Decision making and risk aversion under uncertainty in energy renewable and operational of flexibility of distribution system network

In recent years particular attention has been emphasized to different diversified means of energy production for the security of supply, availability, reliability, and robustness of electrical energy systems. The attention rests on the most effective preventive organization at the cost of an economic investment which will be all the more profitable as the consequences of the breakdown are significant. Given the random nature of the failures of the existing electricity distribution networks and the intermittency of production, the decision to invest preventively in the electricity system is similar to exposure to risk. Will the network manager then take the risk of not investing in a preventive policy, saving investment, but under the threat of a failure requiring a more costly corrective intervention? An expected utility function models the taste and/or aversion to risk. We use the model of von Neumann and Morgenstern, indicating that rational choice amounts to maximizing the expected utility. In this paper, a new standard methodology of uncertainty modeling techniques for decision making process is proposed. The paper provides a decision support tool to the decision maker that allows him to choose a corrective or preventive policy that best suits the electrical system and his preferences. A decision support tool is provided and allows choosing a corrective or preventive policy that best suits the electrical system and the preferences of the decision maker. The objective is to model risk aversion to the choice of a policy leading to the integration of renewable energies into the electricity system. We take into account the probabilities of the occurrence of failures within the framework of a defined policy, the associated costs, and the degree of risk aversion of the decision-maker. Based on these elements, we provide a policy proposal that is the best compromise for the decision-maker. Several examples are treated and allow one to become familiar with the integration of risk aversion modeling to define a preventive policy for the power supply system.