To accurately simulate the impact of distributed photovoltaic (PV) integration on the uncertain power flow distribution in distribution networks

an affine optimization method for the probability interval power flow of the distribution network based on holomorphic embedding is proposed. First

an affine model for bus voltages and power is established

and an embedding factor is introduced to construct the holomorphic embedded affine optimization power flow model. A focal element model for distributed PV output is developed

transforming the probabilistic interval power flow model based on focal elements into the holomorphic embedded affine optimization power flow model. A hybrid box-ellipsoidal uncertainty set model is established to capture the correlation between interval variables

which is then converted into affine constraints and solved simultaneously within the holomorphic embedded affine optimization power flow model. Finally

the probability bounds of the probabilistic interval power flow solution for the distribution network are obtained based on evidence theory. Case study results demonstrate that the holomorphic embedded affine optimization power flow algorithm exhibits lower conservatism and is more suitable for uncertainty analysis under larger fluctuation intervals. Additionally

the hybrid box-ellipsoidal uncertainty set model is more accurate than other correlation models and can effectively reflect the influence of correlation coefficients on the computational results.