Risk-averse capacity planning for renewable energy production

This paper considers the problem of capacity planning and operation of energy grids where the power demands are served from renewable energy sources, such as wind farms, and the transmission network is represented by the high-voltage direct current (HVDC) lines. The principal question considered in this work is whether a risk-averse design of the grid, including the selection of wind farm locations and assignment of power delivery from wind farms to customers, would allow for effective hedging of the risks associated with uncertainties in power demand and production of energy from renewable sources. To this end, the problem is formulated in the general context of supply chain/facility location, with both the supply and the demand being stochastic variates. Several stochastic optimization models are presented and analyzed, including the traditional risk-neutral, or expectation-based model and risk-averse models based on linear and nonlinear coherent measures of risk. Exact solutions algorithms that employ Benders decomposition and polyhedral approximations of nonlinear constraints have been proposed for the obtained linear and nonlinear mixed-integer programming problems. The conducted numerical experiments illustrate the properties of the constructed models, as well as the efficiency of the developed algorithms.