Photovoltaic power one-day and multistep-hourly AI predictions using node-by-node evolved binomial tree structures to form L-transformed PDE modules

Abstract Photovoltaic (PV) power is generated by two common types of solar components that are primarily affected by fluctuations and development in cloud structures as a result of uncertain and chaotic processes. Local PV forecasting is unavoidable in supply and load planning necessary in integration of smart systems into electrical grids. Intra- or day-ahead modelling of weather patterns based on Artificial Intelligence (AI) allows one to refine available 24 h. cloudiness forecast or predict PV production at a particular plant location during the day. AI usually gets an adequate prediction quality in shorter-level horizons, using the historical meteo- and PV record series as compared to Numerical Weather Prediction (NWP) systems. NWP models are produced every 6 h to simulate grid motion of local cloudiness, which is additionally delayed and usually scaled in a rough less operational applicability. Differential Neural Network (DNN) is based on a newly developed neurocomputing strategy that allows the representation of complex weather patterns analogous to NWP. DNN parses the n-variable linear Partial Differential Equation (PDE), which describes the ground-level patterns, into sub-PDE modules of a determined order at each node. Their derivatives are substituted by the Laplace transforms and solved using adapted inverse operations of Operation Calculus (OC). DNN fuses OC mathematics with neural computing in evolution 2-input node structures to form sum modules of selected PDEs added step-by-step to the expanded composite model. The AI multi- 1…9-h and one-stage 24-h models were evolved using spatio-temporal data in the preidentified daily learning sequences according to the applied input–output data delay to predict the Clear Sky Index (CSI). The prediction results of both statistical schemes were evaluated to assess the performance of the AI models. Intraday models obtain slightly better prediction accuracy in average errors compared to those applied in the second-day-ahead evening approach. However, the first-morning strategy application includes a much more complicated and time-consuming procedure, so in conclusion, the second one-mode series processing could be recommended. Model statistics are generally more successful than NWP data processing due to limitations, delays, and unavailability of free radiation or cloudiness forecasts in the systems. An all-day model enables the prediction of complete PVP periods in sequenced computing with acceptable operational quality in the late afternoon, which is inevitable in day-ahead management and load scheduling in smart grids based on PV energy.