Optimal power flow in hybrid AC-DC systems considering N-k security constraints in the preventive-corrective control stage

The optimal power flow methods for AC-DC systems containing VSC-HVDC generally only consider the economy during normal operation, overlooking the distribution of line transmission power in fault conditions. As a result, lines that continue to operate after a fault may experience overloading or operate at full capacity. Thus, a method for optimal power flow calculation is proposed that incorporates N-k security constraints in the preventive-corrective control stage for secure and economic operation of hybrid AC-DC systems. This method ensures that the line transmission power in the system meets the limits in the normal, short-term fault, and long-term fault states. In addition to the optimal power flow in the normal state, the method incorporates the system's imbalance as an indicator to evaluate system resilience. It combines this indicator with the economic, network loss, and performance metrics of the system, forming a two-stage bi-level multi-objective optimization model. Furthermore, to address the curse of dimensionality in anticipating system fault sets, a method for generating the anticipated fault set using non-sequential Monte Carlo simulation is proposed, along with a fault scenario search approach based on robust thinking to identify the most severe faults. Finally, the traditional IEEE 30-bus system was improved, and simulation verification was conducted using examples of an AC/DC system with a three-terminal DC network and a wind-solar-storage hybrid AC/DC system with a three-terminal DC network. The simulation results indicate that the proposed optimal power flow method considering the preventive-corrective control stage with N-k security constraints can effectively enhance system resilience. Furthermore, it improves the economic efficiency while ensuring the secure operation of the system.