Complex Dissipating Energy Flow Based on Voltage Angle Variations
AbstractThe formulation of the Complex Dissipating Energy Flow (CDEF), used for locating sources of forced oscillations, is expressed by the sum of terms that represent the contributions of power system components to the complex energy function of the system. These terms are calculated through integrals that are evaluated over the trajectory of the system. The integrands are the active and reactive power flows through system branches, and the integration variables are the voltage magnitude and the voltage angle. In this letter, we show that the terms whose integration variable is the voltage magnitude can be grouped separately from the terms whose integration variable is the voltage angle. Furthermore, the contribution to the complex energy function of the system of each of these grouped terms is zero. This allows for an alternative definition of CDEF using only the terms whose integration variable is voltage angle (discarding terms whose integration variable is voltage). It is shown that using the alternative definition for CDEF produces a higher success rate compared to the original CDEF. The tests are performed on the WECC 240 system model considering sources of FO located in the governor and the excitation system of conventional generators, as well as in renewable plants, alternatively.