Moment-based distributionally robust joint chance-constrained retrofit planning for wind-storage-thermal systems considering multiple time-scale correlations

Retrofitting existing thermal units effectively improves the power system's flexibility. However, decisions at multiple time scales (planning and operational) exist in the retrofit planning problem. Existing retrofit planning models have ignored the interaction of long- and short-term uncertainties. Correlations between the random variables were also ignored. Neglecting the above issues leads to suboptimal retrofit plans and increases the total cost. This study proposes a coordinated retrofit planning model for wind-storage-thermal systems, considering lowering the minimum load, improving the ramp rates, and configuring energy storage. First, an improved moment-based ambiguity set is constructed considering the multi-time-scale correlations of wind generation and load. Then, to alleviate multiple time-scale uncertainties, a distributionally robust joint chance-constrained retrofit planning model is developed based on the proposed ambiguity set. To ensure computational tractability, the nonconvex distributionally robust planning model is approximately converted to a mixed-integer semidefinite programming problem. The IEEE 39- and 118-bus test systems were modified to verify the proposed model, showing that the proposed distributionally robust coordinated planning model makes optimal tradeoffs between the investment and operational costs to minimize the total cost. Compared to the existing moment-based distributionally robust planning model, the conservatism of the proposed model was reduced by considering the multiple time-scale correlations. The proposed distributionally robust model outperformed the existing methods in terms of lower cost (−9.82%), violation probability (−66.31%), and higher system flexibility.