This paper discusses the state of the art in electric power system state estimation. Within energy management systems, state estimation is a key function for building a network real-time model. A real-time model is a quasi-static mathematical representation of the current conditions in an interconnected power network. This model is extracted at intervals from snapshots of real-time measurements (both analog and status). The new modeling needs associated with the introduction of new control devices and the changes induced by emerging energy markets are making state estimation and its related functions more important than ever.

Electric power system state estimation

An operationally "secure" power system is one with low probability of blackout or equipment damage. The power system control processes needed to maintain a designated security level at minimum operating cost are extremely complicated. They increasingly depend upon on-line computer security analysis and optimization. This on-line technology is still relatively new, with enormous further potential. Since security and optimality are normally conflicting requirements of power system control, it is inappropriate to treat them separately. Therefore, they are slowly becoming coalesced into a unified hierarchical mathematical problem formulation: one that is, however, far too complex to afford anything but an approximate, near-optimal solution. The practical validity of this unifying trend relies on being able to incorporate all significant security constraints within the process. The main two current computational tools in this field are contingency analysis and special operations-oriented versions of optimal power flow (OPF). Contingency analysis identifies potential emergencies through extensive "what if?." simulations on the power system network. OPF is a major extension to the conventional dispatch calculation. It can respect system static security limits, and can schedule reactive as well as active power. Moreover, the advanced versions of OPF include or interface with contingency analysis. This paper reviews present formulations and methods, and tries to point out areas of difficulty that constitute the main challenges for successful practical on-line implementations over the coming years.

Security analysis and optimization

An application of expert system techniques to the restoration of distribution systems is reported. Primary feeders are typically radial in structure. To increase system reliability, neighboring feeders are connected through a normally open tie switch. When load zones on a feeder interrupted due to a fault, system operators need to identify neighboring feeders and try to restore customers through the tie switches. To restore the maximum number of zones, several steps are followed: group restoration, zone restoration and, if necessary, load transfer. Based on the methodology, an expert system is developed which can be utilized as an online aid to system operators in a distribution SCADA (supervisory control and data acquisition) environmental. The proposed expert system is implemented in Prolog. Knowledge representation, portability of the system, and computational efficiency are discussed. Several examples illustrate the capabilities of the system. >

An expert system operational aid for restoration and loss reduction of distribution systems

A three-phase distribution system state estimation algorithm is proposed in this paper. The normal equation method is used to compute the real-time states of distribution systems modeled by their actual a-b-c phases. A current based formulation is introduced and compared with other formulations. Observability analysis for the proposed distribution system state estimation is discussed. Test results indicate that the normal equation method is applicable to the distribution system state estimation and the current based rectangular form formulation is suitable for this application. >

Distribution system state estimation

This article provides a survey on state estimation (SE) in electric power grids and examines the impact on SE of the technological changes being proposed as a part of the smart grid development. Although SE at the transmission level has a long history, further research and development of innovative SE schemes, including those for distribution systems, are needed to meet the new challenges presented by the requirements of the future grid. This article also presents some example topics that signal processing (SP) research can contribute to help meet those challenges.

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State Estimation in Electric Power Grids: Meeting New Challenges Presented by the Requirements of the Future Grid

Two algorithms are presented; one for (i) testing the observability of a network and (ii) identifying the observable islands when the network is unobservable, and the other for selecting a minimal set of additional measurements to make the network observable. The two algorithms are based on triangular factorization of the gain matrix and are characterized by (i) being extremely simple, (ii) using, subroutines already in a state estimation program, and (iii) incurring very little extra computation. The design and testing of the algorithms are presented in this paper.

Network Observability: Identification of Observable Islands and Measurement Placement

Recently a triangular-factorization based observability analysis has been proposed. The method uses subroutines already existing in a state estimation software using the standard normal equations approach. The normal equations approach works well in most applications. However, occasional numerical ill-conditioning of the gain matrix has been observed in practice. Orthogonal transformation methods have been suggested to alleviate this problem. A hybrid approach combining the sparsity of the normal equations method and the numerical robustness of the orthogonal transformation methods has recently been developed. The method solves the normal equations using the orghogonal transformation of the Jacobian matrix. This paper extends the basic idea of the triangular-factorization based observability analysis to orthogonal transformation and hybrid state estimators. The observability analysis is performed during the process or orthogonal transformation (Householder or Givens) of the Jacobian matrix. The deailed algorithm is given. Test results are presented.

Observability Analysis for Orthogonal Transformation Based State Estimation

The standard approach to the solution of the weighted least square (WLS) state estimation in power system is the iterative normal equations method. Occasional ill-conditioning has been experienced with this method. Recently alternative solution approaches based on orthogonal transformations have been proposed. Sparsity generally suffers in these methods. In this paper, the network condition which causes ill- conditioning is studied. A hybrid approach which enjoys the same numerical robustness of the orthogonal methods with sparsity close to the standard WLS method is presented. The modification needed to implement the hybrid method on an existing standard WLS state estimation program is quite small.

A Hybrid State Estimator: Solving Normal Equations By Orthogonal Transformations

A conceptual framework for computer-aided monitoring and assessment during system restoration using analytical tools is proposed. The basic structure is similar to one for security monitoring and assessment (ibid., vol.3, no.1, p.1-9, 1988). State estimation and the related functions, such as observability analysis, bad-data identification and external network modeling which are used in security analysis, are modified for application to system restoration monitoring. In addition to the load flows and optimal power flows that are used in security assessment, a host of analysis/optimization programs is required. These analytical tools are identified and categorized. A knowledge-based expert system architecture is suggested for synthesizing possible control sequences and to select and coordinate analysis procedures for assessing restoration plans. The conceptual design of the knowledge-based system and its interface with analytical tools are presented. >

Analytical tools for power system restoration-conceptual design

A method that combines internal state estimation and external network modeling is developed. The external system is represented by an unreduced load flow model. One state estimation covering both the internal system and the external system is used. The external system operating data on power injections and bus voltages are entered as pseudo-measurements. At each iteration the set of active pseudo- measurements are selected to conform with the specified variables in a load flow program. Because such a set of non-redundant measurements is used, the internal state estimation is not affected by the external system pseudo-measurements. External generation MVAR and controlled bus voltage limits are enforced. A technique is developed to make a pseudo-measurement dormant. Using the dormant-measurement technique, it is possible to maintain the same external system state estimation formulation while the PV-PQ switching takes place from iteration to iteration. The method can easily be implemented by modifying an existing state estimation program. It has been implemented in a fast model-decoupled estimation program. Because of the dormant measurement technique, the constant gain matrix evaluated at flat voltage is used in every iteration. The method has been tested on the IEEE 14- bus, 30-bus, and Brazilian 66-bus systems. Excellent results are obtained. The number of iterations for the method to converge is usually the same as the regular state estimation runs. Thus the method presented here achieves simultaneously the internal state estimation and the external network modeling without adversely affecting the internal state estimation.

A. Monticelli

Papers

Network Observability: Identification of Observable Islands and Measurement Placement

Observability Analysis for Orthogonal Transformation Based State Estimation

A Hybrid State Estimator: Solving Normal Equations By Orthogonal Transformations

Analytical tools for power system restoration-conceptual design

A Method That Combines Internal State Estimation and External Network Modeling