Improved Affine Arithmetic-Based Power Flow Computation for Distribution Systems Considering Uncertainties

The randomness characteristics of large-scale grid-integrated intermittent distributed energy resources (DERs) and loads for power consumption pose significant power flow uncertainties to distribution networks. Although affine arithmetic (AA) is popularly and effectively used for uncertain power flow analysis, its nonlinear operation increases the conservatism of the identified solutions. Based on the interval Taylor formula, an improved AA (IAA) is developed to decrease conservatism and then an IAA-based power flow computation is proposed for distribution systems considering uncertainties. First, a multinoise elements affine model is established to predict the DERs' generation, which considers the different effects and correlations of multiple uncertain factors of DERs. Second, an IAA based on the interval Taylor formula was proposed, which linearizes the nonlinear operation of affine division, and avoids the generation of new noise elements. Finally, the IAA is combined with forward/backward power flow computation to solve the uncertain power flow of the distribution network. The effectiveness and advantages of the proposed method are examined on IEEE 33, 69, and 118 systems. The results demonstrate that the proposed method has lower conservatism and higher computational efficiency, and it can provide guidance for power system operators to effectively monitor and control distribution systems under various uncertainties.