Two-stage stochastic mixed integer optimization models for power generation capacity expansion with risk measures

We present two-stage stochastic risk averse optimization models for the power generation mix capacity expansion planning in the long run under uncertainty. Uncertainty is described by a set of possible scenarios in the second stage and uncertain parameters are the unit production costs of the existing power plants as well as those of the candidate plants of new technologies among which to choose, the market electricity price, the price of green certificates and the emission permits and the potential market share of the producer. The problem is expressed as a two-stage stochastic integer optimization model subject to technical constraints, market opportunities and budget constraints. First stage variables represent the number of new power plants for each candidate technology to be added to the existing generation mix every year of the planning horizon. Second stage variables are the continuous operation variables of all power plants in the generation mix along the time horizon. We solve the problem of the maximization of the net present value of the expected profits along the time horizon using both a risk neutral approach and different risk averse strategies (conditional value at risk, shortfall probability, expected shortage and first- and second-order stochastic dominance), under different hypotheses of the available budget, analysing the impact of each risk averse strategy on the expected profit. Results show that risk control strongly reduces the possibility of reaching unwanted scenarios as well as providing consistent solutions under different strategies.