A novel OPF analysis for optimizing wind power curtailment in AC/multi-terminal VSC-HVDC systems under frequency constraints

This graphical abstract illustrates the integrated optimization framework for hybrid AC/multi-terminal voltage-source converter-based high-voltage direct-current systems, highlighting how steady-state and dynamic constraints are simultaneously incorporated in the optimal power flow formulation to determine wind power curtailment levels. 1. Constraint Layer (Top) The framework is distinguished by its dual-constraint approach. Steady-state constraints ensures the system satisfies power flow limits (thermal ratings, voltage limits). Dynamic constraints (Highlighted in Red): This is the core novelty. It enforces stability limits determined by time-domain simulations, specifically frequency nadir (after a disturbance) and DC voltage deviations in the VSC-HVDC system. 2. System & Control Layer (Middle) The constraints are applied to the physical components of the hybrid grid. Wind output curtailment (Green): The primary control variable used to balance generation cost against system stability. hybrid AC / Multi-terminal VSC-HVDC system: These represent the hybrid network model where the interaction between AC frequency support and DC voltage stability is analyzed. 3. Optimization Layer (Bottom) OPF Optimizer: This block represents the evolutionary algorithm that processes the inputs from the layers above. It iteratively adjusts control variables (like wind power curtailment) to find the solution that minimizes generation cost without violating the critical dynamic constraints. • Novel optimal power flow framework integrates dynamic frequency and DC voltage constraints. • Wind curtailment optimized considering frequency support by multi-terminal voltage-source converter-based high-voltage direct-current systems. • Evolutionary algorithm couples steady-state analysis with dynamic constraints. • Lowest curtailment achieved when all voltage-source converters provide frequency regulation. • DC voltage limits significantly increase required wind curtailment levels. A novel optimal power flow formulation for AC/multi-terminal voltage-source converter-based high-voltage direct-current systems is developed to calculate the wind power curtailment level considering frequency constraints. The objective function minimizes the total generation cost. Steady-state and dynamic behaviors of the power system, including wind generation and the frequency support of the multi-terminal high-voltage direct-current system, are included as additional constraints. The frequency support provided by a multi-terminal high-voltage direct-current system requires adjustments in the active power flow of voltage-source converters, which leads to DC grid voltage fluctuations. A DC voltage constraint is incorporated to prevent excessive DC voltage deviation. Multiple scenarios with different multi-terminal control methods are simulated. The optimal power flow problem can be solved using an evolutionary optimization process. First, the steady-state constraints are evaluated based on power flow analysis for each control vector. Time-domain simulations are conducted to check dynamic constraint violations. The lowest wind curtailment levels are obtained when all voltage-source converter stations participate in frequency support. However, the curtailment level increases once DC voltage constraints are imposed. The most significant curtailment level increase occurs when all converters contribute to frequency regulation.