Interval Total Transfer Capability for Mesh HVDC Systems Based on Sum of Squares and Multi-Dimensional Holomorphic Embedding Method

Total transfer capability evaluation is an effective method to analyze the backbone transmission capability among regions. To address renewable energy uncertainties, an interval total transfer capability model based on the multi-dimensional holomorphic embedding method and sum of squares relaxation technique is proposed to solve the regional total transfer capability in meshed high voltage direct current systems. First, the multi-dimensional holomorphic embedding method is used to derive the analytical expressions of regional tie lines. Second, the interval total transfer capability model can be reformulated by two bi-level optimization models. Third, sum of squares relaxation is employed to solve the two optimization problems. Numerical results on a 40-bus European Synthetic System and the Chinese meshed high voltage direct current system validate the effectiveness of the proposed model and method.