Testing and Validation of Power System Dynamic State Estimators ...

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Testing and Validation of Power System Dynamic State Estimators Using Real Time Digital Simulator (RTDS) A. Sharma, Member, IEEE, S. C. Srivastava, Senior Member, IEEE, and S. Chakrabarti, Senior Member, IEEE

Abstract—This paper presents an approach to test and validate a number of power system dynamic state estimation (PSDSE) algorithms, utilizing Real Time Digital Simulator (RTDS), a real-time simulation tool. WSCC 9-bus and IEEE 30-bus systems have been utilized to demonstrate the proposed approach. The test systems are developed on the RSCAD software of the RTDS. The conventional remote terminal unit (RTU) measurements and the phasor measurement unit (PMU) measurements are sent from the RTDS runtime environment to the MATLAB based PSDSE application at regular intervals for the estimation of the states, using software-inthe-loop (SIL) configuration. The PSDSE is solved by utilizing the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the cubature Kalman filter (CKF) approaches, and their relative performances are studied with the help of the simulation results on the two test systems. Index Terms—Cubature Kalman filter, dynamic state estimation, extended Kalman filter, Real Time Digital Simulator, unscented Kalman filter.

I. INTRODUCTION

C

ONVENTIONALLY, the power system state estimation (PSSE) has been considered as an offline tool to estimate the states of the power system. The PSSE is utilized at the control centers for the visualization of the power system states. To perform the PSSE, generally the static state estimation (SSE) approaches, such as weighted least squares (WLS) approach [1]–[3], are utilized at the control centers due to their simplicity, accuracy, and satisfactory performance under steady state conditions. Normally, the SSE estimates the states of the power system at regular intervals of 30–60 s, utilizing the measurements received from the remote terminal units (RTUs), which refresh at every 1–5 s. Therefore, SSE does not consider updated measurements received from the RTUs during its execution process, and its results fall behind in time with the actual

Manuscript received January 25, 2015; revised April 13, 2015 and May 27, 2015; accepted June 28, 2015. Date of publication July 28, 2015; date of current version April 15, 2016. This work was support in part by the Department of Science and Technology, New Delhi, India,under Project DST/EE/20100258. Paper no. TPWRS-00100-2015. The authors are with the Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur, India (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2015.2453482

system states. Hence, it is difficult to utilize the SSE approach for the online visualization of the power system states. Under the purview of the smart grid, online visualization of the power system states is highly demanded due to the growing complexity in the operation of the power system networks. With the advent of the phasor measurement units (PMUs), the measurement data reporting rate has increased up to 50 frames per seconds for the 50-Hz system, and up to 60 frames per seconds for the 60-Hz system [4], which is much faster as compared to that of the RTUs. Hence, the PMU measurements can be best utilized for the online visualization of the power system states. However, due to large cost of the PMU's deployment, online visualization of the power system states, using only PMUs, is not carried out at present. Accordingly, there have been various dynamic state estimation (DSE) algorithms developed to solve the PSSE problem utilizing all the available field measurements from the RTUs and the PMUs, for online visualization of the power system states. Before deploying the DSE algorithms in the control centers, the performance of the algorithms need to be tested and validated under a simulated real-time environment. With the introduction of the real-time simulation tools, such as the Real Time Digital Simulator (RTDS) [5], the real-time test and validation of the power system DSE is achievable. Such simulations will provide the required confidence in the design of the DSE, and also validate its performance in a real-time environment. There have been efforts to design, test, and validate the algorithms and methodologies using real-time simulation tools to solve problems in various areas of the power system, such as protection, renewable integration, and Flexible AC Transmission System (FACTS). In [6], a real-time test bed is developed using the RTDS for the power system operation, control and cyber security study. In [7], the real-time implementation of an intelligent reconfiguration algorithm for microgrid is studied using RTDS as a real-time test bed. In [8], RTDS is utilized to test the performance of the distance relays on shunt-FACTS compensated transmission lines. In [9], a multi-agent system (MAS) for real-time operation of a microgrid using RTDS is presented. A 12-bus power system with the plug-in electric vehicles (PEVs) and wide area controllers (WACs) has been implemented on the RTDS in [10] to show the improvement in the stability of the power system, when PEVs are integrated. There have been a few efforts to execute the state estimation approaches using RTDS. In [11], RTDS is used to validate the state estimator under real-time environment using the low

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SHARMA et al.: TESTING AND VALIDATION OF POWER SYSTEM DYNAMIC STATE ESTIMATORS USING REAL TIME DIGITAL SIMULATOR (RTDS)

voltage measurements from secondary substations and smart meters. A precision time protocol based synchronization approach for the power system state estimation with PMUs is proposed in [12] utilizing the RTDS as a test bed. However, to the authors' best of knowledge, there is no literature available on the simulation of the DSE problem in real-time using the real-time simulators, such as the RTDS. Efforts have also been made in recent years to solve the Power System Dynamic State Estimation (PSDSE) problem using Kalman filters in the non-real-time simulation environment. In [13], extended Kalman filter (EKF) was used to estimate the states of the power system. The EKF utilizes first order approximation of the Taylor series to solve the measurement function. Since EKF ignores the nonlinearity of the measurement function, its state estimation (SE) results deviate from the actual values. In [14]–[16], unscented Kalman filter (UKF) was utilized to estimate the states of the power system. In [17], an unscented transform (UT) based hybrid SE, utilizing conventional as well as PMU data, was proposed. Since the performance of the UKF deteriorates with the increase in the number of state variables [18], it is not suitable for the SE of large power systems. In [19], a comparative study of various Kalman filters, using a second-order kinematic model in 2-D space, is presented. Recently, the introduction of the cubature Kalman filter (CKF) [18], [20], [21] has demonstrated potential benefits, such as accuracy and stability for the large state vector, over other Kalman filtering techniques. The CKF has been proposed in this paper to develop, test, and validate the PSDSE problem on the real-time simulator, utilizing both the RTU data and the PMU data. This paper proposes a new testing and validation methodology of various Kalman filter (KF) based DSE approaches under a simulated real-time environment, using RTDS [5]. To the authors' best knowledge, there is no methodology available to assess the performance of the developed DSE algorithms in a real-time environment. Therefore, an approach has been proposed for testing and validation of the DSE algorithms utilizing a simulated real-time environment on the RTDS. Generally, RTDS is designed to test and validate the hardware, such as controllers and relays, using hardware-in-the-loop (HIL) configurations. To validate the software algorithms, software-in-the-loop (SIL) feature, is not available in the RTDS. Therefore, to implement the proposed methodology, a new SIL scheme is developed for the RTDS in this work. The SIL scheme helps in automation and execution of the proposed approach in a closed loop configuration. It integrates the information and measurement data exchanges between the RTDS and the PSDSE applications in a time bound manner through communication network. This helps in validating whether the PSDSE approaches, under test, will work effectively under the real-time operating conditions. The proposed methodology has been explained with the help of the CKF based PSDSE approach, proposed by the authors in [22]. The relative performance of the CKF based PSDSE is compared with the UKF and the EKF based PSDSE formulations under the real-time environment. In the proposed approach, the power system model is developed on the RTDS. The measurement devices and the PMUs, connected at the buses of the power system model, send

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TABLE I MEASUREMENT TYPES AND CORRESPONDING STANDARD UNCERTAINTIES

the voltage magnitudes, the voltage angles, the power injections, and the line power flows from the RTDS to the MATLAB based PSDSE application, installed in a computer, for estimation of the states. The load variations are triggered regularly from the PSDSE application to the RTDS and, accordingly, the measurements are captured for the PSDSE execution using the SIL configuration. The real-time simulation of the proposed approach is used to identify the best approach among the CKF, the UKF, and the EKF based PSDSE approaches that can be implemented in the real operating conditions. II. POWER SYSTEM MODEL Generally, the load variations in the power system are slow. Therefore, the power system states, i.e., bus voltage magnitude and bus voltage angle, under various loading conditions are considered as quasi-static. Under such scenario, fast estimation of the power system states can effectively track the variations in the states of the power system. The DSE, in this work, is mainly used for the prediction of the power system states in advance, and then to execute the state estimator by utilizing the predicted states and the latest available measurements [23]. Predicting the states in advance helps in filling the gap in the measurements, arising due to varying communication delays in the networks, and generates the pseudo measurements, which can be used in the measurement update step, in case of incomplete information or the communication link failure. The power system model utilized in this work has been explained by the authors in [22]. However, for ready reference, it is summarized in this section. The non-linear dynamic power system states and measurements can be represented using the following difference equations: (1) (2) (3) (4) is the state vector at the th instance, is the meawhere surement vector, is a Gaussian process noise with zero mean and covariance, is a Gaussian measurement noise with zero mean and covariance, the and are the non-linear state transition function and measurement function, respectively. It is assumed that all the measurements are independent of each other. Hence, is considered as a diagonal matrix. Various measurement types and their standard uncertainties (i.e., ), used in the present work, are given in Table I [22]. The process noise error covariance represents the Gaussian noise added in the state estimation process due to the small random fluctuations around the operating points. The value of is derived through offline simulations [22].

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In the PSDSE formulation, Holt's two-parameter linear exponential smoothing technique [24] is used to define the state transition function as given in the following:

through the transition function . is the size of the state vector. • Calculate the predicted state error covariance

(5) where

(6)

and

(7)

The and are the parameters at th instant containing values between 0 and 1, is the predicted state vector, and are the vectors defined by (6) and (7) at th instant. To define the measurement function for the power system, the standard real and reactive power balance and line flow equations are used, which are given by [25] (8)

(13) where

is the process noise error covariance.

B. Measurement Update Step After receiving the estimated values of the state vector and the state error covariance from the time update step at the th time step, the measurement update step is executed to estimate the measurement vector and its innovation and cross covariance, as follows: • Calculate the estimated value of the measurement vector at the th time step (14)

(9)

(10)

(15)

(11) is the real power injection at bus is the reacwhere tive power injection at bus is the real power flow between buses and is the reactive power flow between buses and is the voltage magnitude at bus is the conductance of the line between buses and is the susceptance of the line between buses and is the conductance of the shunt at bus , and is the susceptance of the shunt at bus . III. CKF BASED PSDSE The CKF based PSDSE approach has been proposed and explained by the authors in [22]. For the sake of ready reference, this approach is summarized below. The CKF based PSDSE approach is executed in two steps: the time update and the measurement update. The execution process assumes a flat start, with the initial voltages and angles at all the buses of the power system assumed to be at 1 p.u. and zero radians, respectively. The individual steps, to be executed by the CKF based PSDSE approach, are as follows. A. Time Update Step The time update step computes the estimated value of the state vector and the corresponding state error covariance matrices using state transition function , just before the arrival of every fresh field measurement set, as follows: • Calculate the estimated value of the state vector (12)

is the propagated cubature point vector for the th cubature point input, processed through the measurement function. • Calculate the estimated value of the innovation covariance

(16) is the measurement noise error covariance. where • Calculate the estimated value of the cross covariance

(17) On arrival of the fresh field measurements, the estimated mean of the state and its associated error covariance matrix along with the Kalman gain are updated at the th time step by using the standard Kalman filtering approach, given by (18) (19) (20) The time update and the measurement update steps are executed sequentially and iteratively for every measurement cycle to estimate the states of the power system. IV. REAL-TIME SIMULATION OF PSDSE USING RTDS

where is the propagated cubature points set at the th instant, calculated by processing cubature points

For the real-time simulation of the PSDSE, the mimic of the power system network is developed on the RTDS. The RTDS

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Fig. 2. Data flow sequence for the real-time simulation of the PSDSE approach in the software-in-the-loop (SIL) configuration. Fig. 1. Lab setup of the RTDS for the PSDSE execution.

uses nodal approach to convert the power system model into mathematical equations by converting the sources into Norton equivalents [5], [23]. The RTDS executes the electromagnetic transient simulation in real-time with the help of hardware and software process synchronization. The RTDS utilizes the algorithms, such as the one proposed by Dommel [5], and the Trapezoidal rule of integration [24], to simulate the dynamics of the power system. The simulation of the power system in real-time is executed by the RTDS, with a typical time step of integration of 50 s. In order to execute the real-time simulation of the proposed PSDSE approach, the six rack RTDS available at the real-time simulation lab in the host Institute is integrated with the computer, having MATLAB installed, through the local area network (LAN). The simulation is performed in two stages: the RTDS simulation and the PSDSE execution. The details are as follows. A. RTDS Simulation The RTDS is a real-time simulation platform, which utilizes a combination of hardware and software in a synchronized manner to perform the simulation. It uses PB5 processor cards to simulate the power system network on the real time operating system (RTOS) installed in it. The simulation is executed in parallel on various 1.7-GHz PB5 processor cards using RTOS in such a way that the power system simulation output is perceived as if it is executed in the real-time. The simulation on the RTDS is executed with the typical time step of 50 s to experience the real-time processing. The Gigabit Transceiver Network (GTNET) card is utilized to connect the RTDS to the LAN. The RTDS, used for the present work, is equipped with the GTSYNC card to receive the 1 pulse per second (pps) signal from the satellite through GPS clock. This signal is used to synchronize the software PMUs, called as GTNET PMUs in the RTDS, with the GPS clock. One GTSYNC card can synchronize a maximum of 24 GTNET PMUs of the RTDS. The schematic diagram of the lab setup with the RTDS, for simulation of the present work, is shown in Fig. 1. The GTNET card can support various protocols, out of which, one can be selected at a time, based on the simulation requirement. In the present work, IEEE C37.118-2011 [4] protocol was

Fig. 3. CKF processing sequence of the PSDSE approach.

selected, to send the time stamped GTNET PMU measurement set from the simulation environment to the computer executing the PSDSE. The OpenPDC [25], a software Phasor Data Concentrator (PDC), is utilized in the present work to consolidate, time-align, and store all the available PMU measurements in the database. In this work, a new SIL scheme is developed to simulate the proposed methodology. In this scheme, RTDS and the PSDSE host system were connected in a closed loop configuration for the information exchange. The measurements, the time-stamps and the status information were sent from the RTDS to the PSDSE host system for the estimation of the states. The monitor and the control commands for the RTDS are issued from the PSDSE host system to change the load profiles and synchronizing the complete execution process. The process flow in the SIL configuration is shown in Fig. 2. The model of the test power system is developed on the RSCAD software, installed in a computer. The developed model is, then, loaded into the RTDS racks for simulation.

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Fig. 4. WSCC 9-bus system developed in RSCAD.

To acquire the RTU measurement set, the simulation output from the RTDS was taken through the voltage and the power meters available in the run-time environment of the RTDS. The readings of the meters are captured through a Java based network packet reading utility, and the readings are sent to the MATLAB based PSDSE process. To acquire the PMU measurement set, the simulation output of the GTNET PMUs from the RTDS is received by the OpenPDC through LAN. The PSDSE process acquires the PMU measurements from the OpenPDC. To capture the measurements at various operating conditions, load variation commands are sent to the RTDS from the PSDSE application at regular intervals. B. PSDSE Execution In the present work, the readings of the voltage and the power meters, available in the run-time environment of the RTDS, are

considered as the RTU measurements, and the measurements provided by the GTNET PMU are considered as the PMU measurements. Further, the GTNET PMU is configured to provide measurements at the rate of 25 frames per second for the 50-Hz system. The RTDS run-time is also configured to provide one RTU measurement set per second. Hence, between two consecutive RTU measurement sets, 25 PMU measurement sets are reported. The GTNET PMU of the RTDS is configured to provide the measurements of the states, i.e., the voltage magnitude and voltage angles, for the buses where PMUs are installed. This keeps the measurement equation for the PSDSE process linear in nature during the CKF execution of the PMU measurement set between the two consecutive RTU measurement sets [22]. On arrival of the RTU and the PMU measurement set, the PSDSE application first groups the conventional and the PMU data sets based on the time stamp. The CKF based PSDSE [22]

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Fig. 5. WSCC 9-bus system execution snapshot of the run-time environment on the RSCAD.

process is, then, executed using the latest available RTU and the PMU measurements. During the period of the two consecutive RTU measurement sets refresh, the CKF based PSDSE process is executed, normally at the rate of the PMU measurement data refresh, by utilizing the forecasted state estimates of the non-PMU buses and the latest available measurements from the PMU buses [22], as shown in Fig. 3. The details of the PSDSE process can be found in [22]. Using SIL configuration, the PSDSE execution process is repeated for various loading conditions, at various instants, by automatically changing the loads of the test system, running at RTDS. The PSDSE process is executed in SIL, using the CKF, the UKF, and the EKF based approaches, and their relative performance has been compared. V. SIMULATION RESULTS The proposed test and validation methodology for the PSDSE has been demonstrated on the Western System Coordinating Council (WSCC) 9-bus system [26] and the IEEE 30-bus system [27]. The developed RSCAD models of the above test systems are executed on the RTDS with the help of an automated test script to capture the measurement data over the LAN. Generally, the RTDS measurements are much more accurate [5], when compared with the measurements obtained from actual measurement devices installed in fields. To make the RTDS measurements closely resemble real field measurements, Gaussian noise is added to the measurements obtained from the RTDS, using corresponding values of the measurement uncertainties shown in Table I. These measurements are used by the developed MATLAB based application to test and verify the proposed CKF based PSDSE approach. For the sake of comparison, the EKF and the UKF based PSDSE approaches are also executed for the above test systems. The estimated states, obtained from the proposed CKF based PSDSE, the EKF based PSDSE, and the UKF based PSDSE are compared with the actual values of the system states to determine the accuracy of the above approaches. The actual values of the system states at various instants are obtained by running the load-flow repeatedly for those operating conditions, at which the measurements are taken from the RTDS.

To capture measurements continuously from the RTDS runtime environment at various loading conditions, the loads of the test systems are varied randomly by % to %, using automated scripts, to generate various measurement snapshot cases to be used in the PSDSE execution. Accordingly, the readings of the RTUs and the PMUs are captured, and the PSDSE process is executed. The MATLAB and Java based simulations are carried out on Intel Core-i7 3.4-GHz processor based computer with 4 GB of RAM. A. WSCC 9-Bus System To execute the proposed approach using RTDS, the model of the WSCC 9-bus system is developed on the RSCAD, as shown in Fig. 4. The PMU measurements are captured through the GTNET-PMU24 component of the RSCAD. The analog measurements are captured through the analog meters used in the run-time environment of the system, as shown in Fig. 5. The bus no. 5, 6, and 8 are the load buses of the WSCC 9-bus system, as shown in Fig. 4, and considered as having RTUs to report the measurement data. Accordingly, the readings of the analog meters for these buses are captured from run-time environment of the RTDS at a regular interval of every 1 s, and considered as the RTU measurements for the PSDSE. A Java based network packet reading utility is used to read the analog meters in real-time. Using the RTU and the PMU measurements received from the RTDS, the PSDSE is run for the WSCC 9-bus system for 400 times by considering various loading conditions. During the period of 400 simulations, the loads at the buses 5, 6, and 8 are varied randomly by % to % from their base case values. The sliders, available in the run-time environment of the RTDS and shown in Fig. 5, are utilized to change the loads automatically at a regular interval with the help of automated scripts written in the PSDSE application. The loads at these buses are varied after every 25 simulations. Between the two consecutive RTU measurements, 25 PMU measurement sets are also acquired and processed. The PMU measurement data processing is optimized in such a way that it completes the execution of all the 25 PMU measurement data sets before the arrival of the next conventional measurement data. Comparison of the voltage

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Fig. 6. Comparison of voltage angle error for CKF, UKF, and EKF based PSDSE at bus no. 6 of the WSCC 9-bus system.

Fig. 7. Comparison of voltage magnitude error for CKF, UKF, and EKF based PSDSE at bus no. 6 of the WSCC 9-bus system.

TABLE II ERROR COMPARISON OF VARIOUS KF APPROACHES FOR PSDSE WITH RESPECT TO THE ACTUAL VALUES FOR WSCC 9-BUS SYSTEM

angle and magnitude errors for the CKF, the UKF, and the EKF based PSDSE at bus no. 6 in the WSCC 9-bus system are shown in Figs. 6 and 7, respectively. From these figures, it can be seen that, under sudden load change conditions, the error and the rate of change of error in the CKF based PSDSE are lesser than the UKF and the EKF based PSDSE approaches. Table II compares the estimation errors of the CKF, the UKF, and the EKF based dynamic state estimation results, as compared to the actual values of the states for the WSCC 9-bus system. From Table II, it can be seen that the PSDSE using the CKF is more accurate as compared to that with the EKF and the UKF. Table III compares the execution time of the CKF, the UKF, and the EKF based PSDSE approaches. From Table III, it can be seen that, for PMU measurement data refresh rate of 40 ms, all the above three KFs in the proposed PSDSE approach will finish the processing of one PMU measurement data set well before the arrival of next PMU measurement data set. Further, out of the above three KF approaches, CKF is the fastest. On comparing the execution

TABLE III EXECUTION TIME COMPARISON OF VARIOUS KF APPROACHES FOR WSCC 9-BUS SYSTEM

time for the hybrid (PMU as well as RTU) measurement set, it can be seen that the PSDSE completes its execution for the hybrid measurement set, well before the arrival of the next RTU measurement set, which arrives at the rate of 1 s. Again, out of the above three KF approaches, the CKF is the fastest. B. IEEE 30-Bus System Another system considered to demonstrate the effectiveness and validation of the proposed methodology is IEEE 30-bus system [30]. As in the WSCC 9-bus system, for this system also, the PSDSE is executed 400 times by considering various loading conditions. Similar to the WSCC 9-bus system, for this system also, between the two consecutive RTU measurement data simulation time steps, 25 simulation time steps of the PMU measurements are processed. Since the GTNET-PMU of the RTDS can be utilized to provide the measurements of the 24 PMUs, it is assumed that the 24 buses of the IEEE 30-bus system are having PMUs installed to provide the measurements at a

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Fig. 8. Comparison of voltage angle error for CKF, UKF, and EKF based PSDSE at bus no. 12 of the IEEE 30-bus system.

Fig. 9. Comparison of voltage magnitude error for CKF, UKF, and EKF based PSDSE at bus no. 12 of the IEEE 30-bus system.

regular interval. The buses having large size of loads, i.e., the bus no. 2, 5, 7, 8, 26, and 30, are considered as non-PMU buses having RTUs to report the measurement data, to execute the proposed approach on the IEEE 30-bus system. As in case of the WSCC 9-bus system, in this case also, during the period of 400 simulations, the loads at the buses 2, 5, 7, 8, 26, and 30 are varied randomly by % to % from their base case values. The sliders, available in the run-time environment of the RTDS, are utilized to change the loads automatically at a regular interval with the help of automated scripts written in the PSDSE application. In this case also, the loads at these buses are varied after every 25 simulations. The PSDSE is executed by using the EKF, the UKF, and the CKF based approaches, and the state estimation results are compared. Figs. 8 and 9 compare the voltage angle and magnitude errors for the CKF, the UKF, and the EKF based PSDSE at bus no. 12 in the IEEE 30-bus system, respectively. These figures again confirm that, under sudden load change conditions, the error and the rate of change of error in the CKF based PSDSE are lesser than the UKF and the EKF based PSDSE approaches. Table IV compares the estimation errors of the CKF, the UKF, and the EKF based dynamic state estimation results, with the actual values of the states for the IEEE 30-bus system. From Table IV, it can be seen that, in this system also, the CKF based PSDSE is more accurate as compared to that with the UKF and the EKF. Table V compares the execution time of the CKF, the UKF, and the EKF based PSDSE approaches.

TABLE IV ERROR COMPARISON OF VARIOUS KF APPROACHES FOR PSDSE WITH RESPECT TO THE ACTUAL VALUES FOR IEEE 30-BUS SYSTEM

TABLE V EXECUTION TIME COMPARISON OF VARIOUS KF APPROACHES FOR IEEE 30-BUS SYSTEM

From Table V, it can be seen that, for this system also, for the PMU measurement data refresh rate of 40 ms, all the above three KFs in the proposed PSDSE approach will finish the processing of one PMU measurement data set well before the arrival of next PMU measurement data set. Further, out of the above three KF approaches, CKF is the fastest. On comparing the execution time for the hybrid (PMU as well as RTU) measurement set, it can be seen that, in this case also, the PSDSE completes its

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execution for the hybrid measurement set, well before the arrival of the next RTU measurement set, which arrives at the rate of 1 s. Out of the above three KF approaches, the CKF is the fastest. VI. CONCLUSION The main contribution of this paper is to model, test, and validate the PSDSE approach, developed by the authors in [22], under the real-time environment. A new SIL scheme is developed, in this work, to execute the proposed methodology with the RTDS in the closed-loop and synchronized manner. It has applied the CKF for the estimation of system states. The effectiveness of the CKF based PSDSE approach has been established by comparing the results with the EKF and the UKF based approaches on WSCC 9-bus and the IEEE 30-bus systems. The simulation results show that the proposed test and validation methodology of the PSDSE can help in selecting the correct approach, which can ensure the utilization of all the available RTU and the PMU measurements in a time bound manner. It also shows that the PSDSE can be used for the online visualization of the power system states under the real-time operating conditions. Therefore, the proposed approach may be utilized as a benchmark for the testing and validation of the performance of various DSE algorithms under a real-time environment. Comparison of the simulation results of the proposed PSDSE approach based on the EKF, the UKF, and the CKF, reveals that, being reasonably fast under the given time constraints of the conventional and PMU measurements data refresh rate, i.e., 1 s and 40 ms, respectively, and being more accurate and stable under sudden load change conditions, the CKF based PSDSE approach is better suited than the EKF and the UKF based PSDSE approaches. ACKNOWLEDGMENT The authors would like to thank RTDS Inc. for their technical support. REFERENCES [1] F. C. Schweppe and J. Wildes, “Power system static state estimation, part I: Exact model,” IEEE Trans. Power App. Syst., vol. PAS-89, no. 1, pp. 120–125, Jan. 1970. [2] F. C. Schweppe and D. B. Rom, “Power system static state estimation, part II: Approximate model,” IEEE Trans. Power App. Syst., vol. PAS-89, no. 1, pp. 125–130, Jan. 1970. [3] F. C. Schweppe, “Power system static state estimation, part III: Implementation,” IEEE Trans. Power App. Syst., vol. PAS-89, no. 1, pp. 130–135, Jan. 1970. [4] IEEE Standard for Synchrophasor Measurements for Power Systems, C37.118.1-2011, Dec. 2011, IEEE Std. [5] Real Time Digital Simulator (RTDS) [Online]. Available: http://www. rtds.com/ [6] R. M. Reddi and A. K. Srivastava, “Real time test bed development for power system operation, control and cyber security,” in Proc. North Amer. Power Symp. (NAPS), 2010, Sep. 26–28, 2010, pp. 1–6. [7] F. Shariatzadeh, C. B. Vellaithurai, S. S. Biswas, R. Zamora, and A. K. Srivastava, “Real-time implementation of intelligent reconfiguration algorithm for microgrid,” IEEE Trans. Sustainable Energy, to be published. [8] T. S. Sidhu, R. K. Varma, P. K. Gangadharan, F. A. Albasri, and G. R. Ortiz, “Performance of distance relays on shunt-FACTS compensated transmission lines,” IEEE Trans. Power Del., vol. 20, no. 3, pp. 1837–1845, Jul. 2005.

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SHARMA et al.: TESTING AND VALIDATION OF POWER SYSTEM DYNAMIC STATE ESTIMATORS USING REAL TIME DIGITAL SIMULATOR (RTDS)

S. C. Srivastava (SM’91) received the Ph.D. degree in electrical engineering from the Indian Institute of Technology Delhi, India. He is currently a Professor in the Department of Electrical Engineering, Indian Institute of Technology Kanpur. His research interests include energy management systems, synchrophasor applications, power system security, stability, and technical issues in electricity markets. Prof. Srivastava is a Fellow of INAE (India), IE (India), and IETE (India).

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S. Chakrabarti (S’06–M’07–SM’11) received the Ph.D. degree in electrical engineering from Memorial University of Newfoundland, Canada, in 2006. Currently he is working as an Associate Professor in the Indian Institute of Technology Kanpur, India. His research interests include power system dynamics and stability, state estimation, and synchrophasor applications.