Adaptive latency compensator considering packet drop and packet disorder for wide area damping control design

Electrical Power and Energy Systems 106 (2019) 477–487

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Adaptive latency compensator considering packet drop and packet disorder for wide area damping control design

T

Bibhu Prasad Padhy Department of Electrical Engineering, IIT Ropar, India

ARTICLE INFO

ABSTRACT

Keywords: Power system stabilizer Extended Kalman filter TSfuzzy controller Flexible AC transmission system Phasor measurement unit Network delay compensation

Network based wide-area controls will form an important part of smart grid implementation to improve power system stability. The performance of such control systems can seriously deteriorate under various network uncertainties such as time-varying delays, packet loss, and packet disorder. To address these issues, an Adaptive Time Delay Compensation (ATDC) scheme has been suggested to design wide area damping controller for a Flexible AC Transmission System (FACTS). The proposed TDC scheme is based on a direct phase advancement methodology that requires the signal modal information such as amplitude, frequency, and damping. This information has been utilized to compensate the latency by predicting the future trajectories of oscillatory response. An Adaptive Extended Kalman Filter (AEKF) is employed to estimate the low-frequency oscillatory modes with missing measurement data. To compensate the error due to packet disorder, a new methodology of packet-reordering, has been proposed. Further, the Wide-Area Damping Controller (WADC) is designed addressing the issue of sampled data control. The performance of the proposed scheme has been validated on the 16-machine, 68-bus power system.

1. Introduction Small signal oscillations have been observed in the power systems since past few decades, which have, sometimes, resulted into system instability and blackout. The traditional cost-effective way to damp-out these oscillations is through Conventional Power System Stabilizer (CPSS) [1], forming part of the generator excitation system or FACTS supplementary controller. These controllers usually employ local signals as inputs, and may not always be effective in damping out the inter-area modes of oscillations due to lack of global observation [2]. The Synchrophasor technology based Wide-Area Measurement, and Control System (WAMCS) forms an important component of the smart grid to enhance the system reliability and security [3,4]. The WAMCS employs Phasor Measurement Units (PMUs), which utilize voltage and current measurements from the field to generate synchronized time stamped phasors in real time. These phasor data can be effectively utilized for various applications, including design of wide area damping controllers [2,5–9]. The WADC requires remote feedback input signals from the PMUs, which are transmitted over a communication medium to the control center, and forms a Networked Control System (NCS). The WADC has significant capability to damp out the inter-area mode of oscillations in an effective manner and to improve overall stability of the system. The communication link between the sensors, i.e. PMUs and

the controller play a very crucial role in any NCS [10]. However, due to the inherent reliability issues associated with the communication network, the wide-area signal transmission is often subjected to fading and congestion, leading to latency, packet dropping and packet disorder errors [10–12]. As per author’s knowledge, no literature is available by considering all these issues together in the power systems, which are the dominant problems in the NCS. Few literatures have addressed the issue of network communication latency [10] which is usually time varying and random in nature. The communication latency on the widearea network comprises of transmission delay, propagation delay, processing delay and queuing delay. As mentioned in [13], by utilizing an optical fiber cable based communication link, the one way associated delay could be of the order of 100–150 ms, gives the least latency and large band width, which is an important advantage for any widearea real-time based application. As reported in [14], the resulting latency may vary from few miliseconds to hundreds of milliseconds. The system performance may degrade significantly, and can even be unstable in case this issue is not addressed. A control design, based on the Padé approximation model of nominal delays, has been used in [5]. However, the controller has been designed with certain maximum delay bound, which is not suitable for time varying delay. A gain scheduling approach based design has been employed in [14]. This requires multiple controllers to be designed for different delays, out of which; a

E-mail address: [email protected]. https://doi.org/10.1016/j.ijepes.2018.10.015 Received 18 July 2018; Received in revised form 25 September 2018; Accepted 13 October 2018 0142-0615/ © 2018 Elsevier Ltd. All rights reserved.

Electrical Power and Energy Systems 106 (2019) 477–487

B.P. Padhy

suitable controller is scheduled depending on the actual delay encountered. Robust control methodologies are also proposed by selecting the filter weight in [7]. To compensate variable delay, Lyapunov–Krasovskiis (LK) functional based approach was used in [8]. However, consideration of appropriate LK functional to obtain less conservative result and compensation of large random network delay are still challenging task. From the literature, it appears that very little work has been done to simultaneously take into account packet delay, the packet drop, and the packet disorder. Hence, the motivation behind the present work has been to address these issues in design of WADC. A wide-area Time Delay Compensation (TDC) technique has been proposed in this work, so that a delay-free input signal can be effectively applied to the controller. However, this requires exact signal modal information in real-time, that poses many challenges. Several methods have been suggested recently, such as those based on FFT [15], Prony [16], and ESPRIT [17] approach, to estimate the low-frequency modes. Among these, the FFT based methodology [15] is simple to implement and fast. However, it suffers from poor resolution, that results in inaccuracy in estimation of fractional parameters. The Prony based methodology [16] is the most popular and widely being adopted. However, sensitivity towards noise restricts its use. The ESPRIT based method [17] is highly robust towards noise, and performs well for low Signal to Noise Ratio (SNR). However, sliding block processing by Prony, ESPRIT reduces the effectiveness towards tracking of modes in time varying signals. This problem can be well addressed by utilizing an Extended Kalman Filter (EKF) based methodology [18]. Realizing its potential capability, the EKF is being extensively used in many fields such as signal processing, tracking, detection, control, and optimization. It has also been applied in many power system applications like oscillation mode estimation [18], harmonic estimation [19], dynamic state estimation [20], etc. However, since the packet drop creates loss of information, it affects the stability of the EKF [11], specifically for a critical the loss probability above which the error covariance matrices become unbounded [11]. Hence, an adaptive EKF (AEKF) has been utilized to address the packet drop. The main contributions of the paper are as following:

the control center. To incorporate the variable time delay with packet drop, it is modeled by a discrete-event driven architecture utilizing the Matlab SimEvent toolbox [21], which is an effective tool to develop the model of the discrete event system and simulate queues, servers and other event-based blocks. The network buffer of finite length has been used to store incoming data packets from the network. The EKF algorithm is executed at a fixed sampling rate. However, the packets may arrive in the random manner, not necessary at the sampling rate. This may result in an additional packet drop. To avoid this, an event-driven network buffer of sufficient length NB has been considered, which works on the Last-In-First-Out (LIFO) principle. The data is, then, exported to the Networked Packet Disorder Compensation (NPDC) block to remove any out of order packet. The synchrophasor data has a major advantage of being accurate and time aligned to the UTC, which can be utilized for precise latency calculation, essential for the latency compensation. The latency has been compensated by providing appropriate phase lead to compensate the phase lag, created while communicating and processing (mainly PDC processing) of the signal. The amount of phase lead not only depends upon the latency, but also on the frequency of oscillation of the signal. The frequency dependence is due to highly complex and non-linear behavior of the power system. This can be also verified from an event in the WSCC system that took place on Aug. 10, 1996 and resulted in different trends of frequency oscillations [22]. The random load variation can also affect the system dynamics. Hence, the modal analysis and conventional lead lag compensators may not be a better choice to solve this issue effectively. The Extended Kalman Filter (EKF) has been used to estimate the low-frequency oscillation modes using the PMU measurements taking into account the packet drop. This has been utilized further for the delay compensation. 2.1. Extended Kalman filter with packet drop The EKF is an efficient computational tool to estimate the unknown variables of a system or process, utilizing the measurements containing noise or other uncertainties. The dynamics of a nonlinear system can be expressed as,

• It proposes a new methodology for continuous compensation of • •

k)

(1)

k)

(2)

X k + 1 = f (X k ,

large time-varying latencies through phase advancement, along with continuous monitoring of modes from online PMU measurement data. A new algorithm for active packet disorder compensation technique based on data-realignment is proposed. Extensive simulation is carried out to study the controller performance at different operating condition and compared with a fixed delay compensation using Padé approximation.

S (k ) = h (X k,

where X k denotes the state of the system, and S (k ) is the measurement taken from the system. The stochastic variable k is the process noise with co-variance Qk , and k is the measurement noise with covariance Rk . The EKF, with intermittent observation, consists of the following steps [11,23]: Step 1: Initialize the state and co-variance matrix at k = 0 n

(3)

X 0 = E [X 0]

The proposed approach has been used to design the WADC for a Static Var Compensation (SVC) and its performance has been demonstrated on 16-machine, 68-bus power system considering various test scenarios.

P0 = E [(X 0

E (X 0 ))(X 0

(4)

E (X 0 ))T ]

Step 2: Predictor step for k = 1, 2. .

2. Proposed methodology for time delay compensation The proposed methodology for time delay compensation includes (1) modeling of communication network, (2) Networked Packet Disorder Compensation (NPDC), (3) online low frequency mode estimation from PMU measurements, (4) latency calculation from time stamped data, and (5) phase advancement leading to latency compensation. 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) networked buffer. The sensor node measures the analog current and voltage signals. The PMUs are utilized to extract the synchronized phasor information. In the NCS, the communication network allows the signal information transportation between the PMUs to

Xk

k 1

= f (X k

Pk

k 1

= Jk 1Pk

(5)

1 k 1) T 1 k 1Jk 1

+ Qk

(6)

1

where X k k 1 and Pk k 1 are the predicted estimation of the state and error co-variance matrix P at kth instant of time and state transition matrix Jk [i, j] = f[i] (Xk,0) Xj . The error co-variance matrix and states can be updated in the corrector step, as given in step 3. Step 3: Predictor step for k = 1, 2. .

Gk = Pk

Pk

k

T T k 1Hk 1 (Hk 1Pk 1 k 1Hk 1

= Pk

k 1

k Gk Hk Pk k 1

+ R k)

1

(7) (8)

where the matrix Hk [i, j] = h[i] (X k,0) Xj . The estimated state vector can be updated as, 478

Electrical Power and Energy Systems 106 (2019) 477–487

B.P. Padhy

Remote Location

PMU n

Sensorn

Sdcn

rr

rr rr

• • •

PDC2 • • •

mn (KT)

m1 (KT -

Communication Network

• • •

Yn (t)

m2 (KT)

rr

PMU 2

PDC1

rr

Sensor2

• • •

m1 (KT)

rr

Y2 (t)

PMU1

PDCn

1

m 2 (KT -

m n (KT -

moden

Delay Compensatorn

1

Sn (k)

S 2 (k)

EKF2

mode1

Delay Compensator1

Buffern

• • •

M dn Sdc 2 mode 2 Delay Compensator U 2 Td2 X Sdc

WADC

n

Buffer2

EKFn

• • •

Vs

2

• • •

Power System

Sensor1

Buffer1

• • •

Y1 (t)

NB

Other PMUs

• • •

GPS Clock

• • •

Sa Satellite

S1 (k)

EKF1

NPDCn

NPDC2

NPDC1

Td1 Time Stamp of Incoming Data Packets

Satellite

Logic To Calculate Time Delay

Control Center

GPS Clock

Fig. 1. Schematic diagram of a power system with the proposed network based delay compensation methodology.

Xk

k

= Xk

k 1

+

k Gk (S (k )

h (X k

N

(9)

k 1))

S (k )

g ( k , p) =

p k (1

gi, k = ai, k exp(

X i, k = [

+

i, k )

+

k

sin(

(14)

i, k

i, k

i, k

Ji =

where N is the number of mode frequency components present in the signal, ai, k is the amplitude of the signal, i, k is the angular frequency of the signal in rad/s, and i, k is the phase angle of the signal for ith mode at time k . Further, the signal can be reduced to the following form:

sin(

i, k )

+

k

for i = 1,2. ..m

where i, k = ln(ai, k ) written as,

i, k kTs

and

i, k

=

i, k kTs

+

= X i = Xi

1 0 0 0

Ts 1 0 0

0 0 1 0

J = diag ( J1 J2 ... Ji ... JN ) H = [ H1 H2 ... Hi ... HN ]

(11) i, k .

f (X i ) Xi

0 0 Ts 1

(17)

(18)

In a scenario when more than one signal modes are present, as in (12), the (17), (18) can be written in generalized form as,

N i, k )

(15)

(16)

Hi = [exp(X i, k (3)) cos (X i, k (1)) 0 exp(X i, k (3)) sin (Xi, k (1)) 0] (10)

ai, k exp(

= [ X i, k (1) X i, k (2) Xi, k (3) Xi, k (4)]

The measurement/observation matrix and state transition matrix of the signal model in Eq. (14) can be calculated by differentiating the function in (13) and (16), respectively, as,

for i = 1,2. ..m

i=1

T i, k ]

X i, k (1) + Ts X i, k (2) X i, k (2) Xi, k (3) TS X i, k (4)

i=1

S (k ) =

(13)

i, k )

X i, k (4)

N i, k kTs

(12)

where the ith mode state variable Xi, k at kth instant of time, related to the physical quantities in the Eq. (14) can be denoted as,

The power oscillation signals can be represented as sum of exponentially damped sinusoidal signals. Therefore, the measurement signal S (k ) , at time k , can be represented as,

sin(

i, k )

X i, k + 1 = f (Xi, k ) gi, k = Hi X i, k

and f (X i, k) =

i, k kTs )

for i = 1,2. ..m

The signal representation in Eq. (13) can be expressed in state space form as,

p k ) for k {0, 1} 0 Otherwise

ai, k exp(

k

where the ith mode of oscillation component is represented as,

2.2. Signal modeling

S (k ) =

gi, k + i=1

where Gk is the Kalman filter gain at kth instant of time. The packet loss between PMUs and the controller takes place when a phasor measurement data packet does not arrive after a certain interval of time. It is assumed to be random in nature as it depends on the variable network conditions, such as network traffic, and congestion. The variable k is an independent stochastic binary variable. If a measurement arrives at kth time step, k is set to 1, and if no measurement arrives, k is set to 0. It has been assumed that k has Bernoulli process with probability P [ k = 0] = p and P [ k = 1] = 1 p. The packet drop probability p , is related to independent variable k , through a probability distribution can be defined as,

(19)

From the above signal modeling, given in (12), (14), (16), and by applying EKF using (3)–(9), the signal model information such as modal

This can be 479

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B.P. Padhy

frequency damping and time varying amplitude i, k , i, k , ai, k = exp( k + k kTs ) at kth time instant can be extracted from the online PMU measurement data S (k ) . The latency can be compensated using the proposed methodology based on the estimated information from the time stamped PMU measurement signals. The performance of the EKF depends on the accurate system modeling, better model order selection, good initial estimate of the states and covariance matrices. The uncertainties in the nominal model, can be approximated by fictitious process noise and covariance of the fictitious process noise, Q. 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 specifying the appropriate noise levels in selecting better initial process noise covariance Q0 . However, incorrect specification of these statistics can even result in the filter to diverge. Usually, the specification of the Q is often done through trial-and-error approach. However, the highly nonlinear and time-varying processes like power systems dynamics, the specification of a constant matrix Q might not be sufficient in order to provide a sufficiently accurate filter performance. Further, the convergence of EKF highly depends on an appropriate order of the selected model. 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 0.1–0.8 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. Hence, the process noise covariance Q accounts for the model uncertainty and inaccuracy whereas, the measurement covariance matrix R accounts for the amount of noise content in the measurement. Hence, an improper initial guess of Q0 and R 0 results in unsatisfactory transient and steady state performance by the EKF. Moreover, by choosing a higher value of Q0 , the gain matrix G will increase. This will result in

faster transient performance but poor steady-state response. By considering a larger R 0 , the filter gain will decrease resulting in a poor transient performance. The prior information about the noise present in the measurement is generally unknown or sudden change in the noise condition is generally unpredictable. This requires adaptive estimation of the covariance matrices to improve the performance of the EKF. The recursive update of Q can be performed as proposed, and the measurement covariance can be estimated recursively, as given in [24]. The measurement covariance can be estimated recursively, as given in [25]. These have been applied to improve the performance of the EKF. 2.3. Time delay compensation (TDC) In a Wide-Area Networked Control Systems (WANCS), the signal delay is basically due to PDC processing, routing, and long distance signal transportation. For efficient operation of the proposed TDC scheme, it is necessary to calculate the feedback latency while sending the packets from PMU to the controller. The latency calculation is an important issue for the viability of the synchrophasor based measurement system to the protection and control applications. The total signal latency, including the buffer queue delay, can be easily estimated by comparing the time skew information in the phasors with the GPS clock time at the instant of comparison. This can be written as, Td = TGPS TStamp , where, TGPS and TStamp are the present clock time and time tag, respectively. The signal state components [ i i i i ] of the ith mode are estimated online at each time step from the delayed measurement data by the AEKF, and are exported to the Time-Delay Compensator (TDC) block as shown in Fig. 2. The latency can be compensated by time advancing the signal in equation (12), equal to the total time delay in the network, Td . Hence, for a time step TS , the signal should be advanced by Td Ts times the time step. By advancing the signal in (12) by Td TS times the time step and applying the conditions in (15), the delay compensated signal at kth instant can be represented as,

GPS Clock

TGPS

Tstamp

-+

Td

γ k ,S(k)

AEKF

φk ,ωk ,λ k ,ζk

Sdc (kTs ) = N

e

(λ i,k -ξ i,k Td )

i=1

NPDC Compensation

sin(

i ,k

Sdc (kTs ) WADC

yj

yk

+ ω i,k Td )

y3

y1 Buffer TOP

Network Buffer Incoming Data

Fig. 2. Schematic diagram of the proposed TDC.

480

Vs Power System

TDC

Electrical Power and Energy Systems 106 (2019) 477–487

B.P. Padhy

Sdc, k = S (k + Td TS )

= =

N

respectively. The PD in the network makes the control input signal distorted due to time misalignment. To compensate for the latency in case of the PD in the network, a new approach of data realignment has been proposed having two stages. In the first stage, the Network Buffer (NB) data has been sorted and restored in chronological sequence as incoming data packets are time-stamped. The sorting algorithm should start after accumulation of a certain minimum number (Nmin ) of packet data, which depends upon the Td , and should satisfy Nmin < [round (2 Td TS ) 1]. This results in an additional delay of Nmin × TS , which has to be also compensated by the TDC. An insertion sort algorithm has been used for chronological sequence restoration of the data, which is simple to implement, and also efficient for the data which have already been substantially sorted. Here, the order of computational complexity is only O (n + d ), where d is the number of the data to be inserted. This operation has been carried out in the eventdriven mode as soon as the new packets arrive, as shown in Fig. 3, to avoid any recent data loss. In the second stage, the sorted data packets have been sent to the AEKF sequentially in every phasor time step. This requires a free-running clock scheduled to generate time-stamp in every phasor time step. The clock time format is also assumed to be

exp(Xi, k (3) + Td TS ) sin(Xi, k (1) + Td TS )

i=1 N

exp(X i, k (3)

Td X i, k (4)) sin(X i, k (1) + Td TS )

i=1

=

N i=1

exp(

i, k

Td

i, k )

sin(

i, k

+ Td

i, k )

(20) The synthesized signal Sdc, k is the delay free signal at kth instant of time. Hence, the above signal Sdc, k can be effectively applied as input to the controller. 2.4. Networked packet disorder compensation (NPDC) Packet disorder is a phenomenon in which the data packets generated later arrives at the control center earlier or vice versa [12]. The Packet Disorder (PD) occurs when delay bound, Td = Td max Td min > TS , where, TS is the sampling period, Td max and Td min are the upper bound, and the lower bound on the delay

Fig. 3. Flow chart of the proposed NPDC algorithm. 481

Electrical Power and Energy Systems 106 (2019) 477–487

B.P. Padhy

equivalent to the PMU time stamp. For time synchronization, a bias time T0 has been added to the clock timing, equal to the first incoming data packet time tag. A search algorithm has been applied to find out the index position corresponding to the free-running clock time in the sorted data base. If the data corresponding to the free-running clock is present in the buffer, k is set to one and data value and its corresponding time-stamp are exported to the AEKF. Else, k is set to zero, so that the AEKF only runs the time update. This methodology has the advantage over the packet rejection logic [12], to compensate the packet disorder, in which the older data packets are discarded when the data generated later are received. The methodology in [12] is easy to be realized, but additional packet loss occurs due to packet rejection, which increases with the increase in Td , and may deteriorate the control performance. The proposed approach is quite efficient and restores the complete signal information by data realignment and, hence, improves the control performance. The total computational time observed is 0.03 ms on Intel i7, 3.39-GHz CPU and 3-GB RAM PC, as obtained from the MATLAB simulink profile report.

control input signals which require 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 output signal of the Wide-Area Damping Controller (WADC) has been applied to the SVC as a supplementary voltage reference signal. A few critical line contingencies have been applied to capture the coherent groups, identified by the above mentioned methodology. The severity of the contingencies is determined by a dynamic contingency ranking index [27]. The tieline 28–29 outage is found to be the most severe, followed by L25 26 , L8 9 , and L5 6 line contingencies, having the index values 0.13083, 0.05661, 0.03532, and 0.02819, respectively. From the clustered groups, a few signals have been selected based on the PCA score vectors. The signals P21 22 , P23 24 , P17 27 , and P36 37 are selected as optimal inputs to the WADC. It is assumed that the PMUs are installed to measure these remote signals. Among these, P21 22 is a local signal and all others are remote signals. A Multi Input and Single Output (MISO) controller has been designed with the power system model linearized at nominal operating point and also at other system loading conditions. A three rule fuzzy controller has been designed with triangular membership function. The controller gains have been calculated by solving the LMIs in Theorem provided in [6]. The controller gains, obtained by solving the LMIs, are

3. System description and implementation results The test system considered in this work is a reduced order model of the interconnected New England and the New York Power System. This system consists of 68-buses and 16-generators, divided into five-areas, as shown in Fig. 4. Each generator is assumed to be provided with governor and IEEE ST1A type static exciter. To damp out the local mode of oscillations, generators 3, 7, 9, 13 and 16 are assumed to be provided with the CPSS. The system data is taken from [26]. The parameters of the IEEE ST1A type static exciter and CPSS are given in Tables 1 and 2 respectively. A SVC of 300 MVar capacity is placed at 345 kV bus 21 to regulate the voltage. The SVC has a 109 MVar Thyristor Controlled Reactor (TCR) bank and three 94 MVar Thyristor Switched Capacitor (TSC) banks, interfaced to the system through a coupling transformer of 345 kV/16 kV, 333 MVA capacity. The input/output signal selection has been carried out using a coherency based approach [27], in which a combined Principal Component Analysis (PCA) and Self Organizing Map (SOM) clustering approach has been applied to select the optimal

F1 = [ 7.5895 2.22681 2.71525 F2 = [ 8.1431 3.50618 2.96853 F3 = [ 5.7517 4.62663 3.38793

0.528617] × 10 04 0.757625] × 10 04 0.885364] × 10 04

3.1. Performance evaluation of the proposed AEKF based estimator To demonstrate the performance of the proposed AEKF based estimator, a test signal considered is Z (t ) = S (t ) + (t ) , where, S (t ) is the signal component, and (t ) is the noise. The S (t ) is of the form, S (t ) = A exp( t ) cos(2 ft + ) , where, A is the amplitude, is the damping factor, f is the frequency of oscillation in Hz, is the phase. In this study the frequency of oscillation of 0.4 Hz, damping factor of 0.07, zero phase, and magnitude ( A ) as 1 p.u. are used for the parameter estimation. The accuracy of the proposed methodology has been

Fig. 4. Schematic diagram of New-England and New-York Power Systems. 482

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B.P. Padhy

TLS ESPRIT [17] approach for the two SNR levels. The proposed methodology is more suitable for the online application, since it estimates modes at each time step and, hence, it is very effective for any abrupt change in the mode. However, the modified Prony [16] and the modified TLS ESPRIT [17] require at least one cycle data window before estimating these modes. Consideration of larger window length will increase the accuracy of the mode estimation. But, it will also increase the weight of the past event, which prevents it to act on any temporal change in the signal parameter. Hence, one normally decides a trade-off between the window length and the accuracy. However, this reduces the effectiveness towards estimating the modes of the signals, which are non-stationary in nature and poses a challenge for real-time tracking applications. AEKF based estimator is efficient to report the results, at each phasor sampling rate of PMU, with no prior knowledge other than the state estimation for the previous time instant. Hence, it is capable of responding to any variation in the signal parameter, making it suitable for tacking the modes of non-stationary signals.

Table 1 Parameters Used for the CPSS. Lead-lag time constant #1

Lead-lag time constant #2

KP

T1

T2

T3

T4

7.25

0.1124

0.0874

0.1035

0.9100

Table 2 Parameters Used for the Excitation System. KA

TR

200

0.01

Table 3 Performance results for the test signal considered. Parameters

Methodology

3.2. Estimation of modes in WECC system [17]

SNR No noise

50 dB

40 dB

Frequency

Prony [16] TLS ESPRIT [17] Proposed

0.4 Hz 0.4 Hz 0.4 Hz

0.4 Hz 0.4 Hz 0.4 Hz

0.4007 Hz 0.4 Hz 0.3998 Hz

Amplitude

Prony [16] TLS ESPRIT [17] Proposed

1.00 1.00 1.00

1.0048 1.0034 1.0004

1.0986 1.0089 1.0006

Damping

Prony [16] TLS ESPRIT [17] Proposed

0.07 0.07 0.07

0.0708 0.0706 0.0698

0.0875 0.0715 0.0688

The performance of the proposed estimator is further evaluated by estimating the mode components for the field data of Western Electricity Coordinating Council (WECC) system obtained on Sept. 14, 2005 [17]. The detailed sequence of the data can be found in [17]. The analysis applied for ambient and probing data corresponds to the oscillation of the real power in the line MALN-Round Mountain 1, as shown in Fig. 5. The analysis window-1 (20:10:11:967–20:10:26:267 UTC) corresponds to the probing data, and the window-2 (20:30:07:234–20:30:20:867 UTC) corresponds to the ambient data. The analysis is carried out at PMU sampling rate of 30 frames/s for the 60 Hz system. The comparative performances of the three methodologies are presented in Table 4. However, for the probing signal, TLSESPRIT methodology is found to be the best in [17]. The results obtained for the window-1 show that the proposed method estimates the frequency as 0.31776 Hz and the damping ratio as 8.023%, which are close to the actual modal frequency of 0.318 Hz and damping of 8.3% [17]. Similarly, for the case of the ambient data considered in window 2, the proposed methodology provides an estimate of frequency as 0.32276 Hz and damping ratio as 2.112%, which are close to the estimated values by the TLSESPRIT methodology, which provides frequency as 0.3236 HZ and damping as 1.908%. However, the modified Prony method gives slightly higher frequency and damping values. Thus, the proposed method shows comparable estimation accuracy as the existing proven methodologies.

evaluated by comparing its results with a modified Prony based method [16] and modified TLS ESPRIT approach [17]. With the Prony and TLS ESPRIT approaches, the modes are estimated for a 20 s data window length with a sampling interval of 20 ms. In case of the AEKF, the results obtained in each iteration are averaged over the whole window to get the final value of the estimated mode. To test the robustness towards noise, Gaussian white noise, with SNR 50 dB and 40 dB, has been added. The results, showing the comparative performance for the signal considered with the three methodologies are presented in Table 3. It can be observed that, without any noise in the signal, all the three methodologies, give satisfactory results. With the increase in the noise, the performance of the modified Prony [16] significantly worsens. The proposed AEKF approach gives better performance than the modified 600

Real Power (MW)

550

Window 1

500

Window 2

450 400 350 300 250 0

500

1000

1500

2000

Time(Seconds)

2500

Fig. 5. Field data correspond to the flow of real power. 483

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been kept at 4%. The uniform random delays applied to various input channels, are given in Table 5. The delay in the output channel is neglected, as the controller is local to SVC device. The network latency can be characterized as constant, variable and random in nature. However, from the practical point of view, it is advisable to consider the empirical results obtained in [10,10], that gives generic idea of the characteristics of the delay. However, the main motivation in this work was to test the performance in the worst network condition, that exhibits random delay behavior, so that it will also be effective for constant and variable nature of delay. The low frequency modes, estimated by the three methodologies, are presented in Table 6. The results obtained from the AEKF are applied as input to the TDC. The proposed delay compensator has compensated the random delay and is able to retrieve the PMU output signal from the online delayed measurement data, as shown in Fig. 6. It accurately tracks the original delay free PMU output signal, and effectively predicts the future dynamics of the system from the measured PMU data. As depicted in Table 5, the delay bound Td = 80 ms > TS . Hence, it will result into packet disorder in the network. With the application of the proposed NPDC compensation technique, the packet disorder has been effectively compensated, and the packet disorder free waveform is retrieved. Thus, it improves the performance of the AEKF and WADC, and, hence, the stability of the system. The simulation result reveals that proposed method (AEKF) can estimate the low-frequency modes of a signal within 0.0235 ms in an Intel core i7, 3.39-GHz CPU and 3-GB RAM PC hardware environment, which is much faster compered to the PMU data rate. Thus, the proposed algorithm is fast enough can be implemented in the online control systems. The major advantage with the proposed method is that the controller design requirement is independent of the amount and nature of the delay characteristics. Hence, the controller can be designed independently without considering the input delay. Since, the proposed TDC scheme effectively cancels out the occurrence of random nature of the channel latency, this leads to better utilization of the control effort in improving the system damping and stability. Moreover, since the existing methodologies are designed robustly to the input latency, its control performance depends on the delay characteristics. Due to this requirement, one should tradeoff between the delay margin and the robust control performance. This will have the detrimental impact, if the delay encountered deviates from the nominal value.

Table 4 Performance results for WECC system field signal. Parameters

Freq. (Hz) Damp. (%)

TLS-ESPRIT

Prony [17]

Proposed

Ambient

Ambient

Probing

Ambient

Probing

0.3236 1.908

0.3479 5.167

0.32473 1.705

0.32276 2.112

0.31776 8.023

Table 5 Input latency in various channels (NE-NY system). Ch. no

Control signal

1 2 3 4

P21 P23 P17 P36

Random delay

22

24

27 37

Packet drop

Minimum

Maximum

0 ms 320 ms 420 ms 920 ms

0 ms 400 ms 500 ms 1000 ms

0% 4% 4% 4%

Table 6 Performance Results for NE-NY system. Estimated parameter

Proposed AEKF method

Prony [16]

TLS ESPRIT [17]

Amplitude Damping Frequency (rad/s)

630.99 0.1956 3.6782

636.98 0.1592 3.7722

621.71 0.1454 3.6919

3.3. Performance evaluation of the proposed TDC and NPDC The effectiveness of the proposed TDC has also been assessed on the 68-bus system. A self-clearing 3-phase fault has been applied at bus-16 for 70 ms, to create low-frequency oscillations in the order of less than one Hz. For estimation of the low-frequency modes by the AEKF, the initial values of the states, state covariance matrix, process noise covariance and measurement covariance considered are, X 0 = [0 3 0 0.2], P0 = diag [50 50 50 50], Q0 = diag [0.01 0.01 0.01 0.01], R 0 = 0.2 respectively. For this simulation study, the packet loss probability has

Delay (Sec)

(1-γ )

1 0.5 0 10

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28

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15.6

-800 10

16

(c) Time(Seconds)

12

14

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Fig. 6. Plots for (a) packet drop with time, (b) delay with time, (c) effect of NPDC and (d) tracking of PMU signal with delayed measurement (68 bus system).

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3.4. Performance of proposed delay compensation technique

TDC scheme. To test the effectiveness of the proposed approach for different network topology configurations and operating conditions, line and load contingency cases were also considered. A heavily loaded line, connecting buses 32 and 30, carrying power of 320.19 MW and 26.30 MVar, was taken out 15 s after the start of the simulation, so that the pre-fault operating condition is quite different from the post-fault condition. Due to this disturbance, the power generated by Gen-11 gets diverted to the line connecting buses 32 and 33, which makes it highly stressed, resulting in large power swing. The comparative performance results are given in Fig. 8(b). To test the robustness under wide variation in operating condition, another line contingency L15–16 was simulated. The plot of speed difference of gen-5 and 16 is shown in Fig. 8(a). From this result, it can be observed that, without any delay compensation, the system performance deteriorates severely, and the system becomes unstable. However, with the proposed TDC scheme based WADC, the system damping has significantly improved and the system stability is restored. Similarly, to test the performance under load change condition, a large load at bus-8, of value 522 MW and 177 MVar, was taken out. Severe oscillations are observed without any WADC. However, with the proposed control action, significant improvement in the damping is observed, as shown in Fig. 8(c). Similar conclusions are also drawn by reducing the load at bus-37 by 900 MW from its nominal operating value of 6000 MW and 300 MVar, 15 s after the start of the simulation, as shown in Fig. 8(d).

The effectiveness of the proposed time delay compensator, in presence of the network uncertainties along with the WADC, has been evaluated for various scenarios and test cases through time-domain simulation. A comparison has been made for the cases, without any control action, with WADC without compensation, and with compensation. In the first test study, a self-clearing three-phase fault for 70 ms was applied at bus-16 near to the SVC bus 10 s after the start of the simulation. During the nonlinear simulations, the packet loss probability of 4% has also been considered. As the delay bound Td = 80 ms > TS . Hence, packet disorder is also taken place during the simulation study. Fig. 7(a) and (b) show the power flow deviation in the line connecting buses 21 and 22 and rotor speed difference between gen-5 and gen-16. It is evident from these results that, without any control action, poorly damped oscillations are generated, while with the WADC and without delay compensation, a negative damping is observed, which fails to restore the stability of the system. On the contrary, with the proposed compensation, the system performance improves because of the improved damping of the dominant inter-area mode of oscillation. Another test case of large disturbance was considered by applying a 3-phase fault at bus-1 for 70 ms. The comparative study results are presented in Fig. 7(c) and (d). It is evident from these results that adequate damping has been obtained with the proposed

W5-W16 (pu)

P21-22(MW)

800 700 600 500 10

15

Time(Seconds)

20

(a)

W5-W16 (pu)

P21-22(MW)

600

12

14

16

Time(Seconds)

18

(c)

-3

x 10

2 0 -2 -4 10 -3

700

500 10

4

20

22

2

x 10

15

20

25

30

15

20

25

30

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0 -2 10

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-4

W6-W16 (pu)

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5

x 10

20 25 Time(Seconds)

(a)

30

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-5 x 10

-5 15 20 Time(Seconds)

0

-5

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10

5

x 10

15

W15-W16 (pu)

W5-W16 (pu)

5

-4

(d)

-4

x 10

15

(b)

Fig. 7. (a) and (b) plots for 3 − φ fault at bus 16, (c) and (d) 3 − φ fault at bus 1, (a)–(d) solid blue line: without WADC, dot line: with WADC and without delay compensation, and solid black line: the performance with WADC and delay compensation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

30

20 25 30 Time(Seconds)

35 (b)

40

2 0 -2 -4 15

20 25 Time(Seconds) (d)

30

Fig. 8. (a) L15–16 outage, (b) L30–32 outage, (c) bus-8 load outage, (d) load at bus-37 variation, (a)–(d) solid blue line: without WADC, dot line: with WADC and without delay compensation, and solid black line: the performance with WADC and delay compensation. 485

Electrical Power and Energy Systems 106 (2019) 477–487

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0 -2 -4 10

∆ P36-37(MW)

∆ P17-27 (MW)

2

50 0 -50 -100 -150 15

15

20

Time(Seconds)

25

(a)

30

50 0 -50 10

20

25

30

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35

(c)

15

-5

x 10

W15-W16 (pu)

W2-W16 (pu)

x 10

40

20

Time(Seconds)

25

(b)

30

2 0 -2 15

20

25

30

Time(Seconds)

35

(d)

40

Fig. 9. (a) 3 − φ fault at bus 16, (b) bus-8 load outage, (c) load at bus-37 variation, (d) L30–32 outage, (a)–(d) dash line represents with Padé Approximation, solid line represents the performance with proposed approach.

References

3.5. Comparison of results with Padé approximation based delay compensation

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The performance of the proposed technique has also been compared with a constant delay compensation based on Padé approximation technique. For this purpose, the delay has been modeled with Padé approximation of 3rd order. An augmented system model is obtained by embedding the delay approximated model with the linear power system model. The wide area TS fuzzy controller was designed based on the augmented state space model. The upper bound of delays, as shown in the Table 5, are considered to develop the Padé approximation model. The packet drop probability of 4% was considered in all the input delayed channels. The packet disorder was also assumed and compensated by the proposed TDC technique. To evaluate the comparative performance under a wide variation of operating conditions, various types of disturbances have been applied in the system. The comparative performances of both the methodologies are shown in Fig. 9(a)–(d). The proposed TDC scheme gives better performance than the constant delay scheme in all the cases. As the nature of the delay is variable and considerably large, the Padé approximation based method is unable to compensate the delay, whereas the proposed method accurately compensates the delay. 4. Conclusion A network based latency compensation technique for Static Var Compensator (SVC) controller has been proposed in this work. The AEKF based estimator provides accurate estimation of the modes for the test signal with different noise scenario and the field signal data available for the WECC system with accuracy comparable with the existing methods. Also the estimation results obtained at every sampling interval confirms the fast and accurate mode estimation capability of the proposed method, making it suitable for online applications. The network time delay has been compensated accurately by time advancing the signal equal to the total delay occurring in the communication. It is also found that the proposed Network Packet Disorder Compensation (NPDC) has effectively compensated the active packet disorder in the networked control system. The performance evaluations for various test cases under random delay, packet drop and packet disorder, demonstrate promising results of the proposed control for its online applications. It has also been observed that the system performance significantly deteriorates without any delay compensation. The proposed method also performs better than an existing delay compensation technique using Padé approximation. 486

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