Optimization-Based Cost-Frequency Trade-Off Analysis of Active Power Reallocation in Bipolar MTDC Systems

In multi-terminal DC (MTDC) systems, converter outages require immediate active power reallocation among healthy converters to maintain the stability of interconnected AC grids. While previous studies mainly focused on control strategies for DC power flow, the economic implications for AC systems including operational costs and frequency stability impacts remain insufficiently addressed. This study proposes an optimization framework to simultaneously minimize the total adjustment cost and frequency deviation by determining optimal active power reallocation among converter stations. The proposed model incorporates multiple types of balancing reserves characterized by distinct cost structures and activation conditions. A four-terminal bipolar VSC-MTDC system is simulated during a converter trip scenario, and the impact of active power reallocation is evaluated in terms of system stability and adjustment cost. By varying the cost-weighting factor, a Pareto front is obtained with three representative operating points: cost-minimization,compromise, and frequency-minimization cases, yielding total adjustment costs of 5.524-5.973 million JPY and cumulative frequency deviations across all interconnected AC systems of 10.125-10.884 Hz. Compared with a baseline scenario without optimization, the proposed framework achieves 20.7-26.7% cost reduction and 26.1-31.3% frequency improvement. The results show that the system operator can select the operation point of the MTDC system based on the specific priorities and system conditions.