Wind and photovoltaic power generation exhibit strong randomness and volatility. Improving the prediction accuracy is of great significance for constructing new power systems. Considering the certain correlation between wind and photovoltaic output in the same region, a short-term wind and photovoltaic power correlation probability interval prediction model based on similar day clustering and whale optimization algorithm-bidirectional long short-term memory neural network-Copula（WOA-BiLSTM-Copula) algorithm is proposed. Firstly, the K-means clustering algorithm is adopted to divide the numerical weather prediction （NWP） dataset, and wind and photovoltaic joint output typical similar day scenarios with correlation are extracted based on Kendall and Spearman correlation coefficients. Secondly, the non-parametric kernel density estimation method is used to establish Copula model for similar day scenes, and the optimal Copula function types of wind and photovoltaic output are determined. Then, the WOA is trained to optimize the BiLSTM and perform point predictions on wind power and photovoltaic power. Finally, the Monte Carlo method is used to sample the optimal Copula function, and the correlation probability prediction interval is generated based on wind and photovoltaic point prediction values. The simulation results show that the proposed model can effectively extract the correlation characteristics of wind and photovoltaic output, and the accuracy is higher than the existing models, which verifies the effectiveness of the model.