426 IEEE Transactions on Power Systems, Vol. 14, No. zyx 2, May 1999 zy Bayesian Network Model for Reliability Assessment of Power Systems David C. Yu Thanh C. Nguyen Peter Haddawy Department of Electrical Engineering and Computer Science University of Wisconsin-Milwaukee Milwaukee, WI 53201 zyxwvu Abstract -This paper presents an application of Bayesian networks (BN) to the problem of reliability assessment of power systems. Bayesian networks provide a flexible means of representing and reasoning with probabilistic information. Uncertainty and dependencies are easily incorporated in the analysis. Efficient probabilistic inference algorithms in Bayesian networks permit not only computation of the loss of load probability but also answering. various probabilistic queries about the system. The advantages of BN models for power system reliability evaluation are demonstrated through examples. Results of a reliability case study of a multi-area test system are also reported. Keywords zyxwvutsrqpo - Power system reliability, LOLP, load uncertainty, area load dependency, Bayesian network. I. INTRODUCTION Probabilistic reliability indices serve as an accurate and consistent basis for assessing and comparing reliability of power systems, where component’s outage and load demand are of stochastic nature. Analytical mathematical models [ 1 - zyxwvu 51 or Monte-Carlo simulation [6-71 are usually used for computing these indices. While existing methods can efficiently evaluate the probabilistic reliability indices of a power system, they usually reveal few details about the role of various components and subsystems in overall system reliability. Conversely, when the states of certain components in the system are known, existing methods do not offer a direct way to assess the conditional probabilities of the causes and/or the effects in the rest of the system. These conditional probabilities, if readily available, can be very useful for improving the assessment of system reliability. For example, one can use this information to determine the system weak points from the point of view of system reliability. The proposed model for reliability assessment of power systems can address the issues mentioned above This model is based on Bayesian network (BN) technique. [t provides a probabilistic representation of the balance between the supply availability and the load demand at various points in the system. Probability of the loss of load states as well zy as other probabilities are computed efficiently by BN propagation algorithms [8,9]. The main advantages of the proposed BN model for reliability assessment of power sysiems can be summarized as follows: Simple and intuitive model building that is closely based on the physical power network topology. Easy incorporation of uncertainty and dependency in reliability assessment. Capability to monitor the probability of any variable in the system. Propagation of probabilistic information that allows a wide range of what-if analysis. The proposed BN models can provide answers to important questions conceming power system reliability, such as: Is the given supply configuration reliable, enough to meet certain demand forecast in the system? What is the most likely cause of some contingency condition at a certain site? Given some probability distribution of failure of a certain part of the network, what is the reliability of power supply to downstream sites? zyx 0 0 11. BAYESIAN NETWORK MODEL, OF POWER SYSTEM A. Bayesian Networks A Bayesian network is a directed acyclic graph in which nodes represent random variables and links represent direct probabilistic influences. The variables depicted in the BN represent key parameters characterizing the system being modeled, The direction of a link between nodes is PE-058-P~RS-0-07-1998 A Paper “-rImended and approved by Committee of the IEEE Power Engineering Society for publication in the 2, 1997; made available for printing June 22, 1998. the IEEE Power System Analysis, Computing and Economics IEEE Transactions on Power Systems. Manuscript submitted October usually chosen to indicate a causal-effect or cla,ss-propem relationship between variables denoted by these nodes. In a zy 0885-8950/99/$10.00 0 1998 IEEE