Three-phase power flow calculation considering probability and interval uncertainties for power distribution systems

Factors such as the stochastic nature of weather condition and arbitrariness of loads make power flow have both probability and interval properties. In order to solve power flow considering probability and interval uncertainties for power distribution systems, an approximate method, which combines affine linear three-phase power flow and Latin hypercube sampling (LHS) method, is proposed. The formulation of affine node voltage is derived based on affine inverse operation and conservative estimation method. Bound influences of interval variables (BIIVs) of affine node voltage are used to determine the upper bound and lower bound of the result of probabilistic power flow. Further decomposition of BIIVs, which contributes to reduce the conservation of results, is given. The effectiveness of the proposed method is verified using the modified IEEE 13-bus system and IEEE 123-bus system by comparing with LHS-Monte-Carlo simulation method.