Identifying Critical Measurements in the Power System Network

Identifying Critical Measurements in the Power System Network 1 Kenedy Aliila Greyson and 2 Anant Oonsivilai School of Electrical Engineering, Institute of Engineering, Suranaree University of Technology 111 University Street, Muang District, Nakhon Ratchasima, 30000 THAILAND Abstract-The main objective of this research work is to obtain the minimum number of measurements and their weights (index) in the power system network. The use of singular value decomposition (SVD) is used to find a simpler approximation that speed up the search dramatically. The SVD is used to solve the problem of minimum number of measurements placement while maintaining accuracy as well as network observability. In this paper, the weights (index) of the measurements are obtained by their effect measured by the respective relative error in state estimation. The critical and non critical measurements are identified in the system. Keywords: Measurement placement, accuracy, measurement weight (index), state estimation, critical measurements. I. INTRODUCTION A. Motivation Due to the complexities power systems, the demand of modern energy management systems (EMS) has also increased. It is impractical to install each measuring unit at each location; therefore, several locations will be unmetered. The role of the state estimation is to obtain the best estimate of the system with the available measuring units in the network [1]. Noise from the meter readings received at the control room can severely impact the quality of state estimation. Therefore, the fundamental question is which measuring unit from which location can severely distort the quality of state estimation? Answering this question will draw the attention of operators to monitor those measuring equipments very closely. B. Aim Owing to the limited number of measuring units as well as minimization of the installation cost, the minimum number of measuring units is a key factor. However, the cost of minimizing the measuring units is the introduction of the state estimation errors and moreover the limited network observation. This research intends to workout both the minimization of state estimation errors (accuracy) as well as to obtain the effect of each measurement in the power system. C. Background The goal of placement algorithms is to achieve full system observability with a minimum number of PMUs so as to minimize the installation cost. A reliable estimate of the state of the system must be determined before any security assessment or control actions taken. In order to obtain the optimal number of measurements while maintaining the guarantee the accuracy for measurement to establish energy management system (EMS), the placements of these measurements is the critical in the power system network. The aim of minimal measurement placement is to obtain a metering distribution system that is observable with established accuracy and cost. There are several proposed measurement placement methods. In [1], the importance of bus injection measurements over the line measurements is explained. As it has been presented in [2] and [3], algorithm used for measurement placement for power system nonlinear state estimation has a reduced number of possible combinations to be considered using condition number method. The gain or measurement matrix has to be formulated first. Each row of the gain matrix is temporarily removed one at a time to obtain the objective function of measurement matrix. The possible location that has a minimum objective function is removed so as to reduce the possible location. Other methods such as the use of binary genetic algorithm [5], tabu search algorithm, an iterative search that starts from some initial feasible solution and attempt to determine a better solution in the manner of hillclimbing algorithm [8], etc. D. Paper Organization This paper is organized as follows. Section I, is the introduction. Section II provides the background of power system state estimation. Section III is the theory of network observability. Section IV is the illustration of the algorithm used. Section V gives results obtained and section VI provides relevant conclusions. II. POWER STATE ESTIMATION A. Background In this section, development of method of state estimation problem is explained. Various methods are possible; the most common widely used is the Weighted Least Square (WLS). Therefore, WLS is used in this section for clarification. For a power system, measurements are nonlinear and iterative solutions are required and they are based on the model ISSN: 1790-5117 61 ISBN: 978-960-474-026-0

H (1) where is the measurement vector, H. is the measurement quantities in terms of the state variables, and is the Gaussian random variable noise terms. In estimating N unknown parameters using N measurements, the weighted least-square estimator is used, and expressed in Equation (2) [1], [9] min,,, N N,,, N σ (2) where; f is the function used to calculate the value being measured by i measurement. σ is the variance for the i measurement J is the measurement residual N is the number of independent measurements z is the i measured quantity In AC power system ( -bus system), the state variables are: voltage magnitude at each bus ( ), the phase angle at all buses except the reference bus N 1, and the transformer tap. In order to minimize the objective function, equation (2), Firstly, form the gradient of as (3) = σ σ z f z f Solution of state variable in the iterative algorithm to equation (1) is obtained by solving (3) to make equal zero yields, z f T [ T ]z f (4) T (5) where; = σ σ,, T, and z f z f Therefore, it can be see that, the state estimation which is a function of, and it is also a function of system parameters except for the case of observability analysis [9]. In this paper the simulation is carried with the network parameters throughout by using MATLAB [7]. B. Singular Value Decomposition The study of singular value decomposition is used to obtain a minimum rank matrix. The numerical rank of a matrix is the number of singular value of the matrix that is greater than max,.where is the largest singular value of a matrix and is a machine epsilon. In this study, the network system measurements will include injected active power, injected reactive power and voltage measurements. For a bus system, there will be: possible location for active power measurements, possible location for reactive power measurements, and possible location for voltage measurements. Therefore, there will be 3 possible locations which forms the number of matrix rows. Similarly, there will be 2 1 state variables which will form the column of the matrix. Therefore, the measurement matrix will be where is the total number of possible locations, and is the number of state variables. In this case, for a minimum measurement placement while maintaining observability the rank of the measurement matrix is considered. The results obtained in this paper are based on the status of measurements matrix formed by inspecting its relative errors given by III. where xx NETWORK OBSERVABILITY As stated in section I, in order to minimize the cost of measurement installation, which depends on the number of measurements, the objective function becomes the minimization of the measurement placement subject to the observability constraints. It is explained in [4] and [6] that the network observability analysis is concerned with the power flows in the network and measurements made on the network. That is to say, a network is said to be observable if it satisfy the conditions in Equation (6): 0 H RR V 0 and 0 (6) where H AA is the decoupled Jacobian for the real (active) power measurement, H RR is the decoupled Jacobian for the reactive power measurement, θ is the phase angle estimated state, V is the magnitude voltage estimated state, and P is the vector of branch flow. ISSN: 1790-5117 62 ISBN: 978-960-474-026-0

The vector of branch flow is given by P Aθ (7) where is the branch-bus incidence matrix, and is the vector of bus voltage phase angle The system observability is independent of the branch parameters as well as operating state of the system so all system branches can be assumed to have an impedance of 1.0 p. u.and all bus voltages can be set equal to 1.0 p. u. More explanations on this can be reviewed in [6]. The unobservable branch can be obtained by the use of Cholesky method as explained in [6]. IV. ILLUSTRATION OF THE METHOD USED In this paper, The algorithm used is shown in Fig. 1. In order to obtain the optimum measurement unit placement, the algorithm proposed in [2] is used. However the number of measurements to be obtained is 2 measurements instead of the proposed 2 1, so that the removal of the measurement to obtain the relative error does not affect the observability of the network, and scale of the matrix. That is, the remaining 2 1 is still available in the network. Other methods can be used for the similar purpose. The next step is to remove each measurement and relative error is calculated. Finally, classify measurements according to their relative errors, and measurements are classified such as a critical and non critical as well as their weight (index). It can be seen that, the weight of the measuring unit is observed by their effect of accuracy and the critical measuring units have more effect in the accuracy of the system estimation. V. RESULTS A. Application Example The algorithm has been tested using IEEE 14-bus test system shown in Figure 2. Same as [2] the measurement covariance matrix in Equation (4) is determined by assuming Gaussian distributions with standard deviation of 0.001 for error in injection measurements and 0.04 in voltage measurements. Then MATLAB is used to simulate the algorithm and Newton-Raphson is applied to obtain the values for state variables. Table 1 is the results obtained when IEEE 14-bus test system was in test. In this case three measuring units are considered, active injected power, reactive injected power as well as voltage measuring unit. Measurements are as follows: Thirteen (13) injected active power measurements at bus 1-3, and 5-14. Eight (8) injected reactive power measurements at bus 1-2, and 8-13. And Six (6) voltage measurements at bus 3-5, 7, 12 and 14. The voltage measurement at bus bar number 13 was obtained as a 28 th measurement. Table 2, gives the weight of the measurement unit based on the power flow error and the state estimation effect when the measurement unit is removed. It was also observed that, when some measurements are removed, the Matrix becomes close to singular or badly scaled, here the weight of these measurements are given weight (index) to identify them as critical measurements. In this simulation three (3) measurements are identified as critical measurements, they are injected reactive measurements at bus 1, 2 and 8. Twelve (12) measurements are classified as non critical measurement since their absence does not affect the relative error; however the values of state variables are affected. Form Jacobian Measurement Matrix, H(MN), where M-possible locations Find the CN when each row is removed one at a time Minimum condition is permanently removed NO is 2 YES Remove each measurement and obtain the relative error Classify the measurement units by their relative errors, Fig. 1, Flowchart of proposed algorithm used Fig. 2. IEEE 14-bus test system ISSN: 1790-5117 63 ISBN: 978-960-474-026-0

Table 1 IEEE 14-bus system, True value (measured) of bus bar voltage, estimated voltage, and errors between true and estimated voltage Bus # True voltage Est. voltages estimated error 1 1.060 0.00 1.034 0.00 0.026 0.00 2 1.045-4.98 1.030-4.81 0.015-0.16 3 1.010-12.74 1.010-12.75 0.000 0.01 4 1.019-10.28 1.019-9.91 0.000-0.37 5 1.020-8.76 1.020-8.52 0.000-0.24 6 1.070-14.22 1.057-13.88 0.013-0.34 7 1.062-13.34 1.062-13.02 0.000-0.32 8 1.090-13.34 1.063-13.02 0.027-0.32 9 1.056-14.92 1.052-14.62 0.004-0.30 10 1.051-15.08 1.053-14.78-0.002-0.30 11 1.057-14.78 1.055-14.46 0.002-0.32 12 1.055-15.07 1.055-14.76 0.000-0.31 13 1.050-15.15 1.053-14.93-0.003-0.22 14 1.036-16.02 1.036-16.18 0.000 0.16 TABLE 2 IEEE 14-bus test system, the relative error and measurement weight Removed measurement Relative weight Error (Index) Bus # Type - - 0.025-1 1 0.116 4.6 2 1 0.185 7.4 3 1 0.0986 3.9 5 1 0.025 1.0 6 1 0.025 1.0 7 1 0.025 1.0 8 1 0.025 1.0 9 1 0.025 1.0 10 1 0.1 4.0 11 1 0.2175 8.7 12 1 0.025 1.0 13 1 0.025 1.0 14 1 0.025 1.0 1 2 2 2 8 2 9 2 0.635 25.4 10 2 1.6075 64.3 11 2 4.6425 185.7 12 2 0.025 1.0 13 2 0.025 1.0 3 3 23.217 928.7 4 3 2.17 86.8 5 3 1.57 62.8 7 3 0.985 39.4 12 3 0.025 1.0 14 3 0.025 1.0 Note: Measurement types: 1- injected active power measurement 2- injected reactive power measurement 3- voltage measurement B. Case Study: TANESCO Network This method is also applied to the Tanzania Electric Supply Co. (TANESCO) network shown in Figure 3. The system includes 32 which imply that there are 96 measurement locations. Transmission lines use pylons made of steel. Almost all the transmission lines are radial single circuit lines. The transmission lines are estimated to comprise of 2,624.36 km of system voltages 220 kv; 1441.50 km of 132 kv; and 486.00 km of 66 kv, totaling to 4551.86 km. The system is all alternating current (AC) and the system frequency is 50 Hz [10]. Table 3 is the simulation results for TANESCO power system. In this network 31 injected active power measurements at bus 1-20 and 22-32. 21 injected reactive power measurements at bus 2-7, 9, 12-14, 16-20,22-23,26-28 and 32. 11 voltage measurements at bus 1, 7, 12, 16-17, 22, 24, 27 and 29-31. The voltage measurement at bus bar number 5 was obtained as a 64 h measurement. Key: 1-Kihansi, 2- Kidatu, 3- Moro-a, 4 Moro-b, 5- Chalinze, 6- Ubungo-a, 7-Ubungo b, 8-Ubungo c, 9-Mtoni (Zanzibar), 10-Hale, 11-New Pangani, 12-Tanga, 13-Same, 14-Kiyungi-a, 15-Kiyungi-b, 16- Nyumba ya Mungu, 17- Njiro-a, 18- Njiro-b, 19-Babati, 20- Singida, 21-Shinyanga-a, 22-Shinyanga-b, 23-Tabora, 24-Bulyankulu, 25-Mwanzaa, 26- Mwanza-b, 27-Musoma, 28-Dodoma, 29-Mtera, 30-Iringa, 31-Mufindi and 32-Mbeya Fig.3. TANESCO power network ISSN: 1790-5117 64 ISBN: 978-960-474-026-0

Table 3: TANESCO Network True value (measured) of bus bar voltage, estimated voltage, and errors between true and estimated voltage Bus # True voltage Est. voltages estimated error 1 1.67 0.00 1.47 0.00 0.2 0.00 2 1.67-5.11 1.61-6.13 0.06 1.02 3 1.67-2.41 1.63-2.47 0.04 0.06 4 1.00-7.02 1.00-9.02 1e-4 2.00 5 1.00-2.17 1.00-2.14 1e-5-0.03 6 1.67-2.91 1.67-2.21 1e-3-0.70 7 1.00-5.71 1.00-4.91 1e-6 0.20 8 1.00-3.82 1.00-4.01 1e-3 0.19 9 1.00-4.01 1.01-4.01 1e-2 1e-3 10 1.00-7.77 1.00-8.74 1e-4 0.97 11 1.00-4.04 1.01-8.01 1e-2 3.97 12 1.00-8.98 1.00-9.98 1e-8 1.00 13 1.00-3.19 1.00-3.07-1e-8-0.12 14 1.00-2.99 1.00-2.91-1e-7-0.08 15 0.50-3.86 0.52-4.01 0.02 0.15 16 0.50-9.81 0.50-9.50 1e-3-0.31 17 1.00-3.86 1.00-4.86 1e-4 1.00 18 1.67-8.01 1.67-7.02 1e-3-0.99 19 1.67-9.45 1.67-10.01 1e-3 0.56 20 1.67-8.81 1.67-9.02 1e-5 0.21 21 1.67-1.59 1.67-1.29 1e-7-0.30 22 1.00-7.64 1.00-7.64 1e-3 1e-4 23 1.00-9.08 1.00-8.96 1e-4-0.12 24 1.67-1.03 1.67-1.00 1e-4-0.03 25 1.67-6.05 1.67-6.02 1e-3-0.02 26 1.00-5.94 1.02-5.69 0.02-0.25 27 1.00-4.01 1.00-4.00 1e-5-0.01 28 1.67-7.05 1.69-6.99-0.02-0.06 29 1.67-9.82 1.78-9.81-0.11-0.01 30 1.67-6.20 1.67-6.30 1e-6 0.10 31 1.67-3.42 1.67-3.41 1e-5-0.01 32 1.67-3.05 1.67-3.02-1e-4-0.02 Table 4, gives the weight of the measurements and the state estimation effect when removed. It is observed that injected active power measurement in bus 3, 26, and injected reactive measurement in bus 5, 6, 16 are critical measurements. The higher indexed measurements as shown in Table 4, are injected active in bus 3, injected reactive power in bus 23, etc. TABLE 4 IEEE 14-bus test system, the relative error and measurement weight Removed measurement Bus # Type Relative error Weight (index) - - 0.023-1 1 0.117 5.087 2 1 0.912 39.652 3 1 4 1 0.023 1.00 5 1 0.035 1.52 6 1 0.176 7.65 7 1 0.25 10.87 8 1 0.046 2.00 9 1 0.023 1.00 10 1 0.023 1.00 11 1 0.023 1.00 12 1 0.023 1.00 13 1 0.023 1.00 14 1 0.1 4.348 15 1 0.90 39.13 16 1 4.98 216.52 17 1 29.54 1284.45 18 1 0.023 1.00 19 1 0.023 1.00 20 1 0.023 1.00 22 1 0.023 1.00 23 1 7.01 7.01 24 1 0.023 1.00 25 1 0.023 1.00 26 1 27 1 0.231 10.04 28 1 0.023 1.00 29 1 0.023 1.00 30 1 0.023 1.00 31 1 0.023 1.00 2 2 0.023 1.00 3 2 0.023 1.00 4 2 0.023 1.00 5 2 6 2 7 2 0.023 1.00 9 2 0.822 35.74 12 2 0.792 34.43 13 2 0.023 1.00 14 2 0.023 1.00 16 2 17 2 0.111 4.83 18 2 0.093 4.04 19 2 0.023 1.00 20 2 0.023 1.00 22 2 0.023 1.00 23 2 17.421 757.43 26 2 0.771 33.52 27 2 0.023 1.00 28 2 9.101 395.70 32 2 0.023 1.00 1 3 0.023 1.00 7 3 0.215 9.35 12 3 0.023 1.00 16 3 0.023 1.00 17 3 0.023 1.00 22 3 0.023 1.00 24 3 0.023 1.00 27 3 0.023 1.00 29 3 0.023 1.00 30 3 0.023 1.00 31 3 0.023 1.00 Note: Measurement types: 1- injected active power measurement ISSN: 1790-5117 65 ISBN: 978-960-474-026-0

2- injected reactive power measurement 3- voltage measurement VI. CONCLUSION Weight of the measurement in optimal measurement placement can be used to identify measurement unit effect in state estimation. That is, the state estimation is more affected when bad readings come from the high weighted measuring units. Operators may take a special measure to ensure that, the high weighted measuring units are given priority in obtaining their readings accurately. REFERENCES [1] M. P. Young, H. M. Young, B. C. Jin and W.K. Tae, Design of Reliable Measurement System for State Estimation, IEEE Trans. Power System, vol. 3(3), pp. 830-836, 1988. [2] C. Madtharad, S. Premrudeepreechacharn, N.R. Watson, and D. Saenrak, Measurement placement method for power system state estimation: part I, in Proc. of IEEE Power Engineering Society General Meeting, vol. 3, pp. 1632-1635, July 2003. [3] C. Rakpenthai, S. Premrudeepreechacharn, S. Uatrongjit, and N. R. Watson, An Improved PMUs Placement Method for Power System State Estimation, IEEE Trans. Power [4] Weerakorn Ongsakul and Thawatch Kerdchuen, Optimal Measurement Placement with Single Measurement Loss Contingency for Power System State Estimation Using Refined Genetic Algorithm, 28th Electrical Engineering Conference (EECON28), Phuket, Thailand. [5] A. Ketabi and S.A. Hosseini, A New Method for Optimal Harmonic Meter Placement, American Journal of Applied Sciences 5 (11): 1499-1505, 2008 [6] A. Abur, and A. G. Expόsito, Power System State Estimation: Theory and Implementation, Marcel Dekker, Inc. 2004 [7] MATLAB Software (Version 7.5), Mathwork Inc. [8] A. Oonsivilai and P. Pao-la-or, 2008, Optimum PID Controller Tuning for AVR System using Adaptive Tabu Search Conference Greece. [9] M. Shahidehpour and Y. Wang Communication and Control in Electric Power Systems: Applications of Parallel and Distributed Processing John Wiley & Sons, Inc. 2003. [10] TANESCO, Tanzania Electric Supply Company, http://www.tanesco.com, accessed on May 10, 2008. ISSN: 1790-5117 66 ISBN: 978-960-474-026-0