Scheduling-control coupling framework for variable-speed pumped storage: Coordinating economics and stability in renewable energy systems

Power systems are evolving toward high variable renewable energy (VRE) penetration, exacerbating the challenge of balancing economics with regulation stability in pumped storage, as frequent output adjustments intensify operational switching demands. Previous studies have separated scheduling and control models, failing to achieve coordinated optimization of economics and stability. Therefore, this paper utilizes the parametric coupling relationships (power, pressure, and water level) between scheduling and control systems to develop a scheduling-control soft-coupling model that incorporates the refined characteristics of fixed-speed units (FSUs) and variable-speed units (VSUs). Additionally, novel economic and stability indicators are proposed, including torque variation range and integral of absolute error for VSU speed. A comprehensive assessment system for operational economics and stability is constructed using the Stochastic AHP-TOPSIS method. Finally, through a Wind-Solar-Pumped Storage Hybrid Energy System (WSPHES) case study, the effects of FSU-VSU configuration ratios, VRE-PS ratios, and optimization strategies b, c, d (corresponding to efficiency-optimal, performance-balanced, and fixed-speed priority, respectively) on economics and stability are investigated. Results demonstrate that in terms of economics, the strategy c outperforms others across all configuration scenarios, enhancing output smoothness while maintaining high operational efficiency. Regarding stability, a fundamental trade-off exists: each additional VSU improves plant efficiency by at least 0.225% but reduces hydraulic stability of power regulation by at least 12.1%. Stochastic AHP-TOPSIS comprehensive assessment reveals that scheduling strategy selection proves more influential than unit configuration itself, with strategy effectiveness ranking (c > d > b) remaining consistent across all renewable energy penetration scenarios. This paper provides a fundamental method for coordinated control of economics and stability.