Pumping systems serve as critical fluid transportation facilities, accounting for a significant proportion of global electricity consumption. In engineering applications, parallel pumping operation is a standard solution to meet large flow and variable operating/load demands. Accordingly, an energy-optimal control strategy for parallel pumping systems is proposed, where optimal frequency switching points are used to schedule pump start/stop decisions and their timing. This strategy is based on the principle of equal-speed operation for identical pumps, and its solution constitutes a complex non-linear constrained optimization problem. To efficiently solve this problem, a customized hybrid intelligent optimization algorithm (ABCG) is developed. By redesigning the initialization, boundary handling, and search operators, the algorithm improves robustness in global optimization. Experimental results indicate that the proposed ABCG algorithm ranks first in the Friedman mean rank tests on benchmark functions and demonstrates rapid convergence. Furthermore, based on this strategy, the optimal frequency switching points were quantitatively determined to be 39 Hz (for single-to-dual pump transition) and 43 Hz (for dual-to-triple pump transition). Compared to traditional sequential operation, the new strategy achieves a maximum relative energy-saving rate of 13.05%, validating the feasibility and effectiveness of this active switching control scheme in practical industrial processes.
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