Polyhedral Risk Measures and Lagrangian Relaxation in Electricity Portfolio Optimization

We present a multistage stochastic programming model for mean-risk optimization of electricity portfolios containing physical components and energy derivative products. We consider a medium-term time horizon of up to one year. Stochasticity enters the model via the uncertain (time-dependent) prices, electricity demand, and heat demand. The objective is to maximize the expected overall revenue and, simultaneously, to minimize a multiperiod risk measure, i.e., a risk measure that takes into account the intermediate time cash values. We compare the effect of different multiperiod risk measures taken from the class of polyhedral risk measures which was suggested in our earlier work. Furthermore, we discuss how such a mean-risk optimization problem can be solved by dual decomposition techniques (Lagrangian relaxation). Hence, the scope of this presentation, beside the model itself, is the impact of polyhedral risk measures on stochastic programming models with respect to both, results and decomposition structures.