Efficient stochastic analysis of power distribution systems using polynomial models

With ever increasing penetration of distributed generation, voltage control has become a new challenge for distribution networks. Conventionally, to control the system, perturb-and-observe or Jacobian matrix inversion approaches are used to evaluate the impact of active and reactive power of distributed generators on voltage magnitudes. However, these approaches require constantly updating the Jacobian matrix or running several power flow simulations for different system states, which can be computationally cumbersome. In this work, we propose developing polynomial surrogates that approximate the voltage level as a function of power consumption, distributed power generation and power factor of distributed generators. Polynomial surrogates can be efficiently used for probabilistic analysis and control of the distribution network. The effectiveness of the proposed surrogate-based method is demonstrated on the IEEE 33-bus system, in the presence of a large number of correlated random inputs.