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Abstract—Traditional state estimation methods employ large weights for zero injection pseudo-measurements, which may result in numerical instability.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 3, AUGUST 2013

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An Efficient State Estimation Algorithm Considering Zero Injection Constraints Ye Guo, Wenchuan Wu, Member, IEEE, Boming Zhang, Fellow, IEEE, and Hongbin Sun, Senior Member, IEEE

Abstract—Traditional state estimation methods employ large weights for zero injection pseudo-measurements, which may result in numerical instability. The normal equations with constraints will increase the order of the coefficient matrix, thus reducing the speed of the calculations. To improve computational performance, this paper presents a modified Newton method to deal with zero injection constraints. The decoupled form of the proposed technique—a modified fast decoupled state estimation method—is also given. The computational speed of the proposed modified Newton method is similar to that of conventional state estimations based on normal equations, since they use the same type of coefficient matrices. Furthermore, it offers the advantage that zero injection constraints can be strictly satisfied, and the numerical stability problem caused by large weights will no longer exist. Extensive numerical results from test systems and a real provincial system are included to verify the performance of the proposed procedure.

State variable vector for zero injection buses. State variable vector for nonzero injection buses. Measurement value vector. Measurement Jacobian matrix. Measurement function vector. Jacobian matrix of

Diagonal measurement covariance matrix. Right-side vector in normal equations, . Gain matrix in normal equations,

Index Terms—Equality constraints, normal equations, reduced method, state estimation, zero injection.

P

NOMENCLATURE SE

State estimation.

WLS

Weighted least squares.

MNM

Modified Newton method.

FDSE

Fast decoupled state estimation.

MFDSE Modified fast decoupled state estimation. NE

Normal equations.

NE/C

Normal equations with constraints. Bus admittance matrix. Real part of

, or the bus conductance matrix.

Imaginary part of matrix.

, or the bus susceptance

Incidence mapping between state variables in orthogonal coordinates and polar coordinates. Incidence mapping between state variables of zero injection buses and nonzero injection buses in polar coordinates. State variable vector. Manuscript received May 04, 2012; revised October 22, 2012; accepted November 30, 2012. Date of publication January 08, 2013; date of current version July 18, 2013. This work was supported in part by the National Key Basic Research Program of China (2013CB228206). Paper no. TPWRS-00471-2012. The authors are with the State Key Lab of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China. 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.2012.2232316

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I. INTRODUCTION

OWER system state estimation is an essential basic function in energy management systems. In actual power systems, most of the high-voltage buses are zero injection buses with neither load nor generation. Power injections into these buses are strictly 0, so based on Kirchhoff’s current law, equality constraints should be used to handle these buses in an SE model. It is a challenge to ensure that these zero injection constraints can be strictly satisfied without losing computational efficiency. The traditional method for processing zero injection constraints is to add zero injection pseudo-measurements with extremely large weights based on NE [1]–[3]. This approximate technique is convenient, but the artificially added large weights may cause the coefficient matrix to be ill-conditioned, thus degrading the convergence [4], [5]. An orthogonal transformation procedure can be used to overcome this difficulty [6]–[8], but imposes additional computational burden. NE/C is a basic type of SE method considering zero injection constraints [9], [10]. One problem arising from this approach is that the coefficient matrix is no longer positive definite. Symbolic optimal ordering and the signed Cholesky factorization technique [11] can be used to solve the SE problem with an indefinite coefficient matrix. Another problem arising from NE/C is that the multipliers increase the order of the coefficient matrix. The computational expense of NE/C is usually about three or four times that of NE, due to the large number of zero injection buses in an actual power system [11]. To reduce the computational expense, a suboptimum algorithm is presented in [12], which corrects the results for the unconstrained state estimation model to satisfy the constraints. Hachtel’s augmented matrix technique [13], [14] is a robust SE method, but its coefficient matrix is also indefinite. The block matrix technique [15], [16] can be employed to increase the numerical stability and computational speed of this type of method. Also, a mixed pivoting approach has been developed

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in [17], focusing on the indefinite matrix factorization problem in SE. The interior point method is another effective technique for solving an SE problem with constraints [18], [19]. A significant advantage of this approach is that it allows any possible equality or inequality constraints to be included. In the interior point method, zero injection constraints are processed in the same general way as other constraints, without considering their individual characteristics. This paper is concerned with how to use these individual characteristics to further improve the computational performance of state estimation. A reduced method, which uses equality constraints to directly eliminate state variables, is introduced in [20] and [21]. This technique offers convergence reliability. Furthermore, the size of its state variable vector decreases as the number of equality constraints increases. However, a critical disadvantage of this method is that its coefficient matrix becomes much denser, which creates a huge computational burden for large-scale power systems. In this paper, a reduced quasi-Newton method is derived to solve SE problems considering zero injection constraints. The proposed method is derived from the reduced method, and zero injection constraints can be strictly satisfied. The coefficient matrix of the proposed reduced quasi-Newton method has the same form as in the NE, and hence, this procedure has a very sparse approximate Hessian matrix and fast computational speed. Since the coefficient matrix of the proposed reduced quasi-Newton method is very similar to that of the NE, this method is referred to as the modified Newton method (MNM) in the present paper. A fast decoupled form (MFDSE) based on MNM is also proposed to further accelerate the computational speed. Both of these proposed methods are suitable for real-time applications. Compared with traditional NE methods with large weights for zero injection pseudo-measurements, MNM provides similar convergence and computational speed, while offering the following advantages: 1) It can strictly satisfy the zero injection constraints, whereas the NE method with large weights is approximate. 2) The numerical stability is improved significantly, since large weights for zero injection pseudo-measurements are no longer necessary. Compared with other SE methods considering rigorous zero injections, such as NE/C, MNM offers the following primary advantages: 1) The computational speed of MNM is much faster than that of NE/C. 2) Only minor modifications are needed to update the existing NE- or FDSE-based SE software to MNM- or MFDSEbased SE software. Numerical results from test systems and an actual provincial power system are given in this paper to verify the performance of the proposed MNM and MFDSE. II. FORMULATION OF ZERO INJECTION CONSTRAINTS

where , and denote the bus admittance matrix, bus complex voltage vector, and bus complex current injection vector; the subscripts and denote zero injection buses and nonzero injection buses, respectively. Expanding the first row of (1) (2) Converting (2) to real number form in orthogonal coordinates

(3) and are the real and imaginary parts of the mawhere trix , and and are the real and imaginary parts of the vector . Let and , where the superscript represents orthogonal coordinates. Then (3) becomes (4) where

is a constant matrix that can be formulated as follows:

(5) It can be concluded from (4) that the zero injection constraints are linear in orthogonal coordinates. B. Zero Injection Constraints in Polar Coordinates Let be the state variable vector in polar coordinates. In polar coordinates, the trigonometric functions introduce nonlinearities to the zero injection constraints. However, using complex number transformation theory, the relationship between and based on the zero injection constraints can be easily formulated. According to complex number theory, the relationship between and can be expressed by (6)

(7) where the subscript denotes the bus index. To simplify the expressions, (6) can be written as (8) and (7) can be written as (9)

A. Zero Injection Constraints in Orthogonal Coordinates Since current injections of zero injection buses are strictly 0, the network equations can be expressed in complex number form as (1)

where is a nonlinear homeomorphism. The nonlinear zero injection constraints in polar coordinates can be expressed as (10)

GUO et al.: AN EFFICIENT STATE ESTIMATION ALGORITHM CONSIDERING ZERO INJECTION CONSTRAINTS

The WLS SE model with zero injection constraints can be expressed as

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values are treated as state variables; In model (16), only the the values are calculated in terms of using (10). The gradient vector and Hessian matrix for this reduced SE model are [22], [23] (17)

(11)

III. MODIFIED NEWTON METHOD (18)

A. Normal Equations The WLS SE model without equality constraints is solved by the normal equations, which can be expressed as follows:

where is the Jacobian matrix of the mapping . The Newton iteration formula for this reduced SE model is

(12) (19)

The coefficient matrix and right-hand vector in (12) are denoted by and , respectively, and (12) becomes

(20) (13) By dividing the set of all buses into zero injection buses and nonzero injection buses, the normal equations (13) can be expressed as (14)

The reduced SE solution is theoretically effective, but a critical disadvantage of this method is that the Hessian matrix in (19) is dense. However, this disadvantage can be resolved by a reasonable approximation, as described below. C. Modified Newton Method By eliminating

, (14) becomes

where (21) The derivative form of (10) is (22) In the solution of NE, the zero injection constraints (22) cannot be strictly satisfied. Assume that (15) (23) is the Jacobian matrix relating all the measurements In (15), and state variables of the nonzero injection buses, and is the Jacobian matrix relating all the measurements and state variables of the zero injection buses. B. Reduced Newton Method By expressing in terms of can be formulated as

The value of mainly depends on the residuals of zero injection pseudo-measurements. Since zero injection pseudomeasurements are accurate without error, which make that is always much smaller than and . Substituting (23) into (21), (24a) (24b)

, the reduced Newton model

can be converted to (16)

(25)

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Substituting (25) into (24b)

Pre-multiplying (24a) by

(30) (26)

(31)

, and then adding the result to (26)

Firstly, (28) is used to transform to orthogonal coordinates, in which the zero injection constraints are linear. By solving (4), the state variables of the zero injection buses can be derived in orthogonal coordinates. However, since the matrix in (4) is dense, the solution of (4) is divided into two steps, (29) and (30), instead of calculating the matrix . Finally, the state variables of the zero injection buses will be transformed to polar coordinates by (31). It should be noted that the matrix in (4) need not be calculated. Similarly, it is not necessary to calculate the matrix Q or the Hessian matrix in (18), either. (28) and (31) are complex number transformations between orthogonal and polar coordinates, with negligible computational burdens. Equation (29) involves the multiplication of a sparse matrix and a vector, and adds little computational burden. Equation (30) involves the solution of a linear equation with a constant, symmetric, and sparse coefficient matrix. Since the coefficient matrix in (30) is constant, its triangular decomposition can be carried out in the initialization step, and only forward and backward substitutions of this sparse coefficient matrix are required in each iteration. The computational burden of these operations is also very slight. In summary, the additional computational burden of MNM is very slight compared with NE methods. Thus, the computational speeds of these two methods are virtually the same. As regards the issue of numerical stability, the structure of coefficient matrix in MNM is exactly the same as that in NE. The only difference is that in NE, large weights are needed for the zero injection pseudo-measurements to make the injection powers of the zero injection buses approximately equal to 0, whereas there are no large weights in MNM. Since the large weights used in NE can degrade the numerical stability, MNM is more numerically stable than the traditional NE-based method. It should be noted that in MNM, zero injection pseudo-measurements should still be used, since they are very helpful in enlarging the observable area and identifying bad data. The main benefit of MNM is that it is no longer necessary to employ extremely large weights for these zero injection pseudo-measurements.

(27) , the second term Since is much smaller than and on the left-hand side of (27) can be neglected. Thus, it has been obtained by NE (14) is very close to that obproved that tained by the reduced Newton method. from NE (14) to update and By using the solution of , and utilizing (10), a reduced quasiin terms of calculate Newton algorithm can be derived. The details of the algorithm are as follows: 1) Start iterations, set the iteration index. 2) Initialize the state vector for nonzero injection buses , typically a flat start. Calculate in terms of using (10). . 3) Calculate the gain matrix 4) Calculate the right-hand side . 5) Decompose and solve for , using NE (14). calculate in 6) Update and terms of , using (10). 7) Test for convergence: If ? 8) If no, and go to step 3. Else, stop. is calculated in terms of In each step of this procedure, using equation (10), which exactly represents the zero injection constraints. Thus, the solution will strictly satisfy the zero injection constraints. It should be noted that the values obtained from (14) are not used in the proposed method. The normal equations are given in (14), and (10) represents the zero injection constraints. If and are obtained from (14) also satisfy (10), the solution of the normal equations can strictly satisfy the zero injection constraints. However, in the normal equations, the zero injection constraints are always expressed in terms of zero injection pseudo-measurements, and cannot be strictly satisfied. Thus, if and are obtained from (14), they will not satisfy (10). To make the SE solution strictly satisfies the zero injection constraints, we should use (10) rather than (14) to calculate . D. Discussion Compared with the NE algorithm, the only modification in the proposed MNM is that is calculated in terms of , using (10). The computational burden for this step is very slight, and is explained as follows. The computational procedure of (10) can be divided into 4 steps:

IV. MODIFIED FAST DECOUPLED STATE ESTIMATOR The fast decoupled state estimation procedure is an efficient SE method [24], and such a technique is widely used in practical SE programs. In fast decoupled state estimation (FDSE), sub-iterations and sub-iterations are solved alternately. The iteration formulas of FDSE can be expressed as (32) (33)

(28) (29)

where and sub-iterations and

are constant coefficient matrices for sub-iterations, and and are right-

GUO et al.: AN EFFICIENT STATE ESTIMATION ALGORITHM CONSIDERING ZERO INJECTION CONSTRAINTS

hand vectors for sub-iterations and sub-iterations, respectively. Based on the same idea used in MNM, a modified fast decoupled state estimation (MFDSE) is developed in this paper. The details of the algorithm are as follows: 1) Initialize the voltages and angles for nonzero injection buses . 2) Carry out triangular decompositions of and . 3) Calculate in terms of using (10). 4) Calculate in terms of . 5) Solve the P sub-iteration equation (32). 6) Check if both and are less than the convergence tolerance. If yes, stop. 7) Update . 8) Calculate in terms of using (10). 9) Calculate in terms of . 10) Solve the Q sub-iteration equation (33). 11) Check if both and are less than the convergence tolerance. If yes, stop. Else, continue. 12) Update . 13) Go to step 3. One may observe that the above algorithm is very similar to the traditional FDSE method. The main differences between them are the following. In MFDSE, only obtained from (32) is used to update , and the value of is calculated according to the zero injection constraints instead of the results of (32). The same is true of the Q-sub-iteration. V. NUMERICAL TESTS A. IEEE 9-Bus Test System The IEEE 9-bus system [25] shown in Fig. 1 is used for this test. A complete measurement set is generated from load flow results for the system. White noise is added to the true values, the standard deviations of the errors are set at 0.09 and 0.009 for the power and voltage measurements, and the measurement weights are set at 123.45 (inverse square of the standard deviation, ) and 12345.6 for the respective power and voltage measurements. A WLS estimator is used in this test. All calculations are carried out on a personal computer with a 2.70-GHz central processing unit. Three SE algorithms are used: 1) NE: The traditional NE based method with large weights for zero injection pseudo-measurements. The weights for the zero injection pseudo-measurements are set at 10 times the weights for normal power measurements. A C++-based commercial grade SE program using the normal equations is used for comparison in this test. This SE program is widely used in China, and the standard Cholesky factorization function for sparse matrices is employed. 2) NE/C: The NE/C-based method. Lagrange multipliers are added to the state variable vector. A scaling technique is used to improve the numerical stability of this method, and NE/C can be modified as in [26] (34)

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Fig. 1. IEEE 9-bus test system.

where is a scalar, is the zero injection Jacobian matrix, and is the multiplier vector added for the zero injection constraints. The NE/C program is based on C++, and uses the same Cholesky factorization function as NE. The weights of the zero injection pseudo-measurements are set equal to the normal power measurements. 3) MNM: The modified Newton method proposed in this paper. The MNM program is also C++-based, with very minor code modifications based on the original NE estimator. The weights of the zero injection pseudo-measurements are also set equal to the normal power measurements. A flat start is used for all the tests. The convergence threshold is set equal to . The estimation error is measured by and , where the superscripts se and true denote estimated values and true values, respectively. These two indices, together with the total unbalanced active power and reactive power of the zero injection buses, are listed in Table I. The CPU time costs of the three algorithms are also listed, in the 7th column of Table I. Some numerical characteristics of their coefficient matrices and Cholesky factors are listed in Table II. Table I indicates that there are some power imbalances at the zero injection buses for NE, while the zero injection constraints are strictly satisfied in MNM and NE/C. MNM exhibits a calculation speed similar to that of NE, while it is about 20% faster than NE/C. In Table II, since Lagrange multipliers are added to the state variables, the size and nonzero entries of the coefficient matrix, as well as the Cholesky factors of NE/C increase significantly. On the other hand, the coefficient matrix of MNM has the same size and nonzero entries as NE. The smaller size and fewer nonzero elements in the coefficient matrix of MNM indicate a faster calculation speed compared with NE/C. As regards the issue of numerical stability, it is concluded from the last row in Table II that the coefficient matrix of MNM has a better condition number than NE, thanks to the elimination of large weights. In summary, it is concluded that MNM offers the advantage of better numerical stability than NE, while its computational speed is faster than that of NE/C. The convergence curves of the three methods are plotted in Fig. 2 in logarithmic coordinates. The figures indicate that these three algorithms have similar convergence. Hence, it is concluded that the proposed modified Newton method is computationally fast and robust in convergence.

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TABLE I STATE ESTIMATION RESULTS FOR THE IEEE 9-BUS TEST SYSTEM

TABLE II COEFFICIENT MATRIX AND CHOLESKY FACTOR CHARACTERISTICS FOR NE, NE/C, AND MNM IN THE IEEE 9-BUS TEST SYSTEM

Fig. 3. Convergence rates of NE and MNM for 9-bus system when the actual state is far from flat start.

Fig. 4. Average iteration times of NE and MNM for 9-bus system when the actual state is far from flat start. Fig. 2. Convergence curves for the three methods in the IEEE 9-bus test system. TABLE III , AND

FOR THE

IEEE 9-BUS TEST SYSTEM

The values of , and are listed in Table III for MNM. is much smaller than and , which proves that it is reasonable to neglect during the iterations. Extensive numerical tests are carried out to verify that it is reasonable to neglect even when the actual state is far from flat start. The detailed procedure is as follows: 1) Add errors to each of the actual state variables for the nonzero injection buses to obtain the test state variables, for the th state variable for non-zero injection buses: (35)

where is a normally distributed random number with standard deviation . 2) Calculate the test state variables for the zero injection buses using (10), so that these variables will strictly satisfy the zero injection constraints. 3) Construct 100 measurement scans around the tested state. 4) Perform SE calculations using NE and MNM, and count the convergence rate and average iteration time for each method. The average value of in the first iteration is also recorded. The convergence rate, average iteration time and average value of in the first iteration are plotted versus in Figs. 3–5. From Fig. 5, is much smaller than and , even when the actual state is very far from flat start (the voltage amplitude can reach about 3.0 or 0.33 p.u. at the last point). As a result, the convergence for MNM is very robust in Figs. 3 and 4. The convergence rate for MNM is higher than that of NE in Fig. 3, and the average iteration time for MNM is less than that of NE in Fig. 4. This is because MNM is more numerically stable than NE. It is concluded that it is reasonable to neglect

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TABLE IV STATE ESTIMATION RESULTS FOR THE IEEE 145-BUS TEST SYSTEM

Fig. 5. Average value of in the first iteration of MNM for 9-bus system when the actual state is far from flat start. TABLE V COEFFICIENT MATRIX AND CHOLESKY FACTOR CHARACTERISTICS FOR NE, NE/C, AND MNM IN THE IEEE 145-BUS TEST SYSTEM

, and that MNM is effective even if the actual state is far from flat start. B. IEEE 145-Bus Test System The calculations are repeated in an IEEE 145-bus test system [27] with 71 zero injection buses, under the same conditions described above. The estimation results are listed in Table IV, which indicates that all of the above conclusions for the 9-bus test system remain valid. The time cost of NE/C increases to nearly 4 times of that of NE and MNM, This is because nearly 50% of the buses in the 145-bus system are zero injection buses (similar to real-world power systems), and thus the dimension of the coefficient matrix of NE/C increases by half, which implies a huge computational burden compared with NE or MNM. These conclusions are in agreement with the results in [11]. A comparison of the coefficient matrices of NE, MNM, and NE/C is given in Table V. The coefficient matrix of NE/C is much larger than those of NE and MNM, and there are many more off-diagonal nonzero entries in the Cholesky factors in NE/C than

Fig. 6. Convergence curves for the 3 methods in the IEEE 145-bus test system. TABLE VI AND ITERATIONS FOR THE IEEE

IN THE FIRST THREE

145-BUS TEST SYSTEM

in NE. This is why the computational speed of NE/C becomes slower. On the other hand, the coefficient matrix of MNM has the same size and the same number of nonzero entries as in NE. The condition number of the coefficient matrix in MNM is much smaller than in NE, and very similar to that of NE/C, which indicates that MNM and NE/C are both numerically stable. The convergence curves of the three methods for the 145-bus test system are plotted in Fig. 6 in logarithmic coordinates. The figure indicates that these three methods have similar convergence properties in this test system. The values of , and for the first three iterations are listed in Table VI for MNM. It is concluded that is much smaller than and . To verify that it is reasonable to neglect , the same type of numerical tests used for the 9-bus system are carried out in the 145-bus system. The results are given in Figs. 7–9, and lead to conclusions similar to those obtained for the 9-bus system. is still much smaller than , and the convergence is better for MNM than for NE. Based on these test results, the characteristics of NE, NE/C, and MNM are summarized in the Table VII. C. Provincial System To evaluate the performance of MFDSE in a practical application, a C++ MFDSE program is developed, based on a commercial grade FDSE software that is widely used in China.

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TABLE VII COMPARISON OF THE THREE METHODS

Fig. 7. Convergence rates of NE and MNM for 145-bus system when the actual state is far from flat start.

TABLE VIII STATE ESTIMATION RESULTS FOR A PROVINCIAL SYSTEM

Fig. 8. Average iteration times of NE and MNM for 145-bus system when the actual state is far from flat start.

VI. CONCLUSION

Fig. 9. Average value of in the first iteration of MNM for 145-bus system when the actual state is far from flat start.

A Chinese provincial system that includes 546 buses and 737 branches is tested via this program. There are 271 zero injection buses in this system. The test results for the two methods are listed in Table VIII. Since a bad data identification loop is needed for a real-world system, multiple SEs are included in the test. As Table VIII indicates, MFDSE is very similar to FDSE in terms of convergence and computational speed. Since conventional FDSE handles zero injection constraints by using the large weight method, a large total power imbalance exists (near 90 MW), whereas the zero injection constraint is strictly satisfied for the proposed method (only 0.05 MW). The computational speeds for the two techniques are virtually the same. Based on the above tests, it is concluded that MFDSE is an efficient SE method considering zero injection constraints, analogous to the modified Newton method.

An efficient zero injection constraint processing method is important for power system state estimation. In this research, modifications to the reduced Newton technique are developed, and a modified Newton method is proposed. A fast decoupled form of the proposed modified Newton method—a modified fast decoupled state estimation method—is also presented. The modified Newton method proposed in this paper has a sparse and positive definite coefficient matrix, is fast in terms of computational speed and is numerically stable. Hence, the proposed modified Newton state estimation procedure has inherited the advantages of the approach based on normal equations and the approach based on normal equations with constraints. It is especially troublesome that the large-weights approach to handling zero injection constraints creates a power imbalance problem. The modified Newton method and modified fast decoupled state estimation method presented in this paper can provide practical solutions to this problem with negligible computing expense, and only minor modifications to the existing state estimation codes are needed to implement these methods. Numerical tests have shown that the proposed procedures are effective and practical for dealing with zero injection constraints. 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.

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[25] P. M. Anderson and A. A. Fouad, Power System Control and Stability. Ames: Iowa State Univ. Press, 1977, pp. 37–39. [26] A. Abur and A. G. Expósito, Power System State Estimation: Theory and Implementation. New York: Marcel Dekker, 2004, pp. 50–73. [27] IEEE Committee Report, “Transient stability test system for direct stability methods,” IEEE Trans. Power Syst., vol. 7, no. 1, pp. 37–43, Feb. 1992.

Ye Guo was born in Hebei, China, in 1988. He received the B.S. degree from the Electrical Engineering Department, Tsinghua University, Beijing, China, in 2008. He is currently pursuing the Ph.D. degree at Tsinghua University. His research interests include state estimation, load flow analysis, parameter identification, as well as other power system modeling technologies.

Wenchuan Wu (M’07) received the B.S., M.S., and Ph.D. degrees from the Electrical Engineering Department, Tsinghua University, Beijing, China, in 1996, 1998, and 2003, respectively. He is currently an Associate Professor in the Department of Electrical Engineering of Tsinghua University. His research interests include energy management system and active distribution system operation and control.

Boming Zhang (SM’95–F’10) received the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 1985. Since 1985, he has been with the Electrical Engineering Department, Tsinghua University, for teaching and research and promoted to a Professor in 1993. His interest is in power system analysis and control, especially in the EMS advanced applications in the Electric Power Control Center (EPCC). He has published more than 300 academic papers and implemented more than 60 EMS/DTS systems in China. Prof. Zhang is a steering member of CIGRE China State Committee and of the International Workshop of EPCC.

Hongbin Sun (M’00–SM’12) received the double B.S. degrees and the Ph.D. degree from the Department of Electrical Engineering of Tsinghua University, Beijing, China, in 1992 and 1997, respectively. He is now a Full Professor in the Department of Electrical Engineering, Tsinghua University, and Assistant Director of the State Key Laboratory of Power Systems in China. During 2007–2008, he was a visiting Professor with the School of Electrical Engineering and Computer Science at the Washington State University, Pullman. His research interests include energy management system, voltage optimization and control, applications of information theory, and intelligent technology in power systems.