PV power intra-day predictions using PDE models of polynomial networks based on operational calculus

Abstract

Precise daily forecasts of photo-voltaic (PV) power production are necessary for its planning, utilisation and integration into the electrical grid. PV power is conditioned by the current amount of specific solar radiation components. Numerical weather prediction systems are usually run every 6 h and provide only rough local prognoses of cloudiness with a delay. Statistical methods can predict PV power, considering a specific plant situation. Their intra-day models are usually more precise if rely only on the latest data observations and power measurements. Differential polynomial neural network (D-PNN) is a novel neuro-computing technique based on analogies with brain pulse signal processing. D-PNN decomposes the general partial differential equation (PDE), being able to describe the local atmospheric dynamics, into specific sub-PDEs in its nodes. These are converted using adapted procedures of operational calculus to obtain the Laplace images of unknown node functions, which are inverse L-transformed to obtain the originals. D-PNN can select from dozens of input variables to produce applicable sum PDE components which can extend, one by one, its composite models towards the optima. The PDE models are developed with historical spatial data from the estimated optimal numbers of the last days for each 1-9-h inputs-output time-shift to predict clear sky index in the trained time-horizon.