Multi-objective optimal allocation of distributed generations under uncertainty based on D-S evidence theory and affine arithmetic.

• The AA is used to represent the uncertainty of DGs and loads, which significantly avoids the interval overestimation problem. • The AA power flow calculation is implemented to obtain the affine value of network loss. It facilitates the solution of multi-objective uncertainty optimization. • A multi-objective interval decision-making model and bi-layer optimization method based on D-S ET and GA is proposed. • GA is used as an outer layer optimization and the ET method is used as the inner layer optimization to guide the evolution direction of GA in the outer layer. • The paper considers (1) the weights of decision makers, (2) the uncertainty of DGs and load (3) the penetration of DGs. Many efforts on distributed generation (DG) allocation are based on deterministic methods in previous studies. However, the influence of stochastic fluctuation characteristics of DGs and loads is enormous. Therefore, affine arithmetic (AA) is used to represent the uncertainty, and a multi-objective uncertainty optimization model for DG allocation with minimum investment cost, highest income, lowest environmental cost, and minimal network loss is built in this paper. Then multi-objective interval decision-making and bi-layer optimization method based on D-S evidence theory (ET) and genetic algorithm (GA) is proposed to achieve the optimal allocation of DGs. In the proposed method, GA is used as an outer layer optimization for multi-point searches to generate different allocation schemes. Moreover, the ET method is employed as the inner layer to evaluate the candidate allocation schemes which from the outer layer optimization. Also, the ET method guides the evolution direction of GA in the outer layer. For validating the effectiveness and performance, the proposed method is applied to a typical 33-bus distribution system. The comparison with the existing TOPSIS method demonstrates the advantages when handling the uncertainty of the proposed method and achieves a more robust optimal solution. [ABSTRACT FROM AUTHOR]