A Network Delay Compensation Technique for Wide-Area SVC Damping Controller in Power System

Bibhu P. Padhy, S.C. Srivastava, Senior Member, IEEE, and Nishchal K. Verma, Senior Member, IEEE Department of Electrical Engineering, Indian Institute of Technology, Kanpur, India

bibhupee@iitk.ac.in, scs@iitk.ac.in, nishchal@iitk.ac.in Abstract— Network uncertainties, such as time-varying delays, packet losses, packet disorder, seriously deteriorate the performance and stability of any network based control system. To address this issue, a systematic approach has been suggested in this paper to compensate for the network latency in the application of synchrophasor assisted wide area control for the Static Var Compensator (SVC). The power oscillation modes are estimated online in presence of packet drop in a communication network. The modes are monitored through a modified Modified Extended Kalman Filter (MEKF) approach. The time delay has been compensated by predicting the dynamics of the delayed measurement signal. A network control system model has been developed incorporating the Phasor Measurement Units (PMUs), event driven communication network and network buffers to mimic the response of a real time communication based control. The wide-area stabilizing controller has been designed based on Takagi-Sugeno (TS) fuzzy approach. The performance of the proposed delay compensation scheme has been tested on 39-bus New England system.

Index Terms-- Power system stabilizer, Extended Kalman filter, TS fuzzy controller, Static Var Compensator, Phasor measurement unit, Network delay compensation.

I. INTRODUCTION N the last few decades, small signal oscillations have been observed in the power systems, which have, sometimes, resulted into instability and blackout in the network. The

traditional approach to damp out these oscillations is through Conventional Power System Stabilizer (CPSS), forming part of the generator excitation system or a part of FACTS supplementary controller. These controllers usually employ local signals as inputs and may not always be effective to damp out the inter area modes of oscillations. The design of CPSS, generally, is based on linearization of the system model at a given operating point, which may not be effective under wide variation in the system conditions. Further, the local controllers, generally, lack the global observation. The synchrophasor technology based Wide Area Monitoring and Control System (WAMCS) forms an important part of the smart grid to enhance the grid security. This employs Phasor Measurement Units (PMUs), which provide synchronized and time stamped real-time measurement data from remote locations to a Phasor Data Concentrator (PDC) at control center. These measurements can be effectively utilized to design wide area damping controllers

[1], [2], [3], [4], [5], [6], [7], [8]. However, a major drawback with the Wide-Area Networked Control System (WANCS) is that its performance gets deteriorated due to the time delays in the network communication. Also, if the communication link, that has been used for the wide-area signal transmission is unreliable, it is often subjected to fading and congestion, leading to packet drop in the network. Several research efforts have been made to address these issues. A power system dynamic model has been presented in [9] to study the impact of time-delays on small-signal stability of the power systems. An iterative Linear Matrix Analysis (LMI) based delay-dependent HVDC-wide area feedback signal controller, with constant delay, has been presented in [8]. An eigenstructure performance index based FACTS controller was suggested in reference [7] considering the time delay. A communication disturbance observer based time delay compensation technique considering time varying delays has been proposed in [10]. A small gain stability criterion based robust control has been proposed in [11] to deal with constant time delays. Although these methods consider variable or constant delay, the performance of these controllers may deteriorate in cases when random delay occurs, packet drop or packet disorder takes place in the network. One of the recent publications [3] addresses the issue of packet drop in the communication network considering varying time delay up to 125ms. LMI based method has been proposed to design the robust controller. The delays in the network, being random in nature, has been experimentally verified in [12] and, as mentioned in [2], the delay can go up to 1sec. To design networked control system to deal with such a large random delay considering the packet drop in the network and ensuring desired control performance is a challenging task. To overcome these difficulties, a wide-area Time Delay Compensation (TDC) technique has been introduced in this work. A time lead has been provided to compensate the time-lag due to the time delay, so that a delay free input signal can be effectively applied to the controller. In literature, few papers have addressed the time delay compensation. In [1], a HVDC controller has been designed and the time delays have been compensated by properly designing a phase lead block to compensate the phase lag due to the time delay. It is critical to tune a phase lead block for variable or random delays. Few approaches are suggested to estimate the low frequency modes, such as Prony method [13], modified TLS-ESPRIT-based method [14], [15], a stepwise-regression

I

978-1-4799-3656-4/14/$31.00 ©2014 IEEE

based method [16]. These methods are good at estimating the low frequency modes, but require at least one cycle data to be stored in a buffer before estimating these modes. These are not good at estimating the non-stationary signals requiring shorter time window. In the proposed approach, signal frequency, phase, and damping factor are estimated online through Modified EKF (MEKF) with random delay. The MEKF is quite robust to the noise, and can effectively track the signals with time-varying amplitude and frequency. The stochastic stability of the MEKF is given in [17]. These components have been estimated in each time step, as shown in Fig. 1, and sent to the Time Delay Compensator (TDC) block to make the signal delay free.

PowerSystem

1y (KT) 1 1y (KT - τ )

2 2y (KT - τ )

n ny (KT - τ )

2Buffer1Sensor1S (t)

nBuffer

1Buffer

nEKFnDelay Compensator

dnTWADC

Satellite

GPS Clock

rr rr

Other PMUs� � �

���

���

��

�MUX

BN

2EKF2Delay Compensator

d2T1EKF1Delay Compensator

d1T

1PMU 1PDC

2y (KT)2Sensor2S (t)

2PMU 2PDC

ny (KT)nSensornS (t)

nPMU nPDC

rr rr� � �

rr rr� � �

Com

mun

icat

ion

Net

wor

k

��

�

Fig. 1 Schematic diagram of the proposed networked based delay

compensation methodology

II. NETWORK ARCHITECTURE A schematic diagram of the proposed network based delay compensation methodology is shown in Fig.1. The network consists of four main components (1) sensor node (2) PMUs (3) communication network, and (4) the networked buffer. The sensor node measures the analog current and voltage signals and discretetizes them at a fixed sampling rate by using a Sample and Hold (S&H) circuit. The PMUs are used to extract the synchronized phasor information of the signal such as amplitude, phase, frequency, Rate of Change of Frequency (ROCOF), as well as the MW and MVar flows. The measurements from the PMUs are time-tagged. To incorporate the PMUs in the simulation, a DFT based algorithm has been used, which reports phasor in every cycle. The communication network is an important part of Wide-Area Networked Control System (WANCS) that allows signal information transportation between the PMUs, to the control center and has been modeled as a discrete-event driven architecture, which helps to incorporate variable time delay with packet drop. The SimEvent toolbox [18] has been used, which is an effective tool to model the communication network with packet drop. The network buffer of finite length

,BN receives data packets from present communication network, as shown in Fig.1. It is due to their arrival in random manner, the packets may reach at other than the sampling period. However, the modified MEKF algorithm is executed at a fixed sampling rate. This may result in losing some of the packet data due to the non-aligned time interval. It is also

required that data should be sufficiently buffered before exporting into the Kalman filter, else the buffer may quickly exhaust. The network buffer works on Last in First Out (LIFO) principle.

III. SVC CONTROLLER The Static Var Compensator (SVC) is one of the most popular Fexible AC Transmission System (FACTS) controllers, for providing fast-acting reactive power support in the network. The primary application of the SVC is to provide dynamic voltage support, which also improves transient stability. It is also provided with supplementary stabilizing controller to damp out power oscillations in the system. A block diagram of basic SVC Controller incorporating conventional PID supplementary controller is shown in Fig.2. The measured bus voltage ( pV ) is passed through a low pass filter ( ( )mH s ) to remove the higher order harmonic components present in the signal. A first order model of SVC with gain SVCK and time constant SVCT has been considered, which generates the desired reference susceptance signal ( ref

SVCB ). Comparing it with the present susceptance value, a distribution unit determines the number of Thyristor Controlled Capacitor (TSC) and firing angle reference ref� for Thyristor Controlled Reactor (TCR). The firing pulse generator generates appropriate pulses for TSC and TCR. The effective impedance of TCR related to firing angle � can be found in [19], [20], as

_( )2 sin 2L L normX X�� ��� �� � � � �

where, _L normX is the total impedance of the reactor relative to its MVA rating. The amount of the reactive power can be controlled by varying the firing angle of the TCR and the TSC branch. The reactive power injection connected to a bus-k is given by, 2

k k SVCQ V B� , where, kV is the bus voltage,

SVCB is the total susceptance. A Supplementary Modulation Controller (SMC) can be designed to improve the performance of the SVC during transient conditions. The SMC in Fig. 2 consists of a PID controller having control inputs obtained from local measurements and provide a voltage reference signal to the regulator. Thus, it modulates directly the SVC bus voltage or its effective susceptance in order to damp out oscillations and, thus, improve the stability.

SVC

SVC

K1+sT

DistributionUnit

refSVCB Firing

PulseGenerator

mH (S)

sB

refV

SV

++

++

To TCR

To TSC

maxB

minB

Low pass filter

TSC Blocking

pV

mV

WADC Control InputsW

W

sT1 + sT

maxsV

minsV

refα

n_TSC

Fig. 2 model of SVC controller

IV. PROPOSED METHODOLOGY In general, a nonlinear system can be represented in discrete form, given as

1 ( , , )( , )

k k k k

k k k

x f x u wy h x v

� ��

(1)

where, nkx R� denotes the state of the system, d

ku R� the control input signal, and m

ky R� the measurement taken from the system. The stochastic variables s

kw R� and t

kv R� denote the process noise and measurement noise, respectively. Both of these are assumed to be uncorrelated and white Gaussian type. In the nonlinear function (1), ( )f �relates the state at time step k to the state at the time step( 1)k � . The nonlinear function ( )h � relates the state at time step k to the measurement at the thk time step. The model in (1) can be expanded by using Taylor’s series approximation as,

ˆ ˆ( , , ) ( , ,0) ( ) K K K k k k k kf u w f u A higher order terms� � �x x x xˆ ˆ( , ) ( ,0) ( ) k k k k k kh u h C higher order terms� � �x x x x

where, ˆ kx is the estimated state at the thk time step. The Jacobian matrix elements [ , ]k i jA and [ , ]k i jC can be calculated as partial derivative of ( )f � and ( )h � with respect to x ,

respectively, and can be defined as,� �[ ]

[ , ][ ]

ˆ , ,0,i k k

k i jj

f u��

�

xA

x

and � �[ ]

[ , ][ ]

ˆ ,0.i k

k i jj

h��

�

xC

x

The packet loss takes place when a data packet does not arrive after a certain interval of time. It is random in nature as it depends on the variable network conditions such as network traffic. Consider stochastic independent binary variable k� assumed to be of Bernoulli type with probability

.p Its probability distribution can be defined as,

� �(1 ) for 0,1( , )

0 otherwise

k kk

k

p pg p

� � ��

� ��� ���

If measurement arrives at thk time step, k� is set to 1, and if no measurement arrives, k� is set to 0, as shown in Fig. 3. Kalman filter, with intermittent observation, consists of the following steps [17]: Step I: Initialization ( 0k � )

0 0ˆ [ ]E�x x (2)

0 0 0 0 0[( ( ))( ( )) ]TE E E� P x x x x (3)

Step II: Time Update ( 1,2,3...k � ) / 1 1 1/ 1ˆ ˆk k K k k �x A x (4)

/ 1 1 1/ 1 1 1T

k k k k k k k � �P A P A Q (5) Step III: Measurement Update

/ 1 1 1/ 1 1 1T

k k k k k k k � �P A P A Q (6)

� � 1

/ 1 1 1 / 1 1T T

k k k k k k k k k

� �G P C C P C R (7)

/ / 1 / 1k k k k k k k k k� � P P G C P (8)

where, kG , Q , R and P are the Kalman filter gain, the process noise covariance, the measurement noise covariance and the error covariance matrices respectively. The estimated state vector can be updated as,

1/ 1 1/ 1 1 1 1/ˆ ˆ ˆ( ( ,0))k k k k k k k k ky h�� � � � � � �� � x x G x (9)

A. Signal Modeling

The power oscillation signals can be represented as sum of exponentially damped sinusoidal signals. The signal with N -modes can be represented in mathematical form as,

1.sin( )i s

NkT

K i i s ii

y Ae kT for k=1,2,...m� � �

�

� �

(10)

where, Ky is the measurement data at time k , iA is the amplitude of ith mode of signal, i� is the angular frequency of

the signal in rad/sec and i� is the phase angle of the signal for ith mode. Further, the signal can be reduced to,

,,

1.sin( )i k

N

K i ki

y e for k=1,2,...m� ��

�

(11)

where, , ln( )i K i i sA kT� �� and ,i k i s ikT� � �� � (12)

This can be written as, ,

, ,1 1

.sin( )i kN N

K i k i ki i

y e g , for k=1,2,...m� �� �

�

(13)

where, the ith mode of oscillation component is represented as,

,, ,.sin( ),i k

i k i kg e for k=1,2,...m� �� (14)

The signal expression in equation (13) can be represented in state space form as,

, 1 ,

, ,

i k i i k

i k i i k

� �

�

x A xg C x

(15)

The four state components of ith mode at thk instant of time can be denoted as,

,1, , ,2, , ,3, , ,4, ,, ,i k i k i k i k i k i k i k i kx , x x x� � � �� � � � (16)

The output and state components at ( 1)thk � instant of time

are related to those at thk instant of time as,

,3,

,1, 1 ,1, ,2, ,2, 1 ,2,

,3, 1 ,3, ,4, ,4, 1 ,4,

, ,1,.sin( )i k

i k i k s i k i k i k

i k i k s i k i k i k

xi k i k

x x T x , x xx x T x , x x

and g e x

� �

� �

!� � ���� � "�

� �#

(17)

The state transaction matrix and measurement/observation matrix of the signal model from equations (14), (15), (16) and (17) can be defined as,

1 0 00 1 0 00 0 10 0 0 1

s

s

T

T

$ %& '& '�& '& '( )

iA

(18)

3, 3,1, 1,cos( ) 0 sin( ) 0k kx x

k ke x e x$ %� ( )iC (19)

For the signal in equation (11), the matrices are defined as,

1 2( , ,.. .. ),i Ndiag A�A A A A * +� 1 2 i NC C C ...C ...C

(20)

thk Step

10111 �01

00

������

1y3y4ykyk+2ymy

Fig. 3 Networked buffer with packet drop

B. Selection of Initial Condition and Tuning of MEKF

The convergence of MEKF highly depends on initial state, order of the selected model, and parameters of the Kalman filter. A good guess of the initial state can be obtained from the linearized model and also considering the fact that the wide-area signal is rich in inter-area modes, having frequencies in the range of 0.1 to 0.8 Hz. The linear analysis also helps in obtaining the model order, which represents the number of mode-frequency components present in the signal. If the model order selected is too large, then, by over fitting the model order, suspicious noise frequency components may appear in state estimation problem. If the order selected is too small, some of the important mode frequencies may be lost due to under-fitting of the model. At any particular instant of time, the model order is unknown and always changes with the change in topology and operating condition of the system. An engineering experience helps in this regard. It is always desirable to filter out the higher frequency modal components present in the signal. The model uncertainty can be further minimized and convergence of the EKF can be guaranteed by selecting better initial covariance 0 ,P process noise covariance 0 ,Q and measurement covariance 0R .

C. Delay Compensation

The total signal latency, including the buffer queue delay, can be calculated by subtracting the present GPS clock time from the time tag of the current data packets available in the buffer. This total delay can be written as, .d GPS StampT T T�

where, GPST and StampT are the present clock time and time tag, respectively. The latency can be compensated by time advancing the signal in equation (11), equal to the total time delay occurred in the network i.e. dT . Hence for a time step

,sT the signal should be advanced by d

s

TT times the time

step. By advancing the signal in (11) by d

s

TT times the time

step the delay compensated signal can be represented at thk instant as,

,3,, ,1,

1.sin( )i k T Td s

d s d s

Nx

dc k k T T i k T Ti

S y e x�

� ��

� �

, ,4, ,4,(ln ),2, , ,2,

1 .sin( )i k i k d i k

NA x T x

i k i k d i ki

e x T x�

�

� � �

,3, ,4,( )

,1, ,2,1

.sin( )i k d i kN

x T xi k d i k

ie x T x

�

� �

, ,( )

, ,1

.sin( )i k d i kN

Ti k d i k

ie T� � � �

�

� �

(21)

The above equation (21) represents the delay compensated signal ,dc kS at thk instant of time, which can be effectively applied to the WADC. A block diagram representation of the proposed methodology is presented in Fig. 4.

Incoming Data

GPS Clock

Buffer TOP

MEKF

Extract the Time Stamp Time

stampTGPST

dT

WADC

Power System

Network Buffer

k k k kφ ,ω ,λ ,ζk k d

dc s(λ -ζ T )

k k d

S (kT ) =

e sin(φ -ω T )

TDC

dc sS (kT )

sV

��� ���

jy ky 3y 1y

Logic to Calculate Time Delay

Fig. 4 Block diagram of proposed TDC scheme

D. Input Signal Selection and Wide-Area Controller Design

The input/output signal selection has been carried out using a coherency approach [8], in which a combined Principal Component Analysis (PCA) and Self Organizing Map (SOM) clustering approach has been applied to select the optimal control input signals that requires less control effort to stabilize the system. The tie-line active power flow deviations are considered as appropriate remote input signals to the WADC. The line contingency 8 9 2 25, ,P P 16 19P have been applied to collect the data for coherency approach. The control signals selected are the power deviation 1 39 16 19,P P , ,

and 26 27P , to the wide-area controller and the controller output signal is the voltage modulating signal to the FACTS controller, the SVC in the present study. A multi-input and single output wide-area TS Fuzzy controller [4] has been designed considering various operating conditions in the system. The fuzzy controller has been designed by satisfying certain Linear Matrix Inequality (LMI) conditions, to stabilize the system at multiple operating points. Triangular membership functions have been used to generate the rules of the fuzzy system. The overall fuzzy model is achieved by blending these rules, which can approximate the non-linear dynamic behavior of the system.

V. SYSTEM DESCRIPTION AND IMPLEMENTATION RESULTS The proposed methodology has been implemented on New

England system [21], which consists of 10-machines and 39-buses as shown in Fig. 5. Each generator is assumed to be provided with governor, AVR and IEEE ST1A type static exciter. The loads in the system are assumed to be constant impedance type. A Static Var Compensator (SVC) of

capacity ±300MVar has been placed at bus-27, with nominal bus voltage of 345kV, which regulates the terminal voltage by absorbing or injecting the reactive power into the network.

Fig. 5 39-New England system power system

The critical modes of the 39-bus system are shown in Table I. There are two inter area modes of oscillation in the system. Out of these mode-1 is the most critical having damping ratio 0.0378 and frequency 0.6030Hz. The dynamic behavior of the system, with the SVC controller, has been studied applying various disturbances in the system. However, results of only few of them are reported in this paper. A 3-phase fault was applied at bus-16 and bus-26 for 70ms. A random input delay of maximum value 1sec has been created in the input channel-1( 1 39P, ), 400 ms in the input channel-2( 16 19P , ), and zero delay created in channel-3( 26 27P , ) as this is a local signal and can be measured locally. The packet drop probability has been kept at 4% at all the delayed channel inputs. The proposed delay compensator has compensated the random delay in the communication channel and is able to retrieve the PMU output signal from the online delayed measurement data. It effectively tracks the original delay free PMU output signal, as shown in Fig. 6. The random time delay bound has been restricted to one phasor sampling period to avoid packet disorder. From the results obtained, it is found that there is a considerable reduction in the overshoot and time of oscillations with the proposed approach. With the proposed approach, the system settles to steady state within 12 sec under the fault at bus-26 and within 13 sec for the fault at bus-26. Whereas, without WADC, the system continues to oscillate up to 24sec in both the cases and also gives slightly higher overshoot and undershoot as compared to those in the presence of WADC, as shown in Fig.7. To study further the effectiveness of the proposed approach, a modified TLS-ESPRIT algorithm [14], was applied to calculate the mode frequency and damping ratio with these disturbances. For that, the speed plot in Fig. 7(B) considered. Without any WADC, mode frequency obtained is 0.60863Hz and damping ratio is 0.03173, and, with the action of WADC, the mode frequency obtained is 0.5787Hz and the damping ratio is 0.06891. A similar conclusion are drawn

from the results of the cases when, loads at buses-16 and 28 of capacity 329MW, 32.3Mvar and 206MW, 27.6Mvar respectively, have been taken out. The performances with and without WADC are shown in Fig. 8.

TABLE I 39-BUS SYSTEM CRITICAL MODES OF OSCILLATIONS

Mode No Eigen value Damping (%) Frequency (Hz)

Mode 1 -0.1432 ± 3.7888i 3.78 0.6030

Mode 2 -0.4731 ± 4.2372i 11.10 0.6744

Mode 3 -0.1901 ± 6.2889i 3.02 1.0009

To test the effectiveness of the proposed approach with different network configurations, two major disturbances were applied in the system, considering a fault along with line contingency and only line contingency cases. The 3-pahse fault has been created at the bus-4, and the breakers at bus-4 and 14 clear the fault after 70 and 80ms, respectively, leading to a large change in operating condition. The tie-line power flow 1 2Pline variation is shown in figure 9(A). A critical line

21 22L contingency has been considered 10sec after start of the simulation, and the results of tie-line power flow 1 2Pline oscillations are shown in figure 9(B). The proposed approach predicts the mode frequency and damping of the signal correctly and effectively has compensated the delay occurred in the communication network. Hence, the stability of the system has considerably improved.

Fig. 6 (A) Packet drop (B) Random time delay (C) Tracking of PMU signal

Fig. 7(A) a 3-phase fault at bus- 26 for 70ms (B) a 3-phase fault at bus- 16 for 70ms

10 15 20 25 30 350

0.5

1

Time(Seconds) (A)

(1-�

)

10 15 20 25 30 350.38

0.4

Time(Seconds) (B)

Pack

et

Del

ay(S

ec)

10 15 20 25 30 35-25-15-55

1525

Time(Seconds) (C)

, P

16_ 19

(p.u

.)

PMU Output Delayed Signal Predicted Signal

9 11 13 15 17 19 21 23 25 27 29 31 33 35-4-2024

x 10-3

Time(Seconds) (A)

W4-W

1 (P.U

.)

9 11 13 15 17 19 21 23 25 27 29 31 33 35-5

0

5x 10-3

Time(Seconds) (B)

W4-W

1 (P.U

.)

Without WADC With Phasor Approach

Without WADC With Phasor Approach

Fig. 8(A) a load outage at bus-16 (B) a load outage at bus-28

Fig. 9(A) a 3-phase fault at bus- 4 followed by 4 14L outage (B) a line

contingency 21 22L

VI. CONCLUSION A network based latency compensation technique for SVC controllers has been proposed in this work. The wide-area controller has been designed based on TS fuzzy approach [4]. The modified EKF based latency compensation offers an effective method to properly compensate the input signals with large latencies from the online measurement data and, hence, can be adopted for real-time applications. The validity and performance of the proposed control scheme have been evaluated for various test cases under random delay, and packet drop, which show the effectiveness of the proposed latency compensation technique.

ACKNOWLEDGMENT

1Authors sincerely thank Dept. of Science and Technology (DST), New Delhi for providing partial financial support under IIT Kanpur project no. DST/EE/20100258 to carry out this research work.

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[17] S. Kluge, K. Reif, and M. Brokate, "Stochastic stability of the Extended Kalman filter with intermittent observations," IEEE Trans. Autom. Control, vol. 55, pp. 514- 518, Feb. 2010.

[18] The MathWorks, Inc. (2011) SimEvents (ver. 4). [Online]. Available: http://www.mathworks.in/products/simevents/.

[19] N. G. Hingorani and L. Gyugyi, Understanding FACTS Concepts and Technology of Flexible AC Transmission Systems.: Piscataway: IEEE press, 2000.

[20] H. Ambriz-Perez, E. Acha, and C.R. Fuerte-Esquivel, "Advanced SVC Models for Newton-Raphson Load Flow and Newton Optimal Power Flow Studies," IEEE Trans. Power Syst., vol. 15, no. 1, pp. 129- 136 , Feb. 2000.

[21] Graham Rogers, Power System Oscillations.: Kluwer Academic Publishers, Norwell MA, 2000.

9 11 13 15 17 19 21 23 25 27 29 31 33 35-1

0

1x 10-3

Time(Seconds) (A)

W4-W

1 (P.U

.)

9 11 13 15 17 19 21 23 25 27 29 31 33 35

-5

0

5

x 10-4

Time(Seconds) (B)

W4-W

1 (P.U

.)

Without WADC With Phasor Approach

Without WADC With Phasor Approach

9 11 13 15 17 19 21 23 25 27 29 31 33 35-100

0100200300

Time(Seconds) (A)

Plin

e 1-

2 (M

W)

9 11 13 15 17 19 21 23 25 27 29 31 33 35-1000

100200300

Time(Seconds) (B)

Plin

e 1-

2 (M

W))

Without WADC With Phasor Approach

Without WADC With Phasor Approach