harmonics are slip dependent. As a result, in a time- frequency decomposition, the trajectory of those harmonics frequency will vary versus time. This is not the case for the stator-related harmonics. This allows for the detection of the fault during transients. Another advantage of the stator current monitoring at start-up is that the rotor current gets its maximum, and as a result, rotor electrical faults are magnified during start-up with respect to the steady state. Aiming to illustrate the application of such methods for the detection of broken rotor bars, Figure 2.21(a) shows the application of the analytical wavelet transform (AWT), whereas Figure 2.21(b) shows the application of the discrete wavelet transform (DWT). 2.1.3.4 Demagnetisation of permanent magnets Demagnetisation is the condition at which the PMs lose partially or fully their ability to magnetise. Motor applications involving PM motors require high power and torque density which cannot be usually supported by electrical machine types applying only electromagnets. If the PMs are demagnetised, the magnetic flux density drops, and with it the output torque and mechanical power. So, the PM machine loses its main selection purpose. It is to be noted that the demagnetisation effect could be irreversible, depending on the operating conditions. As a result, the reliable detection of this fault is crucial for the safe and normal operation of the PM machine. Before discussing the diagnosis of the demagnetisation any further, it is important to explain the phenomenon and its dependence on temperature. The normal curve of a PM material is shown in Figure 2.22(a), following the line described by the points Br; a; a0 ; a00 ; Hc. The curve can be assumed to be linear for high magnetic flux density values followed by a sharp drop until the point of coercive magnetic field strength Hc. The magnet operates at the intersection of the demagnetisation curve and the load characteristic line. Normally, the intersection point exists on the linear part of the curve (around the point a0 ). However, an increase in the load will drive the operation point below the knee of the curve (around the point a00 ). If that happens, the PM will not be able to fully recover its former remanence magnetic flux density when the demagnetising effect disappears. Instead it will be characterised by a new B0 r which is less than the original Br. A similar approach is followed to explain the irreversible demagnetisation due to the temperature increase. The impact of the temperature on the demagnetisation curve of the PM is shown in Figure 2.22(b). An increase in temperature leads to a new curve characterised by less coercive magnetic field strength as well as less remanence magnetic flux density. As a result, the same load line, which for Voltage-source inverter-fed drives 27
- 48. temperature T1; intersected the demagnetisation curve at the linear part, now intersects the curve for T2 T1 at point c0 which is below the knee of the shifted demagnetisation curve. The result is that when the demagnetising effect dis- appears, the new remanence magnetic flux density will be B00 r which is lower than the original Br. Now if the temperature increases back to T1; the remanence magnetic flux density will increase to B0 r with respect to B00 r ; however, it will be less than the original one Br. For applications where the load requirements are fixed, it is evident that demagnetisation will evolve into increased fault levels. Due to demagnetisation, the produced torque capability of the motor for a given current will decrease. So, in order to serve the fixed load/torque requirements, the stator winding is forced to draw more current, leading to increased Joule losses and elevation of temperature, thus accelerating the demagnetisation of the PMs and leading to faster degradation of the windings insulation materials [67]. It is to be noted that demagnetisation in electrical machines might be uniform or partial. Uniform demagnetisation is more difficult to detect since its distorting effect on the magnetic field distribution is minimum [68]. However, partial demagnetisation leads to a strong asymmetry of the motor’s magnetic field which will unavoidably lead to unbalanced magnetic pull (UMP) [69]. UMP will lead to torque oscillations, vibrations and noise and could cause some level of eccentricity [70]. A second level of fault evolution concerns the bearings which are overstressed and degrade faster. The PM demagnetisation effect gives rise to stator current frequencies located at fdm ¼ 1 k p fs; k 2 N (2.14) The effect of partial demagnetisation on the magnetic flux density distribution and stator current frequency spectra is presented in Figure 2.23 for a six-pole PM synchronous machine (PMSM) operating at 6,000 rpm. (a) Demag. effect of current Normal load Normal load Open cct. load Open cct. load B Br B′r B Br B′r B″r H Hc T1 T1T2 T2 H Hc a″ a″ b′ a′ a′ c′ a a b (b) Figure 2.22 PM operating point (demagnetisation curve and load line). Irreversible demagnetisation due to (a) external demagnetising MMF. (b) Operation at high temperature (SmCo- or NdFeB-based magnets). 2017–2018 IEEE. Reprinted, with permission, from Reference [66] Voltage-source inverter-fed drives 29
- 49. 2.1.3.5 Bearing faults Bearings are the electrical machine components which guarantee and secure the appropriate rotor positioning with respect to the stator while allowing rotation. There are two types of bearings, namely rolling elements or ball and sleeve (a) (b) 0 –10 –20 –30 –40 –50 Amplitude (dB) –60 –70 –80 –90 0 1/3 2/3 1 4/3 5/3 2 7/3 8/3 3 10/3 11/3 Harmonic order (xfe) 4 13/3 Healthy motor 50% magnetised Flux density Tesla 352.30751E-6 / 138.14315E-3 138.14315E-3 / 275.9331E-3 275.9331E-3 / 413.72484E-3 413.72484E-3 / 551.51568E-3 551.51568E-3 / 689.30653E-3 689.30653E-3 / 827.09737E-3 827.09737E-3 / 964.88821E-3 964.88821E-3 / 1.10268 1.10268 / 1.24047 1.24047 / 1.37826 1.37826 / 1.51605 1.51605 / 1.65384 1.65384 / 1.79163 1.79163 / 1.92942 1.92942 / 2.06721 2.06721 / 2.20501 Demagnetised motor 14/3 5 16/317/318/3 Figure 2.23 (a) Spatial distribution of the magnetic flux density in a partially demagnetised PMSM. (b) Simulated stator current harmonics in a healthy and a partially demagnetised PMSM when running at 6,000 rpm. 2017–2018 IEEE. Reprinted, with permission, from Reference [71] 30 Diagnosis and fault tolerance
- 50. bearings (Figure 2.24). It was shown earlier in Figure 2.1 that bearing failures are the main fault in low and medium voltage machines, while being of significantly lesser importance in high voltage machines. This is due to the fact that high voltage machines utilise sleeve bearings, while low and medium voltage machines utilise rolling element bearings [3]. For this reason, this section will be focused on the rolling element bearings fault detection. It has been shown that, the location of the fault or in other words the faulty component of the bearing produces a unique vibrating harmonic response. More (a) (b) Vibration accelerometer Vibration accelerometer Shock pulse transducer Shaft rotation Y-axis proximeter High pressure fluid R Reaction F Destabilising components P Pressure W Whirl force Minimum clearance point Low pressure fluid W F P R Roller elements Inner race Housing Shaft Outer race Cage X-axis proximeter Figure 2.24 Bearing types and components: (a) rolling element bearing and (b) forces acting upon a shaft in a sleeve bearing. 2017–2018 IET. Reprinted, with permission, from Reference [2] Voltage-source inverter-fed drives 31
- 51. specifically, the following formulas have been proposed to detect the origin of the bearing fault [3,72]: Outer race defect fo ¼ N 2 fr 1 Db Dc cos b (2.15) Inner race defect fi ¼ N 2 fr 1 þ Db Dc cos b (2.16) Ball defect fb ¼ Dc Db fr 1 Db Dc cos b 2 # (2.17) where N is the number of balls, Db is the ball diameter, Dc is the bearing pitch diameter and b is the contact angle of the balls on the races. As a result, it is possible to monitor each individual defect via the stator current frequency spectrum by applying the following formula [73]: freb ¼ fs mf c; m 2 N (2.18) where fc corresponds to the appropriate vibration frequency described by (2.15)– (2.17). An application of the above formulas can be seen in Figure 2.25 for inner and outer race faults. However, past experience has shown that the use of the above characteristic frequencies is not reliable when trying to detect general bearing faults, such as contamination or degradation. It is to be noted that bearing failures create some level of eccentricity, so there are numerous cases where the detection of eccentricity has led to the detection of bearing failures indirectly. 2.1.4 Alternative diagnostic methods It is to be expected that although the analysis of the stator current for diagnostic purposes is indeed a powerful tool, it still has weaknesses in some applications or specific problems. This is the reason for the existing rich literature where many researchers propose alternative signals or methods to overcome the MCSA draw- backs. Some of the most frequently met will be discussed in this section. 2.1.4.1 Electromagnetic/mechanical torque monitoring The torque monitoring has drawn a lot of interest over the years, whether it is the electromagnetic or the mechanical one. The electromagnetic is difficult to measure directly, this is why methods exist to estimate it from current, voltage and/or flux measurements [75,76]. The mechanical torque can be measured with a torque transducer in the lab, however, has limited application in a real industrial envir- onment. However, the signatures existing in the electromagnetic torque are prac- tically the same in the mechanical torque, so multiple cases exist where researchers do not differentiate between the two. The motor’s torque comes as a result of Lenz law, so it is in some way the end effect of the electromechanical energy conversion. Any fault or imbalance causing 32 Diagnosis and fault tolerance
- 52. an asymmetry in the magnetic field will express itself as torque oscillations. So, the torque is just one signal originating from the synthesis of multiple electrical ones. This is why the torque is considered a diagnostically valuable tool. To enhance understanding, all faults described earlier produce specific side- band harmonics to the fundamental in the stator current. The exact same sidebands (a) (b) 100 260 270 280 290 300 Frequency (Hz) 310 320 330 105 0 –5 –10 –15 –20 Amplitude PSD (dB) Amplitude PSD (dB) –25 –30 –35 –40 –45 –50 –15 –20 –25 –30 –35 –40 –45 110 115 120 125 2fi 5fs + fr fs – fr + 2fi |fs – 2*fo| 7fs – fr fs + 2fi 130 Frequency (Hz) 135 140 Outer raceway defect Healthy machine Inner raceway defect Healthy machine 145 150 Figure 2.25 Application of MCSA to detect bearing faults where (a) outer raceway defect detection of loaded induction motor and (b) inner raceway defect detection of unloaded induction motor. 2017–2018 IEEE. Reprinted, with permission, from Reference [74] Voltage-source inverter-fed drives 33
- 53. (although of different amplitude) exist in the torque spectra around the DC com- ponent. Similarly, higher harmonics also exist. Figure 2.26 illustrates the diagnosis of a broken rotor bar fault located at 2sf s and at 6 2ks ð Þfs in the mechanical torque spectra of a four-pole, 400 V, 4 kW, 50 Hz cage induction motor. 2.1.4.2 Magnetic flux monitoring The main idea of the diagnostic strategies is that a fault will cause an asymmetry in the magnetic field. As a result, many works [35,77–80] have proposed the direct monitoring of the magnetic flux using flux sensors. It is possible to monitor either the radial or axial magnetic flux. The MCSA signatures exist also in the radial flux spectra for radial flux electrical machines. However, the flux sensor is independent from the motor geometry and more specifically does not depend on the number of (a) (b) 270 0 1 2 3 4 5 6 7 8 280 290 –50 –60 –70 –80 –90 –100 –110 –120 –130 –140 300 Frequency (Hz) Frequency (Hz) Amplitude (dB) Amplitude (dB) 310 320 330 –60 –40 –20 0 –80 –100 –120 Figure 2.26 Comparative experimental spectra of the motors’ (healthy and induction motor with a broken rotor bar) torque for s ¼ 0.027 (a) at the low-frequency range and (b) at the frequency range close to 300 Hz. 2017–2018 IEEE. Reprinted, with permission, from Reference [54] 34 Diagnosis and fault tolerance
- 54. poles like the stator phase winding. As a result, the radial flux spectrum is richer in harmonic index than the stator current. The application of a search coil to detect partial demagnetisation of a PM machine is shown in Figure 2.27 [81]. The distortion of the flux waveform is easily noticed. However, in most real cases, the fault needs to be diagnosed at incipient stages where it cannot be noticed by the flux waveform. As a result, spectral ana- lysis is applied. Figure 2.28 illustrates the spectra of the radial flux derivative in an induction motor under healthy condition as well as under broken bar fault [82]. 2.1.4.3 Single-phase rotation test The single-phase rotation test (SPRT) is a test applied offline and aiming to detect rotor defects [83]. The rotor is manually rotated under fixed speed while only one of the stator phases is supplied, thus producing a pulsating magnetic field. The aim is to monitor the phase current and voltage, thus being able to calculate the phase impedance. Variations of the impedance during rotation are strong indicators of rotor asymmetries. The test belongs to the non-intrusive methods, so it does not require the motor disassembly. The setup is shown in Figure 2.29(a). Furthermore, the application of the test to detect different levels and types of eccentricity in an induction machine is shown in Figure 2.29(b). 2.1.5 Fault prognosis of electrical machines There are two end goals in the field of electrical machine prognosis. The first one is to model the degradation mechanisms with accuracy. The second one is to estimate the component or device RUL [84,85]. Degradation is the irreversible process where a material, component or device loses its properties. Usually, the degradation has a strong multi-scientific character, that means many different mechanisms act together to produce the end effect which is the end of the subject’s life [86,87]. In electrical machines, the area of fault prognosis is meaningful and thus has met significant interest and progress in the case of windings insulation materials. This is t (20 ms/div) Measured voltage of the search coil (V) One mechanical round –2 –1 0 1 2 Figure 2.27 Measured voltage of the search coil from the prototype machine with partial demagnetisation Voltage-source inverter-fed drives 35
- 55. Another Random Scribd Document with Unrelated Content
- 56. them, including Colonel Palmer, were killed, a few escaped, and the rest were made prisoners. The commander of the fleet also disregarded the arrangement he had made with Oglethorpe and ordered off the war-ship stationed outside the harbor, with the result that several sloops from Havana with new troops and provisions stole into the channel and reached the Spanish stronghold. The garrison at St. Augustine had begun to feel the pinch of hunger and might soon have surrendered, but these fresh supplies tided them over and enabled them to keep up their defense. General Oglethorpe, discouraged in his plan of a blockade, decided to make one more attempt at carrying the town by assault. The British commodore, Pearse, was to attack with his fleet while Oglethorpe led his soldiers by land. The colonial troops and Indians were ready to open fire, and only waited the signal from the ships. They waited in vain, however. Instead of keeping his agreement, Commodore Pearse quietly sailed away with all his ships, sending word to General Oglethorpe that it was now the season when hurricanes might be expected off the Florida coast and that he didn't intend to risk His Majesty's fleet there any longer. Oglethorpe, who alone seemed really in earnest in his desire to fight the Spaniards, deserted by the English fleet, getting very little support from the officers and men of the Carolina regiments, found it impossible to carry on the campaign. Even his own men from Georgia were worn out by fatigue and the heat of Florida. Reluctantly therefore he gave over his expedition, and returned to Savannah. The campaign, however, had shown the Spaniards that the governor of Georgia was a man whose power was to be respected, and they did not renew their raids into his province for some years. Oglethorpe was a great builder as well as a very skilful military leader, and he used this time of peace to improve the prosperity and beauty of the towns he had settled in his colony. Savannah was already a thriving place, with fine squares, parks, and wide shaded streets.
- 57. Now he turned his attention to Frederica, a town of a thousand settlers. He meant this to be a strong frontier fort, and designed an esplanade, barracks, parade-ground, fortifications, everything that could be of use to protect Frederica from an enemy. Not far from Frederica, on the same island of St. Simons, was a small settlement called Little St. Simons. A road connected the two places, running over a beautiful prairie and through a forest, and at the edge of this forest Oglethorpe built himself a small cottage and planted a garden and an orchard of oranges, grapes and figs. Here he made his home, where he could watch the water and keep an eye on Frederica and its forts. A number of his officers built country-seats for themselves near the general's cottage, almost all of them larger and more pretentious than that of the general. Strange as it may seem, the founder of Georgia never claimed or owned any other land in his province but this one small place, and he lived almost as simply as the poorest colonist, a great contrast to the elaborate state kept by the governors of such colonies as Virginia and Maryland or the luxury of William Penn's home at Pennsbury. Meantime other forts were built in the southern part of Georgia, one on Jekyll Island, another on Cumberland Island, a third at Fort William; and fortunately the governor saw to all this, for his province was to be for some time the buffer between the English and the Spaniards, two peoples who were constantly either on the verge of warfare or actually fighting. The mother-countries of England and Spain were always at swords' points, and those troubles on the other side of the Atlantic were sure to bring the American colonists into the same strife. Each country hectored the other. In the spring of 1740 the British government decided to attack Spain through its American possessions. France also decided to take a hand in the business, and this time joined with Spain. Ships of these two countries set sail for the West Indies and threatened the British colony of Jamaica. The English admiral, Vernon, was despatched with a large squadron to attack the enemy, but instead of sailing to Havana he turned in the direction of Hispaniola to watch the French fleet, and so lost a splendid chance to capture the Spanish stronghold of Havana.
- 58. General Oglethorpe learned of this, and in May, 1641, he wrote to the Duke of Newcastle in England, explaining how matters stood in that part of America and stating what the colonists would need if they were to carry on a successful war with the Spanish Dons of Florida and the West Indies. His letter was laid before the proper officers in England, but, as so often happened in such cases, those officers, far though they were from the scene of action, thought they knew more about conditions in Georgia and Florida than Oglethorpe did. The government delayed and delayed, while the general waited for an answer to his requests. Then he had to write again to England. Either the northern colonies or the mother-country was accustomed to supply his province with flour, but now Spanish privateers were capturing the merchant vessels that brought it. Only two English men-of-war were stationed off the coast, and they were insufficient to protect it from privateers. A Spanish rover had just seized a ship off Charleston Harbor with a great quantity of supplies on board. When Oglethorpe heard of this he sent out his guard-sloop and a schooner he had hired, met three Spanish ships, forced them to fly, attacked one of their privateers and drove it ashore. Then he bought a good-sized vessel and prepared it for service on the coast until the English should send him a proper fleet. A large Spanish ship was sighted off the bar of Jekyll Sound on August 16th. The intrepid governor manned his sloop and two other vessels, the Falcon and the Norfork, and started in pursuit. He ran into a storm, and when the weather had cleared the Spaniard had disappeared. The storm had disabled the Falcon, and she had to put back, but Oglethorpe sailed on with the other two, laying his course for Florida, and a few days later sighted the Spanish ship at anchor. The Spaniard was a man-of-war, and with her was another ship, by name the Black Sloop, with a record as a daring privateer. But Oglethorpe was equal in daring to any Spanish captain. He ordered his small boats put out to tow his two ships, the weather being now a calm, and as they approached the enemy, gave the command to
- 59. board. The two Spanish vessels opened fire, but Oglethorpe's guns answered so vigorously that the Spaniards quickly weighed anchor, and, a light breeze coming to their aid, were able to run across the bar of the harbor. The English followed, and, though they could not board the enemy, fought them for an hour, at the end of which the Spaniards were so disabled that they ran for the town, while half a dozen of their small galleys came out to safeguard their retreat. Other Spanish vessels were lying in the harbor, but none dared to attack the two ships of Oglethorpe, and the governor spent that night at anchor within sight of the castle of St. Augustine. Next day he sailed for the open sea again, and there cruised up and down outside the bar, as if daring the Spaniards to come out to meet him. When they refused to come he sailed back to Frederica, having spread a proper fear of his small fleet of two ships all along the Florida coast. Perhaps the greatest service that Oglethorpe rendered to his colony was his retaining the friendship of all the neighboring Indian tribes. This he did by always treating them fairly and impressing them with his sincere interest in their own welfare. Another man might have let the Indians see that he was merely using them to protect his own white settlers, but Oglethorpe convinced them that he was equally concerned in protecting both red men and white from ill-usage by the French and Spanish. Georgia moreover needed the friendship of the native tribes much more than the other English colonies did. It was nearest to the strong Spanish settlements in Florida, and its neighbor to the north, South Carolina, was able to furnish it very little assistance in times of need, and was often barely able to protect itself. Had the Creeks, the Chickasaws and Cherokees been allies of the Spaniards or the French instead of allies of Georgia the English settlers would have found themselves in hot water most of the time. The general had difficulty in corresponding with England and letting the people there know what he needed. Seven out of eight letters miscarry, he said. Fortunately no more English merchantmen were
- 60. captured by Spanish privateers; the Dons had apparently been taught a lesson by the vigorous attack Oglethorpe had made on their own ships. To keep this lesson in their mind the governor sailed again for St. Augustine, but ran into a storm that almost destroyed his fleet. At nearly the same time a privateer reached the bar outside St. Augustine with large supplies for the garrison. The Spanish governor, as usual in need of fresh supplies, joyfully hailed the privateer, sent out a pilot with two galleys to bring her into the harbor, fired the guns from his castle, and ordered some of his Indians to cut wood and build a welcoming bonfire. Oglethorpe and his Indian allies were on the alert, however. A party of his Creek friends attacked the Spanish Indians and captured five of them. At the same time one of his ships reached the privateer before the tide was high enough to float her over the bar, seized her, and took her to Frederica. Now the settlers of Georgia, and even of South Carolina, praised the general for his vigilance and dashing courage. A merchant of Charleston wrote, Our wrongheads now begin to own that the security of our southern settlements and trade is owing to the vigilance and unwearied endeavors of His Excellency in annoying the enemy. Yet, in spite of this, Carolina continued to fail in providing the men or ships or supplies that Oglethorpe, Commander-in-Chief of His Majesty's forces in Georgia and Carolina, requested of it. Presently the Spaniards, following the policy of England in trying to annoy enemy colonies in America, took the offensive. A Spanish fleet of more than fifty ships, with more than 5,000 soldiers on board, was despatched to attack the English settlements. Fourteen of the ships tried to reach Fort William, but were driven back by the battery there. They then made for Cumberland Sound. Oglethorpe sent out Captain Horton with white soldiers and Indians and followed with more troops in three boats. The Spanish ships attacked him, but he fought his way through their fleet with two of his boats. The third boat made for
- 61. a creek, hid there until the next day, and then returned to St. Simons with the report that General Oglethorpe had been overpowered and killed. A day later, however, the people of St. Simons were delighted to see their general return safe and sound. He had escaped damage from the Spaniards, but had hit them so hard with his guns that four of their ships foundered on the way back to St. Augustine for repairs. At once he prepared ships and men for another conflict. His daring had so inspired his crews that as some of them said, We were ready for twice our number of Spaniards. They soon had their chance. Thirty-six Spanish ships in line of battle ran into St. Simons harbor. The forts and the vessels there opened fire at once. Three times the enemy tried to board the Success, a ship of twenty guns and one hundred men, but each time the crew proved that they really were ready for twice their number of Spaniards. After fighting for four hours the Spaniards gave up the battle and sailed up the river in the direction of Frederica. Oglethorpe called a council of war. In view of the great number of Spanish ships it was decided to destroy the batteries at St. Simons and withdraw all the forces to Frederica. This was quickly done, and that evening some of the enemy landed and took possession of the deserted and dismantled fortifications. Meantime the general learned from some prisoners captured by the Indians that the Spaniards had land forces of 5,000 men and had issued commands to give no quarter to the English. As Mr. Rutledge of Charleston later wrote, The Spaniards were resolved to put all to the sword, not to spare a life, so as to terrify the English from any future thought of re-settling. Oglethorpe was now in a most dangerous situation. The enemy had numerous ships, a great many soldiers, and were evidently determined to settle matters once for all with their neighbors. The fate of the English colonies of Georgia and South Carolina might depend on the outcome of the next few days. Spanish outposts tried to reach the fort at Frederica, but were driven back by Indian scouts. The only road to the town was by the narrow
- 62. highway, where only three men could walk abreast, with a forest on one side and a marsh on the other. Artillery could not be carried over it, and it was guarded by Highlanders and Indians in ambush. Yet, after many attempts, the Spaniards managed to get within two miles of the town. Oglethorpe now led a charge of his rangers, Highlanders and Indians, so fiercely that all but a few of the enemy's advance-guard were killed or made prisoners. The Spanish commander was captured. The English pursued the retreating Spaniards for a mile, then posted guards, while the general returned to the town for reinforcements. The Spaniards again marched up the road and camped near where the English lay hid in ambush. A noise startled them and they seized their arms. The men in ambush fired, many Spaniards fell, and the rest fled in confusion. As a Spanish sergeant said, The woods were so full of Indians that the devil himself could not get through them. For a long time the place was known as the Bloody Marsh. Oglethorpe marched his troops over the road to within two miles of the main Spanish encampment, and there halted for the night. The enemy withdrew to the ruined fort at St. Simons, where they were sheltered by the guns of their fleet. Oglethorpe went back to Frederica, leaving outposts to watch the Spaniards. There he found that his provisions were running low, and he knew that no more could be brought in since the enemy blocked the sound. He told the people, however, that if they had to abandon their settlement they could escape through Alligators Creek and the canal that had been cut through Generals Island, and he assured his little army of 800 men that they were more than a match for the whole Spanish expedition. Presently Spanish galleys came up the river; but Indians, hid in the long grasses, prevented the soldiers from landing. When they approached the town the batteries opened such a hot fire that the galleys fled down-stream much faster than they had come up.
- 63. English prisoners, escaping from the Spaniards, began to bring word that the enemy were much discouraged. Many Spaniards had fallen sick, and the soldiers from Cuba were wrangling with the men from Florida. Oglethorpe therefore planned a surprise for the enemy and marched to within a mile of their camp. He was about to attack when one of his soldiers, a Frenchman who had volunteered but was in reality a spy, fired his gun and ran from the general's ranks. The Frenchman was not caught, and the general knew that he would tell the Spaniards how few English soldiers there were. So Oglethorpe tried a trick of his own, hoping to make the Frenchman appear to be a double spy. He hired a Spanish prisoner to carry a letter to the spy. The letter was in French, Oglethorpe later said, as if from a friend, telling him that he had received the money, and would strive to make the Spaniards believe the English were very weak; that he should undertake to pilot their boats and galleys, and then bring them into the woods where the hidden batteries were. That if he could bring about all this, he should have double the reward, and that the French deserters should have all that had been promised them. The Spanish prisoner got into their camp, Oglethorpe said, and was immediately carried before the general. He was asked how he escaped and whether he had any letters; but denying this, was searched and the letter found. And he, upon being pardoned, confessed that he had received money to carry it to the Frenchman, for the letter was not directed. The Frenchman, of course, denied knowing anything of the contents of the letter, or having received any money or had any correspondence with me. Notwithstanding which, a council of war was held and they decided the Frenchman a double spy, but the general would not suffer him to be executed, having been employed by himself. While the Spaniards were still in doubt as to the strength of Oglethorpe's forces some English ships arrived off the coast. This decided the Spaniards to leave, and they burned the barracks at St. Simons and took to their ships in such haste that they left behind some of their cannon and provisions.
- 64. Hearing that ships had been sighted Oglethorpe sent an officer in a boat with a letter to their commander. But when the officer embarked he found no ships were to be seen. Later the general learned that one of the vessels sighted came from South Carolina, and that the officer in command had orders to see if the Spanish fleet had taken possession of the fort at St. Simons, and if it had to sail back to Charleston at once. Here was further proof that the plucky governor of Georgia could expect little assistance from the sister colony on the north. By now some of the Spanish ships were out at sea, and others had landed their soldiers at St. Andrews in a temporary camp. A couple of days later twenty-eight of their ships sailed up to Fort William and called upon the garrison to surrender. The English officer there answered that he would not surrender the fort and defied the Spaniards to take it. The latter tried; they landed men, who were driven off by the guns of soldiers hidden in the sand-dunes, their ships fired on the fort, but were disabled by the return-fire of the Georgia batteries. After a battle of three hours the Spaniards withdrew from the scene and returned to their base at St. Augustine. With a few ships and eight hundred men Oglethorpe had defeated a Spanish fleet of fifty-six vessels and an army of more than 5,000 soldiers. Small wonder that the people of his province couldn't find praise enough for their leader! George Whitefield, a famous clergyman of Savannah, wrote of this war against the Spanish Dons, The deliverance of Georgia from the Spaniards is such as cannot be paralleled but by some instances out of the Old Testament. The Spaniards had intended to attack Carolina, but wanting water, they put into Georgia, and so would take that colony on their way. They were wonderfully repelled, and sent away before our ships were seen. The governors of the colonies of New York, New Jersey, Pennsylvania, Maryland, Virginia, and North Carolina sent letters to Oglethorpe thanking him for his valiant defense of the southern seaboard and expressing their gratitude to God that Georgia had a commander so
- 65. well fitted to protect her borders. The governor of South Carolina and most of his officers had done little or nothing to help their neighbor, but the people of that colony thoroughly disapproved of this failure to be of assistance and a number of them sent a message to Oglethorpe in which they said, If the Spaniards had succeeded in their attempts they would have destroyed us, laid our province waste and desolate, and filled our habitations with blood and slaughter.... We are very sensible of the great protection and safety we have so long enjoyed by having your Excellency to the southward of us; had you been cut off, we must, of course, have fallen. Even after this defeat, however, the Spaniards of Florida continued from time to time to molest the Georgia borders. A party of rangers was killed by Spanish soldiers, the settlement at Mount Venture was burned by Yamasee Spanish Indians. Oglethorpe had to be on the watch constantly lest the French or the Spanish should raid his territory. And the English government, though he wrote them time and again, neglected to send him proper reinforcements. In the spring of 1743 the general was again camped on the St. Johns River. He heard that a Spanish army was marching against him, and he resolved to attack them before they should attack him. His Indian allies stole up on the enemy, and surprising them, drove them back in confusion. The Spaniards took shelter behind one of their forts, and Oglethorpe could not manage to draw them out to battle. He marched his men back to Frederica, and there by Indian scouts, by sentry-boats, kept an eye on the Spaniards, ready to spring out to meet them should they renew their raids at any time. His soldiers never faltered in their obedience to the general's orders; his Indian allies, though they were often tempted, never forsook their allegiance to him. The Spaniards tried many times to buy the red men over to their side. Similli, a chief of the Creeks, went to St. Augustine to see what was being done there. The Spaniards offered to pay him a large sum of money for every English prisoner he would bring them, and showed him a sword and scarlet clothes they had given a chief of the Yamasees. They said of Oglethorpe, He is poor,
- 66. he can give you nothing; it is foolish for you to go back to him. The Creek chief answered, We love him. It is true he does not give us silver, but he gives us everything we want that he has. He has given me the coat off his back and the blanket from under him. In return for his loyalty to his English friend the Spaniards drove the Indian from St. Augustine at the point of the sword. The general had spent all his own money in protecting his people in Georgia, and the English government would not send him the sums he said were urgently needed for the province. Therefore he decided that he must go to England and see what could be done there. He put his forts on the border in the best possible shape for defense, appointed a deputy governor in Savannah, and sailed for England in July, 1743. Was the colonial hero received with the praise his great services deserved from England? Instead of praise he was harshly criticized for this or that trivial matter; though a few of the wiser men came forward to do him honor. Parliament would not vote him the money his colony needed; he had difficulty in finding enough money to pay his personal debts. Yet he kept on appealing for aid for Georgia, while the government took the same attitude it had taken toward so many of the other American colonies, and appeared of the opinion that the province across the Atlantic must look after itself. Fortunately for Georgia, Oglethorpe had so trained its soldiers, had so befriended its Indian neighbors, had so protected it by forts that the colony was now able to go its own way without English help. In 1744 Oglethorpe married Elizabeth Wright, the heiress of Cranham Hall, a manor in Essex. He was also in that same year chosen as one of the officers to defend England from a threatened invasion by France. His services were not needed for that purpose; but in the next year he was given the rank of major-general and took part in the suppression of the rebellion of the Young Pretender. This kept him in England, and he left the government of Georgia to the care of the men he had trained there. From time to time, however, he bestirred himself to send new colonists across the sea to Savannah.
- 67. When the rebellion was ended General Oglethorpe and his wife settled at Cranham Hall. Here he lived the life of a country gentleman, delighting in the peace and quiet after his many turbulent years in Georgia. He lived to see the American Revolution, though he took no part in it; he said that he knew the people of America well; that they could never be subdued by arms, but their obedience could ever be secured by treating them justly; he learned that his colony of Georgia, with twelve of her sisters, had succeeded in winning her independence from that mother-country he had served so long and on whose lists he was now the senior ranking general; and he seems to have harbored no ill-feeling against the colonists for forming a new nation. Georgia and America owe a great debt of gratitude to General James Edward Oglethorpe. None of the colonies had a more unselfish founder and governor, none were more bravely defended from enemies, and in none was more devotion shown to making a few scattered settlements in the wilderness blossom into the safe homes of a contented people.
- 68. X THE GREEN MOUNTAIN BOYS AND THE YORKERS (Vermont, 1774) I A young fellow, raccoon skin cap on his head, with heavy homespun jacket, with breeches made of buckskin and tucked into the tops of light, supple doeskin boots, was running along the shore of a lake in the Green Mountain country on a winter afternoon in 1774. He went at a comfortable dog-trot, and every now and then he would slow up or stop and look about him with keen eyes. Some people would only have seen the lake, with thin, broken layers of ice floating out from the shore, the underbrush and woods to the other side, powdered with a light fall of snow, and heard only the crackling of frozen twigs and the occasional scrunch of loose ice against the bank. But this tall, slim boy saw and heard a great deal more. He caught the hoot of an owl way off through the forest, and listened intently to make certain that it was an owl and not a signal call of some Indian or trapper; he saw little footprints in the snow that told him a marten had gone hunting small game through the brush, and he spied the thatched roof of a beaver's house in a little scallop of the lake. Then he ran on up the shore of the lake, all his senses alert, his eyes constantly looking for other trails than the one he had made himself on his south-bound journey that morning. The sun had been set a half-hour when he came to a place where the trail led inward a short distance from the shore. A few more yards brought him to a small log cabin. Other ears heard him coming and
- 69. as he stopped a boy and a man looked out from the cabin doorway. You made good time of it, Jack, said the boy at the door. Did you really get to Dutton's? Did I get there? chuckled the runner. I got there a good hour before noon. And what did they say there? asked the man at the door. That the Yorkers mean to settle this land themselves. If they can, he added, with a grin. That's what all the men said down at Dutton's, 'if they can,' and they shook their fists when they said it. Jack Sloan shook his fist in imitation of the men. Not if the Green Mountain Boys can help it! Not by a jugful! No, sir! he added. The man grunted approvingly and stepped back into the cabin. The boy came out. I got a silver fox to-day, he declared proudly. The biggest one I ever saw, too. Did you, Sam? That's fine! I saw plenty of tracks, heard a bull- moose calling, too; but I didn't have time to stop. Gee, but my legs are tired now! I'm going to lie down by the fire and rest a bit. He went inside, where the man was busy frying bacon and boiling coffee, and taking a blanket from a bed in the corner spread it out before the fire and stretched himself comfortably on it. Dutton wanted to know when you'd be sending him some more skins, Peter, he said. He wants to get 'em over to Albany early this year, in case there should be more trouble with the Yorkers. I can send him some next week, was the answer. There's a dozen mink and a dozen otter out in the shed now, an' a lot o' beavers an' martens, and four fine foxes. Did they say anything about Ethan Allen, Jack? They said he was down at Bennington. My, but that bacon smells good! They had corn-cake and molasses down at Dutton's, and I ate so much I didn't think I'd ever be hungry again, but I am all right now.
- 70. Peter Jones, the trapper, laughed. I never saw the time when you and Sam wasn't ready for food. Sam came in soon, like a bear-cub scenting food, and the three had supper and then made things snug for the night. The weather was growing colder. Peter, taking a squint at the sky, allowed that he thought the lake would be frozen clear across by morning. They brought in a good stock of wood and built up the fire, and then sat down in front of it to hear what Jack had to tell them of the news at Dutton's trading-post. At that time, in 1774, there was a great dispute between the two colonies of New Hampshire and New York as to which owned the country of the Green Mountains. New York stretched way up on the west shore of Lake Champlain, and New Hampshire extended from the northern boundary of Massachusetts up along the eastern shore of the Connecticut River. Now Massachusetts reached as far west as a line drawn south from Lake Champlain, and the governor of New Hampshire claimed that his colony extended as far west as Massachusetts. He quoted his colony's grant from the king of England to prove his claim, and he sent word to Governor Clinton of New York that he meant to settle the great Green Mountain tract that lay between the Connecticut River and Lake Champlain. Governor Clinton sent back word to Governor Wentworth of New Hampshire that the province of New York claimed all that land under the charter of King Charles II to his brother the Duke of York. New Hampshire settlers, however, went into this debatable land and built homes and began to farm there. Governor Wentworth granted lands, known as the New Hampshire Grants, to any who would settle there, and a township was organized west of the Connecticut River, and was named Bennington. The country was very fertile, the woods and rivers were full of game, and it was a tempting land to take. But the New Yorkers looked on the land as greedily as did the men from New Hampshire, and soon both provinces were sending their sheriffs and other officers to enforce their own laws there.
- 71. New York appealed to the king of England to settle the dispute, and he declared that the western bank of the Connecticut River should be the boundary line, giving all the Green Mountain country to the province of New York. By this time, however, there were a great many people from New Hampshire living there, and they meant to keep their homes no matter what the New York governor might do. What he did was to order the settlers to give up their grants from New Hampshire and buy their lands over again from New York, which charged twenty times as much as New Hampshire had. A few settlers did this, but most of them refused. A meeting of the latter was held at Bennington, and they resolved, as they said, to support their rights and property in the New Hampshire Grants against the usurpations and unjust claims of the governor and Council of New York by force, as law and justice were denied them. The settlers began to resist all New York officers who came to arrest them or try to eject them from their homes. Surveyors who came to run new lines across lands already granted by New Hampshire were forced to stop. No matter how secretly a sheriff with a party of Yorkers, as the New York officers were called, came to a farm in the disputed land, there were sure to be settlers there to meet the Yorkers and drive them away. The settlers had scouts all through the country; every trading-post was a rallying-point. A military force was organized, and chose Ethan Allen, a rugged, eloquent man, to be its colonel. The governor of New York declared that he would drive these men into the Green Mountains, and when they heard this Ethan Allen's followers took the name of Green Mountain Boys for themselves. Peter Jones was a hunter and trapper. The two boys, Jack and Sam, were the sons of men who had moved into the country on New Hampshire grants and taken up farm land. The boys had wanted to learn more of the woods than they could on their fathers' farms, and so had joined Peter at his cabin. He had taught them woodcraft and Indian lore, how to paddle a canoe, how to shoot straight, how to track the animals they wanted. All three were ready at any time to go
- 72. to the help of settlers who might be driven from their land by New York officers. Jack told the news of Dutton's trading-post, and then the hunter and the boys went to bed. Outside the cabin the wind whistled and sang. By morning the wind had dropped, but the air was very cold. Peter was up soon after dawn, putting fresh wood on the fire. The boys followed him shortly, getting into warm clothes as quickly as they could. They ate breakfast, and went outdoors. The lake was a field of ice, the trees were stiff with frost, the cold air nipped and stung their faces viciously. There was plenty of work to do. Soon Peter set out to visit a line of traps to the south, and the boys went through the woods northwest to look at other traps. They came to the frozen bed of a little stream and a couple of beaver traps. There were no animals there. Perhaps the night had been too cold to tempt them from their homes. I shouldn't think any animals would have gone prowling round last night, said Sam. I know I wouldn't, said Jack, if I was a beaver. They pushed on through the woods until they came to an open pasture. They had started across it when they heard a crow calling overhead. Must be a fox somewhere about, whispered Jack. Let's see if we can find him, even if we haven't got our guns. They went back to the edge of the woods, making as little noise as they could, for they knew that a fox depends more on his ears than on his eyes. They stopped behind the trees and after a few minutes saw a big gray fox trotting slowly along the edge of the woods. Dropping to their knees the boys crept forward to a hummock and hid back of it. The fox stood still, looked about, and then started at a slow gait across the meadow. The fox was more than a hundred yards away from the boys when Jack began to squeak like a meadow-mouse. No Indian or hunter could have heard the sound at half that distance, but the air was very
- 73. still and Jack knew the fox's big ears were very sharp. True enough, the fox did hear it, and stopping, looked around. Again Jack gave the squeak of the meadow-mouse. The fox came leaping lightly over the frozen hassocks of the meadow toward the two hidden boys. Every few yards he would stop and cock his ears over the long grass to listen. Each time he did this Jack squeaked, lower and lower each time, and every time the fox came on again, more and more cautiously, as if he were afraid of frightening the game he was hunting. The fox got within fifty yards, and from there the boys, crouching behind their hummock, were in plain view of him. The fox looked sharply, distrustingly at the hummock. Had either boy moved his head or arm the fraction of an inch the fox would have shot off like an arrow to the woods. Neither did move, however. Jack waited until he judged from the fox's attitude and the set of his ears that his suspicions were vanishing, and then he squeaked again, very faintly now. The fox bounded on, almost up to the hummock. Then he stopped short, and the boys could see from the look on his shrewd face that he judged something was wrong. Instead of coming on he circled round to the left, trusting to his nose rather than to his eyes. Jack squeaked, but the fox went on circling; it was plain he meant to come no farther. What's the matter, old boy? said Jack softly. At the sound of Jack's voice the fox sprang up into the air and then bounded away to the edge of the woods, where he stopped a minute to look back and then disappeared behind the trees. We could have had him easy, said Sam, getting up. We could almost have caught him with our hands. I don't want to try catching a big fellow like that with my hands, said Jack, chuckling. Give me a gun every time. When they got back to the cabin they found that Peter had been more successful than they in his visit to the traps on the south, for the skins of an otter and a mink had been added to the store that
- 74. hung on a line in the drying-shed. After dinner the hunter took from his pocket a piece of wood he had been working over for several days. I'm going to see if I can't fool a pickerel with this, he announced, holding out the little decoy for the boys to look at. The wood was cut to represent a minnow, was weighted on the bottom with lead, and had fins and a tail made of tin. He had painted a red stripe on each side, a white belly, and a brilliant green back. A line fastened to the minnow would allow Peter to pull it about in the water as if it were swimming. Armed with a long-shafted fish-spear and a hatchet Peter and the boys went out on the ice. Choosing a smooth place Peter cut a square of ice. Then through the open space the hunter dropped his wooden minnow and made it swim about in a very lively way. In his right hand he held the spear poised, ready to strike at any venturesome fish. For some time they waited; then the long nose of a pickerel showed in the water; Peter jerked the minnow and struck with the spear. The pickerel, however, slipped away unharmed. They had to wait fifteen minutes before another appeared. This time the pickerel stopped motionless, and seemed to be carefully considering the lively red- striped minnow. Then the fish shot forward, Peter aimed his spear, and the shining pickerel was caught and thrown out on the ice. Peter caught two more fish before he let Sam have a try at it. Sam and Jack each caught a pickerel, and then they brought their five trophies back to the camp to cook for supper. They had just sat down to supper when there came a rap on the door followed by the entrance of a tall man in a fur jacket with a gun slung across his back. He was John Snyder, a hunter from the country north of the lake, and he had met the three in the cabin several times before. H-mm, said he, that fish smells mighty good. I haven't tasted fish for a month o' Sundays.
- 75. Pitch right in, invited Peter, setting out another tin plate and pouring a cup of coffee for the new arrival. Snyder pulled off his cap and gloves, and threw off his fur coat, showing a buckskin jacket underneath. He ate like a man who hadn't tasted food for a month. After a while he said, They say up where I come from that thar's trouble down Bennington way. If the Yorkers want trouble I reckon we can supply 'em good and proper. I'm on my way to Dutton's, and thar's more of the Boys comin' on down through the woods. Why don't you come along with me in the morning? We was planning to go when we'd got a few more skins, said Peter. But we've got a fair-sized stock, an' I don't know but what we might go along with you. That's what the word is, said Snyder. Green Mountain Boys to Bennington. He looked hardy and tough, a typical pioneer, quite as ready to fight as he was to hunt or farm. That night the guest slept on the floor before the fire, rolled in a blanket, and soon after dawn next morning the four set out, pulling two heavy sleds to which the furs and skins were securely strapped. All four of the party were used to long trips on foot, often carrying considerable baggage. There were few post-roads through that part of the country, and horses would have been little use in traveling through such rough and wooded stretches. So most of the new settlers, and particularly those who were hunters, copied the customs of the Indians and trained themselves to long journeys afoot, varied occasionally by canoeing when they reached open water. The party of four traveled fast, in spite of the heavy sleds. Peter Jones, not very tall but very wiry, all sinew and muscle, and Sam, red-haired, freckle- faced, and rather stocky, pulled one sled, and big, raw-boned, weather-beaten Snyder, and slim, Indian-like Jack the other. Presently they left the lake and came into more open country, where they could see snow-powdered hills stretching away to the clear blue horizon. Now they made better time, for there was no underbrush to
- 76. catch the sleds and stop them. On they went until they saw a number of cabins grouped about a larger frame building, then they broke into a run, and dashed up with a shout before Dutton's trading- post. The shout brought three or four men out to see what was the matter. They called the newcomers by name, and Big Bill Dutton, seeing the sleds, told Peter Jones to bring his furs inside. Jack and Sam and Peter unstrapped the furs and carried them into the house, where they were spread out on a long counter, over which Dutton was accustomed to buy whatever farmers and hunters and trappers might have for sale, and in return to sell them provisions or clothing or guns or powder and shot or whatever he might have that they wanted. There was always a great deal of haggling over the sale of furs. Peter had to point out what unusually fine skins of otter and beaver and mink, of marten and fox he had brought, and Dutton had to argue that this fur was rather scanty, that other one very much spotted. But at last they reached an agreement, Peter was paid in cash for the pelts, and they were carefully stowed away by the trader, to be sent at the first good opportunity over to Albany, from where they would go by boat down the river to New York. Meantime Jack and Sam, outside the house, were listening to the stories of the men who had gathered at Dutton's. They were exciting stories of conflicts between Green Mountain settlers and the Yorkers or those who sided with them. One man told how a doctor, who had openly talked in favor of the Yorkers, had been swung in an armchair for two hours under the sign of the Green Mountain Tavern at Bennington, on which sign stood the stuffed hide of a great panther, a monster who showed his teeth at all enemies from New York. Most of the stories were of the exploits of Ethan Allen and his band of Green Mountain Boys. They said that Ethan Allen had caught a surveyor marking out claims for Yorkers, and had taken him prisoner and had ordered him out of the country on pain of death if they caught him there again. Then Allen had marched on to the First Falls of Otter Creek, where Yorkers had driven out some New Hampshire
- 77. settlers who had built a sawmill. The Boys had sent the intruders flying at the point of their guns, and had burned their log houses and broken the stones of a gristmill the enemy had built. Then they had brought the original owners back and settled them again in possession of their houses and sawmill. All through that part of the country similar things were taking place. The men said they had word that Yorkers were planning to drive settlers off their farms not very far to the west of Dutton's. If they do it, cried Snyder, striking his open palm with his great fist, I want to be there to settle accounts with them! So said all the rest; Ethan Allen and his men shouldn't have all the glory there was going. Big Bill Dutton's frame house was tavern and post-office as well as trading-post and meeting-place for the settlers of the neighborhood. When Mrs. Dutton rang the dinner bell all the strangers trooped into the room back of the store and sat at the long table. Jack and Sam marched in with the others and ate their share of dinner while they listened to the talk of the men. Some of the latter were for setting out south toward Bennington immediately, in order to learn at first hand what was going on. After dinner they all stood about the stove in the store, talking, talking, talking. Sam and Jack went outdoors and looked about the little group of cabins. A boy of near their own age came out from one of the houses and talked with them about hunting moose. As they were swapping yarns a man rode into the settlement from the southwest. At sight of the three he flung out his right arm. Yorkers down to Beaver Falls! he called out. They're coming to drive our people out o' their homes! Are there any Green Mountain Boys hereabouts? In there! exclaimed Jack, pointing to the store. Tell 'em about it in there! The horseman sprang from his saddle. Fetch a blanket for my horse, will you? said he. The boy who lived there ran indoors to get a covering. Meantime the rider strode up to Dutton's door and flung it
- 78. open. He walked up to the group of men about the stove, announcing his news briefly. At his heels came Sam and Jack, and back of them came the boy from the log house opposite. II They started from Dutton's next morning, a troop of a dozen men and three boys, bound for Beaver Falls. Big Bill left his store in charge of his wife, and took command of the troop. They were all hardy and strong, and they covered the twenty miles to Beaver Falls by the middle of the afternoon. Here there stood a sawmill on the river, with a score of log houses, and farms scattered through the neighborhood. The place looked perfectly quiet as the fifteen Green Mountain Boys trooped up to it. But they soon found there was plenty of excitement in the mill. There were gathered most of the men of the Falls, and they were very glad to see the reinforcements. Yorkers been found prowling round in the woods! Surveyors been caught in the act of staking claims! Jim Murdock found a paper stuck on his door, saying we'd better get out peaceful-like, and let the lawful owners have their land! Such were some of the items of information given to Dutton's band. Let 'em come! exclaimed Snyder, slapping his hand round the muzzle of his gun. This is the law of the land we'll read to them! After a time Jack and Sam, having heard all there was to hear, struck out on a line of their own. They followed the bank of the river until they came to woods, and then skirted the forest southward. This brought them at length to a wide trail with frozen wheel ruts. Down this road they went, passing occasional cabins, until they came to a crossroad where they found a man looking perplexedly about him, as if undecided which road to take.
- 79. Where's Farmer Robins' place? he asked. The place that used to belong to Elijah Robins. We don't know, said Jack. We're strangers here. There's a maple grove back of it, said the stranger, that's all I know about it. I was told to stick to this road, but they didn't say nothing about any forks in it. This goes to Beaver Falls, said Sam, pointing to the one they had taken, and that, he added, indicating the crossroad to the right of him, would take you through thick woods to the river. I don't reckon it's either o' those roads then, said the man, and, bobbing his head at Sam, he stalked off to the left. The two boys watched until the man was almost hidden by the trees. Then Jack turned to Sam. You don't want to tell all you know to strangers, he said. Make the other man tell you what he's up to first. Sam's round face, not nearly so shrewd as the older boy's, looked perplexed. Why shouldn't I tell him about those other roads? he asked. Because I think he may be one of the Yorkers, and the less we tell them about the lay of the land round here the better. Do you really think he was? exclaimed Sam, his tone of voice showing that he had expected a Yorker to be a much more terrifying looking creature than this stranger. What did he want of Farmer Robins' place then? I don't know, answered Jack. But I think we might be able to find out something more about it if we follow his tracks. They turned to the west, following the road where the prints of the man's big hob-nailed boots could now and then be seen in the frozen crust of snow. The sun was setting, and the wind was rising, and they pulled their fur caps down over their ears and stuck their hands
- 80. in their pockets as they trudged along. It grew dark rapidly. They passed two cabins where they looked closely for a clump of maples and then scoured the road to find the prints of the hob-nails. The man's tracks went on, and they followed, only speaking in whispers now lest they should be overheard. At the third log house they stopped. Jack, catching Sam by the sleeve, pointed to the back of the house, where the starlight unmistakably showed a grove of trees. Smoke came from the chimney, and the front door, not quite plumb in its frame, showed there was a light inside. Jack crept round the cabin, Sam following him, each as silent as if they were stalking moose. There were four windows, but each was securely shuttered from the inside, and though light came through the cracks, the boys could see nothing of what was going on inside nor catch a sound of voices. Then Jack made the circuit of the house again, this time examining the logs and the filling of clay between them with the greatest care. At last he found a place that seemed to interest him, and he pulled out his hunting knife from its sheath and began to pick at a knot-hole in the wood. His knife was very sharp, and he dug into the circle round the knot and then into the clay just below it. He worked swiftly and very quietly. In a short time he had the wood loosened; pressing inward with his blade he forced the knot out, and then scraped some of the plaster away. Now he had a hole that enabled him by stooping a little to look into the cabin. He put his eye to the opening and saw about a dozen men in the room. He could hear what they said. They were, as he had suspected, Yorkers, planning to make an attack on the people at Beaver Falls. As Jack listened he pieced one remark to another, and caught the gist of their plans. They meant to march down to the Falls that night, stop at each house, rout the people out, make them prisoners in the sawmill, and take possession of houses and farms under orders from officers of the province of New York.
- 81. Jack drew away from the hole, and let Sam have a chance to look into the log-house room. When Sam had watched and listened for a few minutes he nodded to Jack, and the two stole away from the cabin as noiselessly as they had circled round it. Out on the road, as they went hurrying back by the way they had come, they whispered to each other, telling what each had overheard. Then they went at a dog-trot to the path along the river and came to the sawmill at Beaver Falls. Peter, Big Bill Dutton, Snyder, and most of the other men were at the mill, though some had been stationed on sentry-duty in the fields and woods. Jack told his story without interruption, and then the men began to plan how they should welcome the Yorkers. It was Big Bill's plan they finally adopted, and set to work to carry it into effect at once. All the people at the Falls had had their supper, the women were busy cleaning up, most of the children were in bed. The men went to the houses, and told the women that they and the children must spend the night in the sawmill. Children were bundled into warm clothes, and, wondering what was happening, were hurried to the mill by their mothers. Half a dozen men under command of Snyder were stationed at the mill, the others were allotted to the different houses in the village. Two were told off to each house, and it happened that Peter and Jack stood on guard at the house nearest the Falls. Every house at that time had its store of firearms, its powder and balls. Peter and Jack sat inside their cabin, muskets ready to hand. From time to time they threw fresh wood on the fire, for the night was cold. Jack stood at a window, looking out at the open space along the river and the road on the opposite bank, both faintly lighted by the stars. Midnight came, but there was no sign of the Yorkers; presently it seemed to Jack that it must be nearly dawn. Peter, standing at a window on the other side of the door from Jack, suddenly said, Look! There, coming through the trees to the left of
- 82. the mill! Jack looked and saw men coming into the road, a good many of them, more than he thought he had seen at Farmer Robins' house. They came along the road, crossed the wooden bridge below the Falls, passed by the mill, evidently taking it for granted there would be no one there at this hour, and marched into the clearing before the log houses. There they divided into small parties, each party heading for a separate cabin. Ready now! cautioned Peter. We've got two to handle. I'll take the first. Jack stepped back from the window and laid his hand on the bolt of the door. Wait till I give the word, whispered Peter. From outside there came a loud voice. Open your door in the name of the Sheriff of New York! There followed knocks on the door, and other orders, all to the same intent. Peter waited until the owner might be supposed to rouse and get to the door. Then he whispered, Now! Jack drew back the bolt and opened the door enough for the men to enter single file. One man stepped in, the other followed at his heels. Peter caught the first man in his arms, and, taking him altogether unawares, threw him to the floor with a wrestler's trip. Jack, throwing his arms round the second man's knees, brought him down with a crash. Lithe and quick as an eel, Jack squirmed up to the man's chest and gripped the Yorker's throat in his hands. In a minute or two the man underneath was almost breathless. Do you surrender? panted Jack. The Yorker tried to nod. Peter had wrenched his man's gun away, and was copying Jack's tactics. His man was partly stunned by the sharpness of the fall and made little attempt to free himself from Peter's grasp. Finding himself attacked by a thoroughly-prepared and resolute man, he had no
- 83. notion as to how many other such men there might be in the house. It was clearly a case where it was best to save one's skin as whole as one could. So, when Peter said, Keep still there, will you! the Yorker grunted, I will, and made no attempt, unarmed as he was, to try further conclusions with the sinewy hunter. Peter had a coil of rope ready. Now he cut two lengths of this, tossed one over to Jack, who still kept his knee on the chest of his man, and used the other to tie the arms of his own prisoner. Then he helped the Yorker to his feet. Meantime Jack had followed his example with the other, and shortly both prisoners were standing before the hearth while their captors searched their pockets for firearms and knives. I must allow, said one of the Yorkers, you two were mighty sharp! We figured that when you people here heard we were acting under sheriff's orders you'd do as you were told. We don't pay no more attention hereabouts to what a Yorker sheriff says than if he was a catamount,—no, not so much as that! returned Peter. What do you men mean by marching into a peaceful village an' trying to turn people out o' their lawful homes? Well, the village certainly looked peaceful enough, said the Yorker, but I don't see as how we've turned many folks out o' their homes yet. And I don't think you will! Peter assured him. Jack, take a look outside and see what's happened. Jack went out, and going from house to house, found that wherever the Yorkers had demanded admittance the Green Mountain Boys had worked their trick beautifully. In two or three houses it had taken some time to make the enemy prisoners, but in each case the elements of surprise and determination had won the day. The Yorkers had expected to meet frightened villagers; instead they had found themselves confronting well-prepared Green Mountain Boys. Under direction of Big Bill Dutton the prisoners, all with their arms securely tied behind them, were marched out into the road. You say
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