A probabilistically constrained extension of the integrated portfolio investment model

In recent years, new methods concerning risk mitigation techniques in energy planning strategies have become popular. Delarue et al. introduced the integrated portfolio investment model to account for supply–demand constraints. This paper proposes a model which is suitable to the energy management problem of planning the capacity factors of renewable energy technologies used in a strategy with stochastic supply–demand constraints under reliability limitations and evaluating their associated costs. Therefore, we introduce the concept of Power-at-Risk, following the Value-at-Risk formulation to quantify risks on the supply side in an adequate way. This paper extends the integrated portfolio model and introduces a reliability level to account for issues related to the unpredictability in the power output. We analyze cost effects by considering increasing levels of reliability in the supply–demand constraint. The energy planning problem, illustrated in a use case, is solved numerically by the sample approach based on locally calibrated probability density functions of both wind and solar power available. The results quantify risk diversification in renewable energy technologies and show that the associated costs increase exponentially with increasing levels of reliability. Keywords: Risk management, Reliability based design optimization, Stochastic energy planning