Dynamic Ward equivalents for transient stability analysis

In an effort to reduce the computing time of transient stability assessment, the paper presents a dynamic equivalent which results from the elimination of the load buses provided with voltage-dependent loads. The elimination is performed through a new version of the Ward equivalencing method. In this approach, the equivalent current injections are expressed in terms of the retained bus angles and a sensitivity matrix W_¯. The nonlinearity of the load flow model is accounted for through piecewise linear approximations by updating the W_¯ matrix whenever the operating point moves beyond the validity of the linearization. The paper also derives the expressions of the incremental changes in the generator electric power and the transient energy function for the reduced system. The approach has been tested on several systems with different sizes and characteristics