A Probabilistically Constrained Extension to the Generation Expansion Problem

This paper presents a probabilistic modeling approach to the generation expansion problem, where the energy manager of a firm aims at minimizing the investment costs of an energy park subject to the stochastic supply-demand balance constraint. We consider a reliability-based framework, where the energy manager determines robust generation expansion by imposing a probabilistic guarantee on the demand coverage distribution, specifying the required system reliability. We compare two solution methodologies to solve the probabilistically constrained generation expansion problem, i.e. (i) the sample approach and (ii) the sample average approximation. Applicability of the model is demonstrated in the use case, where the two renewable energy sources wind and solar technology are considered. We recover the energy manager's efficient frontier characterizing the optimal level of investment in renewable energy technologies as a function of the ex-ante imposed level of reliability, which quantifies the substitution rate of investment and reliability. The portfolio selection depends on the required reliability and is shifted towards a higher share in solar power when required reliability increases. Within the probabilistically constrained framework we demonstrate the potential of Demand Side Management (DSM) in reducing capital expenditures. With increasing participation in DSM, the energy manager is able to reduce the necessary level of investment to obtain required reliability, thereby mitigating investment risks