-
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International Journal of Advanced Research in Engineering and
Technology (IJARET)
Volume 11, Issue 4, April 2020, pp. 219-229, Article ID:
IJARET_11_04_022
Available online
athttp://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=11&IType=4
ISSN Print: 0976-6480 and ISSN Online: 0976-6499
© IAEME Publication Scopus Indexed
MULTIMACHINE POWER SYSTEM STABILITY
ENHANCEMENT WITH UPFC USING LINEAR
QUADRATIC REGULATOR TECHNIQUES
Brijesh Kumar Dubey
Department of Electrical and Electronics Engineering,
Pranveer Singh Institute of Technology, Kanpur, India
Dr. N.K. Singh
Department of Computer Science Engineering,
Director, ITM Gida, Gorakhpur, India
ABSTRACT
It is well known that for computer simulation and analysis of
power systems both
planning and operation are necessary. Computer simulation
requires an appropriate
mathematical model that many inter-related linear, nonlinear,
differential and
algebraic equations of the system. Such mathematical model is
needed for analysis and
improves power system dynamic stability performance and also
design a suitable
controller. This paper provides comprehensive development
procedure and final forms
of mathematical models of a power system installed with UPFC and
controller UPFC
using linear quadratic regulator techniques for stability
improvement. The impacts of
control strategy on power system multi machine installed with
UPFC, without UPFC
and with controller UPFC at different loading and operating
conditions are discussed.
The accuracy of the developed models is verified through
comparing the study results
with those obtained from detailed MATLAB programming. In this
paper settling time
analysis also have been done for justification of the stability
improvement.
Keywords: Modelling; LQR; UPFC; Eigen value analysis; dynamic
stability; Power
oscillation damping controller
Cite this Article: Brijesh Kumar Dubey and Dr. N.K. Singh,
Multimachine Power
System Stability Enhancement with UPFC using Linear Quadratic
Regulator
Techniques, International Journal of Advanced Research in
Engineering and
Technology (IJARET), 11(4), 2020, pp. 219-229.
http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=11&IType=4
1. INTRODUCTION
The expansion of electric power systems are not always
favorable, because along with the
complexity of the network, the damping torque of the whole
system is also reduce and the result
can make the power system unstable. On the other hand, the main
drawbacks of the electrical
power systems are deteriorating voltage profiles and issues
related to power system stability
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Multimachine Power System Stability Enhancement with UPFC using
Linear Quadratic Regulator
Techniques
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and security; the major cause of this problem is the overloading
of the electrical power
transmission lines [1]. The main parameters which are
responsible to determine the transmitted
electrical power over a power transmission line are power
transmission line impedance, the
receiving and sending end voltages, and phase angle between the
two voltages. Therefore,
controlling one are more of these power transmission parameters,
it is possible to control the
active and reactive power flow over a power transmission lines.
To improve power system
stability power system stabilizers have been widely used. The
equilibrium of the dynamics of a
large-scale power system is uncertain due to nonlinear and
interconnected system, and physical
limitations of the controllers are also present. Controllers are
designed as a part of excitation
system of the generator and feedback linearization scheme is
developed by Deqiang Gan and
et.al [9]. However, due to some drawbacks of the conventional
PSSs, the need for finding a
better substitution still remains. Therefore, in this paper, the
application of the FACTS devices
such as unified power flow controller (UPFC) to improve dynamic
stability of a multi-machine
electric power system is presented and a supplementary
stabilizer based on the FACTS device
is incorporated. Investigations involve the analysis of the
linearized state space equations of the
power system dynamics. To damp out the low power oscillation
frequency and increase system
oscillations stability, the installation of Power System
Stabilizer (PSS) is both economical and
effective [2]. Recently appeared FACTS (Flexible AC Transmission
System)-based stabilizer
offer an alternative way in damping power system oscillation.
The primary function of the
FACTS controllers is not only it Damping Duty, but also to
increase the overall power system
oscillation damping characteristics [3]. The objective of this
paper is to design a UPFC based
Power Oscillation Damping (POD) controller to damp the low
frequency electromechanical
oscillations over wide range of operating conditions [4-6]. The
objective and steps involved are
as follows:
• The model of the multi machine power system installed with
UPFC is obtained by linearizing the non-linear equations around a
nominal operating point.
• To present systematic approach for designing UPFC based power
oscillation damping controller.
• Eigenvalue analysis technique has been used as this is a
powerful tool for analyzing oscillatory instability and yields
information about the frequency and damping of each
oscillation mode.
• Design a POD controller using linear quadratic regulator
technique which places the eigenvalue corresponding to mode of
oscillation at desired location such that
eigenvalues get placed within a vertical degree of
stability.
• To demonstrate the effectiveness of the designed POD
controller under different controlling parameter.
2. INVESTIGATED SYSTEM
Figure 1 depicts a multi machine power system installed with
unified power flow controller
between bus 2 and bus 3 on the transmission line. It consists of
the components:
Excitation transformer (ET), (ii) Boosting transformer (BT),
(iii) Two three-phase GTO
based voltage source converters (VSCs), (iv) Dc link capacitor
nased on pulse width modulation
converters (assumed) [10-11]. This paper considers three
identical machines with same rating
and operating conditions. The system parameters are given in
Appendix-A.
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Brijesh Kumar Dubey and Dr. N.K. Singh
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VtIt
VEt
XtE
IB Xb
VB
Xe
ET
Ii
VSC-E
Cdc
VSC-BBT
XBv
meδe mb δb
I0
IEt
qE
BUS 2
BUS 3
t
qE t
qE
BUS 1
G2
G1
G3
Figure 1 UPFC with MMIB power system
2.1. Unified Power Flow Control
The UPFC is the best controller, because over the line real and
reactive power flows and the
bus voltage, it provides independent control [12], Between the
converter dc link provides a path
to exchange active power. The input control parameter discussed
here are, me, mb , δe, δb of the
UPFC. Here me is amplitude modulation ratio of shunt VSC-E, δe
is phase angle of shunt VSC-
E, mb is amplitude modulation ratio of series VSC-B and δb
represents phase angle of series
VSC-B [5]. The phase angle control method is more efficient than
Amplitude modulation
control methods [13]. Power system which comprises a multiple
synchronous generators
connected to an infinite bus through a transmission line and
stepping up transformer. The
generators are assumed to have Automatic Voltage Regulator (AVR)
controlling its terminal
voltage. The UPFC is used in this study to just analyze the
purpose of power system stability
and its characteristics. The UPFC can fulfill the multiple
control objectives.
Figure 2 Variation of Settling Time with Phase Angle
Figure 3 Variation of Settling Time with Modulation Index
G1, 0.3, 1.0058G1, 0.4, 1.4158
G1, 0.5, 1.8568G1, 0.6, 2.3344
G2, 0.3, 1.7544
G2, 0.4, 2.4183
G2, 0.5, 3.0233G2, 0.6, 3.2889
G3, 0.3, 1.2186
G3, 0.4, 1.1498
G3, 0.5, 1.1168G3, 0.6, 1.0873
Variation in Settling Time with variation in phase angle of the
converters
for G1, G2, G3
G1 G2 G3
Phase angle
G1, 0.3, 2.3218
G1, 0.4, 1.1913G1, 0.5, 1.8997 G1, 0.6, 1.8997
G2, 0.3, 4.3069
G2, 0.4, 3.4188 G2, 0.5, 3.0233 G2, 0.6, 3.0882
G3, 0.3, 0.944
G3, 0.4, 1.0361 G3, 0.5, 1.1168G3, 0.6, 1.1913
Variation in Settling Time with variation in modulation index of
the
converters for G1, G2, G3
G1 G2 G3
Modulation Index
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Multimachine Power System Stability Enhancement with UPFC using
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2.2. Phillips-Heffron model for Multimachine System with
UPFC
A single-line diagram of 3-generator installed with a UPFC is
shown in Figure 1. Figure 4
shows the Phillips-Heffron model of power system installed with
UPFC, developed by Wang
[6, 14] with the modification of the basic Phillips-Heffron
model including UPFC. Around a
nominal operating point, by linearizing the nonlinear model,
this model has been developed.
The parameters of the model depend on the system parameters and
the operating condition. In
this model [Δu] is the column vector while [Wpu], [Wqu], [Wvu]
and [Wcu] are the row vectors. Where,
[Δu] = [Δme Δδe Δmb Δδb]T, [Wpu] = [Wpe Wpde Wpb Wpdb]
[Wqu] =[Wqe Wqde Wqb Wqdb],[Wvu] = [Wve Wvde Wvb Wvdb]
[Wcu] = [Wce Wcde Wcb Wcdb]
The control parameters of the UPFC in which me and mb are the
amplitude modulation ratio
of shunt and series converters respectively. By controlling me,
the voltage at a bus where UPFC
is installed, is controlled through reactive power compensation.
The magnitude of series
injected voltage can be controlled by controlling mb. δe and δb
are the phase angle of shunt and
series converters respectively. Phase angle of the shunt
converter, which regulates the dc
voltage at dc link, phase angle of the series converter when
controlled results in the real power
exchange control [15-16].
-1
(sM+D)
ω0
s
Δω
W1
W4 W5
-
W2
W6
- Ex(s)1
(K3+sTd0)
WpuW8 Wqu Wqd Wvu Wvd Wpd
-Wcu1
(W9+s)W7
Δδ
ΔEfd
Δu
Δu
ΔE’q
ΔVdc
Figure 4 Phillips-Heffron model of power system installed with
UPFC
2.3. Model Analysis
The constant parameters of the model computed for nominal
operating condition and system
parameters are
Table 1 Model Analysis data
W1 = 0.1372 Wpb = 0.0715 Wpde = -0.2514
W2 = 0.4350 Wqb = -0.0223 Wqde = - 0.2243
W3 = 0.4727 Wvb = 0.0145 Wvde = 0.0782
W4 = 0.0598 Wpe = 0.7860 Wcb = 0.1763
W5 = -0.0159 Wqe = -0.2451 Wce = 0.0018
W6 = 0.5092 Wve = 0.1597 Wcdb = 37.7306
W7 = 80.9318 Wpdb = -0.0229 Wcde = 77.2952
W8 = 21.0677 Wqdb = - 0.0204 Wpd = 0.4287
W9 = 40.6634 Wvdb = 0.0061 Wqd = -0.1337
Wvd = 0.0871
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2.4. Design of POD Controller (Linear Quadratic Regulator
Technique)
The linearized state-space model of multi machine power system
is obtained by phillip-heffron
model as expressed by,
�̇� = 𝐴𝑋 + 𝐵𝑈 (1)
Where A and B are the matrices of the system and input
respectively. X is the system state
vector, and U is the input state vector. The matrices A and B
are constant under the assumption
of system linearity. If we use state feedback, that is, if we
set U= -KX where K is the chosen
gain matrix, the equation (1) becomes [7],[8],
�̇� = (𝐴 − 𝐵𝐾)𝑋 (2)
And the problem is to allocate any set of eigenvalues to closed
loop matrix by choosing the
gain matrix K [9].
Steps for controller design
• Required data – A, B, Q, R and N matrix
• Data for calculation- K matrix, P matrix and eigen value
• Set N matrix is zero
• Q and R are the positive definite real symmetric matrix.
• Calculate the P matrix
• Find the value of K matrix
UPFCPower
System
POD
Controller
y(t)u(t)
-x(t)
uin(t)
uoPOD(t)
Figure 5 Generalized Diagram of POD Controller
3. SIMULATION RESULTS UNDER DIFFERENT SYSTEMS AND AT
VARIOUS LOADING CONDITIONS
The proposed model of UPFC in multi machine power system figure
1 has been used in order
to study the damping performance. To study the performance of
the proposed controller,
simulation results under different system conditions and at
various loading conditions i.e. at
normal operating point corresponding to line loading of 1.0 pu
and at 20 percent decrease and
increase in line loading are shown. It can be readily seen that
the proposed controller performs
better in terms of reduction of overshoot and settling time than
system without UPFC and with
system with UPFC only. This is consistent with the eigenvalues
analysis results. Simulation
results with variation in system- state, rotor angle (δ) of
generator is only considered.
Case-1: [pf=0.85, me =.5, δe =0.5, mb =0.5, δb =0.5, Load= 0.8
PU, D=4]
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Table 2 Settling Time and Overshoot for Multimachine system
Settling Time and Overshoot analysis
System Settling Time Overshoot
System Without UPFC (G1) 7.1299 3.3065
and without (G2) 9.8276 3.8700
controller UPFC (G3) 19.2541 3.4422
System With UPFC
(G1) 1.1128 3.1854
(G2) 3.0233 5.1764
(G3) 1.1168 3.3337
System With controller (G1) 0.4311 2.5789
UPFC (G2) 0.8307 2.6178
(G3) 0.772 2.5874
Table 3 Eigen values for Multimachine system.
Eigen Value Analysis
System Without UPFC and controller UPFC
Generator(G1) Generator(G2) Generator(G3)
-28.3671 + 0.0000i -45.9363 + 0.0000i
-28.3680 +
0.0000i
-0.4291 +10.3486i -0.3185 + 9.1082i
-0.1565
+10.3624i
-0.4291 -10.3486i -0.3185 - 9.1082i -0.1565 -10.3624i
-5.5149 + 0.0000i -4.3082 + 0.0000i -5.5083 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
System With UPFC only
-88.4236 + 0.0000i -73.2065 + 0.0000i
-88.4178 +
0.0000i
-6.5628 +29.2773i
-26.4028 +
0.0000i
-6.5492
+29.2205i
-6.5628 -29.2773i
-11.8046 +
0.0000i -6.5492 -29.2205i
-2.9793 + 4.8762i -1.1876 + 5.7775i -2.7204 + 5.0381i
-2.9793 - 4.8762i -1.1876 - 5.7775i -2.7204 - 5.0381i
System With controller UPFC
-7.5417 + 0.0000i -7.8567 + 0.0000i -7.5417 + 0.0000i
-0.6782 + 0.0000i -0.4661 + 0.0000i -0.6782 + 0.0000i
-0.0038 + 0.0074i -0.0044 + 0.0057i -0.0038 + 0.0074i
-0.0038 - 0.0074i -0.0044 - 0.0057i -0.0038 - 0.0074i
-0.0005 + 0.0000i -0.0005 + 0.0000i -0.0005 + 0.0000i
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Figure 6 Systems(G1, G2, G3) with and without (UPFC and UPFC
controller)
Figure 7 Systems[G1 (Blue), G2 (Red), G3(Orange)] with UPFC
controller
Figure 8 Systems[G1 (Blue), G2 (Red), G3(Orange)] with UPFC
only
Case-2: [pf=.85, me =.5, δe =.5, mb =.5, δb =.5, Load= .8 PU,
D=8]
Table 4 Settling Time and Overshoot for Multimachine system
Settling Time and Overshoot analysis
System Settling Time Overshoot
System Without UPFC (G1) 3.7132 3.3197
and without (G2) 4.6897 3.6575
controller UPFC (G3) 7.1299 3.3065
System With UPFC
(G1) 1.4938 3.4864
(G2) 2.0513 4.789
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(G3) 1.1128 3.1854
System With controller (G1) 0.8120 2.5422
UPFC (G2) 0.8436 2.607
(G3) 0.4311 2.5789
Table 5 Eigen values for Multimachine system
Eigen Value Analysis
System Without UPFC and controller UPFC
Generator(G1) Generator(G2) Generator(G3)
-0.8406 + 9.7780i -45.9362 + 0.0000i -28.3671 + 0.0000i
-0.8406 - 9.7780i -0.6625 + 9.0878i -0.4291 +10.3486i
-10.3168 + 6.1200i -0.6625 - 9.0878i -0.4291 -10.3486i
-10.3168 - 6.1200i -4.3099 + 0.0000i -5.5149 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
System With UPFC
-78.2843 + 0.0000i -73.2089 + 0.0000i -88.4236 + 0.0000i
-6.6486 +15.0308i -26.4507 + 0.0000i -6.5628 +29.2773i
-6.6486 -15.0308i -11.5876 + 0.0000i -6.5628 -29.2773i
-2.2194 + 7.5799i -1.6158 + 5.7241i -2.9793 + 4.8762i
-2.2194 - 7.5799i -1.6158 - 5.7241i -2.9793 - 4.8762i
System With controller UPFC
-5.4454 + 0.0000i -7.8567 + 0.0000i -7.5417 + 0.0000i
-0.1653 + 0.0000i -0.4661 + 0.0000i -0.6782 + 0.0000i
-0.0043 + 0.0066i -0.0045 + 0.0057i -0.0038 + 0.0074i
-0.0043 - 0.0066i -0.0045 - 0.0057i -0.0038 - 0.0074i
-0.0015 + 0.0000i -0.0005 + 0.0000i -0.0005 + 0.0000i
Figure 9 Systems(G1, G2, G3) with and without (UPFC and UPFC
controller)
Figure 10 Systems[G1 (Blue), G2 (Red), G3(Orange)] with UPFC
controller
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Figure 11 Systems[G1 (Blue), G2 (Red), G3(Orange)] with UPFC
only
Case-3: [pf=.85, me =.5, δe =.5, mb =.5, δb =.5, Load= 1.0 PU,
D=4]
Table 6 Settling Time and Overshoot for Multimachine system
System Settling Time Overshoot
System Without UPFC (G1)8.1609 3.2915
and without (G2) 10.1817 3.5377
controller UPFC (G3)19.8206 3.2929
System With UPFC
(G1) 1.6356 3.4154
(G2)2.7273 4.6552
(G3) 1.0089 2.9598
System With controller (G1)0.7377 2.4151
UPFC (G2) 0.7759 2.4456
(G3) 0.7433 2.4956
Figure 12 Systems(G1, G2, G3) with and without (UPFC and UPFC
controller)
Figure 13 Systems[G1 (Blue), G2 (Red), G3(Orange)] with UPFC
controller
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Multimachine Power System Stability Enhancement with UPFC using
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Figure 14 Systems[G1 (Blue), G2 (Red), G3(Orange)] with UPFC
only
4. CONCLUSION
In this paper, the power system low frequency electromechanical
oscillation was damped via
linear quadratic regulator technique (using MATLAB tool) based
POD controller when applied
independently with UPFC and investigated for multimachine power
system. For the proposed
controller design problem, an eigenvalue-based objective
function to maximize the system
damping ratio among all complex eigenvalues concept was
developed.
Method have been described in this paper. As compared The
effectiveness of the proposed controller in damping the low
frequency EM mode of oscillations and hence improving power
system stability have been verified through eigenvalue analysis
and simulation results with
different system condition and under different line loading and
without any line loading.
APPENDIX A
System Data-Generator data:
• [M] = [8, 8, 8] M J/ MVA;
• [Xd] = [1, 1, 1];
• [X’d] = [0.3, 0.3, 0.3];
• [Td0] = [5.0, 5.0, 5.0] sec;
• [Xq ] = [0.6, 0.6, 0.6];
• [δ ]= [0.6981, 0.6981, 0.6981] radian;
• [E’q ]=[1.0, 1.0, 1.0]
Excitation System data:
• [Ka] = [10, 10, 10];
• [Ta] = [0.01, 0.01, 0.01] sec.
Transformers data:
• [Xb] = [0.03, 0.03, 0.03];
• [Xe ]= [0.03, 0.03, 0.03]
Transmission line data:
• [XBV] = [0.3, 0.3, 0.3];
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• [XtE ] = [0.3, 0.3, 0.3]
Operating conditions:
• Vb= 1.0;
• pf = 0.85;
• Frequency = 50 Hz.
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