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Solar energy constitutes an effective supplement to traditional energy sources. However, photovoltaic power generation (PVPG) is strongly weather-dependent, and thus highly intermittent. High-precision forecasting of PVPG forms the basis of the production, transmission, and distribution of electricity, ensuring the stability and reliability of power systems. In this work, we propose a deep learning based framework for accurate PVPG forecasting. In particular, taking advantage of the long short-term memory (LSTM) network in solving sequential-data based regression problems, this paper considers the specific domain knowledge of PV and proposes a physics-constrained LSTM (PC-LSTM) to forecast the hourly day-ahead PVPG. It aims to overcome the shortcoming of recent machine learning algorithms that are applied based only on massive data, and thus easily producing unreasonable forecasts. Real-life PV datasets are adopted to evaluate the feasibility and effectiveness of the models. Sensitivity analysis is conducted for the selection of input feature variables based on a two-stage hybrid method. The results indicate that the proposed PC-LSTM model possesses stronger forecasting capability than the standard LSTM model. It is more robust against PVPG forecasting, and more suitable for PVPG forecasting with sparse data in practice. The PC-LSTM model also demonstrates superior performance with higher accuracy of PVPG forecasting compared to conventional machine learning and statistical methods. • Domain knowledge of PV is firstly considered into the deep-learning model. • A two-stage hybrid method is proposed to select the input feature variables. • PC-LSTM is more robust against PV power output forecasting than the basic LSTM. • PC-LSTM has advantages in the forecasting of PV power generation with sparse data. [ABSTRACT FROM AUTHOR]