As for the problem of the series and parallel resonance between the capacitors and the system impedance and load impedance

in order to achieve the optimal allocation of capacitors and to avoid resonance

the relationship between the capacitive reactive power and series and parallel resonant frequency is put as a constraint in the mathematical model

considering the resonant case.The improved particle swarm optimization（PSO） that is time-varying nonlinear trigonometric functions to control parameters is proposed to optimize the allocation of the capacitor.Comparing the net loss and economic costs etc before and after the optimal allocation of capacitors

the results show that after the optimal allocation of the capacitors

it will be more economical

and effectively avoid the occurrence of resonance.