Periodic steady-state solution methods of electric power transmission and distribution networks
In power quality studies, the total harmonic distortion (THD) at a system bus often needs to be calculated. To find the THD, the steady-state solution of a power system is required. This calculation is often computationally intensive--especially for low-loss systems. For this reason, the rapid calculation of periodic steady-state (PSS) solution of electric power systems are desired. In order to calculate PSS solutions very rapidly, it is undesirable to calculate the transient response of the system. This work focuses on deriving new methods of calculating the PSS solutions and their application to power systems. Two major methods are derived in this work. The first method is applicable to linear, time-invariant (LTI) systems with periodically time-varying forcing functions. This method is based on superposition and time-shifting properties of the system response to only one period of the input. This PSS solution method yields exact solutions. The second method is termed the gain shift formula (GSF) method and is applicable to linear and periodically time-varying (LPTV) systems with periodically time-varying forcing functions. Quasi-periodic systems may also be solved by the GSF method. The calculations of the GSF method are carried out in the Fourier domain; thus, all of the harmonic components of the response are captured at the end of the calculation.
Heydt, Purdue University.
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