94310-6767 IJET-IJENS

International Journal of Engineering & Technology IJET Vol: 9 No: 10

94310-6767 IJET-IJENS @ International Journals of Engineering and Sciences IJENS

47

TCSC Control of Power System oscillation and Analysis using Eigenvalue Techniques

M.W. Mustafa. MIEEE ,Nuraddeen Magaji, IEEE Student Memberand Z. bint Muda Universiti Teknologi Malaysia, Department of Power Engineering, Johor Bahru, Malaysia

[email protected]

Abstract—TCSC devices are used to improve real power and eliminate line loses in ac systems. An additional task of TCSC is to increase transmission capacity as result of power oscillation damping. In this paper eigenvalue-based methods for analysis and control of power system oscillations using TCSC have been developed. The characterization of power system oscillations using the eigenvalues and eigenvectors of the state matrix is detailed. Design of power system damping controllers using residue method is addressed for two area four machine systems. The result shows the effectiveness of the method used

Keywords—TCSC, Power system oscillations, linear models, eigenvalues, eigenvectors, participation factors and residue.

I. INTRODUCTION he concept of flexible ac transmission systems is made possible by the application of high power electronic devices for power flow and voltage control [l]. In

addition a number of TCSC devices have already been installed to aid power system dynamics which help to mitigation a low frequency oscillations often arise between areas in a large interconnected power network [2]. Eigenvalue sensitivities are one important outcome of the modal analysis and control of oscillatory behaviour and dynamic stability in power systems. The pioneering work [3] considers the local oscillation of a single machine by means of a transfer function model. The usually complex pattern of oscillations in a large power system can be studied through linear, time invariant, state-space models based on the perturbations of the system state variables from their nominal values at a specific operating point Power system oscillations occur due to the lack of damping torque at the generators rotors. The oscillation of the generators rotors cause the oscillation of other power system variables (bus voltage, bus frequency, transmission lines active and reactive powers, etc.). Power system oscillations are usually in the range between 0.1 and 2 Hz depending on the number of generators involved in [4]. Local oscillations lie in the upper part of that range and consist of the oscillation of a single generator or a group of generators against the rest of the system. In contrast, inter-area oscillations are in the lower part of the frequency range and comprise the oscillations among groups of generators. In addition, power system oscillations exhibit low damping compared to oscillations found in other dynamic systems: an

oscillation of 10% damping is commonly accepted as well damped. To improve the damping of oscillations in power systems, supplementary control laws can be applied to existing devices. These supplementary actions are referred to as power oscillation damping (POD) control This paper reviews the basic concepts of eigenvalue analysis of linear systems. The physical meaning of eigenvalues, eigenvectors, participation factors, residues and controllability and observability indices will be introduced and illustrated in small scale power systems. This technique has been successfully used in location and tuning of power system stabilizers [5] and FACTS devices. The application of sensitivity measures to the design of power system damping (POD) controllers has been applied to TCSC. The design method utilizes the residue approach; this presented approach solves the optimal sitting of the TCSC device, selection of the proper feedback signals and the controller design problem [6].

II.LINEAR SYSTEM ANALYSIS TOOLS IN POWER SYSTEMS Low frequency electromechanical oscillations range from less than 1 Hz to 3 Hz other than those with sub-synchronous resonance (SSR) [6,15]. Multi-machine power system dynamic behavior in this frequency range is usually expressed as a set of non-linear differential and algebraic (DAE) equations. The algebraic equations result from the network power balance and generator stator current equations. The initial operating state of the algebraic variables such as bus voltages and angles are obtained through a standard power flow solution. The initial values of the dynamic variables are obtained by solving the differential equations

A. Eigenvalues, Eigenvectors and Modes Let us start from the mathematical model a dynamic system expressed in terms of a system of non-linear differential equations:

( , )x F x t=& (1)

If this system of non-linear differential equations is Linearized around an operating point of interest x=x0, it results in:

T



48

( )Δ = Δ&x A x t (2)

A meaningful solution method of (2) is based on the eigenvalues and eigenvectors of the state matrix A. An eigenvalue iλ of the state matrix A and the associated right vi and left wi eigenvectors are defined according to:

i i iAv vλ=

In a matrix with all distinct eigenvalues (not a necessity but it is easier to understand when it is so), all the right eigenvectors and eigenvalues can be expressed as a compact matrix expression

=AV VA (3) Where,

( ..... , )1 2 n 1 n

1 2 n-1 n

V v ,v v v = diag ( ... , )λ λ λ λ

−=Λ

(4)

Pre-multiplying both sides of (3) by V-1 gives 1V AV − = Λ (5)

A similar expression holds for the left eigenvectors W such that

WA W= Λ (6) Where

1 2 1[ ..... ]t t t t tn nW , ω ω ω ω−= (7)

Post-multiplying both sides of (6) by W-l, gives 1− = ΛWAW (8)

The transformed physical state variables (x) can be put into modal variables (2) with the help of eigenvector matrices V and W

x Vzz Wx==

(9)

In power system literature, the right eigenvector matrix v is known as the mode shape matrix, that is, eigenvector vi is known as the ith mode shape, corresponding to eigenvalue λi. The mode shape provides important information on the participation of an individual machine or a group of machines in one particular mode. solution of (2) can be expressed in terms of the eigenvalues and eigenvectors of the state matrix as:

i

Ntt T

i ii

x(t) Ve W x( ) v e [w x( )]1

0 0λΛ

=

Δ = Δ = Δ∑ (10)

The analysis of equation (10) allows drawing the following conclusions:

i. The system response is the combination of the system response to each of the N modes.

ii. The eigenvalues determine the system stability. A real positive (negative) eigenvalue determines exponentially increasing (decreasing) behavior. A complex eigenvalue of positive (negative) real part results in a increasing (decreasing) oscillatory behavior.

iii. The components of the right eigenvector vi measure the relative activity of each variable in the ith mode.

iv. The components of the left eigenvector wi weight the initial conditions in the i-th mode

B. Participation factors It is natural to suggest that the significant state variables influencing a particular mode are those having large entries corresponding to the right eigenvector of λi. The participation factor of the j-th variable in the k-th mode is defined as the product of the j-th's components of the right vjk and left wki eigenvectors corresponding to the k-th mode [7]

jk jk kjP =W V (11)

The product jk kjW V is a dimensionless measure which is called participation factor. In other words, they are independent on the units of the state variables. In addition, both the sum of the participation factors of all variables in a mode and the sum of the participation of all modes in a variable are equal to one. Other interesting measure is the subsystem participation. The subsystem participation is the magnitude of the sum of the participation factors of the variables that describe a subsystem in a mode.

C. Modal controllability and observability factors

The effectiveness of control in power system can be indicated through controllability and observability indices. This is important as control cost is influenced to a great deal by the controllability and observability of the plant. These issues are addressed through modal controllability and observability 1) Controllability index

Assume that an input Δu(t) and an output Δy(t) of the linear dynamic system (2) have defined

x(t) A x(t) B u(t)y(t) C x(t)

Δ = Δ + ΔΔ = Δ

& (12)

The application of a linear transformation defined by the eigenvectors of the state matrix to the system as described by (12) results in: equation (13): Let v and w be the right and left eigen vector matrices of A, respectively. If eigenvalues of A are distinct, then wTv = I, where wT is conjugate transpose of w and I is the identity matrix. Substituting Δx =wΔz in (12), we obtain

T Tz(t) w Aw z(t) w B u(t)y(t) cw z(t)

Δ = Δ + ΔΔ = Δ

& (13)

Equation (13) can be written for kth eigen mode as m

Tk k k i i

iz t z t w B v t

1=Δ = λ Δ + Δ∑&( ) ( ) ( ) (14)

Where wk is the left eigenvector corresponding to kth mode and Bi is the ith column vector of matrix B. From (14), one can find the controllability of kth eigen mode with respect to the ith input. The controllability index (CI) of an ith input to the kth mode [8] is defined as

Ti k iCI = w B (15)



49

The input i, for which the value of Tk iBw is maximum, is

considered the suitable parameter to be controlled for affecting the kth eigen mode to maximum extent. 2) Observability index The observability index (cvi) of an ith input to the kth mode is defined as

i i kOI = C w (16) The study of equations (15) and (16) leads to the following conclusions:

i. iCI Measures the controllability of the mode

associated to the variable ix t( ) from the input

u t( )Δ .In other words, if the mode iλ can be

controlled from the input u t( )Δ

ii. iOI Measures the observability of the mode

associated to the variable ix t( ) form the

output y t( )Δ . In other words, if the mode iλ

can be observed from the variable y t( )Δ Therefore, a mode can be controlled if only if it is controllab

D. Residues Considering (12) with single input and single output (SISO) and assuming D = 0, the open loop transfer function of the system can be obtained by

1−

Δ=Δ

= −

y( s )G( s )u( s )

C( sI A ) B (17)

The transfer function G(s) can be expanded in partial fractions of the Laplace transform of y in terms of C and B matrices and the right and left eigenvectors as

1

1

φψλ

λ

=

=

=−

=−

∑

∑

Ni i

i i

Ni

i i

C BG( s )

( s )R

( s )

(18)

Each term in the denominator, Ri, of the summation is a scalar called residue. The residue Ri of a particular mode i gives the measure of that mode’s sensitivity to a feedback between the output y and the input u; it is the product of the mode’s observability and controllability. Figure 4 shows a system G(s) equipped with a feedback control H(s). When applying the feedback control, eigenvalues of the initial system G(s) are changed. It can be proven, that when the feedback control is applied, the shift of an eigenvalues can be calculated by

i i i = R H( )λ λΔ (19)

It can be observed from (19) that the shift of the eigenvalue caused by the controller is proportional to the magnitude of the corresponding residue. For a certain mode, the same type of feedback controls H(s), regardless of its structure and parameters can be tested at different locations. For the mode of the interest, residues at all

locations have to be calculated. The largest residue then indicates the most effective location to apply the feedback control.

III TCSC MODEL Thyristor-controlled series capacitor (TCSC) is a series FACTS device which allows rapid and continuous changes of the transmission line impedance It has great application potential in accurately regulating the power flow on a transmission line, damping inter-area power oscillations, mitigating sub synchronous resonance (SSR) and improving transient stability. A typical TCSC module consists of a fixed series capacitor (FC) in parallel with a thyristor controlled reactor (TCR) as shown in figure 1. The TCR is formed by a reactor in series with a bi-directional thyristor valve that is fired with an angle ranging between 900 and 1800 with respect to the capacitor voltage [9] The model to be adopted for any device in power systems analysis must be in accordance with the type of study involved and the tools used for simulation. Since this work is concerned with the application of the TCSC for stability improvement, the TCSC model used must rely in the assumptions that are typically adopted for transient stability analysis, i.e., voltages and currents are sinusoidal, balanced, and operate near fundamental frequency. In [9], a TCSC model suitable for voltage and angle stability applications and power flows studies is discussed. In that model, the equivalent impedance Xe of

the device is represented as a function of the firing angle α, based on the assumption of a sinusoidal steady-state controller current. The TCSC is modeled here as a variable capacitive reactance within the operating region defined by the limits imposed by the firing angle α. Thus, Xemin ≤ Xe ≤ Xemax, with Xemax = Xe(αmin) and Xemin = Xe(180o) = XC, where XC is the reactance of the TCSC capacitor. (In this paper, the controller is assumed to operate only in the capacitive region, i.e. αmin > αr, where

cvc

tcrltcri

TCR α

Fig. 1 TCSC Model

kmP maxα

B+ I

PK K s

1

rT s+1

PODv

+−

refP

+

−( , )αcB x

min α

rK

0α α

Fig. 2 small-signal dynamic model of TCSC



50

αr corresponds to the resonant point, as the inductive region associated with 90o < α < αr induces high harmonics that cannot be properly modelled in stability studies [10]. The dynamic model characteristics of the TCSC are assumed to be modeled by a set of differential equations as follows [11] and model in figure 2. α&1 0 r POD 1 rx = ( + K v -x )/T (20) &2 I km refx = K (P -P ) (21) Where α0 P km ref 2 = K (P -P ) + x (22)

The state variable x1=α0, for firing angle model of TCSC. The PI controller is enabled only for the constant power flow operation mode [11]. According to D Jovic [12 ] the value of susceptance B is given as:

( ) ( ) ( )(( ) ( ) ( )

( ) ( )( ) ( ))2

1

2 2

2 2

4

α π π α π π α

π π α α π α α π α

α π α α π α

α π α α α π α

+ − −

− − − + −

− +

⎡⎣

⎤⎦

−

− − −

x

4 2 4x x C x x

4 2x x x x x

4 2x x x x

3 2x x x x

B( ) = k -2k cos k / x k cos k

- cos k k cos k k cos k

-k sin cos k k sin cos k

k cos sin k -4k cos sin cos k

(23)

Where k X=XC/XL., The limits of the controller are given by the firing angle limits, which are fixed by design.

A TCSC POD Controller Design Supplementary control action applied to TCSC devices to increase the system damping is called Power Oscillation Damping (POD). Since TCSC controllers are located in transmission systems, local input signals are always preferred, usually the active or reactive power flow through TCSC device or TCSC terminal voltages. Figure 3 shows the considered closed-loop system where G(s) represents the power system including TCSC devices and H(s) TCSC POD controller In order to shift the real component of λi to the left, SVC POD controller is employed. That movement can be achieved with a transfer function consisting of an amplification block, a wash-out block and mc stages of lead-lag blocks. We adapt the structure of POD controller given in [13, 9] , i.e. the transfer function of the TCSC POD controller is

1

111 1 1

⎛ ⎞+= ⎜ ⎟⎜ ⎟+ + +⎝ ⎠=

cm

w lead

m w lag

sT sTH s K

sT sT sT

KH s

( ) * *

( )

(24)

Where K is a positive constant gain and H1 is the transfer function of the wash-out and lead-lag blocks. The

washout time constant, Tw, is usually equal to 5-10 s. The lead –lag parameters can be determined using the following equations:

0180comp iarg( R )ϕ = − (25)

comp

clead

complag

c

1-sin mTc

T 1+sin m

ϕ

αϕ

⎛ ⎞⎜ ⎟⎝ ⎠= =⎛ ⎞⎜ ⎟⎝ ⎠

(26)

1lag lead c lag

i

T , T = Tc

αω α

= (27)

Where arg(Ri) denotes phase angle of the residue Ri, iω is the frequency of the mode of oscillation in rad/=sec, mC is the number if compensation stages (usually mC = 2). The controller gain K is computed as a function of the

desired eigenvalue location λides according to equation 26:

1

λ λλ

−=

( )i d

i i

KR H

(28)

VI EIGENVALUE ANALYSIS OF POWER SYSTEMS

The concepts detailed in the previous section will be illustrated considering two small-scale power systems. The size of these systems allows the computation of all eigenvalues and eigenvectors of the state matrix without employing advance techniques due to small sizes of the system.

A Analysis of single machine connected to an infinite bus with TCSC The case of a single generator connected to an infinite bus is considered first with and without TCSC. The generator model contains accurate representations of the synchronous machine, the excitation and the speed-

governing systems. It has been assumed that the generator is equipped with a static excitation system [14]. A thyristor controlled series capacitor is connected between bus 2 and 3 as shown in figure 5. The linear model of this system is described by 11 state variables. The synchronous machine, the TCSC and the exciter are described respectively by 6, 3 and 2 state

( )H s

( )G s ue ( )Y s( )refY s

+ -

sTwsTw+1msT+

11

lead

lag

sTsT

++

11PK

lead

lag

sTsT

++

11

tEP Q

BE

j0.15

j0.932200MVA

j0.5



51

variables. The eigenstructure of the state matrix contains 3 pairs of complex eigenvalues and 5 real eigenvalues which are detailed in tables I and I1 respectively. Eigenvalues accurately determine linear systems stability: this system is close to instability due to the presence of a poorly damped oscillatory mode. However, if the connections between eigenvalues and state variables are sought, participation factors have to be used. Table III details the participation of the generator subsystems: rotor dynamics, synchronous machine, exciter, and TCSC in all modes. Table III clearly indicates that the poorly damped oscillatory mode (eigenvalues 1 and 2) is associated to the rotor dynamics and that the other oscillatory mode (eigenvalues 3 and 4) describes the interaction between the synchronous machine and the exciter. The mode associated to the rotor dynamics is also known as electromechanical mode. Table III also shows that three exponential modes are associated to the machine (damper windings), other two to TCSC and the remaining mode to the exciter. The slower modes correspond to the TCSC dynamics whereas the fastest mode is associated to the exciter B Power system stabilizer Design of power system stabilizers or power oscillation damper (POD) in case of FACT can also be addressed using eigenvalue methods. Eigenvalue sensitivities with respect to the parameters of the stabilizer provide a first order approximation of the eigenvalue movement in the complex plane when those parameters are varied. Precisely, the residue of the transfer function between the stabilizers output (reference of the excitation system, ΔVr) and the stabilizer input (speed, Δ w, terminal voltage, ΔVt , electric power, ΔPg) indicates the magnitude and direction of the eigenvalue movement in the complex plane when a static controller is considered able. Table IV contains the residues of transfer functions relevant in stabilizer design corresponding to the electromechanical mode. The phase of the residue informs about the phase compensation required at the eigenvalue frequency so the phase of the eigenvalue sensitivity becomes 1800 and the magnitude of the residue determines the gain required to achieve the desired damping. A speed stabilizer requires almost 900

of phase compensation whereas accelerating power or electric power stabilizers do not require phase compensation. The gain of the speed stabilizer will be greater than the gains of either accelerating or electric power stabilizers.

C Analysis of two areas four machine with TCSC In this study, a two area interconnected four machine power system shown in Fig.6 is considered. The system consists of four machines arranged in two areas inter-connected by a weak tie line [14]. Figure 7 contains a plot of the eigenvalues in the complex plane. Three pairs of poorly damped eigenvalues are found. They result to be associated to the rotor dynamics. The slowest eigenvalues are associated to the speed-governing systems whereas the fastest are associated to

the excitation systems. The synchronous machine modes are in between. From the table V, we see that the system is stable. There are four rotor angle modes. There mode shapes are described by the component of the right eigenvector corresponding to the generator speed

V DESIGN OF TCSC POD CONTROLLER USING RESIDUE METHOD

The uncontrolled system, Fig.6, has one inter-area oscillatory mode characterized by λ = -0.1211 ± j3.7559 with damping ratio ζ= 3.22%. According to Table VII, the bus 8 has the largest residue and therefore the most effective location of the SVC and to apply the feedback control. Using the method presented in

-80 -70 -60 -50 -40 -30 -20 -10 0-8

-6

-4

-2

0

2

4

6

8

Real

Imag

Egenvalue of two area four machine test system

Fig.7 Eigenvalue of two area test system

TABLE I COMPLEX EIGENVALUES OF SMIB WITH TCSC

Mode No.

Eigenvalue Frequency (Hz)

Damping %

1,2 -13.494 ±17.304i

2.7541 61.5

3,4 -0.257±6.772i 1.0777 3.8

TABLE II

REAL EIGENVALUES OF SMIB WITH TCSC MODE

NO Eigenvalue TIME CONSTANT (S)

5 14658.0 0.0001 6 -1000.0 -0.0010 7 -78.9 -0.0127 8 -22.5 -0.0445 9 -1.9 -0.5382 10 -0.2 -5.0531 11 -1.0 -1.0000



52

Section 3, POD controller parameters are calculated in order to shift the real part of the oscillatory mode, to the left half complex plane. The obtained transfer function for the SVC POD controller is

1 10 1 0 1329 1 0 13291 0 1 1 10 1 0 4325 1 0 4325

s s sH s Ks s s s

+ +=

+ + + +. .( ) * * *

. . .

Eigenvalue of our interest moves form the original location λ = -0.1211 ± j3.7559 to the desired location λd= -0.745 ± j3.638 to give about 20% damping as:

1

25 8963.( )

i d

i i

KR Hλ λ

λ−

= =

VI SIMULATION RESULTS The effectiveness of the proposed method of POD designed was tested on two- area four -machine systems. The analysis results for the two systems are presented in tables I to IX. A three phase fault is applied for second test model at the bus 8 and cleared after 74ms. The original system is restored upon the fault clearance. The transient stability performances of the system with TCSC without POD and TCSC with POD controller are shown in figures 8-11. The TCSC with damping controller stabilizes system as can be seen from figure 8-11.The oscillations of the system from figure 8 to 11 also are well damped with POD controller.

ACKNOWLEDGMENT

The authors would like to express their appreciation to the Universiti Teknologi Malaysia (UTM) and Ministry of Science Technology and Innovation (MOSTI) for funding this research

TABLE III

EIGENVECTOR AND NORMALIZED PARTICIPATION FACTOR CORRESPONDING POOR MODE -0.29835+J7.8548

S/N

Right eigenvect

or

Left eigenvector

Participation factor

Participation state

1 -0.09 – j0.55

-1.8*10-7 +j1.8*10-17

0.47159

Machine angle 1δ

2 0.012 – j0.0015

-214-j2.25*10-16

0.47159

Machine speed 1ω

3 0.016 - j0.016

-151 +j1.66 *10-15

0.00959 ′q

q-axis damper e

4 -0.028 - j0.008

5.81 + j0.0 0.01886 ′d

d-axis damper e

5 0.026+ j0.022

34.58 +j45.61

0.00292 ′′q

q-axisdamper e

6 -0.047- j0.07

34.58 -j45.61 0.02466 ′′d

d-axisdamper e

7 -0.004 - j0.00

0.16 -j0.067 0.0006 Exiter mv

8 0 0.16 +j0.067 0 Exiter r1v 9 0.7553 0.12 + j0.0 0.0004

5 Exiter fv

10 -0.029 - j0.32

-2.28*10-6 +j2.09*10-

19

0.0001 1x of Tcsc

11 -0.0096 + 0.0003i

0 0.00004 2x of Tcsc

TABLE IV RESIDUE CORRESPONDING TO LOCAL MODE -0.257-J6.772 Transfer function Residue Phase

angle

g

r

PV

ΔΔ

-56.15- 133.27 67.150

rVωΔ

Δ -0.1252 + 0.0585i -25.044

1

r

VV

ΔΔ

0.0429 - 0.0087i -11.46

TABLE V

COMPLEX EIGENVALUE OF TWO AREA FOUR MACHINE TEST

Mode No. Complex Eigenvalue

Frequency (Hz)

Damping ratio %

1,2 -12.3267±j 20.5784 0.08 99.99 3,4 -12.0224 ±j19.9823 0.08 99.99

5,6 -15.2167±j15.8377 0.53 97.97

7,8 -14.8232 ±j 5.6141 0.43 -98.63

9,10 -1.7779 ±j 6.4726 1.20 10.05 11,12 -1.9176±j 6.7494 1.16 10.23

13,14 -0.11727±j 3.6383 0.60 3.22

15,16 -5.1493±j 0.04188 0.10 99.72

17,18 -0.07742±j .22111 0.09 99.76

TABLE VI PARTICIPATION OF THE GENERATORS IN THE ELECTROMECHNICAL

MODES OF THE TWO AREA TEST SYSTEM

Mode No.

Eigenvalue G1 G2 G3 G4

9,10 0.7647 ±7.5680i

0.01145

0.0429

0.41007

0.55216

11,12 0.7514 ±7.3036i

0.41104

0.53642

0.02767

0.01232

13,14 0.1211 ±3.7559i

0.24613

0.14199

0.34591

0.24344

TABLE VII

SITING INDICES OF TCSC FOR TWO AREA FOUR MACHINE TEST

Mode residues of the transfer function

ΔP/Δkc TCSC location

Normalised Residue |Ri|

6-7 0.001 5-6 0.735 7-8 1.000 9-8 0.181 10-9 0.000

11-10 0.788



53

CONCLUSION This paper has reviewed methods for analysis and control of power system oscillations with TCSC device based on the eigenstructure of the state matrix of the linear model of the power system. Residue-based methods also provide valuable information on how to design power system damping controllers. Although eigenvalue based methods are very powerful, the complexity of the power system stability problem requires the complementary use of other methods such as non-linear time domain simulation. All the simulations were done with PST toolbox in Matlab environment.

APPENDIX TCSC data

Tr = 10 ms, XL = 0.2, XC=0.1,.Kc=50% Kr=10, TW = 10 s, αMAX =3.1416, αMIN =- 0.314

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[17] Einar, V.L., and Joe, H.C.: ‘Concepts for design of SVC controllers to damp power swings’, IEEE Trans. Power Syst., 1995, 10, (2), pp. 948–954

0 5 10 15 20 25-150

-100

-50

0

50

100

150

200

250

300

Time(s)

Act

ive

pow

er in

MW

Fault at bus 8

without POD controllerwith POD controller

Fig.8 Active power flow with and without POD in line 7-8

0 2 4 6 8 10 12 14 16 18 20-60

-50

-40

-30

-20

-10

0

10

20

Time(s)

Ang

le dev

iato

n (G

1-G3)

Fault at bu 8

without PODwith POD

Fig.9 Angle response of G1

0 2 4 6 8 10 12 14 16 18 20-200

-150

-100

-50

0

50

Time (s)

Rea

ctiv

e po

wer

in M

Var

Faut at bus8

Without PODWith POD

Fig.10 Reactive power response for Bus 7

0 5 10 15 20-20

-15

-10

-5

0

5

10

Time(s)

Spee

d de

iatio

n in

rad/

s

Fault is applied at bus 8

Without PODWith POD

Fig11 speed response of G1

Documents

94310-6767 IJET-IJENS