Solar power forecasting is essential for optimizing energy management and ensuring stable grid operations. Accurately forecasting solar irradiance is a key factor to improve solar power forecasts because of a strong relationship between solar power generation and solar irradiance. However, the accuracy of solar irradiance forecasting is affected largely by the limits inherent in Numerical Weather Prediction (NWP). Thus, there exists a notable opportunity to improve the forecast beyond NWP by using data processing technologies. Among them, one is based on the classification of weather patterns. This paper aims to propose several PV power forecasting methods based on weather patterns, and to develop appropriate models for each classification. The proposed five clustering methods include the use of K-Means or SOM algorithm, a time-based classification, an amplitude threshold-based classification using PSO and GWO algorithms, and a season-based classification. Moreover, three up-to-date AI models including XGBoost, GRU, and Transformer were then applied to predict one-day-ahead PV power. Through a systematic experimentation and comparative analysis, the developed forecasting method considering weather classifications with Transformer training model achieves the highest forecasting accuracy on both deterministic and probabilistic forecasts. Furthermore, the forecasting results also reveal the potential advantages for different clustering methods. The time-based and season-based classification models can capture specific climate characteristics of different time periods and seasons, respectively.