Chance-Constrained Equilibrium in Electricity Markets With Asymmetric Forecasts

We develop a stochastic equilibrium model for an electricity market with asymmetric renewable energy forecasts. In our setting, market participants optimize their profits using public information about a conditional expectation of energy production but use private information about the forecast error distribution. This information is given in the form of samples and incorporated into profit-maximizing optimizations of market participants through chance constraints. We model information asymmetry by varying the sample size of participants' private information. We show that with more information available, the equilibrium gradually converges to the ideal solution provided by the perfect information scenario. Under information scarcity, however, we show that the market converges to the ideal equilibrium if participants are to infer the forecast error distribution from the statistical properties of the data at hand or share their private forecasts

Commitment and Dispatch of Heat and Power Units via Affinely Adjustable Robust Optimization

The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem is in essence a multi-stage one. We propose a formulation based on robust optimization where recourse decisions are approximated as linear or piecewise-linear functions of the uncertain parameters. This approach allows for a rigorous modeling of the uncertainty in multi-stage decision-making without compromising computational tractability. We perform an extensive numerical study based on data from the Copenhagen area in Denmark, which highlights important features of the proposed model. Firstly, we illustrate commitment and dispatch choices that increase conservativeness in the robust optimization approach. Secondly, we appraise the gain obtained by switching from linear to piecewise-linear decision rules within robust optimization. Furthermore, we give directions for selecting the parameters defining the uncertainty set (size, budget) and assess the resulting trade-off between average profit and conservativeness of the solution. Finally, we perform a thorough comparison with competing models based on deterministic optimization and stochastic programming.Comment: 31 page

Modelling Dynamic Constraints in Electricity Markets and the Costs of Uncertain Wind Output

Building on models that represent inter-temporal constraints in the optimal production decisions for electricity generation,the paper analysis the resulting costs and their impact on prices during the day. We linearise the unit commitment problem to facilitate th