Short-term power load forecasting with ordinary differential equation substitutions of polynomial networks

• A new neural network type – the differential polynomial neural network is presented.
• Power load historical time-series are described by a general ordinary differential equation.
• Daily load similarity cycle relations combined with time-series are applied for predictions.
• 4 different soft-computing methods are compared in 2 real data sets experiments.

The purpose of the short-term electricity demand forecasting is to forecast in advance the system load, represented by the sum of all consumers load at the same time. Power load forecasting is important for an economically efficient operation and effective control of power systems and enables to plan the load of generating units. A precise load forecasting is required to avoid high generation costs and the spinning reserve capacity. Under-prediction of the demands leads to an insufficient reserve capacity preparation and can threaten the system stability, on the other hand, over-prediction leads to an unnecessarily large reserve that leads to high cost preparations. Differential polynomial neural network is a new neural network type, which decomposes and solves the selective general partial differential equation, which can model a searched function on the bases of observed data samples. It produces an output sum combination of convergent series of selected relative polynomial derivative terms, which can substitute for an ordinary differential equation solution to describe and forecast real data time-series. Partial derivative terms of several time-point variables substitute for the time derivatives of the converted general ordinary differential equation. The operating principles of the proposed method differ significantly from other conventional neural network techniques.