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 is 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 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, due to inclusion of differential equations representing DC dynamics directly in the TEF, the calculation of post-fault equilibrium point is done only once. This leads to considerable reduction in CPU time. The method is validated using 12-bus and 30-bus AC/DC test systems by comparing results with those obtained from time simulation.