Risk-sensitive optimal switching

We propose a new practical methodology for risksensitive stochastic optimal control, showing that material decreases in risk indices are possible with relatively little loss of average case performance. Cost optimisation of energy system assets has typically been carried out under the assumption of risk-neutrality, minimising average operational costs. The risk profile of control strategies is thereby ignored, despite the fact that liberalised electricity markets can be highly volatile and financial risk is a material consideration. In a flexible energy system with cogeneration and heat storage, however, it is possible to exploit variation in wholesale price level or volatility (or both) by shifting heat demand through time and varying electricity demand, achieving a balance between low average cost and low volatility which takes account of risk preferences. Based on least squares Monte Carlo regression, our proposed method optimises an exponential objective function containing a risk sensitivity parameter which may then be tuned to achieve the desired tradeoff. We provide a realistic case study of a flexible district energy system, where local heat and electricity demand must be satisfied at minimum cost subject to stochastic price dynamics and the physical constraints of the system. In this example we compare risk-neutral and risk-sensitive optimal strategies and show consistent changes in economic risk under two different risk measures. Keywords—risk-sensitive control, storage, risk measures, optimal switching, district energy systems.