Modal-Coherent Equivalents Derived from an RMS Coherency Measure

An algebraic formula is derived which relates the rms coherency measure, evaluated over an infinite interval for step disturbances in mechanical input power, to the parameters of the power system state model and the disturbance vector. This expression eliminates the need for simulation to determine the coherency measure as is required when a max-min coherency measure is used to identify coherent groups. It is shown that specific probabilistic disturbances cause the rms measure to be a function of system structure alone, allowing coherent equivalents to be constructed which do not depend on the location of any particular disturbance when these probabilistic disturbances are used to determine the coherent generators for aggregation.