Mean‐risk optimization of electricity portfolios

Abstract

We present a mathematical model with stochastic input data for mean-risk optimization of electricity portfolios containing several physical components and energy derivative products. The model is designed for the optimization horizon of one year in hourly discretization. The aim consists in maximizing the mean book value of the portfolio at the end of the optimization horizon and, at the same time, in minimizing the risk of the portfolio decisions. The risk is measured by the conditional value-at-risk and by some multiperiod extension of CVaR, respectively. We present numerical results for a large-scale realistic problem adapted to a municipal power utility and study the effects of varying weighting of risk

Optimization of Electricity Retailer's Contract Portfolio Subject to Risk Preferences

“…These, however, have not included the correlation between price and load. For example, [13] simulates uncertainties accounting for mean-reversion based on an extended Ornstein-Uhlenbeck process [14], [15] construct their scenario trees using Monte Carlo simulation and a scenario reduction technique [6], [16] uses scenarios that are based upon user-specified moments; while various financial market models have been used in electricity markets to model options and the dynamics of the forward prices [17]- [21]. Overall, there exists an extensive line of research in scenario generation techniques [22]- [27], but, as far as we are aware, contract portfolio optimization within power risk management has not adequately reflected the correlation between load and spot prices.…”

“…Consequently, conditional-VAR (CVAR), which measures the weighted average loss of the tail events, for a given fractile, is "coherent" and theoretically preferable [35]. Furthermore, since it can be formulated using linear programming [37], CVAR constraint portfolio optimizations have gained popularity [13], [15], [38]- [40]. Hence, we use CVAR as our key risk measure and show that by specifying multiple constraints in intermediate time periods as well as at the end, it is possible to control for risk throughout the contract spanning horizon.…”

“…The retailer seeks to minimize the expected cost of establishing these contracts subject to various risk constraints [13], [15], [38]. The problem is also analogous to that faced by an electricity generator who must produce electricity at an uncertain load level and sell this electricity at an uncertain spot price in a setting where it can also use forward contracts for hedging [42], [43].…”

Polyhedral risk measures in electricity portfolio optimization

“…The only integer variables in the model are the decisions whether a certain contract is to make or not. See [4] for further details.…”

“…In this paper, such risk measures and their effect in stochastic programs will be compared in a simulative study of a real world application model. We use the electricity portfolio optimization model presented in [4] which is a multistage stochastic programming model set up for a municipal power utility to optimize power production and electricity trading under uncertainty over a period of one year. The objective is to minimize the expected overall cost and a multiperiod risk measure simultaneously.…”