A Performance Comparison of DFIG using Power Transfer Matrix and Direct Power Control Techniques

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 5, No. 2, October 2014, pp. 176~184
ISSN: 2088-8694  176
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
A Performance Comparison of DFIG using Power Transfer
Matrix and Direct Power Control Techniques
K. Viswanadha S Murthy, M. Kirankumar, G.R.K. Murthy
Department of Electrical and Electronics Engineering, KL University, Andhra Pradesh, India
Article Info ABSTRACT
Article history:
Received Mar 13, 2014
Revised Jun 5, 2014
Accepted Jul 2, 2014
This paper presents a direct power control and power transfer matrix model
for a doubly-fed induction generator (DFIG) wind energy system (WES).
Control of DFIG wind turbine system is traditionally based on either stator-
flux-oriented or stator-voltage-oriented vector control. The performance of
Direct Power Control (DPC) and Power transfer Matrix control for the same
wind speed are studied. The Power transfer matrix Control gave better
results. The validity and performance of the proposed modelling and control
approaches are investigated using a study system consisting of a grid
connected DFIG WES. The performance of DFIG with Power Transfer
Matrix and Direct Power Control (DPC) techniques are obtained through
simulation. The time domain simulation of the study system using MATLAB
Simulink is carried out. The results obtained in the two cases are compared.
Keyword:
Doubly-fedInduction generator
(DFIG)
Direct Power control (DPC)
Power Transfer Matrix
Pulse width modulation (PWM)
Wind energy
Copyright © 2014 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
G.R.K. Murthy,
Departement of Electrical and Electronics Engineering
KL University
Greenfields, Vaddeswaram, Guntur District, Andhra Pradesh 522502, India
Email: drgrkmurthy@kluniversity.in
1. INTRODUCTION
Generation of electricity has been largely dominated by nuclear, hydro and fossil-fueled thermal
plants. Generally this type of generation is considered as conventional power generation. The main drawback
of most conventional power plants is the adverse impact on the environment. The gradual depletion of fossil-
fuel (such as coal, gas) reserves is also a concern. The solution to these problems lies in adopting non-
conventional methods such as wind, solar etc. in power generation. Wind is regarded as the best suitable
renewable energy resource for production of power and the best alternative to the conventional energy
resources mainly because of availability of large wind turbines [1].
For the last two decades, research is being carried out specifically on Wind Energy Systems to
capture more power at fluctuating wind speeds. With the improvement in the power electronic technology
constant speed constant frequency (CSCF) generators were replaced by variable speed constant frequency
(VSCF) generators in WES. The Doubly Fed Induction Generator (DFIG) is currently the choice of generator
for multi-MW wind turbines .The aerodynamic system must be capable of operating over a wide wind speed
range in order to achieve optimum aerodynamic efficiency by tracking the optimum tip-speed
ratio.Therefore, the generator’s rotor must be able to operate at a variable rotational speed. TheDFIG system,
therefore operates in both sub- synchronous and super-synchronous modes with a rotorspeed range around
the synchronous speed. The stator circuit is directly connected to thegrid while the rotor winding is connected
via slip-rings to a three-phase converter. Forvariable - speed systems where the speed range requirements are
small, (for example ±30% ofsynchronous speed) the DFIG offers adequate performance and is sufficient for
the speedrange required to exploit typical wind resources.
The doubly fed induction generator (DFIG) based wind turbine with variable speed and variable
pitch control scheme is the most popular wind power generation system in the wind power industry. This

IJPEDS ISSN: 2088-8694 
A Performance Comparison of DFIG using Power Transfer Matrix and Direct… (K.Viswanadha S Murthy)
177
machine can be operated either in grid connected mode or in standalone mode. This system has recently
become very popular as generator for variable speed wind turbines. The major advantage of the doubly fed
induction generator (DFIG), which has made it popular, is that the power electronic equipment has to handle
only a fraction (20-30%) of the total system power [2], [3]. That means the losses in the power electronic
equipment can be reduced in comparison to power electronic equipment that has to handle the total system
power as for a direct-driven synchronous generator, apart from the cost saving of using smaller converters.
Control of the DFIG is more complicated than the control of a standard induction machine. In order to
control the DFIG rotor current is controlled by a power electronic converter. One common way of controlling
the rotor current is by means of Field oriented (vector) control. Direct torque control (DTC) of induction
machines, provides an alternative to vector control [5]. Based on the principles of DTC strategy, direct power
control (DPC) was developed for three-phase pulse width modulation (PWM) converters.
Power transfer matrix is a control technique of DFIG which uses instantaneous real and reactive
power instead of dq components of currents in a vector control scheme. The main features of the proposed
model compared to conventional models in the dq frame of reference are [6].
a) Robustness: The waveforms of power components are independent of a reference frame;
therefore, this approach is inherently robust against unaccounted dynamics such as PLL.
b) Simplicity of realization: The power components (state variables of a feedback control loop) can
be directly obtained from phase voltage/current quantities, which simplify the Implementation of the control
system.
Figure 1. Structure of DFIG wind power generating system
2. WIND TURBINE MODEL
The wind turbine characteristics must be analyzed for getting optimum power curve (Popt). The
power output of Wind turbine is given by [4]:
P0= Cp*PV = 0.5 Sw V3
Cp (1)
Where ‘’is the air density; Sw is wind turbine blade swept area in the wind, V is wind speed. Cp represents
the power conversion efficiency of the wind turbine. It is a function of (Tip-speed Ratio).
=
ᴨ
=      

Where ‘R’ is the blade radius;  is the angular velocity of the rotating blades; N is the rotational speed in
revolutions per second, and V∞ is thewind speed without the interruption of rotor. Cp can be calculated by
using the formula:
Cp=0.5716* (116*- 0.4 21 λ  
1 1
0.08
0.035
1

Maximum power from the wind turbine is:
Pmax=K        


 ISSN: 2088-8694
IJPEDS Vol. 5, No. 2, October 2014 : 176 – 184
178
Where 0.5Sw *Cp
3. DIRECT POWER CONTROL OF DFIG
Figure 2. Equivalent circuit of DFIG in the
synchronous d-q reference frame
Figure 3. Stator and rotor flux vectors in
synchronous d-q frame
The equivalent circuit of a DFIG in the synchronous d–qframe, rotating at the speed of ω1, is shown
in Figure 2. The d-axisof the synchronous frame is fixed to the stator flux, as shown in Figure 3. With
reference to Figure 2, the stator voltage vector in the synchronousd–q reference frame is given as:
Vs
s
= Rs Is
s
+ (dΨs
s
/dt) + jΨs
s
(5)
Under balanced ac voltage supply, the amplitude and rotating speed of the stator flux are constant.
Therefore, in the synchronous d–q frame, the stator flux maintains a constant value [5]. Thus;
Ψs
s
= Ψsd
(dΨs
s
/dt) = 0 (6)
Considering Equation (5) and neglecting the voltage drop across the statorresistance, Equation (6)
can be simplified as:
Vs
s
= jΨs
s
= jΨsd (7)
The stator current in the synchronous d-q frame is given as:
rs
s
rm
s
s
s
mrs
s
rm
s
srs
s
LL
L
LLLL
LL
I







 2
(8)
Thus the stator active and reactive power inputs can be calculated as:
 









 





 








rd
m
sdr
sdrqsdss
rs
rqrdm
s
sd
sds
rs
s
rm
s
s
s
sdss
L
L
jkjQP
LL
jL
LjjQP
LL
L
LjjQP









1
1
1
2/3
2/3
(9)
Splitting Equation (9) into real and imaginary parts yields:








sd
m
r
rdsds
rqsds
L
L
kQ
kP




1
1
(10)

179
As the stator flux is constant, according to Equation (10), the active and reactive power changes
over a constant period are given by :
rdsds
rqsds
KQ
KP






1
1
(11)
Equation (10) indicates that the stator reactive and active power changes are determined by the changes of
the rotor flux components on the d-q axis, i.e. , ∆Ψrd and ,∆Ψrq, respectively.
4. ACTIVE AND REACTIVE POWER CONTROL
The active and reactive power control calculates the required rotor voltage that will reduce the
active and reactive power errors to zero during a constant sampling time period of Ts. A PWM modulator is
then used to generate the applied rotor voltage for the time period of Ts.
Within the time period of Ts, the rotor voltage required to eliminate the power errors in d-q
reference frame are calculated as [7]-[9]:
rds
sd
s
s
rq
rqs
sd
s
s
rd
k
P
T
V
k
Q
T
V












1
1
1
1
(12)
However, its accuracy could be affected by the variation of Lm (Mutual inductance). An alternative method
based on Equation (11) gives:
sd
s
rq
sd
m
r
sd
s
rd
k
P
L
L
k
Q







1
1



(13)
From the Equation (12) and (13) we get:












sd
m
r
sd
s
s
sd
s
s
sd
s
s
sd
s
s
L
L
k
Q
k
P
T
k
P
k
Q
T









11
rq
11
rd
1
V
1
V
(14)
The first terms on the right hand side reduce power errors while the second terms compensate the
rotor slip that causes the different rotating speeds of the stator and rotor flux.
Figure 4. Schematic diagram of the DPC for a DFIG system

 ISSN: 2088-8694
180
5. PRINCIPLES OF POWER TRANSFERMATRIX
The schematic diagram of a DFIG wind turbine generator is represented in Figure 1. The power
Converter includes Rotor-side-converter (RSC) to control speed of the generator and Grid-side converter
(GSC) to inject reactive power to the system. The instantaneous real and reactive power components of the
grid side converter, pg(t)and qg(t)in the synchronous d-q frame of reference are [6]:



















gq
gd
sdsq
sqsd
g
g
i
i
vv
vv
tq
tp
2
3
)(
)(
(15)
6. MODEL OF DFIG USING INSTANTANEOUS POWER COMPONENTS
The change in real power and reactive power can be expressed as [12]-[14]:
rdsdsqsssl
s
rdsqsdssls
s
uggqgp
dt
dq
uggqpg
dt
dp




541
541
(16)
Where,
rs
sdm
rs
ssrs
rqrdrq
s
s
rqrdrd
LL
vL
g
LL
rLLr
g
vgvgu
L
v
vgvgu
'2'1
23
'
2
32
2
3
;
2
3










 






 


rs
sqrrsdr
rs
sqrrsdr
rs
sqm
LL
vLvr
g
LL
vLvr
g
LL
vL
g
'5
'4
'3
2
3
2
3
2
3

 (17)
The electromechanical dynamic model of the machine is:
 me
r
TT
J
P
dt
d

 (18)
Where P,J and Tm are the number of pole pairs, inertia of therotor, and mechanical torque of the machine,
respectively. Theelectric torque is given by [10], [11]:
 sdsqsqsde iiPT  
2
3 (19)
mss
r
T
J
P
qgpg
dt
d
 76
 (20)
Where,
2
2
7
2
2
6
s
sqsqsdsd
s
sqsdsdsq
v
vv
J
P
g
v
vv
J
P
g






(21)

181
Figure 6. Schematic diagram of the study system of power transfer matrix
6. RESULTS AND COMPARISION
The following parameters are used to verify the real power, Reactive power and dc link voltages:
Parameters Values Units
Rated power(P) 1.5 MW
Rated voltage(V) 0.575 KV
Rated frequency(F) 60 Hz
Rated wind speed(Vw) 12 m/s
Stator resistance(Rs) 1.4 mΩ
Rotor resistance(Rr) 0.99 mΩ
Stator leakage inductance(LS) 89.98 H
Rotor leakage inductance(LR) 82.08 H
Magnetizationinductance(Lm) 1.526 mH
Stator/rotor turns ratio 1 -
Poles 6 -
Turbine rotor diameter 70 M
Lumped inertia constant 5.05 S
Figure 7. Trapezoidal pattern for wind speed
Figure 8(a). Real power from power transfer matrix control

 ISSN: 2088-8694
182
Figure 8(b). Reactive power from power transfer matrix control
Figure 9(a). Real power from DPC
Figure 9(b). Reactive power from DPC
Figure 10(a). Vdc from Power transfer matrix

183
Figure 10(b). Vdc from DPC
The results are obtained at a wind speed of 12 m/sec. The trapezoidal wave form shown in Figure 7
shows the pattern of step change in the reactive reference which is applied to both the control techniques.The
trapezoidal pattern wasselected to examine the system behavior following variation inthe wind speed with
both negative and positive slopes. The selectedwind speed pattern spans an input mechanical wind
powerfrom 0.7 to 1 p.u. (70 to 100% of the turbine-generator ratedpower).
Figures 8(a) and 8(b) show the Real and Reactive power tracking of DFIG against disturbances
present in the given wind speed pattern. Because of coupling of all powers interlinked to each other, the
coupling effect is obtained at t=0.3 sec.
Figure 9(a) shows the Real power tracking of DFIG against disturbances in the given wind speed
pattern. Here the dip in the wave form shows the start of real power generation at t=0.2 sec. Figure 9(b)
indicates the reactive power absorption for 0.4 sec.
Figures 10(a) and 10(b) show the dc link voltages of Power transfer matrix control and DPC.The
change in wind speed leads to the fluctuations of the dc link voltage. Due to the coupling of all powers vdc of
power transfer matrix have some variations. Where as in DPC there is no coupling of the powers and the dc
link voltage is constant. Change in wind speed does not affect dc link voltage
7. CONCLUSION
Upon examining the results of both Power transfer matrix and DPC techniques for the same
disturbances the Real power generation is better in power transfer matrix control than with DPC. Also the
generation of power starts in DPC with a delay of 0.2 sec. Hence power transfer matrix method is giving
better results than the DPC method.
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Power Electronics For Wind Turbines. Riso national laboratory.
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proc.elctr.powerappl. 1998; 145(4): 360-368.
[4] SN Bhadra, D Kastha, S Banarjee. Wind Electrical Systems. Oxford University press
[5] Dawei Zhi, Lie Xu. Direct Power Control of DFIG with Constant Swtching Frequency and Improved Transient
Performance”IEEE Transactions on Energy Conversion. 2007; 22(1).
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