Stefano Zigrino

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.

A stochastic model for investments in different technologies for electricity production in the long period

We present a single stage stochastic mixed integer linear model for determining 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, maintenance costs, purchase and sale of

Stochastic optimization models for power generation capacity expansion with risk management

{CO}_2

Optimal Planning and Economic Evaluation of Trigeneration Districts

CO2 emission trading certificates and green certificates, in order to satisfy regulatory requirements. The power producer is assumed to be a price-taker. Stochasticity of future fuel prices, which affect the generation variable costs, is included in the model by means of a set of scenarios. The main contribution of the paper, beyond considering stochasticity in the future fuel prices, is the introduction of CVaR risk measure in the objective function in order to limit the possibility of low profits in bad scenarios with a fixed confidence level.

A time consistent risk averse three-stage stochastic mixed integer optimization model for power generation capacity expansion

We present deterministic and stochastic models for determining the optimal mix of different technologies for electricity generation, ranging from carbon, nuclear and combined cycle gas turbine to hydroelectric, wind and photovoltaic, taking into account the actual sites and the cost of investment in new sites, the cost of of mantainance, the use of emission quotas and the relative constraints as well as the green certificates one may use. The stochasticity is related to the future price of energy and to the future price of emissions, in this paper we limit our study to the variaility of fuels. The stochasticity appears in the expected costs and the probability that the total cost do not overcome a specific threshold is taken into account by considering CVaR risk measure. A comparison between the deterministic solution and the stochastic solution shows the role of using the risk the importance to use risk measure in the stochastic long run approach.

A Procedure for the Optimal Management of Medium-voltage AC Networks with Distributed Generation and Storage Devices

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.

A stochastic model for the single producer capacity expansion problem in the Italian electricity market

We present a decision support procedure for the configuration of distributed generation systems in residential districts, where various types of energy demands (electrical load, high and medium temperature thermal load, cooling load) have to be served. In the configuration process alternative solutions have to be compared, both from a technical and an economical point of view, taking into account the energy consumption profiles that vary along the day and along the year, due to the weather conditions. The decision support procedure consists of two steps. In the first step, by solving a mixed integer linear programming model, the annual optimal dispatch of the distributed generation system is determined with a hourly discretization, taking into account technical constraints, load profiles and fuel costs. The optimal dispatch is then used for the economic evaluation of the investment, taking into account prices of commodities, taxation and financial aspects (debt/equity). The decision support procedure allows to compare different alternative plant configurations; it can also be used as a simulation tool, for assessing the system sensitivity to variations of parameter values.

A stochastic model for capacity planning in the electricity production sector in the long run

Trigeneration, or combined cooling, heat and power (CCHP), is the process by which electricity, heating and cooling are simultaneously generated from the combustion of a fuel. Trigeneration systems for serving the electricity, thermal and cooling loads in residential districts are a possible solution to enhance energy efficiency, reduce fossil fuel consumption and increase the use of renewable energy sources in the residential sector. Technical, economical and financial issues have to be taken into account when planning a trigeneration system or when expanding an existing generation system. In this chapter a two-step decision support procedure is presented for analysing alternative system configurations. The first step is based on a mixed integer linear programming model that allows to describe the system components in great detail and computes the annual optimal dispatch of the distributed generation system with a hourly discretization, taking into account load profiles, fuel costs and technical constraints. The optimal dispatch is then used for the economic evaluation of the investment, taking into account prices of commodities, taxation, incentives and financial aspects. The procedure allows to compare alternative plant configurations and can be used as a simulation tool, for assessing the system sensitivity to variations of model parameters (e.g. incentives and ratio debt/equity).