A modified affine arithmetic-based power flow analysis for radial distribution system with uncertainty

In a distribution system, the loads and distributed generators connected at a bus have lot of uncertainty due to which the power injections at that bus become uncertain. These uncertainties need to be incorporated in distribution system power flow analysis to get an idea of the uncertainty in the power flow solution. One of the methods used for finding solution intervals for power flow is Monte Carlo simulations. However, Monte Carlo simulations approach suffers from the drawback of large time consumption due to repeated power flows. To overcome this limitation, affine arithmetic based power flow analysis is introduced in literature which is capable of generating solution intervals to the interval power flow problem without the need of repeated power flow analysis. Multiplication operation between two affine terms in conventional affine arithmetic generates an extra noise term in the affine product. In affine based power flow analysis for distribution system, multiplication operation is used repeatedly since backward/forward sweep algorithm is iterative in nature. This generates a large number of noise terms in certain affine parameters which ultimately leads to larger solution intervals for the problem. In the present work, a new formulation of complex affine multiplication is introduced for the affine arithmetic based distribution power flow analysis which does not generate any extra noise term for the resulting complex affine product. The proposed modified affine arithmetic based distribution power flow analysis is tested on IEEE 33, 69, 202 and 874 bus radial distribution systems. All the four test systems are assumed to have distributed generation. The solution intervals obtained are compared with the solution intervals of conventional affine arithmetic based distribution power flow analysis. Results show that the solution intervals of the proposed method are closer to Monte Carlo solution intervals as compared to conventional affine arithmetic based distribution power flow analysis.