Stochastic optimization models for power generation capacity expansion with risk management Maria Teresa Vespucci, Marida Bertocchi, Stefano Zigrino Department of Management, Economics and Quantitative Methods University of Bergamo Via dei Caniana 2, Bergamo 24127, Italy email: maria-teresa.vespucci@unibg.it Laureano F. Escudero Department of Statistics and Operations Research Universidad Rey Juan Carlos c/Tulipan, 28933 Mostoles, Spain email: laureano.escudero@urjc.es Abstract—We propose a two-stage stochastic optimization model for maximizing the profit of a price-taker power producer who has to decide his own power generation capacity expansion plan in a long time horizon, taking into account the uncertainty of the following parameters: fuel costs; market electricity prices, as well as prices of green certificates and CO2 emission allowances; market share. The parameter uncertainty is represented by scenarios on their values along the planning horizon and the associated probability of occurrence. We first discuss the risk neutral stochastic model, that maximizes over all scenarios the net present value of the expected profit along the planning horizon. The risk neutral model does not take into account the variability of the objective function value over the scenarios and, then, the possibility of realizing in some scenarios a very low profit. Several approches have been introduced in the literature for measuring the profit risk. In this work we consider the Conditional Value at Risk, that requires a confidence level to be defined, and the First- order Stochastic Dominance constraints, for which a benchmark need to be assigned. By using a realistic case study, we report the main results of considering risk averse strategies under different hypotheses of the available budget, analysing the impact on the expected profit. I. I NTRODUCTION The incremental selection of power generation capacity is of great importance for energy planners. In this paper we deal with the case of the single power producer who wants to deter- mine the optimal mix of different technologies for electricity generation (ranging from coal, nuclear and combined cycle gas turbine to hydroelectric, wind and photovoltaic), taking into account the existing plants, the cost of investment in new plants, the maintenance cost, the purchase and sales of CO 2 emission allowances and Green Certificates to satisfy regulatory requirements over a long term planning horizon (typically 30 years, or more). Uncertainty of prices (fuels, electricity, CO 2 emission allowances and Green Certificates) should be taken into account, see [5]. However, in practice, producers generally use the Levelized Cost of Electricity (LCoE) to compute the convenience of investments in new power generation technology, i.e. to find the technology that gives the lowest price of electricity or, equivalently, the net present value of the investments equals to zero. In this work, we assume that the producer is a price-taker, i.e. he cannot in- fluence the price of electricity, and propose alternative models for finding an optimal trade-off between the expected profit and the risk of getting a negative impact on the solution’s profit, due to a not-wanted scenario to occur. So this weighted mixture of expected profit maximization and risk minimization undoubtedly may be perceived as a more general model than LCoE. See some approaches in [2], [5], [6], [8], [9], [10], [13], [15], among others. Our model is based on the approach introduced in [15], which we extend by introducing the following elements: 1) consideration of fixed and variable costs in the objective function; 2) design of a risk-averse two-stage stochastic mixed- integer optimization model, by using different risk mea- sures, as an extension of our previous work, see [22]; 3) computational comparison of the risk measures strate- gies, so as to determine the reduction of expected net profit due to risk minimization; We propose a decision support model for a power producer who wants to determine the optimal planning for investment in power generation capacity in a long term horizon. The power producer operates in a liberalized electricity market, where rules are issued by the Regulatory Authorities with the aim of promoting the development of power production systems with reduced CO 2 emissions. Indeed, CO 2 emission allowances have to be bought by the power producer as a payment for the emitted CO 2 . Moreover, the Green Certificate scheme supports power production from Renewable Energy Sources (RES) (e.g. geothermal, wind, biomass and hydro power plants) and penalizes production from conventional power plants (e.g. CCGT, coal and nuclear power plants). Indeed, every year a prescribed ratio is required between the electricity produced from RES and the total electricity produced. In case the actual ratio, attained in a given year, is less than the prescribed one, the power produces must buy Green Certificates, in order to