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Power System Tracking and Dynamic State Estimation by Amit Jain, Shivakumar N. R. in IEEE PES Power Systems Conference Exposition (PSCE) 2009 Report No: IIIT/TR/2009/213 Centre for Power Systems International Institute of Information Technology Hyderabad - 500 032, INDIA March 2009 POWER SYSTEM TRACKING AND DYNAMIC STATE ESTIMATION Amit Jain, Member, IEEE and Shivakumar N. R. Abstract-- State estimation is a key Energy Management System (EMS) function, responsible for estimating the state of the power system. Since state estimation is computationally expensive, it is not easy to execute it repetitively at short intervals, which is a requirement for real time monitoring and control. Hence in order to obtain a computationally inexpensive real time update of the state vector, tracking state estimation algorithms have been proposed and discussed in various research papers available in the literature. Tracking state estimation provides a fast real time update on the state of the power system with out any physical modeling of the time varying nature of the system. Dynamic state estimation models the time varying nature of the system, which allows it to predict the state vector in advance. Hence proves to be a major advantage in security analysis and other control functions. Various techniques for tracking and dynamic state estimation are available in the literature. This paper presents a bird’s view on different methodologies and developments in both of these techniques based on our comprehensive survey of the available literature. Index Terms -- Dynamic state estimation, kalman filter, phasor measurement unit, power systems, square root filter, state estimation, tracking state estimation. A I. INTRODUCTION S the power system grows larger and more complex, real time and monitoring and control becomes very significant in order to achieve a reliable operation of the power system. The energy management system functions are responsible for this task of monitoring and control. State estimation forms the back bone of the energy management system by providing a real time data base of the state of the system for using in other EMS functions [1]. Hence an efficient and accurate state estimation is a pre requisite for an efficient and reliable operation of the power system. The vector consisting of bus voltage magnitudes and phase angles is called the state of an electric power system. Ever since the concept of state estimation was introduced in to the field of power systems, by Schweppe et al [2]-[4], in the early 1970s, numerous methods have been proposed to calculate the state vector of the power system. The state estimation for Dr. Amit Jain is an Assistant Professor with the Power System Research Center at the International Institute of Information Technology (IIIT), Gachibowli, Hyderabad, India (e-mail: [email protected]). Shivakumar N. R. is currently with ABB, Corporate Research in Bangalore, India. (e-mail: [email protected]) a power network involves, collecting the real time measurement data, which includes line flows, injection measurements and voltage measurements, through the SCADA and calculating the state vector, using predefined state estimation algorithms. If the state vector is obtained for an instant of time k, from the measurement set of the same instant of time, then such an estimator is called the static state estimator. In order to know the state of the power system regularly, this process of calculating the state vector is repeated at suitable intervals of time. Static state estimators are widely used in power systems and play a very important role for the reliable operation of the transmission and distribution systems. Under normal conditions, power system is said to be a quasi-static system and hence changes slowly but steadily. Hence in order to have a continuous monitoring of the power system, state estimation must be performed at short intervals of time. But as the power system expands, with addition of generations and loads, the system becomes extremely large for the state estimation to be carried out at short intervals of time as it consumes heavy computing resources. Hence a new technique called “Tracking State Estimation” was developed, wherein the state estimate once calculated, is simply updated for the next instant of time, with new set of measurement data obtained for that instant, instead of again running the static state estimation algorithm fully. Tracking estimators help the EMS to keep track of the continuously changing power system without actually performing the whole state estimation. This allows continuous monitoring of the system, without excessive usage of the computing resources. Hence tracking state estimation plays an important role in the energy management system. The simplest way of following the changes in the system is tracking. But tracking does not include any explicit physical modeling of the time behavior of the system [5]. This allows room for another set of algorithms called the “Dynamic State Estimators” (DSE), where the actual physical modeling of the time varying nature of the system is used. These algorithms have dual advantages of being more accurate and possessing the ability to predict the state of the system one step ahead. That is, from the knowledge of the state vector at an instant of time “t”, and the physical model of the system, the DSE predicts the state of the power system at the next instant of time “t+1”. This forecasting ability has tremendous advantages in performing security analysis and allows more 978-1-4244-3811-2/09/$25.00 ©2009 IEEE Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply. time for the operator to take control actions [5]. Hence DSE algorithms form an important branch of state estimation techniques, with a potential to impact the very nature of operation of the real time monitoring and control. This paper presents a review of the developments in tracking and dynamic stat estimation techniques based on our survey of research papers available in literature on these topics. In our knowledge, no such comprehensive survey has been done for the review of tracking and dynamic state estimation techniques and any work in that direction will be of great importance to the power engineers working on these topics. We have done a comprehensive survey of the literature available on tracking and dynamic estimation techniques and in this paper an attempt has been made to give an overview of the various algorithms, their applications and future trends, on these topics. process all the measurements at one go i.e. the measurements are read in to the state estimation program as one vector. This method is called the snap shot processing of measurements. But if the rate of processing the measurements is greater than τ, then by the time the entire set of data of data is scanned, the power system would have changed, rendering the estimate redundant. Hence we process the measurements as and when they arrive in to the control center and update the estimate. This method is called the sequential processing of measurements [5], [7]. II. TRACKING STATE ESTIMATION As mentioned earlier, the power system is considered to be a quasi static system. Hence the changes in the system occur slowly. It means that the state may not vary much in a short span of time. But some times it becomes very important to have a close monitoring of the system, like during the picking up of load by a generator or during some contingency etc [5]. The SCADA systems, which enable the real time monitoring, and control of power systems capture the field data through sensors and deliver them to the control center at regular intervals of time. In order to have a real time monitoring system, state estimation must be performed as and when every new data set arrives. But as state estimation is computationally heavy (especially as the system size gets bigger), a lot of control centers will not have sufficient computing resources to perform an accurate and fast state estimate at such a high frequency. But if the duration between two estimates is too large, it results in a week co-relation between the estimated states, rendering the bad data detection very difficult [5]. Hence tracking state estimation is used to in order to give the estimation result with a delay and to keep up with the result [6]. The difference between the static and tracking estimators can be understood by the block diagram [7] shown in Fig. 1. F. C. Schweppe, who is a pioneer in the development of static state estimation techniques [2]-[4], was also one of the first to discuss the idea of tracking state estimation in his paper in 1970 [8]. Tracking state estimator merely adds to the existing value of the state vector to give the estimate at a delayed instant and does not need the full execution of the state estimation algorithm at that instant. Hence tracking allows easy and fairly accurate monitoring of the power system in real time. A. Processing of Measurements The measurements that arrive in the control center through the SCADA system can be processed using two methods. If the rate of scanning an entire set of measurements at a given point of time is lesser than the minimum amount of time the power system takes to change its state (τ), then we can Fig. 1. Comparison between static and tracking state estimators B. Mathematical modeling The measurements obtained through the SCADA system include, injection measurements, line flow measurements, voltage and some times current magnitude measurements. These measurements have to be represented by a mathematical model in order to be processed by the estimation algorithm. The measurement vector is represented as: (1) Z = Hx +ν Where Z is the measurement vector (m x 1), H is the Jacobian of measurement function with respect to the state vectors (m x n), “x” is the state vector (n x 1) and “ν” (m x 1) is the zero mean Gaussian error factor in the measurement. Here “m” is the number of measurements and “n” is the number of states. Since the tracking state estimation, unlike the static state estimation has a time factor attached with it, we next have to consider the mathematical model for the time update of the state vector. As we have assumed that the power system state changes very little in a short span of time, we can simply update the old estimate of the state (at the previous instant of time) to obtain the new value of state at an instant, after a short span of time interval. For small time frames, the state is assumed to change linearly and hence if we know the estimate ( xˆk ) at the instant of‘t’, and with the arrival of measurements at t+1’ (t+1 = t + Δ t), we can simply update xk , as: xˆ k +1 = xˆk + Δx (2) Here Δx represents the change in the state due to the changes, power system undergoes during the time interval between ‘k’ and ‘k+1’ instants. The formula for Δx depends on the Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply. method used for tracking state estimation. If a simple WLS method is used, then it is given by: Δx = Gk−1 H kT R −1[Z k +1 − h( xk )] (3) Substituting this in equation (2), we get: xˆ k +1 = xˆk + Gk−1 H kT R −1[ Z k +1 − h( xk )] (4) −1 Where G = [ H k R H k ] is called the Information Matrix, T which remains constant. Hence the computationally heavy G matrix and its inverse are calculated only once, while the estimate is updated as and when the new measurements arrive. It can clearly be seen, that tracking estimation allows an easy update to the existing state vector without much computationally complex operations. Tracking estimation plays its role in between any two predefined execution instants of static estimation. That is, the static state estimation will be performed in the control center at regular intervals or when there is sufficient change in the power system. But these two instants are separated by a large amount of time. Tracking estimation helps the control station to monitor the power system in between these two instants of time. More over, as seen in the equations above, tracking helps to get a real time update of the system with out actually performing the entire state estimation. The concept of tracking views the estimator as a digital feedback loop which uses the new measurements to obtain new estimates, by correcting an old estimate by a feed back gain signal, operating through a gain matrix [8]. C. Methods of calculating Δx Various methods have been proposed to calculate the update vector or the Δx vector. The WLS method, which is one of the widely used techniques of calculating the update vector is as discussed above. In EHV networks, the decoupled nature of the power system states has been widely used to simplify calculations in the static state estimation. It can be easily extended to tracking state estimation as well. In such a case the Δx vector will be split in to two parts, the active part representing the voltage angles and the reactive part representing the voltage magnitudes. This is shown as below [6]. (5) Δθ k = [ H PT R −1 H P ]H PT RP−1[ Z P − h( xk )] ΔVk = [ H RT R −1 H R ]H RT RR−1[ Z R − h( xk )] (6) Where the suffix ‘P’ represents the active set and suffix “R” represents the reactive set. Decoupled estimators are faster, but somewhat less accurate, although reasonably good, in comparison with the fully coupled estimation algorithms. E. Handschin et al [9] suggested associating lesser weight values to measurements with large residuals, to improve the performance of the bad data in state estimation. D. M. Falco et al [6] have suggested that this method can also be successfully extended to tracking state estimation to improve the performance under the presence of bad data. Linear Programming (LP) techniques used in static state estimation are suggested for tracking state estimation as well. In [6], the authors extend one of the LP methods available in literature where, the sum of the moduli of measurement residuals is minimized. Though the filtering capacity of this technique is not as good as WLS, it performs better under the presence of bad data and hence much more robust. W. W. Kotigua [10] discusses Least Absolute Value based tracking algorithm. LAV estimation has the property that the final estimates interpolate a few of the measurements. Hence it has better bad data rejection properties. More over, because of its interpolating feature, the tracking estimator can be updated easily based on the situation, whether interpolated measurements or non-interpolated or both measurements have changed. If only non-interpolated measurements have changed, then the update involves some simple additions else it involves some calculation. Nevertheless the calculation can still be carried out faster as the Jacobian matrix in this case is a very sparse. S. C. Tripathy et al [11] have used the Hessian matrix approach to update the state vector. Where Δx is given by: Δx = M k−1H kT R −1[ Z k +1 − h( xk )] (7) One can clearly see that the information matrix G is replaced by M, which is called the true Hessian matrix. The authors use the Brown Dennis method to obtain the true Hessian matrix. Improved convergence even in case of multiple loss of information or when only injection measurements are used is the advantage of using this particular technique. A.K. Sinha et al [12] proposed a tracking estimator for both AC and DC systems, which uses the Tailor’s series expansion of “h(x)” up to the second order term. This is a constant gain matrix technique (for a given topology) and hence helps in faster convergence Another important technique is the method of tracking by sequential processing of data. As discussed before, when the time to scan all measurements is greater than the time for the system to change its state, then some of the previously mentioned techniques (snap shot techniques) fail to track the system accurately. A sequential time scanning based tracking estimator is needed for that purpose. The expression for time update of the system in such a scheme is given by [5]: xˆ k +1 = xˆk + K k +1[ Z k +1 − h( xk )] (8) −1 Where, K k +1 = Pk H k +1{H k +1 Pk H k +1 + Rk +1} T T (9) Where, Pk is Information Matrix at the instant of time k, Hk+1 is a row vector of partial derivatives corresponding to measurement Zm+1, R is the error covariance of the measurement corresponding to Zm+1 and K is the gain vector. The advantage of this scheme is that, it allows faster update of the system than the snapshot processing by converting the inversions involved in the update equations to scalar inversions. Hence this technique is very well suited for online implementation. Various methods of tracking state estimation for power systems and their uses have been discussed so far. A brief summary of the advantages of tracking state estimators is as below: • Continuous tracking of the system helps the system operator to take better decisions, in case of an emergency. Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply. • • • Techniques proposed are computationally lighter and hence can be easily implemented online Some of the tracking estimation techniques proposed, perform well even under loss of information, bad data or ill conditioning hence make the system more robust. If scanning of measurements takes longer time (especially in large networks) sequential processing techniques can be used to obtain real time update of the system. III. DYNAMIC STATE ESTIMATION An easy way of following the changes in a power system on a real time basis is by using the tracking state estimation techniques. But these techniques, though computationally very efficient, do not use any physical modeling of the time varying nature of the power system [5]. Hence may not be as accurate as desirable. Lack of any physical modeling also results in one of the main drawbacks of a tracking state estimator, which is the lack of the ability to predict the state vector in advance. Dynamic state estimation uses the present (and some times previous) state of the power system along with the knowledge of the system’s physical model, to predict the state vector for the next time instant. This prediction feature of the DSE provides vital advantages in system operation, control, and decision-making. It allows the operator more time to act in cases of emergency, helps in detection of anomalies, bad data etc [5]. The main steps involved in DSE algorithms to achieve an optimized estimate of the state vector are presented below. Throughout the discussion, “k” is used to suggest the present instant of time and “k+1” to suggest the next instant of time. A. Mathematical Modeling This is the first step in DSE and involves the identification of correct mathematical model for the time behavior of the power system and calculation of the corresponding parameters. The general mathematical model used for a dynamic system is given by [1], [13]: xk +1 = f ( xk , uk , wk , k ) (10) Where, k is the time sample, x is the state vector, u is the control actions, w represents the uncertainties in the model and f represents the non-linear function. But such a model is extremely complex, costly and impractical. Hence certain assumptions are made to ease the implementation (some have already been mentioned earlier). They are: • The system is quasi static and hence changes extremely slowly. • Time frames considered are small enough, for the usage of linear models to describe the transition of states between consecutive instants of time • The uncertainties are described using white Gaussian noise with zero mean and constant covariance Q. Considering these assumptions, we can obtain a generic linear model for the DSE as: xk +1 = Fk xk + Gk + wk (11) Here Fk is the function representing the state transition between two instants of time, Gk is associated with the trend behavior of the state trajectory and wk is the white Gaussian noise with zero mean and covariance Q [1], [13]. B. Parameter Identification Fk, Gk and Q are the parameters to be calculated online to evaluate the dynamic model shown in (11). Debs and Larson [13], credited with the seminal paper on DSE, and Nishiya et al [14] have assume a simple linear model with Fk assumed to be an identity matrix and Gk assumed to be zero. But this makes the estimator very simplistic and hampers the forecasting ability of the estimator [1]. In the model proposed by Debs and Larson [13], the change in state vector is considered to be so small that it is replaced by a zero mean, white Gaussian noise. Hence the equation (11) reduces to: xk +1 = xk + wk (12) Other authors in [15]-[17] etc have also used similar mathematical models for describing time update of the state vector. Linear Exponential Smoothing (LES) technique has also been found to be a widely used technique for this purpose. Authors in [5], [17], [18] and [19]-[23] have all used the Holt’s LES technique [24] to obtain the values of Fk and Gk. In this case the equation (11) is reduces to a form: xk +1 = Fk xk + Gk (13) The next parameter to be identified is the error covariance Q. Under normal operating conditions of a quasistatic power system, the Fk and Gk are adjusted such that the value of Q almost remains constant or varies with in a very small range of values or at a constant noise level. This value of Q can be obtained by offline simulation studies [5], [22]. The other parameter to be modeled is the measurement function, which helps to observe the system. The most common measurement model used in the literature is: (14) Z = h( x ) + ν Most of the techniques linearise the above measurement model and use the equation after linearization as shown in (1). C. State Prediction or State Forecasting State forecasting is the next step in DSE where, the nodal voltages or the measurements at the next instant of time are predicted. State vector corresponding to these predicted values is called the predicted state at the instant k+1. The forecasted state vector is obtained by performing a conditional operation on equation (11) [5], [22]. The forecasted state vector, along with its error covariance is given by: xk +1 = Fk xˆk + Gk (15) Where, x is the predicted value at instant k+1. If Σ k is the covariance of the estimate at k, then the covariance of predicted value is given by: M k +1 = Fk Σ k FkT + Qk (16) Many other techniques can be used to predict the state vector. Some authors have also used Artificial Neural Networks (ANN) and Fuzzy Logic techniques [19], [20] to predict the future values of parameters. Other techniques like Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply. auto regression and Box & Jenkins method have also been used as mentioned in [1]. D. State Filtering Once the predicted state vector for the next time instant (k+1) is obtained, it can be purified as and when the measurements arrive at the instant “k+1”, to obtain an optimized and a higher quality estimate for the instant k+1. The most commonly used filtering technique is the kalman filter technique [13], [25]. Since the measurement vector is non linear in nature, Extended Kalman filter is used in most cases. As the predicted state vector is used for obtaining the final estimate in DSE, the objective function is taken as a sum of measurement residuals and the predicted state vector residuals. Hence, the objective function becomes: J ( x) = [ z − h( x)]T R −1[ z − h( x)] + [ x − x ]T M −1[ x − x ] (17) Where, M is the covariance of the predicted state vector. Minimizing this objective function will yield an expression for the update of the state vector as: (18) xˆk = xk +1 + K k +1[ Z k +1 − h( xk +1 )] Where K = ΣH T R −1 = [ H T R −1 H + M −1 ]−1 H T R −1 (19) Here H is the Jacobean of h(x) evaluated at xˆ k , ∑ is the covariance of the estimated state vector and M is the covariance of the predicted state vector. The term K is called the Kalman gain, which acts as the gain matrix for the measurement residuals at instant k+1. The measurement update is carried out either for the entire measurement set or for each such sequential measurement. Once all the measurements at that instant have been processed, the entire procedure (time and measurement update) is repeated again, by replacing time instant k with k+1. The authors in [5], [13]-[16], [19], [21]-[23], [26] and [27] have all used the Kalman filter or techniques based on Kalman filter for their DSE algorithms. Other techniques have also been proposed and implemented in the literature, though Kalman filter techniques seem to dominate in most of the DSE algorithms. As shown in Eq. (18), the filtering step improves up on the predicted values to obtain an accurate estimate with the help of measurements at the instant k+1. The equation (18) is quite similar to the tracking state estimator equation. But the essential difference between the two is that, on the RHS we have xk +1 (the predicted state vector) being improved up on instead of xˆ k (state vector at previous instant) as in case of tracking state estimation. Hence it is the ability to predict the state vector, which differentiates the dynamic and tracking state estimators. The advantages of using a predicted state vector in filtering are that it provides additional measurement redundancy, reduces the effects of bad data and reduces uncertainty levels of the final estimated values [1]. IV. ALTERNATIVE FORMULATIONS OF DSE So far the basic dynamic state estimation technique available in the literature has been presented. Now we can look various other techniques, which try to improve up on the existing technique or have provided a new direction to it. As discussed earlier, the nonlinear measurement function is approximated to a linear model in the conventional DSE. Hence to take care of the error arising due to this, J. K. Mandal et al in [27] have proposed two schemes to incorporate non linearities in to the kalman filter based DSE. In the first method, local iterations are carried out during the calculation of measurement residuals, at each time sample. This increases the reference trajectory and hence gives a better estimate in presence of nonlinearities. In the second scheme the Tailor’ series expansion of the measurement function is retained until the second order in rectangular co ordinates. This helps in retention of full nonlinearity as the measurement function is related to state vector through nonlinear quadratic functions [27]. Another method of tackling the problem of non-linearities has been proposed by Sakr. M. M.F et al in [28], [29]. Here instead of linearising the measurement vector, a nonlinear transformation of the measurement vector is carried out. This transformation is carried out at each node in three different steps. Once the transformation is completed, the measurement vector will be related to the state vector by a constant, sparse matrix, and all linearization errors would be nullified. This method is also extremely useful in anomaly detection. The above technique has one difficulty that the measurement covariance matrix (R) is non sparse and hence computationally intensive. Hence the authors propose another method called a two level estimation technique [15]. Here, in the first level, called the low level estimation, the overall network is divided in to several small sub systems, which have small number of buses, and hence there will be no computation problems related to calculation of R. The next level of estimation, called the upper level estimation, is only for coordination among the various sub systems to obtain a single state vector for the entire system. This technique is comparable to single level estimator in accuracy, but is much faster and in most cases the algorithm converges in the first iteration. The Kalman filter method has another disadvantage that it cannot handle large changes in the load and generation. Hence, K. R. Shih and S. J. Huang in [17], [21] have proposed an algorithm where the weight vector Wk is replaced with the term Wk e −| z − h ( xk )| . If the load variation is large, the weight associated with that measurement automatically gets reduced as the term ‘|z-h(x)|’ appears as a negative exponential term. Under normal conditions, the value of the residual remains insignificant, making exponential term close to 1 and allowing normal weights for the measurements. Another interesting Kalman filter based DSE technique, described and analyzed by Da Silva et al in [23], can be found in [30] and [31]. The technique is primarily used by Da Silva et al to compare the results of their proposed technique in [23] with those in [30] and [31]. This technique uses a model Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply. based on equation (13), to represent the time variation of the system. To reduce the dimension of the problem, Fk is assumed diagonal and its elements are used to define a parameter vector ck . A model for time evolution of ck is defined based on the measurement model. Then the Kalman filter technique is used to find out, the value of ck . Once ck is found, we can calculate the value of Fk based on which the State-forecasting step is carried out. Once the predicted state vector is obtained, the Kalman filter technique is applied in order to filter the predicted state vector and obtain the estimated state vectors. So far we have looked at Kalman filter based techniques, But Isabel et al in 1994 proposed a Square Root Filter (SRF) for DSE instead of Kalman filter [18]. They used the linear exponential smoothing for calculating the predicted state vector and used the SRF for filtering the predicted state vector and obtaining the optimized state vector. The SRF technique reduces the uncertainty level in measurements, saves time and computer memory as compared to the traditional kalman filter technique. The kalman filter based techniques assume Gaussian distribution of noise. But frequently, the noise distribution deviates from the assumed model resulting in outliers. The performance of kalman filter based techniques degrades in the presence of these outliers. Hence, to counter this, G. Durgaprasad et al [32] and S. S. Thakur et al [33] have come up with a robust dynamic estimation technique based on Mestimation. The modeling is based on the assumption that the complex bus voltage at a given point is not only dependent on the previous voltage level but also on the latest available voltage change at the buses to which it is connected. The two essential features based on which the technique has been developed are realistic modeling based on nodal analysis and M-estimation to have robust filtering. The M-Estimation technique reduces the uncertainty level under bad data conditions, uses a filtering technique which is more effective in presence of outliers and is also easy to implement in comparison to the conventional kalman filter based techniques. The ability of artificial intelligence techniques in prediction and pattern recognition can be put to good use in DSE. A. K. Sinha and J. K. Mandal [19] have proposed an Artificial Neural Network (ANN) based DSE algorithm which is based on the popular Short Term Load forecasting (STLF) technique. Since the bus loads are the driving factors of system dynamics, ANN is used to predict the loads at all buses. From these values the generations at various buses is also calculated. Once the injections at various buses are known, it is transformed in to complex bus voltages through load flow solution. These predicted state vectors are in turn used in the filtering stage to obtain accurate state estimates. To counter the linearization errors in Kalman filter based techniques, the nonlinearities in the measurement were taken in to account. But this resulted in increased computation time. Hence to overcome these problems a sliding surface enhanced Fuzzy logic based technique has been proposed by Jeu-Min Lin et al in [20]. The sliding surface enhanced fuzzy control approach to DSE is found to have a higher computational performance than other methods. V. PMU BASED DYNAMIC STATE ESTIMATION In the past two decades a new measuring device called the Phasor Measurement Unit (PMU) has been developed. Its advantage lies in the fact, that it can measure both voltage and current phasors at the installed bus. More over, PMU measurements are much more accurate than the normal SCADA measurements. The importance of PMUs can be gauged by the fact that for the first time both voltage magnitude and voltage angular measurements could be obtained directly from PMU. With their high accuracy of measurement and their ability to directly measure the voltage phasor, the PMUs are destined to play an important role in modern day state estimators. Hui Xue et al. [34] have proposed a technique which predicts the load flow data at the next instant of time by a historical data base and combines the PMU data at the next instant of time for dynamic state estimation of power systems. Another method presented by the authors in [35], [36] uses the model proposed by Leite da Silva et al. [23] for the implementation of PMU based DSE. The DSE technique uses the Holts double exponential smoothing technique for predicting the state vector one timestamp ahead and the extended Kalman filter technique for filtering. To understand the impact of the PMUs on the DSE, it is important to understand how the location and the weightage associated with the PMU measurements affect the estimation procedure. From the literature it can be seen that PMU measurements are in general, given a weightage of a few hundred times the normal SCADA measurements. Hence, in the study presented [35], PMU measurements are given a weightage of around 100, 200, 400 and 1000 times the normal SCADA measurements and tested for their effect on the estimation process. The other implementation and simulation details can be found in [35]. The paper [35] clearly shows that the PMU based DSE greatly reduces the estimation errors in comparison to the case of DSE with no PMU. To obtain a clear of view of how the addition of PMU affects the error percentages in the predicted and filtered states, the results of the study on the variation of the average estimation error when PMU was placed at each bus of the system with the weight of PMU measurements being fixed at 100, is as shown in Fig. 2 and Fig. 3. From the graphs shown in Fig. 2 and Fig. 3, it is seen that in most of the cases the error in the predicted angular estimates of the PMU based DSE is much lower than the filtered values of no PMU case. This again has a direct impact on the security analyses performed at the control center, since better quality of predicted estimate means more accurate prediction of security risks and hence, enables better risk evading strategies. The results also show that location of the PMU is important to obtain a better estimate. Though a PMU at any location provided more accurate estimate than the case when there was no PMU, there are certain PMU locations in the network, Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply. which seem to provide much higher reduction in error than at any other bus in the network. Better PMU placement algorithms can be followed to quickly find out the optimal location of PMU, especially in the case of large networks. • It allows security analysis to be carried out in advance and hence allows the operator to have more time during emergencies. • It helps to identify and reject bad data and hence improves the estimator performance. • In cases where pseudo measurements are to be used, DSE readily provides high quality values and hence avoids ill conditioning. • DSE can be used for data validation, as the states are predicted one time stamp before. Similarly, with the help of the predicted state vector we can identify sudden changes in the system, topological errors and other anomalies. VII. Figure 2. Variation of predicted and filtered voltage magnitude estimate errors, when weight of PMU is fixed at 100 Figure 3. Variation of predicted and filtered voltage angular estimate errors, when weight of PMU is fixed at 100 Simulation studies with multiple PMUs have also been presented in [35]. An important observation in the study of multiple PMUs is that the reduction in error with increase in the number of PMUs seems to saturate after a particular point. Though a great reduction in estimation error can be obtained from a few PMUs, the optimal number of PMUs for a given network should ideally be chosen from the point of view of both state estimation accuracy and observability of the network. This helps to improve the ability of the estimator to detect bad data in the measurement set, especially in critical SCADA measurements. Since DSE can play a major role in monitoring and risk prediction with their unique ability of predicting the state vector one time stamp ahead, their association with phasor measurement units is a great advantage for real time monitoring, detection and control of power systems. From this point of view the PMU based DSE techniques are of extreme importance for the modern day energy management systems. VI. ADVANTAGES OF DYNAMIC STATE ESTIMATION The ability of predicting the state vector one step ahead is a very important advantage of DSE. Some of the advantages of that includes: CONCLUSIONS Real time monitoring and control of power systems is extremely important for an efficient and reliable operation of a power system. Sate estimation forms the backbone for the real time monitoring and control functions. Since a repeated operation of state estimation functions with in short intervals of time is computationally expensive, tracking estimation has been conceived to update the state vector at instant of time. In tracking estimation the changes in the system between two successive instants of time is assumed to be extremely small and hence the state vector is simply updated by an amount proportional to the measurement residual at every instant. Various techniques proposed in the literature to improve the computability, accuracy and the ease of implementation have been discussed. Certain techniques also help in better detection of bad data, anomalies and perform well even under the presence of ill conditioning. Since power system changes continuously, the operator has to be extremely alert in taking decisions on real time, especially in cases of emergency. In such a scenario a technique which can predict the possible state of a power system in the immediate future is a boon. Though tracking monitors the power system continuously, it lacks any physical modeling of the system and hence no realistic prediction of the states can be obtained. Hence researchers have proposed dynamic state estimation techniques, which provide the predicted state vector at the next time instant to the operator, with which the operator will be able to take any suitable control actions. Once the measurements at the next instant arrive, the predicted state vector is filtered to obtain an optimized estimate. Various DSE techniques proposed in the literature, their advantages, disadvantages and specialties if any, have been briefly described in this paper. Keeping in mind the importance of a review paper for future research in the area, a comprehensive survey of the available literature on tracking and dynamic state estimation techniques has been presented. It is sincerely hoped that this will help the community of power engineers to further research on tracking and dynamic state estimation topics. VIII. REFERENCES [1]. M. B. Do Coutto Filho, J. Duncan Glover, A. M. Leite da Silva, “State estimators with forecasting capability”, 11th PSCC Proc., Vol. II, pp.689-695, France, August 1993. Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply. [2]. F. C. Schweppe, J. Wildes, and D. Rom, ‘Power system static state estimation, Power Syst. Eng. Group, M.I.T. Rep. 10, Nov. 1968 [3]. F. C. Schweppe and J. Wildes, “Power system static-state estimation, part I: Exact model,” IEEE Trans. Pourer App. Syst., vol. PAS-89, pp. 120125, Jan. 1970. [4]. F. C. Schweppe and D. B. Rom, “Power system static-state estimation, part 11: Approximate model,” IEEE Trans. Power Apparatus and Systems, Vol. PAS-89, pp. 125-130, Jan. 1970. [5]. Sunita Chohan, “Static and Tracking State Estimation in Power Systems with Bad Data Analysis”, PhD Dissertation, Centre for Energy Studies, IIT-Delhi, July 1993. [6]. D. M. Falco, P. A. Cooke, A.Brameller, “Power System Tracking State Estimation And Bad Data Processing”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-101, No. 2 February 1982 [7]. E. Handschin, "Real-Time Data Processing Using State Estimation in Electric Power Systems", in Real-Time Control of Electric Power Systems, E. Handschin, Ed., Elsevier, Amsterdam, 1972. [8]. R. D. Massiello and F. C. Schweppe, “A Tracking Static State Estimator” , IEEE Trans. PAS, March/April 1971, pp 1025 -1033 [9]. E. Handschin, F. C. Schweppe, J. Kohlas, A. Fiechter, "Bad Data Analysis for Power System State Estimation", IEEE Trans. Power App. Syst., vol. PAS-94, pp.329-337, Mar/Apr.1975. [10]. W. W. Kotiuga, “Development of a Least Absolute Value Power System Tracking State Estimator”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 5, May 1985. [11]. S. C. Tripathy, S. Chohan, “On Line Tracking State-Estimation in Power Systems”, IE (I) Journal-EL, 1992. [12]. A. K. Sinha, L. Roy, H. N. P. Srivaetava, “A New and Fast Tracking State Estimator for Multi terminal Dc/Ac Power Systems”, TENCON '89. Fourth IEEE Region 10 International Conference, Page(s): 949-952. [13]. Atif. S. Debs and Robert. E. Larson, “A Dynamic Estimator for tracking the state of a Power System”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS 89, NO.7, September-October, 1970. [14]. K. Nishiya, J. Hasegawa and T. Koike, “Dynamic State Estimation including anomaly detection and identification for power systems”, IEEE PROC, Vol 129, Pt. C, No. 5, September 1982. [15]. A. Bahgat, M. M. F. Sakr, A. R. El-Shafei, "Two level dynamic state estimator for electric power systems based on nonlinear transformation", IEE Proceedings, Vol. 136, Pt. C, No. I, JANUARY 1989. [16]. Husam. M. Beides, G. T. Heydt, “Dynamic State Estimation of Power System Harmonics Using Kalman Filter Methodology”, IEEE Transactions on Power Delivery, Vol. 6, No. 4, October 1991. [17]. K. R. Shih and S. J. Huang, “Application of a Robost Algorithm for Dynamic State estimation of a Power System”, IEEE Transactions on Power Systems, Vol. 17, No. 1, February 2002. [18]. Isabel. M. F and F. P. Macel Barbosa, “Square Root Filter Algorithm for Dynamic State Estimation of Electric Power Systems”, Proceedings, Electro technical Conference, 7th Mediterranean, vol.3. Pages 877-880, April 1994. [19]. S. K. Sinha and J. K. Mandal, “Dynamic State Estimator Using ANN based Bus load Prediction”, IEEE Transactions on Power Systems, Vol. 14, No. 4, November 1999. [20]. Jeu-Min Lin, Shyh-Jier Huang, and Kuang-Rong Shih, “Application of Sliding Surface Enhanced Fuzzy Control for Dynamic State Estimation of a Power System”, IEEE Transactions On Power Systems, VOL. 18, NO. 2, MAY 2003. [21]. S. J. Huang and K. R. Shih, “Dynamic-state-estimation scheme including nonlinear measurement-function considerations”, IEE PROC. Generation, Transmission and Distribution, Vol 149, No. 6, November 2002. [22]. A. M .Leite da Silva, K. B. Do Ceutto Filho, J.M.C. Canterra, “An Efficient Dynamic State Estimator Algorithm Including Bad data Processing”, IEEE transactions on Power Systems, Vol PWRS-2, No.4, and November 1987. [23]. A. M. Leite da Silva, M. B. Do Coutto Filho, J. F. de Queiroz, “State forecasting in electric power systems”, IEE Proceedings, Vol. 130, Pt. C. No. 5, September 1983. [24]. Methodology of Monthly Index of Services, “Annex B: Holt-Winter’s exponential Forecasting Method”, Available: http://www.statistics.gov.uk/iosmethodology/downloads/Forecasting.pdf [25]. Greg Welch and Grey Bishop, “An Introduction to the Kalman Filter”, Department of Computer Science, University of North Carolina at Chapel Hill, Course 8, SIGGRAPH 2001. [26]. K. Srinivasan, Y. Robichaud, “A Dynamic Estimator for Complex Bus Voltage Determination”, IEEE PES Winter Meeting, New York, N.Y., January 27-February 1, 1974. [27]. J. K. Mandal, A. K. Sinha, L. Roy, “Incorporating nonlinearities of measurement function in power system dynamic state estimation”, IEE Proc.-Generation. Transmission. Distribution, Vol. 142, No. 3, May I995. [28]. Sakr. M. M. F., Bahgat. A., and El-Shafei, A.R, “Dynamic state estimation in power systems with abnormalities detection, identification and correction”. IEE ‘Control 85’ Conference, Cambridge, Conference Publication 252,1, pp. 245-251, 9-1 1 July 1985. [29]. Sakr. M. M. F., Bahgat. A., and El-Shafei, A.R, “Modified estimator applied to electric power systems”, Proc. of Int. AMSE Conf. Modeling and Simulation, Tunisia, November 1985, pp. 131-146. [30]. A. K. Mahalanabis, K. K. Biswas, G. Singh, “An algorithm for decoupled dynamic state estimators of power systems”, IEEE PES summer meeting, paper A 78 573-8, Los Angeles, CA, July 1978. [31]. M. B. Do Coutto Filho, A. M. Leitte Da Silva, J. F. De Queiroz, “Dynamic state estimation in electric power systems using Kalman filter”, Proceedings of the 4th Brazilian Congress on automatic control (in Portuguese), 1982, pp. 152-157. [32]. G. Durgaprasad, S. S. Thakur, “Robost Dynamic State Estimation of Power Systems based on M-Estimation and realistic Modeling”, IEEE Transactions on Power Systems, Vol. 13, No. 4, November 1998. [33]. S. S. Thakur, A. K. Sinha, “A Robust Dynamic State Estimator for Electric Power Systems”, IE (I) Journal-EL, August 2000. [34]. Hui Xua, Qing-quan Jia, Ning Wang, Zhi-qian Bo, Hai-tang Wang, and Hong-xia Ma, “A Dynamic State Estimation Method with PMU and SCADA Measurement for Power Systems,” Proceedings of the 8th International Power Engineering Conference (IPEC 2007), Singapore, 2007, pp. 848-853. [35]. Amit Jain and Shivakumar N. R, "Impact of PMUs in dynamic State Estimation of Power Systems", Proceedings of the North American Power Symposium (NAPS), Calgary, Canada, September 28-30, 2008. [36]. Amit Jain and Shivakumar N. R, "Phasor Measurements in Dynamic State Estimation of Power Systems", accepted for publication in the proceedings of IEEE TENCON 2008, to be held in Hyderabad from November 18-21, 2008. IX. BIOGRAPHIES Amit Jain graduated from KNIT, India in Electrical Engineering. He completed his masters and Ph.D. from Indian Institute of Technology, New Delhi, India. He was working in Alstom on the power SCADA systems. He was working in Korea in 2002 as a Post-doctoral researcher in the Brain Korea 21 project team of Chungbuk National University. He was Post Doctoral Fellow of the Japan Society for the Promotion of Science (JSPS) at Tohoku University, Sendai, Japan. He also worked as a Post Doctoral Research Associate at Tohoku University, Sendai, Japan. Currently he is an Assistant Professor in IIIT, Hyderabad, India. His fields of research interest are power system real time monitoring and control, artificial intelligence applications, power system economics and electricity markets, renewable energy, reliability analysis, GIS applications to power systems, parallel processing and nanotechnology. Shivakumar N R has obtained his Electrical Engineering Degree from RVCE Bangalore and his masters in Power Systems, from IIIT, Hyderabad. He is currently working in ABB Corporate Research Center, Bangalore, India. His areas of interest include real time monitoring and control of power systems, power system protection, AI applications to power systems and condition monitoring and diagnostics of electrical equipment. Authorized licensed use limited to: INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY. Downloaded on October 14, 2009 at 08:38 from IEEE Xplore. Restrictions apply.