A Fast Relax-and-Round Approach to Unit Commitment with Sub Hourly Mechanical and Ramp Constraints

TL;DR

The paper tackles scalable unit commitment under sub-hourly and ramping constraints by relaxing the binary commitment variables and applying a rounding scheme, achieving substantial speedups over traditional MIPs. It extends the Relax-and-Round UC (RRUC) framework to include runtime constraints and high-resolution ramp dynamics, introducing must-run/discretionary classifications, startup penalties, and ramp-state variables to model transitions. The approach demonstrates favorable computational scaling (roughly $O(n^{3/2})$ to $O(n^{4/3})$) with only modest increases in the per-unit cost as the system size grows, and shows robustness to non-constant ramp rates. The results suggest that RRUC can enable large-scale, sub-hourly UC analyses relevant to increasingly distributed and volatile generation, with promising avenues for incorporating transmission constraints and fully temporally coupled objectives in future work.

Abstract

We propose a novel computational method for unit commitment (UC), which does not require linearized approximation and provides several orders of magnitude performance improvement over current state-of-the-art. The performance improvement is achieved by introducing a heuristic tailored for UC problems. The method can be implemented using existing continuous optimization solvers and adapted for different applications. We demonstrate value of the new method in examples of advanced UC analyses at the scale where use of current state-of-the-art tools is infeasible. We expect that the capability demonstrated in this paper will be critical to address emerging power systems challenges with more volatile large loads, such as data centers, and generation that is composed of larger number of smaller units, including significant behind-the-meter generation.

Figures (4)

• Figure 1: Test results for 46-1840 generating units Regev2025. (Top) convergence time for both solvers, RRUC outperforms MIP by orders of magnitude. (Bottom) deviation in objective value calculated as (RRUC-MIP)/MIP. For larger problems, the deviation is below the tolerance set for the solvers.
• Figure 2: Runtime and objective function value for RRUC algorithm including runtime constraints with 462-14784 generators. With $n$ as the number of generators, the runtime scales as $\approx O(n^{3/2})$. This is believed to be ideal in the general case morrison2016. The objective function per generator increases less than 5% for each doubling of the system size.
• Figure 3: A typical production cycle for generator $i$. When the generator is on, it can change its production power between $P_{\min,i}$ and $P_{\max,i}$, provided it does not exceed its ramping power. It can also turn off if it is close enough to $P_{\min,i}$ compared to its ability to ramp down. The only other decision can be made when the generator is off, to prepare for ramping up. During all other periods, the generator is uncontrollable.
• Figure 4: Runtime and objective function value for RRUC algorithm with runtime constraints and ramping constraints for 462-14784 generators. The runtime scales as $\approx O(n^{4/3})$, where $n$ is the number of generators. The objective function per generator increases less than 2% for each doubling of the system size.