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Highlights • Mid-to-long term wind and solar joint generation prediction model established. • Copula for extracting nonlinear and non-Gaussian distributed key weather factors. • Long short term memory network to construct the prediction model with fewer data. • The proposed method is able to improve prediction accuracy validated by real cases. Abstract The accurate estimation of mid-to-long term wind and photovoltaic power generation is important to the power grid's plan improvement, dispatching optimization, management development, and consumption enhancement. These constitute key factors for the realization of power mutual assistance and complementary dispatch of power generation in the broad area of renewable energy. However, owing to the large time scale of mid-to-long term prediction, the low accuracy of weather prediction, the limited data samples of historical power generation, and the significant difference between power generation prediction and short-term power prediction, short-term power prediction technology cannot be directly copied. Thus, the industry has not established yet an effective approach for mid-to-long term wind and photovoltaic power generation predictions. To solve these problems, this study proposed a method for the mid-to-long term wind and photovoltaic power generation prediction based on copula function and long short term memory network to achieve an effective extraction of the key meteorological factors that affect power generation owing to nonlinear effects and tendencies, and to deeply exploit the long-term dependencies and tendencies from the limited available data samples. Therefore, the proposed approach is suitable for mid-to-long term wind and photovoltaic power generation prediction using limited data samples. Firstly, the non-linear effects and tendency correlation measurements of the copula function were used to extract the key meteorological factors that influence wind and photovoltaic power generation. Secondly, independent wind/photovoltaic prediction models were established based on long short term memory network using the best input condition obtained by comparing these models to the persistence model. Additionally, the independent wind/photovoltaic models were further compared to support vector machine model with the optimal input condition. Thirdly, the joint prediction models of wind and photovoltaic power generation based on long short term memory network were established using different inputs. The persistence model and the support vector machine model were used as benchmarks to compare the elicited performances. Finally, the validity and applicability of the proposed approach were extensively evaluated using actual data from wind farms and photovoltaic power stations in China and the United States. The independent and joint power generation prediction results demonstrated that the proposed approach outperforms both the persistence model and the support vector machine model, and can have widespread applicability in limited data sample cases. [ABSTRACT FROM AUTHOR]