Short-term optimal scheduling of a cascade hydropower-wind-photovoltaic-concentrated solar power hybrid power system considering dynamic frequency security constraints and flexible load response

As the penetration of renewable energy sources such as wind and photovoltaic generation continues to rise, the inherent randomness and intermittency of their output pose significant challenges to system frequency stability. To address the limited frequency regulation capability under high renewable penetration, this paper proposes a short-term optimal scheduling approach for a cascade hydropower-wind-photovoltaic-concentrated solar power hybrid system that explicitly incorporates dynamic frequency security constraints. First, a dynamic frequency constraint framework is developed that simultaneously accounts for inertial response, the rate of change of frequency and nadir frequency limits, and these constraints are embedded in the short-term scheduling framework as a mixed-integer linear programming formulation. Second, a coordinated frequency regulation strategy is then proposed for cascade hydropower and concentrated solar power units, with additional frequency support provided through reserved capacities of wind and photovoltaic units. Furthermore, a price-responsive flexible load model is introduced to achieve refined source–load coordination. Simulation studies on an extended IEEE 30-bus system demonstrate that the proposed approach improves the frequency nadir from 49.62 Hz to 49.94 Hz and reduces the maximum rate of change of frequency from 0.8357 Hz/s to 0.1378 Hz/s, thereby significantly enhancing the frequency-security margin. Meanwhile, the flexible load strategy reduces unnecessary hydropower cycling, increases renewable utilization, and improves overall economic performance. Thus, the proposed joint optimization of multi-energy coordinated frequency regulation and flexible load response can substantially improve the frequency security and economy of high-RES penetration power systems, providing a feasible solution for developing safe, economical, and efficient low-carbon power systems.