FIRING ANGLE SVC MODEL FOR ANALYZING THE PERFORMANCE OF TRANSMISSION NETWORK USING NEWTON RAPHSON LOAD FLOW
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This paper presents a study on the Newton-Raphson method of power flow analysis in power systems, particularly focusing on the impact of Static Var Compensator (SVC) devices on voltage stability and power loss minimization. It investigates the optimal placement and firing angle of SVCs to enhance power flow, using simulations on IEEE bus systems. The findings of this research are intended to assist future researchers in understanding power flow control with facts devices in power systems.
![Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load
Flow
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1. INTRODUCTION
The operation of power system is becoming more and more challenging because of continuously
increasing load demand which is leading to an augmented stress of the transmission lines, voltage
instability, increase in loss and cost. To meet the ever increasing demand it is now essential to maximize
the utilization of the existing transmission system. In recent years, due to advancement in high power
solidstate switches, transmission controllers have been developed which provides more flexibility and
controllability. A new solution for controlling power flow known as FACTS was introduced in 1988 by
Hingorani [1]. FACTS devices have made the power system operation more flexible and secure. They have
the ability to control, in a fast and effective manner. FACTS controllers minimizes loss, enhance the
voltage profile and the load ability of power systems. FACTS devices include Thyristor Controlled Series
Compensator (TCSC), Static VAR Compensator (SVC), Static Compensator (STATCOM), Unified Power
Flow Controller (UPFC), etc.
In this paper, SVC is used for several reasons. The most widely used shunt FACTS devices within
power networks is the SVC due to its low cost and good performance in system enhancement. It is more
conventional and available. SVC can control voltage with higher level of accuracy. It is a shunt connected
static VAR generator or absorber whose output is adjusted to exchange capacitive or inductive current so
as to provide voltage support and when installed in a proper location, it can also reduce power losses [27].
For these reasons, SVC is chosen over other FACTS devices in this paper.
2. LITERATURE SURVEY
In the literature many people proposed different concepts about the placement and sizing of the SVC.
Hadi Saadat Presented Real and Reactive Power flow equations in polar form by considering two bus
power system. A Jacobean matrix is then constructed and Newton Raphson method is used to solve these
equations [1]. Hingorani N.G et.al presented about the Fast development of power electronics introduces
the use of flexible ac transmission system (FACTS) controllers in power systems. The main benefit of
FACTS devices is reduction of operation and transmission investment costs, increasing the power transfer
capabilities, system security, controlling power flow in the lines and in improving stability [2]. [3]-[4]
papers refer that , SVCs are the combination of mechanically controlled and thyristor controlled shunt
capacitors and reactors. Ref [5]-[6] papers proposed the most popular model of SVC's is the combination
of either fix capacitor and thyristor controlled reactor or thyristor switched capacitor and thyristor
controlled reactor .Ref[7]-[10] papers proposes Existing Basic model of SVC and the novel Firing angle
model for Static VAR Compensator (SVC) FACTS devices. In that paper, it explains the power electronic
development, fixed capacitor and reactor reactive power compensator has replaced with variable reactance
reactive power compensator. Kumar, G.R et.al presented about load flow analysis with incorporated
FACTS controllers in multimachine power systems from different operating conditions viewpoint. The
Newton Raphson Methods have been proposed in literatures includes for different types of Modeling of
Series FACTS controllers[11] .B.Venkateswara rao et.al explains the Implementation of Static VAR
Compensator for Improvement of Power System Stability[12] Sahoo et.al (2007) proposed the basic
modeling of the FACTS devices for improving the system performance[13].Zhang, X.P et.al explains
Jacobian Matrix of Power flow Newton Raphson algorithm and Newton Raphson strong convergence
characteristics [14].Gotham.D.J and G.T Heydt (1998) detailed about the optimal location of FACTS
devices allows controlling its power flows and thus enhances the reliability of the power systems
[15].Povh.D(2000) proposed the nice concepts of the modeling of the power systems and the impact of the
FACTS devices on the transmission network [16]. Ref [17]-[20] papers presented the lot of techniques
have been developed in predicting the closeness of the system to voltage instability in order to counteract
this effect. The prediction is based on voltage collapse prediction index [VCPI] have been used to identify
the bus which is more prone to voltage instability. Modelling of the FACTS devices with various
techniques with complete computer programming and the operating state determine the maximum power](https://image.slidesharecdn.com/ijeet0705005-161102082459/85/FIRING-ANGLE-SVC-MODEL-FOR-ANALYZING-THE-PERFORMANCE-OF-TRANSMISSION-NETWORK-USING-NEWTON-RAPHSON-LOAD-FLOW-2-320.jpg)
![A.Hema Sekhar and Dr.A.Lakshmi Devi
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carrying capability of the network elements is proposed by Acha et.al. [21].The impact of multiple
compensators in the system was proposed by Radman.G and R.S Raje [22].The important concepts of the
power systems with different load flow was proposed by Stagg.G.W et.al(1968) [23]. Tong Zhu and Gamg
Haung proposed (1999) the accurate points of the buses which were suitable for the FACTS devices
installation [24].P.Kessal and H. Glavitsch (1986) proposed increase the transmission capability,
improvement of stability by installing FACTS devices in transmission network [25].
3. NEWTON RAPHSON METHOD OF POWER FLOW
The Newton-Raphson method is widely used for solving non-linear equations. It transforms the original
non-linear problem into a sequence of linear problems whose solutions approach the solutions of the
original problem. Load-flow studies [7] are very common in power system analysis. Load flow allows us
to know the present state of a system, given previous known parameters and values. The power that is
flowing through the transmission line, the power that is being generated by the generators, the power that
is being consumed by the loads, the losses occurring during the transfer of power from source to load, and
so on, are iteratively decided by the load flow solution, or also known as power flow solution. In any
system, the most important quantity which is known or which is to be determined is the voltage at different
points throughout the system. Knowing these, we can easily find out the currents flowing through each
point or branch.
Since within the power flow problem real power and voltage magnitude are nominal for the voltage-
controlled buses, the power flow equations [1] are developed in polar type. For the standard bus of the
facility system shown in Figure 1
Vi V1 V1
V2
Ii
Vn
Vj yi0
Figure1 A Typical bus of the power system
The current entering bus i is given by
Ii = Vi ∑=
n
j 0
yij - ∑=
n
j 1
yijVj j = i (1)
This equation can be written in terms of the bus admittance matrix as
Ii = ∑=
n
j 1
Yij Vj (2)
In the above equation, j includes bus i. expressing this equation in polar form, we have
Ii = ∑=
n
j 1
|Yij| |Vj|∟θij+ δj (3)
yi1
yi2
yin](https://image.slidesharecdn.com/ijeet0705005-161102082459/85/FIRING-ANGLE-SVC-MODEL-FOR-ANALYZING-THE-PERFORMANCE-OF-TRANSMISSION-NETWORK-USING-NEWTON-RAPHSON-LOAD-FLOW-3-320.jpg)
![Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load
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6. FIRING ANGLE MODEL S
The SVC consists of a group of shunt
means of thyristor switching. The firing angle model for SVC is shown in figure 2.
SVC's normally include a combination of mechanically controlled and thyristor controlled shunt
capacitors and reactors [3], [4]. The most popular configuration for continuously controlled SVC's is the
combination of either fix capacitor and thyristor contr
thyristor controlled reactor [5], [6]. As far as steady
modeled along similar lines. The SVC structure shown in Fig. 2 is used to derive a SVC model t
considers the TCR firing angle α
than those currently available in open literature. The variable TCR equivalent reactance, X
fundamental frequency, is given by [5] ,
!"# = !.
%
& %'( )* &(
Where α is the thyristor's firing angle.
The SVC effective reactance X
"#
+,.+-
.,
/
. & %'( )* &( '+-
In general, the transfer admittance equation for the variable shunt compensator is,
)()( iVjBiI svcsvc =
Where
The SVC equivalent susceptance is given by (4) whilst its profile, as function of firing angle,
(
1
−=−=
Lc
TCRcsvc X
XX
BBB
XL = wL.XC = 01
and the reactive power equation is,
Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load
Flow
EET/index.asp 49
FIRING ANGLE MODEL STATIC VAR COMPENSATOR
The SVC consists of a group of shunt-connected capacitors and reactors banks with fast control action by
means of thyristor switching. The firing angle model for SVC is shown in figure 2.
Figure 3 The Firing angle model of SVC
SVC's normally include a combination of mechanically controlled and thyristor controlled shunt
capacitors and reactors [3], [4]. The most popular configuration for continuously controlled SVC's is the
combination of either fix capacitor and thyristor controlled reactor or thyristor switched capacitor and
thyristor controlled reactor [5], [6]. As far as steady-stale analysis is concerned, both configurations can be
modeled along similar lines. The SVC structure shown in Fig. 2 is used to derive a SVC model t
as state variable. This is a new and more advanced SVC representation
than those currently available in open literature. The variable TCR equivalent reactance, X
fundamental frequency, is given by [5] ,
(9)
is the thyristor's firing angle.
The SVC effective reactance Xeq is determined by the parallel combination of X
(10)
In general, the transfer admittance equation for the variable shunt compensator is,
(11)
susceptance is given by (4) whilst its profile, as function of firing angle,
])2sin)(2[ ααπ
π
+−− c
L
X
X (12)
(13)
and the reactive power equation is,
Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load
editor@iaeme.com
connected capacitors and reactors banks with fast control action by
means of thyristor switching. The firing angle model for SVC is shown in figure 2.
SVC's normally include a combination of mechanically controlled and thyristor controlled shunt
capacitors and reactors [3], [4]. The most popular configuration for continuously controlled SVC's is the
olled reactor or thyristor switched capacitor and
stale analysis is concerned, both configurations can be
modeled along similar lines. The SVC structure shown in Fig. 2 is used to derive a SVC model that
as state variable. This is a new and more advanced SVC representation
than those currently available in open literature. The variable TCR equivalent reactance, XLeq,, at
is determined by the parallel combination of XC and XLeq,
In general, the transfer admittance equation for the variable shunt compensator is,
susceptance is given by (4) whilst its profile, as function of firing angle,](https://image.slidesharecdn.com/ijeet0705005-161102082459/85/FIRING-ANGLE-SVC-MODEL-FOR-ANALYZING-THE-PERFORMANCE-OF-TRANSMISSION-NETWORK-USING-NEWTON-RAPHSON-LOAD-FLOW-6-320.jpg)
![A.Hema Sekhar and Dr.A.Lakshmi Devi
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]}2sin)(2[{
2
svcsvc
c
L
Lc
k
k
X
X
XX
V
Q ααπ
π
+−−
−
=
(14)
From the equation (14) , the linearized SVC equation is given by as
∆
∆
−=
∆
∆
svc
k
svc
L
k
i
k
k
X
V
Q
P
α
θ
α
π
]1)2[cos(
2
0
00
2
)(
(15)
7. VOLTAGE COLLAPSE PREDICTION INDEX (VCPI)
The technique [VCPI] is derived from the basic power flow equation. The technique is applicable for any
number of buses in a system. It needs the voltage phasor information of the participating buses in the
system and the network admittance matrix. Using the measured voltage phasors and the network
admittance matrix of the system, the voltage collapse prediction index (VCPI) is calculated at every bus.
The values of these indexes determine the proximity to voltage collapse at a bus. The detailed derivation of
the technique [VCPI] is given in Appendix 7 of the Ref [17] paper. The power flow equations are resolved
by Newton Raphson methodology that creates a partial matrix. By setting the determinant of the matrix to
zero, the index at bus k is written as follows:
k
N
km
m
m
k
V
V
VCPI
∑
≠
=
−=
,1
'
1
(16)
Where,
23
4
=
567
∑ 568
9
8:;,8<6
23 (17)
Vk is the voltage phasor at bus k
Vm is the voltage phasor at bus m
Ykm is the admittance between bus k and m
Ykj is the admittance between bus k and j
k is the monitoring bus
m is the other bus connected to bus k
N is the bus set of the system
The value of VCPI varies between zero and one. If the index is zero, the voltage at bus k is taken into
account stable and if the index is unity, a voltage collapse is claimed to occur. VCPI is calculated solely
with info of voltage phasor of taking part buses and impedance of relating lines. The calculation is
straightforward while not matrix conversion. The technique offers quick calculation which may be applied
for on-line watching of the power system
8. SIMULATION RESULTS
The proposed system is applied is two different test cases which are IEEE 14 and IEEE 57 bus systems by
using MATLAB software.](https://image.slidesharecdn.com/ijeet0705005-161102082459/85/FIRING-ANGLE-SVC-MODEL-FOR-ANALYZING-THE-PERFORMANCE-OF-TRANSMISSION-NETWORK-USING-NEWTON-RAPHSON-LOAD-FLOW-7-320.jpg)
![A.Hema Sekhar and Dr.A.Lakshmi Devi
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REFERENCE
[1] Power System Analysis - Hadi Saadat , Tata MC Graw Hill, Edition
[2] Hingorani, N.G. and L. Gyugyi. 2000. Understanding FACTS: Concepts and Technology of Flexible AC
Transmission Systems. Wiley–IEEE Press: New York, NY. ISBN: 0-7803-3464-7.
[3] CIGRE. Working Group 38-01, Task Force N0.2 on SVC. - static VAR compensators.". I. A. Enrimez.
EL. 1986
[4] L.Guigyi,”Power Electronics in Electric Utilities:Static VAR Compesators”,proc.of the IEEE.,Vol
76,No.4 PP.483-494,Apr.1988.
[5] T.J.E.Miller ,”Reactive Power Control in Electric Systems,Wiley inter-science,1982.
[6] IEEE Special Stability Controls Working Glaup, Working Group 38-01, Task Force No. 2 an SVC,
"Static VAR compensator models for power flow and dynamic performance simulation," IEEE Tran. on
Power Systems, vol. 9, no. I, pp. 229-240, Feb. 1995
[7] Amit Debnath, Joseph Rualkima Rante, Champa Nandi,” Stability Enhancement with SVC”,
International Journal of Computer Applications (0975 – 8887) Volume 72– No.5, May 2013.
[8] . Ramaprasad Panda,” Determination of Firing Angle for Multiple SVCs Connected to a Large System to Improve
Voltage Stability”, https://www.researchgate.net/publication/262070156
[9] Arihit Sode-Yome, and N.Mithulanathan , Comparison of Shunt Capacitor, SVC and STATCOM in
Static Voltage Stability Margin Enhancement.International Journal of Electrical Engineering Education,
UMSIT, Vol 41, No.3, July 2004
[10] H. Amhriz-PBrez, E. Acha, and C. R. Fuerte-Esquivel,” Advanced SVC Models for Newton-Raphson Load Flow
and Newton Optimal Power Flow Studies”, IEEE TRANSACTIONS ON POWER SYSTEMS. VOL. 15. NO. 1,
FEBRUARY 2000 PP.129-136
[11] Kumar, G.R.; Rao, R.K.; Ram, S.S.T., Power Flow Control and Transmission Loss Minimization model
with TCSC and SVC for Improving System Stability and Security” Industrial and Information Systems,
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[12] B. Venkateswara Rao, G.V. Nagesh Kumar, M. Ramya Priya and P.V.S. Sobhan, "Implementation of
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[15] Gotham, D.J. and G.T. Heydt. 1998. Power Flow Control and Power Flow Studies for Systems with
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[16] Povh, D. 2000. Modeling of FACTS in Power System Studies. Proc. IEEE Power Eng. Soc. Winter Meeting.
2:1435–1439.](https://image.slidesharecdn.com/ijeet0705005-161102082459/85/FIRING-ANGLE-SVC-MODEL-FOR-ANALYZING-THE-PERFORMANCE-OF-TRANSMISSION-NETWORK-USING-NEWTON-RAPHSON-LOAD-FLOW-17-320.jpg)
![Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load
Flow
http://www.iaeme.com/IJEET/index.asp 61 editor@iaeme.com
[17] V. Balamourougan, T. S. Sidhu, M. S. Sachdev, “Technique for online prediction of voltage collapse”,
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[18] C. Taylor, “Indices predicating voltage collapse including dynamic phenomena.” CIGRE Task Force
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[21] Acha, E., C.R. Fuerte-Esquivel, H. Ambriz-Pe´rez, and C. Angeles-Camacho. 2004. FACTS: Modelling
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[22] Radman, G. and R.S. Raje. 2007. Power Flow Model/Calculation for Power Systems with Multiple
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May 1999
[25] P.Kessal H.Glavitsch Estimating the voltage stability of a power system IEEE Transaction on Power
Delivary .vol.PWRD-1.N3.july 1986
[26] L.Jebaraj, C.Christober Asir Rajan, S.Sakthivel ,” Performance Evaluation of TCSC and SVC on
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(IJEET), 3(1), 2012,pp. 326–343.
[28] Reza Sirjani, Azah Mohamed, Hussain Shareef, “Optimal placement and sizing of Static Var
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[30] P.Balachennaiah, Dr. M.Suryakalavathi and P.Suresh Babu, “Optimal Location of SVC for Real Power
Loss Minimization and Voltage Stability Enhancement using Harmony Search Algorithm”.
International Journal of Electrical Engineering & Technology (IJEET), 5(1), 2014,pp. 26–34.](https://image.slidesharecdn.com/ijeet0705005-161102082459/85/FIRING-ANGLE-SVC-MODEL-FOR-ANALYZING-THE-PERFORMANCE-OF-TRANSMISSION-NETWORK-USING-NEWTON-RAPHSON-LOAD-FLOW-18-320.jpg)
FIRING ANGLE SVC MODEL FOR ANALYZING THE PERFORMANCE OF TRANSMISSION NETWORK USING NEWTON RAPHSON LOAD FLOW
- 1. http://www.iaeme.com/IJEET/index.asp 44 [email protected] International Journal of Electrical Engineering & Technology (IJEET) Volume 7, Issue 5, September–October, 2016, pp.44–61, Article ID: IJEET_07_05_005 Available online at http://www.iaeme.com/IJEET/issues.asp?JType=IJEET&VType=7&IType=5 ISSN Print: 0976-6545 and ISSN Online: 0976-6553 Journal Impact Factor (2016): 8.1891 (Calculated by GISI) www.jifactor.com © IAEME Publication FIRING ANGLE SVC MODEL FOR ANALYZING THE PERFORMANCE OF TRANSMISSION NETWORK USING NEWTON RAPHSON LOAD FLOW A.Hema Sekhar Research Scholar, Department of EEE, S.V.University College of Engineering, Tirupati, India. Dr.A.Lakshmi Devi Professor & HOD, Department of EEE, S. V. University College of Engineering, Tirupati, India. ABSTRACT This paper deals with Power flow, which is necessary for any power system solution and carry out a comprehensive study of the Newton- Raphson method of power flow analysis with and without SVC. Voltage stability analysis is the major concern in order to operate any power system as secured. This paper presents the investigation on N-R power flow enhancement of voltage stability and power loss minimization with & without FACTS controllers such as Static Var Compensator (SVC) device. The Static Var Compensator (SVC) provides a promising means to control power flow in modern power systems. In this paper the Newton-Raphson is used to investigate its effect on voltage profile and power system lossess with and without SVC in power system.. Simulations investigate the effect of voltage magnitude and angle with and without SVC on the power flow of the system. This survey article will be very much useful to the researchers for finding out the relevant references in the field of Newton-Raphson power flow control with SVC in power systems. In order to reach the above goals, these devices must be located optimally. In this paper the Optimal placement of SVC is carried out by Voltage collapse Prediction Index (VCPI).The size of the SVC is determined by suitable firing angle which reduces the losses in the system. Simulations have been implemented in MATLAB Software and the IEEE 14 and IEEE 57-bus systems have been used as case studies. Key words: Flexible AC Transmission System (FACTS), Voltage collapse Prediction Index (VCPI), Static VAR Compensator (SVC) and Newton Raphson Method. Cite this Article: A.Hema Sekhar and Dr.A.Lakshmi Devi, Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow. International Journal of Electrical Engineering & Technology, 7(5), 2016, pp. 44–61. http://www.iaeme.com/IJEET/issues.asp?JType=IJEET&VType=7&IType=5
- 2. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow http://www.iaeme.com/IJEET/index.asp 45 [email protected] 1. INTRODUCTION The operation of power system is becoming more and more challenging because of continuously increasing load demand which is leading to an augmented stress of the transmission lines, voltage instability, increase in loss and cost. To meet the ever increasing demand it is now essential to maximize the utilization of the existing transmission system. In recent years, due to advancement in high power solidstate switches, transmission controllers have been developed which provides more flexibility and controllability. A new solution for controlling power flow known as FACTS was introduced in 1988 by Hingorani [1]. FACTS devices have made the power system operation more flexible and secure. They have the ability to control, in a fast and effective manner. FACTS controllers minimizes loss, enhance the voltage profile and the load ability of power systems. FACTS devices include Thyristor Controlled Series Compensator (TCSC), Static VAR Compensator (SVC), Static Compensator (STATCOM), Unified Power Flow Controller (UPFC), etc. In this paper, SVC is used for several reasons. The most widely used shunt FACTS devices within power networks is the SVC due to its low cost and good performance in system enhancement. It is more conventional and available. SVC can control voltage with higher level of accuracy. It is a shunt connected static VAR generator or absorber whose output is adjusted to exchange capacitive or inductive current so as to provide voltage support and when installed in a proper location, it can also reduce power losses [27]. For these reasons, SVC is chosen over other FACTS devices in this paper. 2. LITERATURE SURVEY In the literature many people proposed different concepts about the placement and sizing of the SVC. Hadi Saadat Presented Real and Reactive Power flow equations in polar form by considering two bus power system. A Jacobean matrix is then constructed and Newton Raphson method is used to solve these equations [1]. Hingorani N.G et.al presented about the Fast development of power electronics introduces the use of flexible ac transmission system (FACTS) controllers in power systems. The main benefit of FACTS devices is reduction of operation and transmission investment costs, increasing the power transfer capabilities, system security, controlling power flow in the lines and in improving stability [2]. [3]-[4] papers refer that , SVCs are the combination of mechanically controlled and thyristor controlled shunt capacitors and reactors. Ref [5]-[6] papers proposed the most popular model of SVC's is the combination of either fix capacitor and thyristor controlled reactor or thyristor switched capacitor and thyristor controlled reactor .Ref[7]-[10] papers proposes Existing Basic model of SVC and the novel Firing angle model for Static VAR Compensator (SVC) FACTS devices. In that paper, it explains the power electronic development, fixed capacitor and reactor reactive power compensator has replaced with variable reactance reactive power compensator. Kumar, G.R et.al presented about load flow analysis with incorporated FACTS controllers in multimachine power systems from different operating conditions viewpoint. The Newton Raphson Methods have been proposed in literatures includes for different types of Modeling of Series FACTS controllers[11] .B.Venkateswara rao et.al explains the Implementation of Static VAR Compensator for Improvement of Power System Stability[12] Sahoo et.al (2007) proposed the basic modeling of the FACTS devices for improving the system performance[13].Zhang, X.P et.al explains Jacobian Matrix of Power flow Newton Raphson algorithm and Newton Raphson strong convergence characteristics [14].Gotham.D.J and G.T Heydt (1998) detailed about the optimal location of FACTS devices allows controlling its power flows and thus enhances the reliability of the power systems [15].Povh.D(2000) proposed the nice concepts of the modeling of the power systems and the impact of the FACTS devices on the transmission network [16]. Ref [17]-[20] papers presented the lot of techniques have been developed in predicting the closeness of the system to voltage instability in order to counteract this effect. The prediction is based on voltage collapse prediction index [VCPI] have been used to identify the bus which is more prone to voltage instability. Modelling of the FACTS devices with various techniques with complete computer programming and the operating state determine the maximum power
- 3. A.Hema Sekhar and Dr.A.Lakshmi Devi http://www.iaeme.com/IJEET/index.asp 46 [email protected] carrying capability of the network elements is proposed by Acha et.al. [21].The impact of multiple compensators in the system was proposed by Radman.G and R.S Raje [22].The important concepts of the power systems with different load flow was proposed by Stagg.G.W et.al(1968) [23]. Tong Zhu and Gamg Haung proposed (1999) the accurate points of the buses which were suitable for the FACTS devices installation [24].P.Kessal and H. Glavitsch (1986) proposed increase the transmission capability, improvement of stability by installing FACTS devices in transmission network [25]. 3. NEWTON RAPHSON METHOD OF POWER FLOW The Newton-Raphson method is widely used for solving non-linear equations. It transforms the original non-linear problem into a sequence of linear problems whose solutions approach the solutions of the original problem. Load-flow studies [7] are very common in power system analysis. Load flow allows us to know the present state of a system, given previous known parameters and values. The power that is flowing through the transmission line, the power that is being generated by the generators, the power that is being consumed by the loads, the losses occurring during the transfer of power from source to load, and so on, are iteratively decided by the load flow solution, or also known as power flow solution. In any system, the most important quantity which is known or which is to be determined is the voltage at different points throughout the system. Knowing these, we can easily find out the currents flowing through each point or branch. Since within the power flow problem real power and voltage magnitude are nominal for the voltage- controlled buses, the power flow equations [1] are developed in polar type. For the standard bus of the facility system shown in Figure 1 Vi V1 V1 V2 Ii Vn Vj yi0 Figure1 A Typical bus of the power system The current entering bus i is given by Ii = Vi ∑= n j 0 yij - ∑= n j 1 yijVj j = i (1) This equation can be written in terms of the bus admittance matrix as Ii = ∑= n j 1 Yij Vj (2) In the above equation, j includes bus i. expressing this equation in polar form, we have Ii = ∑= n j 1 |Yij| |Vj|∟θij+ δj (3) yi1 yi2 yin
- 4. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow http://www.iaeme.com/IJEET/index.asp 47 [email protected] The complex power at bus i Pi-j Qi = Vi * Ii (4) Substituting from 2.3 for Ii in 2.4 Pi-jQi=|Vi|∟δi ∑= n j 1 |Yij||Vj|∟θij+δj (5) Separating real and imaginary parts P = ∑ |V | V Y Cos θ + δ − δ = P |V|, δ 6 Q = ∑ |V | V Y Sin θ + δ − δ = Q |V|, δ 7 The power mismatch equations ΔP and ΔQ are expanded around a base point (θ(0),V(0)) and, hence, the power flow Newton–Raphson algorithm is expressed by the following relationship. ∆ ∆ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ = ∆ ∆ V V V V QQ V V PP Q P θ θ θ (8) Where P∆ is the change of real power at the bus. Q∆ is the change of reactive power at the bus. θ∂ ∂P is the change in real power w.r.t angle at the buses V V P ∂ ∂ is the change in real power w.r.t change in voltage magnitude at the buses θ∂ ∂Q is the change in reactive power w.r.t angle at the buses V V Q ∂ ∂ is the change in reactive power w.r.t change in Voltage magnitude at the buses ∆ V is the change in voltage at the bus θ∆ is the change in angle at the bus 4. SHUNT COMPENSATION Shunt compensation is widely used in power system to enhance loadability and to improve voltage stability. At buses where reactive power demand increases, bus voltage can be controlled by connecting capacitor banks in parallel to a lagging load . Capacitor banks supply part of or full reactive power of load, thus reducing magnitude of the source current necessary to supply load. Consequently the voltage drop between the sending end and the load gets reduced, power factor will be improved and increased active power output will be available from the source. Depending upon load demand, capacitor banks may be permanently connected to the system or can be varied by switching ON or OFF the parallel connected capacitors either manually or automatically (M.L.Soni, P.V.Gupta and U.S.Bhatnagar, 1994). Shunt compensation is of two types:
- 5. http://www.iaeme.com/IJEET 4.1. Shunt Capacitive Compensation This method is used to improve the transmission line, power factor lags because of lagging load current. To connected which draws current leading the source 4.2. Shunt Inductive Compensation This method is used either when charging the receiving end. Due to very low, or no load capacitance in the transmission line causes voltage amplification ( voltage may become double the sending end voltage (gen compensate, shunt inductors are connected across the transmission line. The Examples of shunt compensation are Thyristor controlled reactor (TCR), Static Synchronous Compensator (STATCOM), Thyristor etc. 5. STATIC VAR COMPENSAT A static var compensator ( SVC ) is the first generation shunt compensator. It has been around since 1960s. In the beginning it was used for load compensat loads, for flicker mitigation etc. However with the advancement of semiconductor technology, the SVC started appearing in the transmission systems in 1970s. Today a large number of SVCs are connected many transmission systems all over the world. An SVC is constructed using the thyristor technology and therefore does not have gate turn off capability. A typical SVC consists of Thyristor (TSCs) or a fixed Capacitor in parallel. The output of the compensator is controlled in steps by sequentially switching of TCRs and TSCs . The need for harmonic filtering as part of the compensator scheme could be eliminated by stepwise switching of reactors r construction model of SVC device. Figure2 A.Hema Sekhar and Dr.A.Lakshmi Devi EET/index.asp 48 ompensation This method is used to improve the power factor. Whenever an inductive load is connected to the transmission line, power factor lags because of lagging load current. To compensate, a shunt capacitor is connected which draws current leading the source voltage. The net result is improvement in power factor. ompensation either when charging the transmission line, or, when there is very low load at the receiving end. Due to very low, or no load – very low current flows through the transmi capacitance in the transmission line causes voltage amplification (Ferranti effect voltage may become double the sending end voltage (generally in case of very long transmission lines). To compensate, shunt inductors are connected across the transmission line. The Examples of shunt compensation are Thyristor controlled reactor (TCR), Static Synchronous Compensator (STATCOM), Thyristor Switched reactor (TSR), Thyristor Switched Capacitor (TSC) and STATIC VAR COMPENSATOR (SVC) is the first generation shunt compensator. It has been around since 1960s. In the beginning it was used for load compensation such as to provide var support for large industrial loads, for flicker mitigation etc. However with the advancement of semiconductor technology, the SVC started appearing in the transmission systems in 1970s. Today a large number of SVCs are connected many transmission systems all over the world. An SVC is constructed using the thyristor technology and therefore does not have gate turn off capability. A typical SVC consists of Thyristor-Switched Reactors (TSRs) and Thyristor s) or a fixed Capacitor in parallel. The output of the compensator is controlled in steps by sequentially switching of TCRs and TSCs . The need for harmonic filtering as part of the compensator scheme could be eliminated by stepwise switching of reactors rather than continuous control.. The figure shows the basic construction model of SVC device. Figure2 The basic construction model of SVC device. [email protected] . Whenever an inductive load is connected to the compensate, a shunt capacitor is . The net result is improvement in power factor. , or, when there is very low load at the very low current flows through the transmission line. Shunt Ferranti effect). The receiving end erally in case of very long transmission lines). To The Examples of shunt compensation are Thyristor controlled reactor (TCR), Static Synchronous Switched reactor (TSR), Thyristor Switched Capacitor (TSC) and is the first generation shunt compensator. It has been around since 1960s. ion such as to provide var support for large industrial loads, for flicker mitigation etc. However with the advancement of semiconductor technology, the SVC started appearing in the transmission systems in 1970s. Today a large number of SVCs are connected to many transmission systems all over the world. An SVC is constructed using the thyristor technology and Switched Reactors (TSRs) and Thyristor-Switched Capacitors s) or a fixed Capacitor in parallel. The output of the compensator is controlled in steps by sequentially switching of TCRs and TSCs . The need for harmonic filtering as part of the compensator scheme could be ather than continuous control.. The figure shows the basic
- 6. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load http://www.iaeme.com/IJE 6. FIRING ANGLE MODEL S The SVC consists of a group of shunt means of thyristor switching. The firing angle model for SVC is shown in figure 2. SVC's normally include a combination of mechanically controlled and thyristor controlled shunt capacitors and reactors [3], [4]. The most popular configuration for continuously controlled SVC's is the combination of either fix capacitor and thyristor contr thyristor controlled reactor [5], [6]. As far as steady modeled along similar lines. The SVC structure shown in Fig. 2 is used to derive a SVC model t considers the TCR firing angle α than those currently available in open literature. The variable TCR equivalent reactance, X fundamental frequency, is given by [5] , !"# = !. % & %'( )* &( Where α is the thyristor's firing angle. The SVC effective reactance X "# +,.+- ., / . & %'( )* &( '+- In general, the transfer admittance equation for the variable shunt compensator is, )()( iVjBiI svcsvc = Where The SVC equivalent susceptance is given by (4) whilst its profile, as function of firing angle, ( 1 −=−= Lc TCRcsvc X XX BBB XL = wL.XC = 01 and the reactive power equation is, Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow EET/index.asp 49 FIRING ANGLE MODEL STATIC VAR COMPENSATOR The SVC consists of a group of shunt-connected capacitors and reactors banks with fast control action by means of thyristor switching. The firing angle model for SVC is shown in figure 2. Figure 3 The Firing angle model of SVC SVC's normally include a combination of mechanically controlled and thyristor controlled shunt capacitors and reactors [3], [4]. The most popular configuration for continuously controlled SVC's is the combination of either fix capacitor and thyristor controlled reactor or thyristor switched capacitor and thyristor controlled reactor [5], [6]. As far as steady-stale analysis is concerned, both configurations can be modeled along similar lines. The SVC structure shown in Fig. 2 is used to derive a SVC model t as state variable. This is a new and more advanced SVC representation than those currently available in open literature. The variable TCR equivalent reactance, X fundamental frequency, is given by [5] , (9) is the thyristor's firing angle. The SVC effective reactance Xeq is determined by the parallel combination of X (10) In general, the transfer admittance equation for the variable shunt compensator is, (11) susceptance is given by (4) whilst its profile, as function of firing angle, ])2sin)(2[ ααπ π +−− c L X X (12) (13) and the reactive power equation is, Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load [email protected] connected capacitors and reactors banks with fast control action by means of thyristor switching. The firing angle model for SVC is shown in figure 2. SVC's normally include a combination of mechanically controlled and thyristor controlled shunt capacitors and reactors [3], [4]. The most popular configuration for continuously controlled SVC's is the olled reactor or thyristor switched capacitor and stale analysis is concerned, both configurations can be modeled along similar lines. The SVC structure shown in Fig. 2 is used to derive a SVC model that as state variable. This is a new and more advanced SVC representation than those currently available in open literature. The variable TCR equivalent reactance, XLeq,, at is determined by the parallel combination of XC and XLeq, In general, the transfer admittance equation for the variable shunt compensator is, susceptance is given by (4) whilst its profile, as function of firing angle,
- 7. A.Hema Sekhar and Dr.A.Lakshmi Devi http://www.iaeme.com/IJEET/index.asp 50 [email protected] ]}2sin)(2[{ 2 svcsvc c L Lc k k X X XX V Q ααπ π +−− − = (14) From the equation (14) , the linearized SVC equation is given by as ∆ ∆ −= ∆ ∆ svc k svc L k i k k X V Q P α θ α π ]1)2[cos( 2 0 00 2 )( (15) 7. VOLTAGE COLLAPSE PREDICTION INDEX (VCPI) The technique [VCPI] is derived from the basic power flow equation. The technique is applicable for any number of buses in a system. It needs the voltage phasor information of the participating buses in the system and the network admittance matrix. Using the measured voltage phasors and the network admittance matrix of the system, the voltage collapse prediction index (VCPI) is calculated at every bus. The values of these indexes determine the proximity to voltage collapse at a bus. The detailed derivation of the technique [VCPI] is given in Appendix 7 of the Ref [17] paper. The power flow equations are resolved by Newton Raphson methodology that creates a partial matrix. By setting the determinant of the matrix to zero, the index at bus k is written as follows: k N km m m k V V VCPI ∑ ≠ = −= ,1 ' 1 (16) Where, 23 4 = 567 ∑ 568 9 8:;,8<6 23 (17) Vk is the voltage phasor at bus k Vm is the voltage phasor at bus m Ykm is the admittance between bus k and m Ykj is the admittance between bus k and j k is the monitoring bus m is the other bus connected to bus k N is the bus set of the system The value of VCPI varies between zero and one. If the index is zero, the voltage at bus k is taken into account stable and if the index is unity, a voltage collapse is claimed to occur. VCPI is calculated solely with info of voltage phasor of taking part buses and impedance of relating lines. The calculation is straightforward while not matrix conversion. The technique offers quick calculation which may be applied for on-line watching of the power system 8. SIMULATION RESULTS The proposed system is applied is two different test cases which are IEEE 14 and IEEE 57 bus systems by using MATLAB software.
- 8. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow http://www.iaeme.com/IJEET/index.asp 51 [email protected] 8.1. Test case 1: IEEE 14 Bus System The single line diagram of IEEE 14 bus system is shown in the figure 1 and the voltage profile for IEEE 14 bus system without SVC is shown in figure 2. Figure 4 Single line diagram of IEEE 14 bus system. Figure 5 Voltage profile of IEEE 14 bus system without SVC 8.1.1. Single SVC Placement The placement of shunt compensating device which is SVC is determined by VCPI. The highest value of VCPI reveals the suitable location of SVC The placement of single SVC by using VCPI is implemented on IEEE 14 bus system. The VCPI values of the IEEE 14 bus system is shown in the table 1. From the table 1, the single SVC is placement is decided at 14 bus The VCPI is high at 14th bus, so shunt compensating device such as SVC is optimally placed at 14th bus of the system By placing SVC at 14th bus location of the transmission network the real and reactive power losses are reduced.. The real and reactive power losses are reduced to 9.44 MW and 49.44 MVar. The voltage profile, total real and reactive power losses without placing of SVC and with the placing of single SVC are shown in the figure 3,4and 5 respectively. 0 2 4 6 8 10 12 14 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 busnumbers voltagemagnitudeinp.u Voltage profile without SVC device
- 9. A.Hema Sekhar and Dr.A.Lakshmi Devi http://www.iaeme.com/IJEET/index.asp 52 [email protected] Table 1 Voltage Collapse Prediction Index (VCPI) of IEEE 14 bus system Bus no VCPI 1 0.1760 2 0.0679 3 0.2060 4 0.1529 5 0.1300 6 0.2591 7 0.2319 8 0.2184 9 0.2874 10 0.2967 11 0.2827 12 0.2920 13 0.2993 14 0.3408 Figure 6 Voltage profile of IEEE 14 bus with and without single SVC . 0 2 4 6 8 10 12 14 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 busnumbers voltagemagnitudeinP.U voltage profile with and without SVC without SVC with SVC
- 10. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow http://www.iaeme.com/IJEET/index.asp 53 [email protected] . Figure 7 Total Real power losses of IEEE 14 bus with and without single SVC. Figure 8 Reactive power losses of IEEE 14 bus with and without single SVC. 8.1.2. Placement of Two SVC’s With the inclusion of two SVC’s in the bus system i.e one SVC is locate at 14th bus and second SVC is locate at 13th bus then the power flows are further improved and losses further are reduced which is shown in the table 2. The voltage profile, total real and reactive power losses without placing of SVC and with the placing of two SVC’s are shown in the figure 6,7 and 8 respectively. 1 2 0 1 2 3 4 5 6 7 8 9 10 without SVC with SVC realpowerlosses(Mw)withandwithoutsvc TOTAL REAL POWER LOSSES WITH AND WITHOUT SVC 1 2 0 10 20 30 40 50 60 without SVC with SVC reactivepowerlosses(MVar)withandwithoutsvc TOTAL REACTIVE POWER LOSSES WITH AND WITHOUT SVC
- 11. A.Hema Sekhar and Dr.A.Lakshmi Devi http://www.iaeme.com/IJEET/index.asp 54 [email protected] Figure 9 Voltage profile of IEEE 14 bus with and without two SVCs Figure 10 Total Real power losses of IEEE 14 bus with and without two SVCs Figure 11 Total Reactive power losses of IEEE 14 bus with and without two SVCs 0 2 4 6 8 10 12 14 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 busnumbers voltagemagnitudeinP.U voltage profile with and without SVC without SVC with SVC 1 2 0 1 2 3 4 5 6 7 8 9 10 without SVC with SVC realpowerlosses(Mw)withandwithoutsvc TOTAL REAL POWER LOSSES WITH AND WITHOUT SVC 1 2 0 10 20 30 40 50 60 without SVC with SVC reactivepowerlosses(MVar)withandwithoutsvc TOTAL REACTIVE POWER LOSSES WITH AND WITHOUT SVC
- 12. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow http://www.iaeme.com/IJEET/index.asp 55 [email protected] Table 2 Comparative system parameters of IEEE 14 bus with and without SVC Parameters Without SVC With SINGLE SVC With TWO SVC’S Minimum Voltage(p.u) 1.01 at bus 3 1.0044 at bus 13 0.998 at bus 13 Maximum Voltage(p.u) 1.09 at bus 8 1.049 at bus 2 1.047 at bus 2 Real power losses(MW) 9.682 9.44 9.32 Reactive power losses(MVar) 50.04 49.44 48.44 Location of SVC ---------- 14th bus 14th bus. 13th bus SVC 1firing angle(deg) ---------- 138.3 134.3 SVC2 firing angle(deg) ---------- ------ 124.3 Size of SVC1(kVar) ----------- 2.3 1.3 Size of SVC2(KVar) ---------- ------ 0.983 From the above table, it is shown that without SVC the Real and Reactive power losses are 9.682 MW and 50.04 MVar.In case placing single SVC the losses are Reduced i.e Real and Reactive power losses are 9.44 MW and 49.44 MVar and for two SVC’s 9.32 MW & 48.44 MVar. 8.2. Test case 2 : IEEE 57 bus The single line diagram of the IEEE 57 bus system is shown in the figure 9. The improvement of voltage profile, the reduction of total real and reactive power losses, are shown in the figure 9.. Figure 12 Single line diagram of the IEEE 57 bus system.
- 13. A.Hema Sekhar and Dr.A.Lakshmi Devi http://www.iaeme.com/IJEET/index.asp 56 [email protected] 8.2.1. Single SVC Placement The placement of single SVC by using VCPI is implemented on IEEE 57 bus system. By placing single SVC at 33rd bus location of the transmission network, the real and reactive power losses are reduced.. The real and reactive power losses are reduced to 27.864 MW and 119.27 MVar from 27.964 MW and 121.67 MVar. The voltage profile, total real and reactive power losses without placing of SVC and with the placing of single SVC are shown in the figure 10,11and 12 respectively. Figure 13 Voltage profile of IEEE 57 bus with and without single SVC Figure 14 Total Real power losses of IEEE 57 bus with and without single SVC 0 10 20 30 40 50 60 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 busnumbers voltagemagnitudeinP.U voltage profile with and without SVC without SVC with SVC 1 2 0 5 10 15 20 25 30 without SVC with SVC realpowerlosses(Mw)withandwithoutsvc TOTAL REAL POWER LOSSES WITH AND WITHOUT SVC
- 14. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow http://www.iaeme.com/IJEET/index.asp 57 [email protected] Figure 15 Total Reactive power losses of IEEE 57 bus with and without single SVC 8.2.2. Placement of Two SVC’s With the inclusion of two SVC’s in the bus system i.e one SVC is locate at 33rd bus and second SVC is locate at 51th bus then the power flows are further improved and losses further are reduced which is shown in the table 3. The voltage profile, total real and reactive power losses without placing of SVC and with the placing of two SVC’s are shown in figures 13,14 and 15 respectively. Figure 16 Voltage profile of IEEE 57 bus with and without two SVCs 1 2 0 20 40 60 80 100 120 140 without SVC with SVC reactivepowerlosses(MVar)withandwithoutsvc TOTAL REACTIVE POWER LOSSES WITH AND WITHOUT SVC 0 10 20 30 40 50 60 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 busnumbers voltagemagnitudeinP.U voltage profile with and without SVC without SVC with SVC
- 15. A.Hema Sekhar and Dr.A.Lakshmi Devi http://www.iaeme.com/IJEET/index.asp 58 [email protected] Figure 17 Total Real power losses of IEEE 57 bus with and without two SVCs Figure 18 Total Reactive power losses of IEEE 57 bus with and without two SVCs 1 2 0 5 10 15 20 25 30 without SVC with SVC realpowerlosses(Mw)withandwithoutsvc TOTAL REAL POWER LOSSES WITH AND WITHOUT SVC 1 2 0 20 40 60 80 100 120 140 without SVC with SVC reactivepowerlosses(MVar)withandwithoutsvc TOTAL REACTIVE POWER LOSSES WITH AND WITHOUT SVC
- 16. Firing Angle SVC Model for Analyzing the Performance of Transmission Network using Newton Raphson Load Flow http://www.iaeme.com/IJEET/index.asp 59 [email protected] Table 3 Comparative system parameters of IEEE 57 bus with and without single & two SVCs Parameters Without SVC With SINGLE SVC With TWO SVC’S Minimum Voltage(p.u) 0.936 at bus 31 0.9638 at bus 26 0.9618 at bus 26 Maximum Voltage(p.u) 1.06 at bus1 1.0412 at bus 49 1.0392 at bus 49 Real power losses(MW) 27.964 26.864 26.424 Reactive power losses(MVar) 121.67 119.27 115.27 Location of SVC ---------- 33rd bus 33rd bus, 51 bus SVC 1firing angle(deg) ---------- 122.3 126.3 SVC2 firing angle(deg) ---------- ------- 124.3 Size of SVC1(kVar) ----------- 3.82 1.74 Size of SVC2(KVar) ---------- ------- 2.35 From the above table, it is shown that without SVC the Real and Reactive power losses are 27.964 MW and 121.67 MVar.In case placing single SVC the losses are Reduced i.e Real and Reactive power losses are 26.864 MW and 119.27 MVar and for two SVC’s 26.424 MW & 115.27 MVar. 9. CONCLUSION In this paper, the optimal location and optimal sizing of SVC device is find out to minimize voltage deviation and the active power losses in the power system network using Newton Raphson Technique. The Firing Angle Model of Static VAR Compensator (SVC) using Newton Raphson method has been implemented on IEEE 14 and 57 bus test systems to investigate the performance of power transmission line in absence as well as in presence of single and double SVC devices. It is found that during presence of single SVC there is reduction of real and reactive power losses and also voltage profile improvement as compared to absence of SVC and with double SVCs also there is reduction in losses and there is more improvement in voltage profiles .The results obtained by application of the N-R technique during firing- angle model based control are found to be very much similar with the reactance model. It is noted that as compared to Reactance method, the implementation of the firing-angle based control of SVC using NR technique is much easier. It is also noted that the firing-angle calculation of SVC using firing-angle model based control is much easier as compared to impedance model based control.and this proposed method is better than earlier published works like reactance models and power injection models.
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