Recently, power-supply failures have caused major social losses. Therefore, power-supply systems need to be highly reliable. The objective of this study is to present a significant and effective method of determining a productive investment to protect a power-supply system from damage. In this study, the reliability and risks of each of the units are evaluated with a variance-covariance matrix, and the effects and expenses of replacement are analyzed. The mean-variance analysis is formulated as a mathematical program with the following two objectives: (1) to minimize the risk and (2) to maximize the expected return. Finally, a structural learning model of a mutual connection neural network is proposed to solve problems defined by mixed-integer quadratic programming and is employed in the mean-variance analysis. Our method is applied to a power system network in the Tokyo Metropolitan area. This method enables us to select results more effectively and enhance decision making. In other words, decision-makers can select the investment rate and risk of each ward within a given total budget.
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