A methodology for building generation trajectories to balance continuous-time load profiles

In power systems, maintaining a balance between generation and load is crucial. Traditional discrete-time dispatch methods often fall short, as they do not account for continuous-time changes in the load profiles throughout the time span. This oversight can lead to inaccuracies in tracing load profiles and even cause ramping resource shortages. In this paper, we propose the idea of continuous-time generation trajectories as dispatch results, to align with continuous-time load profiles. To ensure the solvability of the continuous-time dispatch, we propose an iterative dispatch methodology, which includes two stages: trajectory construction and constraint verification. In the trajectory construction stage, we use a parametric programming model to divide the continuous-time load profiles into multiple segments. Subsequently, we build the generation trajectories for each segment using parametric solutions. In the constraint verification stage, we specifically check the continuous-time ramping constraints. This stage identifies the infeasible trajectories, which will be updated during the next iteration. We repeat this iterative process until each unit has a feasible continuous-time generation trajectory throughout the time span. The effectiveness of our methodology is demonstrated in an illustrative 5-bus system and an actual 661-bus system.