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

TL;DR

This paper introduces a robust optimization framework for joint heat and power unit commitment and dispatch, effectively managing uncertainty and multi-stage decision-making to improve system reliability and economic performance.

Contribution

It develops a novel affinely adjustable robust optimization model for heat and power systems, incorporating multi-stage decision rules and providing practical guidelines for uncertainty set selection.

Findings

Piecewise-linear decision rules outperform linear rules in robustness.

The proposed model achieves better trade-offs between profit and conservativeness.

Robust optimization outperforms deterministic and stochastic models in uncertain scenarios.

Abstract

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.