Charging, Generation, and PID Control-Activation Characteristics of a One-Pipe–Two-Unit Hydraulic Short-Circuit Pumped-Storage System: A Simulation Case Study

To address the limited pumping-mode flexibility of fixed-speed pumped-storage units, this paper presents a simulation case study of a one-pipe–two-unit parallel ternary system developed in OpenModelica and coupled with Python 3.7. The study examines pure charging and generation, hydraulic short-circuit (HSC) charging, and the PID control-activation transient at nominal speed. A 50 MW benchmark reproduces published pump and turbine shaft powers to within approximately 0.5%, while the system-efficiency difference is 0.14 percentage points, supporting implementation consistency; no plant-measurement validation is claimed. Dual-pump operation reduces the charging time by approximately 44% relative to single-pump operation but lowers efficiency, whereas dual-turbine operation is slightly more efficient because of improved per-unit flow matching. Across the full-cycle HSC sweep, average efficiency increases from 38.6% at 40 MW to 74.1% at 90 MW as internal recirculation decreases. In the PID sensitivity screen, the proportional gain k has the largest effect on the response, a small integral time Ti amplifies sensitivity to k and can increase overshoot or hydraulic loading, and the derivative coefficient wd has only a minor effect within the tested range. The numerical bounds are specific to the selected characteristic maps, reservoir, and waterway; the results are intended as retrofit-screening guidance rather than universal design limits.