Integration of HVDC control dynamics into transient energy functions

A common approximation used in the formulation of transient energy functions (TEFs) for ac/dc power systems involves the omission of dc control dynamics. The differential equations representing the dc system dynamics are used to track the fault-on trajectory, but not to derive the TEF. This approach leads to an error in TEF-based stability prediction. In this paper, a method is presented to derive the TEF with dc system dynamics explicitly integrated. By using this comprehensive transient energy function, the accuracy of the stability prediction in ac/dc systems is improved. In addition, because differential equations representing dc dynamics are included directly in the TEF, the calculation of the post-fault equilibrium point is done only once. This leads to a considerable reduction in CPU time. The method is validated by comparing results from 12-bus and 30-bus ac/dc test systems with those obtained from time simulation.