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NAPS2001_Huang_Lei

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(IntroductionEvaluation of Measurement SystemTraditional analysis of state estimationCriterion 1: System Redundancy Index PCriterion 2: Leverage PointCriterion 3: Variance of SE errorsImpact of Data ExchangeA network and its measurement systemImpact of raw data exchangeImpact of estimated data exchangeA Heuristic Algorithm for Measurement DesignNUMERICAL RESULTSCase1: Raw data exchange for company ACase2: Estimated data exchange for company AConclusionsReferencesBiographies1 Abstract: With power market deregulation, companies cooperate to share one whole grid system but achieve their own economic goals. This paper focuses on how to improve the state estimation result of one company by exchanging raw or estimated data with other companies or ISO. First fundamentals to evaluate a measurement system are developed based on the concept of system redundancy index, leverage point and state estimation error variance. Then the investigations show the complexity of this interesting new topic. Accordingly a heuristic algorithm for the measurement design for distributed multi-utility operation is presented. The numerical results verify that data exchange does enhance the result of state estimation when some principles are applied. Key words: Measurement placement, Distributed state estimation, Power market, Leverage point, Redundancy index. I. INTRODUCTION State estimation is essential for monitoring, control and optimization of a power system. Regardless of the different estimation algorithms, the locations and types of measurements are always decisive factors for successful state estimation. There have been many measurement placement methodologies proposed in the literature [1,2]. However, though the development of power market is rather rapid, the influence of distributed multi-utility operation on the measurement design has not been discussed in these papers. In the regulated environment, the whole power system is owned by a limited number of locally monopolistic organizations. These utilities have the responsibility and the ownership of the instrumentation in their local region to meet their needs to monitor and control. There is almost no need to exchange data with other organizations. On the contrary, in a deregulated environment, no single company owns the whole system. They must cooperate to run the system and to achieve their own economic goals. Therefore, many new problems arise during the measurement design and state estimation, including: This work is supported in part by a PSERC project. The authors are with the Department of Electrical Engineering, Texas A&M University, College Station, TX 77843, USA E-mail: [email protected], [email protected] 1. How to design the measurement system for each subsystem. 2. How to improve the estimation result of one subsystem by exchanging data with other companies, and especially with ISO. This paper focuses on these problems and is organized as follows: fundamentals to evaluate a measurement system are developed first in Section II. Furthermore, in Section III the preliminary concept and some heuristic principles for data exchange are discussed. Accordingly, a heuristic algorithm for the measurement design of distributed state estimation is presented in Section IV. Implementation issues and numerical tests are discussed in Section V. In the last section, a conclusion is drawn. II. EVALUATION OF MEASUREMENT SYSTEM To develop basic concept and principles for data exchange, the problem on how to evaluate a measurement system scheme will be solved in advance. In this section three evaluation criteria are proposed based on traditional analysis of state estimation. A. Traditional analysis of state estimation Generally speaking, the problem of power system state estimation (SE) can be formulated as [1,3]: exhz += )( (1) Where z represents all measurements, including power injection, power flow and bus voltage magnitude measurements, e is the measurement noise vector, x is the state vector composed of the phase angles and magnitudes of the voltages at network buses, )(•h stands for the nonlinear measurement functions. It is always assumed that the parameters and the topology of the systems are already determined in advance. WLS algorithm has been used to solve the SE problem in many commercial software packages for electric power system, which is based on a nonlinear iteration method. At each iteration i , the following equations is solved: iTiTzRHxHRH∆=∆−− 11)( (2) Where R is the measurement covariance matrix H is the Jacobian matrix, iiixxx −=∆+1is the correction of state variables vector, )(iixhzz−=∆ is the estimated error of the measurements. Garng M. Huang, Senior Member, IEEE, and Jiansheng Lei, Student Member, IEEE Measurement Design and State Estimation for Distributed Multi-Utility Operation2 The network is said to be observable when the state variables of an entire network can be calculated uniquely [1,4,5]; in other words, H is of full column rank and G-1 exists numerically. In most cases, the measurement system is always observable under normal operation condition. SE error is defined as:etxx−=α (3) Where tx is the true value of system state variables, ex is the estimated value of system state variables. The covariance matrix of α is defined as [1]: 11)()(−−==HRHECTTαα (4) where E stands for expectation, Residual sensitivity matrix W is defined by: eWr ⋅= (5) where )(exhzr −= is the measurement residual vector, 111)(−−−−=−= RHHRHHISIWTT. (6) B. Criterion 1: System Redundancy Index P Essential Measurement Set is a set of measurements that make the system observable; and at the same time, removal of any measurement from this set will make the system unobservable. A measurement is said to be essential with respect to the essential measurement set if it is a member of the essential measurement set. However, there always exists more than one essential measurement set in one measurement system. In other words, there are different strategies of choosing an essential measurement set. One measurement is a critical measurement if its removal will make the system unobservable. Obviously a critical measurement is always an essential measurement. A set of measurements is a critical measurement set if removals of all the measurements in this set will make an observable power system unobservable. A measurement is said to


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