Stochastic assessment of distribution system resonance frequencies with capacitors or shunt filters

The paper explores the statistical harmonic response of power systems due to manufacturing tolerances of capacitor and shunt filter banks. Expressions to deterministically locate the resonance frequencies of power systems with capacitors and shunt filters are provided. From these expressions, the stochastic behavior of resonance frequencies due to random variations of system and equipment parameters is studied, and analytical expressions of probability density functions of these frequencies are obtained. Finally, the results are compared with Monte Carlo simulations to check their validity and their practical application is discussed.