We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation.
This paper presents model formulations for generators that have the ability to use multiple fuels and to switch between them if necessary. These models are used to generate different scenarios of fuel switching penetration from a test power system. With these scenarios, for a severe disruption in the fuel supply to multiple generators, the paper analyzes the effect that fuel switching has on the resilience of the power system. Load not served is used as the proxy metric to evaluate power system resilience. The paper shows that the presence of generators with fuel switching capabilities considerably reduces the amount and duration of the load shed by the system facing the fuel disruption.
Here, we develop a stochastic optimization model for scheduling a hybrid solar-battery storage system. Solar power in excess of the promise can be used to charge the battery, while power short of the promise is met by discharging the battery. We ensure reliable operations by using a joint chance constraint. Models with a few hundred scenarios are relatively tractable; for larger models, we demonstrate how a Lagrangian relaxation scheme provides improved results. To further accelerate the Lagrangian scheme, we embed the progressive hedging algorithm within the subgradient iterations of the Lagrangian relaxation. Lastly, we investigate several enhancements of the progressive hedging algorithm, and find bundling of scenarios results in the best bounds.
We present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually nondominated solutions. We study the impact of aggregation on two large-scale UC instances: one from the academic literature and the other based on real-world operator data. Our computational tests demonstrate that, when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Furthermore, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.