Accurate prediction of photovoltaic power is conducive to the application of clean energy and sustainable development. An improved whale algorithm is proposed to optimize the Support Vector Machine model. The characteristic of the model is that it needs less training data to symmetrically adapt to the prediction conditions of different weather, and has high prediction accuracy in different weather conditions. This study aims to (1) select light intensity, ambient temperature and relative humidity, which are strictly related to photovoltaic output power as the input data; (2) apply wavelet soft threshold denoising to preprocess input data to reduce the noise contained in input data to symmetrically enhance the adaptability of the prediction model in different weather conditions; (3) improve the whale algorithm by using tent chaotic mapping, nonlinear disturbance and differential evolution algorithm; (4) apply the improved whale algorithm to optimize the Support Vector Machine model in order to improve the prediction accuracy of the prediction model. The experiment proves that the short-term prediction model of photovoltaic power based on symmetry concept achieves ideal accuracy in different weather. The systematic method for output power prediction of renewable energy is conductive to reducing the workload of predicting the output power and to promoting the application of clean energy and sustainable development.