Under the global energy transition and the "dual-carbon" strategy, photovoltaic power generation has rapidly expanded as a key component of clean energy systems. However, photovoltaic output is strongly influenced by abrupt weather changes and irradiance variability, exhibiting pronounced intermittency, randomness, and fluctuations. Meanwhile, existing forecasting models still suffer from limited adaptability, weak physical consistency, and degraded accuracy under complex weather conditions. In order to meet this challenge, this study proposes a physically constrained hybrid deep learning photovoltaic power prediction framework integrating weather clustering and signal decomposition. First, key meteorological variables are selected using the Spearman correlation coefficient, and K-means is employed to classify the data into five refined weather types-sunny, cloudy, overcast, rain/snow, and dust type-thereby reducing sample heterogeneity and enhancing the extraction of weather-dependent power patterns. Second, an improved grey wolf optimizer adaptively tunes the parameters of variational mode decomposition to achieve high-fidelity component separation and suppress mode aliasing. A temporal convolutional network and extended long short-term memory hybrid model is then constructed, where the temporal convolutional network captures multi-scale local features and the extended long short-term memory enhances long-term dependency modeling. Furthermore, the Softplus activation function is combined with the composite loss function embedded with physical constraints to ensure that the prediction results are strictly consistent with the physical consistency of photovoltaic power generation. Finally, a support vector machine is used to calibrate the initial prediction error sequence, further improving forecasting stability. The validation results of a photovoltaic power station data set in Northwest China show that the proposed model is significantly better than the 11 mainstream models in many evaluation indexes. The effectiveness of each module was verified by ablation experiments. The multi-step prediction and tests on data sets in different regions and different time scales further showed that the model still maintained excellent generalization ability and robustness under complex weather conditions such as rain/snow and dust type. This study provides a new technical path for high-precision prediction of photovoltaic power, so as effectively improve the efficiency of grid dispatching and operation safety.