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Graph theoretic approach to solve measurement placement problem for power system

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  • 1. INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME & TECHNOLOGY (IJEET)ISSN 0976 – 6545(Print)ISSN 0976 – 6553(Online) IJEETVolume 4, Issue 1, January- February (2013), pp. 153-161© IAEME: www.iaeme.com/ijeet.aspJournal Impact Factor (2012): 3.2031 (Calculated by GISI) ©IAEMEwww.jifactor.com GRAPH THEORETIC APPROACH TO SOLVE MEASUREMENT PLACEMENT PROBLEM FOR POWER SYSTEM STATE ESTIMATION R. J. Motiyani1, Dr. A. R. Chudasama2 1 Department of Electrical Engineering, S N Patel Institute of Technology & Research, Bardoli, Surat, India 2 Department of Electrical Engineering, The M S University of Baroda, Vadodara, India ABSTRACT In this paper a new method based on graph theoretic approach is proposed to solve the measurement placement problem for power system state estimation. The developed method allows measurement placement without iterative addition. The simulation study is performed on IEEE 14 bus test system. The P-δ and Q-V observable concepts are used to check network observability by triangular factorization of the gain matrix. The measurement system configuration designed through the proposed method maintains network observability and accomplishes accuracy and bad data processing requirements for state estimator. The developed method can be used for measurement systems planning to maintain overall system observable even under branch contingencies and loss of measurements. Keywords: Bad data processing, Measurement placement, Network observability, Network topology processor, Static state estimator. 1. INTRODUCTION Within the energy management system state estimation is a key function to derive a real time network model by extracting information from a redundant data set consisting telemetred static data items. The state of electrical power system is defined as the vector of voltage magnitude and angle at all network buses [1]. Static state estimator is related to conventional power flow calculations. However, the static state estimator is designed to 153
  • 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEhandle the many uncertainties. Uncertainties arise because of meter and communicationerrors, incomplete metering and unexpected system changes. These uncertainties makedifference between the usual power flow studies done in office and online state estimationdone as a part of energy management system [2].The real-time modeling of a power network usually involves following procedure [3]: • Data gathering • Network topology processing • Observability analysis • State estimation (SE) • Processing of bad data and • Identification of network model An observability test should be executed prior to performing the state estimation. A.Monticelli et al. presented two algorithms; one for testing the observability of a network andidentifying the observable islands when the network is unobservable and the other forselecting a minimal set of additional measurements to make the network observable [4]. Thenetwork observability algorithm will check whether the currently available set ofmeasurement from the power system network provides sufficient information forcomputational requirements of state estimation? If state of power system can be estimatedthroughout by processing a given set of measurement sent by the measuring devices in thesystem, then the network is said to be observable, otherwise it is said to be unobservable.The post state estimation procedure involves identification and elimination of bad data fromthe available set of measurement. Sum of squares of residuals method of bad data detectionand identification is presented in [5]. Selection of measurement system aims at attending to requirements such asobservability and reliability- taking in to account the associated monetary costs is discussedin [6]. In the same paper best measurement system configuration for IEEE 30 bus system ispresented. An optimization algorithm suitable to choose the optimal number and positions ofthe measurement devices for state estimation in modern electric distribution network isdiscussed in [7].2. STATE ESTIMATION The state estimation is a mathematical procedure by which the state of electric powersystem is extracted from a set of measurement. In standard SE, in order to relatemeasurements and non linear equations, the following model is used: z = h (x ) + e (1)Where,z = m×1 measurement vectorh(x) = m ×1 vector of non linear functionsx = 2n ×1 state vectore = m×1 measurement error vectorn = Total number of buses in the system and 154
  • 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEm = Total number of measurementsThe state estimator is a mathematical algorithm formulated to minimize the error between areal time measurement and a calculated value of the measurement. The minimizationcriterion often selected is the weighted sum of error squares of all the measurements. Theestimator favors accurate measurements over the less accurate ones by weighing the errorswith the measurement standard deviation (σj) [8]. 2  ej  mmin J ( x ) = ∑   (2) j =1  σ j The condition for optimality is obtained at a point when the gradient of J(x) is zero. Fromweighted least square (WLS) method, the iterative equation can be obtained as follows: (∆x = H T R −1 H ) −1 ( ( )) H T R −1 z − h x k (3)x k +1 = x k + ∆x (4)Where,  ∂ h1 (x ) ∂ h1 (x ) ∂ h1 (x )   ∂x L ∂x2 ∂ x Ns   1   ∂ h 2 (x ) ∂ h 2 (x ) ∂ h 2 (x )  ∂ h (x ) L (5) H = =  ∂ x1 ∂x2 ∂ x Ns  ∂x   M M L M  ∂ h m (x ) ∂ h m (x ) ∂ h m (x )   L   ∂ x1 ∂x2 ∂ x Ns   1   σ 2   1   1  W = R − 1 =  σ 2   2  (6)  L   1   σ 2   m Considering one of the bus as a reference, n-1 angles and n voltage magnitudes (for n bussystem) are to be calculated. The state estimation jacobian (H) always has 2n-1 columns andlarge number of rows based on number of measurements made.The gain matrix is defined asG = H T R −1 H (7)While the power system not only has Supervisory Control and Data Acquisition system 155
  • 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME(SCADA), but also has Phasor Measurement Units (PMUs) placement, the sub problem isformed by PMU placement and SCADA measurements [9]. The state variables measured byPMU are assumed true value and the known state variables are x1. The unknown statevariables are required to be estimated by reduced power system state estimation model.Hence, equations (1), (3) ~ (5) and (7) can be rewritten as follows: z = h (x 2 ) + e (8) ( T∆x 2 = H 2 R −1 H 2 )−1 T ( ( )) H 2 R −1 z − h x 2 k (9) x 2 + 1 = x 2 + ∆x 2 k k (10) G 2 = H 2 R −1 H 2 T (11) ∂h ( x 2 ) (12) H2 = ∂x 2In presence of conventional measurements, one important criterion for PMU placement isthe improvement in state estimator performance [10], [11]. For example frequentlyencountered problem in state estimation is the large value of the condition number of gainmatrix. The PMU placement can be done in such a way that the condition number of thegain matrix is reduced when PMU placements combined with the SCADA measurements.3. METER PLACEMENT State estimator uses a set of measurement consisting of bus injections, branch flowsand bus voltages collected through SCADA System [12]. If all the quantities are measuredas shown in the figure 1, then the possible measurements are 3n + 4b where, n is the totalnumber of network buses and b is the total number of network branches. The stateestimation jacobian will have 3n+4b number of rows. Figure 1. The Per-Phase Representation of Transmission Line- Showing Possible Measurements 156
  • 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME The meter placement problem involves selection of number, type and place ofmeasurement. The main objective in designing a metering scheme is always to satisfy cost,reliability, accuracy and bad data processing requirements. Considering all theserequirements of metering scheme, a meter placement method for IEEE 14 bus system wasdeveloped by Mesut E Baran et al. [13]. The metering scheme designed using hybrid geneticalgorithm and simulated annealing (GA/SA) for 10 and 14 bus system is presented in [14].3.1. PROPOSED METHOD For observability, the presence or absence of the flow is of importance and not thenumerical value of the flow. If a branch that neither has a flow measurement on it nor aninjection measurement at one of its terminal nodes, that branch does not come into thematrix H and thus it does not play any role either in observability analysis or in stateestimation. Proposed measurement placement method is based on network graph theory. Themetering scheme assures that each branch of power system network is incidental by powerinjection measurements at either ends or a flow measurement and an injection measurementat one of its end. Selection of meter locations also assures least requisite of remote terminalunits (RTUs).The proposed meter placement method proceeds as follows: • Read bus data, initialize measurement set of interest by injection measurements at all the zero injection buses in the power system network. • For n bus power system network, read line data and prepare n x n adjacency matrix A= [aij] where; aij =1, if ith bus is incident to jth bus and aij =0, if otherwise. Modify adjacency matrix by making all aii =0, as these elements of matrix represent the bus itself. • Compute total ones of each row of modified adjacency matrix. Identify buses of maximum (p) and minimum (q) adjacency. Place RTUs and measure power injections at the buses of adjacency p, p-1, p-2 ……., till p, p-1, p-2 ……., = q+2. • Identify branches contain no power injection measurement at one of its end, place RTU and measure injection at any end. Add power injection measurements at the buses of q+1 adjacency and voltage measurements at all RTU locations till redundancy becomes ≥ 1. • Update line data file by removing all the lines comprising of injection measurements at both ends. Measure power flows through the remnant lines such that no requisite of additional RTUs.In presence of PMU, the proposed method of measurement placement can be applied tomodified power system network by removing all the buses of PMU locations and branchesconnected to them. The unknown state variables are to be estimated by reduced powersystem state estimation model using the metering scheme obtained through the proposedmethod. 157
  • 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME4. TESTS AND RESULTS The simulation study is performed on IEEE 14 bus test system. Figure 2 showsdesigned metering scheme obtained using proposed method of measurement placement. Themetering scheme consist power injection measurements at buses 2, 4, 5, 6, 7, 9, 10, 12, 13,14; voltage magnitudes at buses 2, 4, 5, 6, 9, 10, 12, 13, 14 and power flows on branchesconnecting buses 2-1, 5-1, 2-3, 4-3, 6-11, 10-11. Figure 2. Metering Scheme Designed for IEEE14 Bus System Using Proposed MethodFor the measurement set power system network was observable. Power flow through the line(4-3) was detected as bad measurement. After removing bad data from the available set ofmeasurement, still network was found observable and redundancy becomes1.44.Table 1 shows the actual state and estimated state obtained by WLS method using meteringschemes of Mesut E Baran et al., hybrid GA/SA and proposed method of measurementplacement. Graph 1 & 2 shows voltage magnitude and bus angle errors at all the buses ofIEEE 14 bus system. 158
  • 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME Table 1. Actual and Estimated State 0.4 0.3 Voltage Error (pu) 0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -0.1 Bus Number -0.2 Proposed Method Mesut E Baran et al. Hybrid GA/SA Graph 1. Voltage error 9 7 Bus Angle Error 5 (Degree) 3 1 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Bus Number Proposed Method Mesut E Baran et al. Hybrid GA/SA Graph 2. Bus angle error 159
  • 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME5. CONCLUSION The developed method avoids iterative addition of measurements and instead allowssimultaneous placement of measurement set. The proposed method accomplishes bad dataprocessing and observability requirements and yields much accurate state of power system.The developed method of measurement placement can be implemented in existing stateestimators as an off- line measurement system planning tool.6. REFERENCES [1] Shayanfar, H. A. and Tabatabaei, N. M (1996). “RCD Rules and Power Systems Observability” International Journal of Engineering, Vol. 9, No. 3, pp. 159-168. [2] Schweppe, F. C. and Wildes, J (1970). “Power System Static- State Estimation, Part І: Exact Model” IEEE Transactions on Power Apparatus and Systems, Vol. 89, No. 1, pp. 120-125. [3] Monticelli, A. (2000). “Electrical Power System State Estimation” Proceedings of IEEE, Vol. 88, No. 2, pp. 262-282. [4] Monticelli, A. and Felix, F.W (1985). “Network Observability: Identification of Observable Islands and Measurement Placement” IEEE Transactions on Power Apparatus and Systems, Vol. 104, No. 5, pp. 1035-1041. [5] Handschin, E., Schweppe, F. C., Kohlas, J. and Fiechter, A (1975). “Bad Data Analysis for Power System State Estimation” IEEE Transactions on Power Apparatus and Systems, Vol. 94, No. 2, pp. 329-337. [6] Alessandra, B. A., Jose, R. A. and Milton, B. D (2001). “Meter Placement for Power System State Estimation Using Simulated Annealing” IEEE Porto Power Tech Conference. Porto, Portugal, September 10-13, Vol. 3. [7] Carlo, M., Fabrizio, P., Giuditta, P. and Sara, S (2006). “Optimal Placement of Measurement Devices in Electric Distribution Systems” IEEE Instrumentation and Measurement Technology Conference, Sorrento, Italy, April 24-27, pp. 1873-1878. [8] Shafiu, A., Jenkins, N. and Strbac, G (2005). “Measurement Location for State Estimation of Distribution Networks with Generation” Proceedings of IEE Generation Transmission and Distribution, Vol. 152, No. 2, pp. 240-246. [9] Fang, C, Xueshan, H., Zhiyuan, P. and Li, H (2008). “State Estimation Model and Algorithm Including PMU” IEEE Electric Utility Deregulation and Restructuring and Power Technologies (DRPT) Conference. Nanging, China, April 6-9, pp. 1097-1102. [10] Gamm, A. Z., Grishin, Yu. A., Kolosok, I. N., Glazunova, A. M. and Korkina, E. S (2007). “New EPS State Estimation Algorithms Based on The Technique of Test Equations and PMU Measurements” IEEE Power Tech Conference, Lausanne, Switzerland, July 1-5, pp. 1670-1675. [11] Chakrabarti, S., Kyriakides, E., Tianshu, B., Deyu, C. and Vladimir T (2009). “Measurements Get Together” IEEE Power & Energy Magazine, Vol. 7, No. 1, pp. 41-49. [12] Kenarangui, R. and Tabatabayee, N. M (1995). “Online Electric Power Systems State Estimation Using Kalman Filtering” Journal of Engineering Islamic Republic of Iran, Vol. 8, No. 4, pp. 233-235. 160
  • 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME [13] Mesut, E. B., Jinxiang, Z., Hongbo, Z. and Kenneth, E. G (1995). “A Meter Placement Method for State Estimation” IEEE Transactions on Power Systems, Vol. 10, No. 3, pp. 1704-1710. [14] Thawatch, K. and Weerakorn, O (2006). “Optimal Measurement Placement for Power System State Estimation Using Hybrid Genetic Algorithm and Simulated Annealing” IEEE International Conference on Power System Technology, Chongquing, China, October 22-26, pp. 1-5. [15] Alsac, O., Vempati, N., Stott, B. and Monticelli, A. (1998). “Generalized State Estimation” IEEE Transactions on Power Systems, Vol. 13, No. 3, pp.1069-1075. [16] D.K. Tanti, M.K. Verma, Brijesh Singh and O.N. Mehrotra, “Optimal Placement Of Custom Power Devices In Power System Network For Load And Voltage Balancing” International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 3, 2012, pp. 187 - 199, ISSN Print : 0976-6545, ISSN Online: 0976-6553 Published by IAEME. [17] Preethi Thekkath and Dr. G. Gurusamy, “Effect of Power Quality on Stand By Power Systems” International Journal of Electrical Engineering & Technology (IJEET), Volume 1, Issue 1, 2010, pp. 118 - 126, ISSN Print : 0976-6545, ISSN Online: 0976- 6553 Published by IAEME.AUTHORS’ INFORMATION R. J. MOTIYANI has received the M.E degree in Electrical Power Engineering in 2005 from The M. S. University of Baroda, Vadodara, India. Currently he is working with S N Patel Institute of Technology & Research Centre as Associate Professor and Head of Electrical Engineering Department. Prof. (Dr.) A. R. CHUDASAMA was born on May 9, 1956. He received the M.E degree in Electrical Power Engineering from The M. S. University of Baroda, India in 1986. He received the Doctoral degree from The M. S. University, Baroda, India in 2003. He published & presented more than 55 research papers. 161