Intensity of solar irradiance directly affects solar power generation and this makes solar irradiance forecasting a vital process in energy management systems. Existing forecasting systems show positive solar irradiance forecasting performance, but most of them are not accurate in real-life especially when there are fast-moving clouds, causing highly fluctuating solar irradiance profile, which is difficult to predict. Moreover, the requirement to pre-train Artificial Intelligence-based forecasting system has made solar irradiance forecasting impractical as long-hour weather profiles need to be collected prior to deployment. This paper proposes a new artificial intelligent algorithm namely the Regression Enhanced Incremental Self-organising Neural Network (RE-SOINN) for accurate (even for highly fluctuating profile) and adaptive solar irradiance forecasting. This algorithm works by learning the time-series solar irradiance data incrementally and predicting it in real-time. It is novel in terms of enabling the learning of data from discrete (as in the conventional) to continuous using the regression method. The proposed algorithm further improves the prediction accuracy by decomposing the input data into two components (low and high frequency components) before feeding into the RE-SOINNs. Results showed that the proposed algorithm achieves higher accuracy compared to the Persistence model, Exponential Smoothing Model and Artificial Neural Networks. (C) 2020 Elsevier Ltd. All rights reserved.