Modelling the Photovoltaic Output Power Using the Differential Polynomial Network and Evolutionary Fuzzy Rules

Abstract

The unstable production of renewable energy sources, which is difficult to model using conventional computational techniques, may be predicted to advantage by means of biologically inspired soft-computing methods. The photovoltaic output power is primarily dependent on the solar direct or global radiation, which short-term numerical forecasts are possible to apply for daily power predictions. The study compares two methods, which can successfully model dynamic fluctuant variances of the solar irradiance and corresponding output power time-series. Differential polynomial network is a new neural network class, which defines and substitutes for the general partial differential equation to model an unknown system function. Its total output is composed from selected neurons, i.e. relative polynomial substitution terms, formed in all network layers of a multi-layer structure. The proposed derivative polynomial regression using relative dimensionless fraction units, formed according to the Similarity analysis, can describe and generalize data relations on a wider range of values than defined by the training interval when using standard soft-computing composing techniques that apply only absolute data. 1-variable time-series observations are possible to model by time derivatives of a converted ordinary differential equation, solved analogously with partial derivative substitution terms of several time-point variables.

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

“…6 afternoon). If it is not possible to obtain an acceptable testing error, then a converted local NWP model forecast of cloudiness [29] can be used [7] instead of statistics.…”

“…The resulting pure rational fraction, which represents the Ltransform F(p) of the function f(t), can be reduced to elementary sum fractions (7). The inverse L-transform using OC definitions is applied to them to obtain the original function f(t) of a real variable t (8) described by the ODE…”

“…1). They convert specific second-order sub-PDEs, analogous to the OC ODE conversion (7). The derivatives of two-variable PDEs (3) correspond to the GMDH polynomial members (5).…”

“…These can process 24-h local forecasts of the meso-scale 'Aladin' NWP model to calculate PVP at corresponding times. However, this conversion and refinement of daily solar radiation forecast series is primarily influenced by the accuracy of processed NWP data [7]. Besides this, artificial neural network (ANN) iterative training may provide slightly different prediction results, and thus the final solution is usually the average of several model runs [8].…”

“…These are applied to the latest morning input data to predict PV power in the trained time‐horizon (Section 3). The presented D‐PNN intra‐day statistical predictions better detail daily PVP progress than those of regression or AI techniques and the converted cloudiness forecasts of regional NWP models [7] (Sections 4 and 5).…”