Sufficient and necessary condition of sensitivity consistency in static equivalent methods

Both power flow states and sensitivities between variables are important information in power system analysis and should be kept consistent before and after equivalence. The general sufficient and necessary condition for sensitivity consistency in equivalent methods is derived. Based on the proposed general condition, it is further derived that Thevenin equivalent method can keep sensitivity consistent before and after equivalence, whereas the specific preconditions for sensitivity consistency are required for the traditional Ward equivalent method and extended Ward equivalent method. These two Ward equivalent methods cannot meet the preconditions in general cases and may lead to significant errors. This conclusion is confirmed by simulation results of the IEEE 39-bus system and an actual power system with 661 buses.