Unit Commitment Without Commitment: A Dynamic Programming Approach for Managing an Integrated Energy System Under Uncertainty

Though variability and uncertainty have always posed challenges for power systems, the increasing use of renewable energy sources has exacerbated these issues. At a vertically integrated utility, the system operator manages many generation units—renewable and otherwise—and storage units to ensure that the total energy produced matches contemporaneous demand. Current industry practice at these utilities involves solving “unit commitment” and “economic dispatch” optimization problems to choose production plans. These models, though complex, do not explicitly incorporate uncertainty. In this paper, we develop a dynamic programming approach to help system operators manage production under uncertainty. We formulate the problem as a stochastic dynamic program and use Lagrangian methods to decompose the system across units. The Lagrangian model relaxes the demand-matching constraint and introduces stochastic Lagrange multipliers that can be interpreted as prices representing the varying marginal value of energy production; each unit is then operated to maximize its own expected “profit” given these uncertain prices. These unit-specific value functions are then used to incorporate longer-term effects in dispatch decisions. The unit-specific value functions also provide a way to value generation and storage units in an uncertain environment. We develop relevant theory and demonstrate this dynamic approach using data from the Duke Energy Carolinas and Progress systems. Our numerical experiments demonstrate that this dynamic approach is computationally feasible at an industrial scale and can improve current practice. Specifically, our results suggest that this dynamic approach can reduce operational costs by about 2% on average in the present Duke Energy system and, in a “future” system with increased solar and storage capacity, can reduce operational costs by 4%–5% on average. Perhaps more strikingly, this dynamic approach, on average, performs within 0.2%–0.3% of production plans based on perfect foresight about future net demands.