Concerns over fossil fuels and depletable energy sources have motivated renewable energy sources utilization, such as solar photovoltaic (PV) power. Utilities have started penetrating the existing primary grid with renewable energy sources. However, penetrating the grid with photovoltaic energy sources degrades the stability of the whole system because photovoltaic power depends on solar irradiance, which is highly intermittent. This paper proposes a prediction method for non-stationary solar irradiance. The proposed method uses an adaptive extreme learning machine. The extreme learning machine method uses approximated sigmoid and hyper-tangent functions to ensure faster computational time and more straightforward microcontroller implementation. The proposed method is analyzed using the hourly weather data from a specific site at Najran University. The data are preprocessed, trained, tested, and validated. Several evaluation metrics, such as the root mean square error, mean square error, and mean absolute error, are used to evaluate and compare the proposed method with other recently introduced approaches. The results show that the proposed method can be used to predict solar irradiance with high accuracy, as the mean square error is 0.1727. The proposed approach is implemented using a solar irradiance sensor made of a PV cell, a temperature sensor, and a low-cost microcontroller.