A risk averse stochastic optimization model for power generation capacity expansion

We present a mathematical model for maximizing the benefit of a price-taker power producer who has to decide the power generation capacity expansion planning in a long time horizon under uncertainty of the main parameters. These parameters are the variable production costs of the power plants already owned by the producer as well as of the candidate plants of the new technologies among which to choose; the market electricity price along the horizon, as well as the price of green certificates and CO2 emission permits; the potential market share that can be at hand for the power producer. These uncertainties are represented in a two stage scenario tree, so the model is a two stage stochastic integer optimization one, subject to technical constraints, market opportunities and budgetarial constraints, whose first stage variables represent the number of new power plants for each candidate technology to be added to the existing generation mix (whose construction has to start in) every year of the planning horizon. The second stage variables (i.e., scenario dependent) are the continuous operation variables of all power plants in the generation mix along the time horizon. We start presenting the maximization of the net present value of the expected profit over the scenarios along the time horizon (i.e., considering the so named risk neutral strategy). Alternatively, we consider different risk averse strategies (i.e., Conditional Value at Risk, Shortfall Probability, Expected Shortage and First- and Second-order Stochastic Dominance constraint integer-recourse strategies). By using a pilot case we report the main results of considering the six strategies under different hypotheses of the available budget, analysing the impact of each risk averse strategy on the expected profit. For that purpose we use a state-of-the-art MIP solver, concluding that 1. the technical advantage of replacing the risk neutral with the risk averse strategies needs a substantial increase in the computing requirements, but it strongly reduces the risk of non-wanted scenarios at a price of a relatively small reduction on the expected profit; 2. the risk averse strategies considered provide consistent solutions, since for all of them the optimal generation mix mainly consists of conventional thermal power plants, for low risk aversion, which are replaced by renewable energy sources plants, as risk aversion increases; 3. it is mandatory to replace the plain use of the solver with ad-hoc decomposition algorithms that have the additional feature of tackling cross-scenario constraints.