Accurate forecasts of photovoltaic power generation (PVPG) are essential to optimize operations between energy supply and demand. Recently, the propagation of sensors and smart meters has produced an enormous volume of data, which supports the development of databased PVPG forecasting. Although emerging deep learning (DL) models, such as the long short-term memory (LSTM) model, based on historical data, have provided effective solutions for PVPG forecasting with great successes, these models utilize offline learning. As a result, DL models cannot take advantage of the opportunity to learn from newly-arrived data, and are unable to handle concept drift caused by installing extra PV units and unforeseen PV unit failures. Consequently, to improve day-ahead PVPG forecasting accuracy, as well as eliminate the impacts of concept drift, this paper proposes an adaptive LSTM (AD-LSTM) model, which is a DL framework that can not only acquire general knowledge from historical data, but also dynamically learn specific knowledge from newly-arrived data. A two-phase adaptive learning strategy (TP-ALS) is integrated into AD-LSTM, and a sliding window (SDWIN) algorithm is proposed, to detect concept drift in PV systems. Multiple datasets from PV systems are utilized to assess the feasibility and effectiveness of the proposed approaches. The developed AD-LSTM model demonstrates greater forecasting capability than the offline LSTM model, particularly in the presence of concept drift. Additionally, the proposed AD-LSTM model also achieves superior performance in terms of day-ahead PVPG forecasting compared to other traditional machine learning models and statistical models in the literature.