MULTIMACHINE POWER SYSTEM STABILITY ENHANCEMENT … · 2020. 5. 4. · Phillips-Heffron model for...

http://www.iaeme.com/IJARET/index.asp 219 [email protected]

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

Multimachine Power System Stability Enhancement with UPFC using Linear Quadratic Regulator

Techniques


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.

Brijesh Kumar Dubey and Dr. N.K. Singh


Vt

It

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, 1.1168 G3, 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


Techniques


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

-Wcu

1

(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



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]


Techniques


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



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]


Settling Time and Overshoot analysis


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


Techniques


(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






Case-3: [pf=.85, me =.5, δe =.5, mb =.5, δb =.5, Load= 1.0 PU, D=4]



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




Techniques



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];



• [XtE ] = [0.3, 0.3, 0.3]

Operating conditions:

• Vb= 1.0;

• pf = 0.85;

• Frequency = 50 Hz.

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