Single-phase residential photovoltaic generation is mainly connected to the low voltage grid，Asymmetry of single-phase photovoltaic generation, distribution network and load can cause significant grid unbalanced voltage, affecting the normal operation of grid and load. This paper considers the correlation and uncertainty of single-phase and three-phase photovoltaic generation and load, and studies the random sampling method that takes into account the correlation between photovoltaic generation and load in three-phase systems. Then, with the goal of maximum allowed capacity of photovoltaic generation, the chance constraints of three-phase voltage unbalance is constructed, and a probability optimization model of allowed capacity considering the correlation between photovoltaic generation and load is established based on grid power balance constraints, the Monte Carlo simulation and immune genetic algorithm are used to solve the model. The proposed method is verified by the photovoltaic generation allowed capacity analysis of an actual 380 V power grid.