Short-term power demand forecasting using the differential polynomial neural network

Power demand forecasting is important for economically efficient operation and effective control of power systems and enables to plan the load of generating unit. 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. A precise load forecasting is required to avoid high generation cost 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 a high cost preparations. Differential polynomial neural network is a new neural network type, which forms and resolves an unknown general partial differential equation of an approximation of a searched function, described by data observations. It generates convergent sum series of relative polynomial derivative terms which can substitute for the ordinary differential equation, describing 1-parametric function time-series. A new method of the short-term power demand forecasting, based on similarity relations of several subsequent day progress cycles at the same time points is presented and tested on 2 datasets. Comparisons were done with the artificial neural network using the same prediction method.Web of Science8230629

Solar and wind quantity 24 h-series prediction using PDE-modular models gradually developed according to spatial pattern similarity

The design and implementation of efficient photovoltaic (PV) plants and wind farms require a precise analysis and definition of specifics in the region of interest. Reliable Artificial Intelligence (AI) models can recognize long-term spatial and temporal variability, including anomalies in solar and wind patterns, which are necessary to estimate the generation capacity and configuration parameters of PV panels and wind turbines. The proposed 24 h planning of renewable energy (RE) production involves an initial reassessment of the optimal day data records based on the spatial pattern similarity in the latest hours and their follow-up statistical AI learning. Conventional measurements comprise a larger territory to allow the development of robust models representing unsettled meteorological situations and their significant changes from a comprehensive aspect, which becomes essential in middle-term time horizons. Differential learning is a new unconventionally designed neurocomputing strategy that combines differentiated modules composed of selected binomial network nodes as the output sum. This approach, based on solutions of partial differential equations (PDEs) defined in selected nodes, enables us to comprise high uncertainty in nonlinear chaotic patterns, contingent upon RE local potential, without an undesirable reduction in data dimensionality. The form of back-produced modular compounds in PDE models is directly related to the complexity of large-scale data patterns used in training to avoid problem simplification. The preidentified day-sample series are reassessed secondary to the training applicability, one by one, to better characterize pattern progress. Applicable phase or frequency parameters (e.g., azimuth, temperature, radiation, etc.) are related to the amplitudes at each time to determine and solve particular node PDEs in a complex form of the periodic sine/cosine components. The proposed improvements contribute to better performance of the AI modular concept of PDE models, a cable to represent the dynamics of complex systems. The results are compared with the recent deep learning strategy. Both methods show a high approximation ability in radiation ramping events, often in PV power supply; moreover, differential learning provides more stable wind gust predictions without undesirable alterations in day errors, namely in over-break frontal fluctuations. Their day average percentage approximation of similarity correlation on real data is 87.8 and 88.1% in global radiation day-cycles and 46.7 and 36.3% in wind speed 24 h. series. A parametric C++ executable program with complete spatial metadata records for one month is available for free to enable another comparative evaluation of the conducted experiments.Web of Science163art. no. 108

Wind speed and global radiation forecasting based on differential, deep and stochastic machine learning of patterns in 2-level historical meteo-quantity sets

Accurate forecasting of wind speed and solar radiation can help operators of wind farms and Photo-Voltaic (PV) plants prepare efficient and practicable production plans to balance the supply with demand in the generation and consumption of Renewable Energy (RE). Reliable Artificial Intelligence (AI) forecast models can minimize the effect of wind and solar power fluctuations, eliminating their intermittent character in system dispatch planning and utilization. Intelligent wind and solar energy management is essential in load scheduling and decision-making processes to meet user requirements. The proposed 24-h prediction schemes involve the beginning detection and secondary similarity re-evaluation of optimal day-data sequences, which is a notable incremental improvement against state-of-the-art in the consequent application of statistical AI learning. 2-level altitude measurements allow the identification of data relationships between two surface layers (hill and lowland) and adequate interpretation of various meteorological situations, whose differentiate information is used by AI models to recognize upcoming changes in the mid-term day horizon. Observations at two professional meteorological stations comprise specific quantities, of which the most valuable are automatically selected as input for the day model. Differential learning is a novel designed unconventional neurocomputing approach that combines derivative components produced in selected network nodes in the weighted modular output. The complexity of the node-stepwise composed model corresponds to the patterns included in the training data. It allows for representation of high uncertain and nonlinear dynamic systems, dependent on local RE production, not substantially reducing the input vector dimensionality leading to model over simplifications as standard AI does. Available angular and frequency time data (e.g., wind direction, humidity, and irradiation cycles) are combined with the amplitudes to solve reduced Partial Differential Equations (PDEs), defined in network nodes, in the periodical complex form. This is a substantial improvement over the previous publication design. The comparative results show better efficiency and reliability of differential learning in representing the modular uncertainty and PDE dynamics of patterns on a day horizon, taking into account recent deep and stochastic learning. A free available C++ parametric software together with the processed meteo-data sets allow additional comparisons with the presented model results.Web of Scienc

Power quality approximation for household equipment load combinations using a stepwise growth in input parameters of AI models

Detached off-grids, subject to the generated renewable energy (RE), need to balance and compensate the unstable power supply dependent on local source potential. Power quality (PQ) is a set of EU standards that state acceptable deviations in the parameters of electrical power systems to guarantee their operability without dropout. Optimization of the estimated PQ parameters in a day-horizon is essential in the operational planning of autonomous smart grids, which accommodate the norms for the specific equipment and user demands to avoid malfunctions. PQ data for all system states are not available for dozens of connected / switched on household appliances, defined by their binary load series only, as the number of combinations grows exponentially. The load characteristics and eventual RE contingent supply can result in system instability and unacceptable PQ events. Models, evolved by Artificial Intelligence (AI) methods using self-optimization algorithms, can estimate unknown cases and states in autonomous systems contingent on self-supply of RE power related to chaotic and intermitted local weather sources. A new multilevel extension procedure designed to incrementally improve the applicability and adaptability to training data. The initial AI model starts with binary load series only, which are insufficient to represent complex data patterns. The input vector is progressively extended with correlated PQ parameters at the next estimation level to better represent the active demand of the power consumer. Historical data sets comprise training samples for all PQ parameters, but only the load sequences of the switch-on appliances are available in the next estimation states. The most valuable PQ parameters are selected and estimated in the previous algorithm stages to be used as supplementary series in the next more precise computing. More complex models, using the previous PQ-data approximates, are formed at the secondary processing levels to estimate the target PQ-output in better quality. The new added input parameters allow us to evolve a more convenient model form. The proposed multilevel refinement algorithm can be generally applied in modelling of unknown sequence states of dynamical systems, initially described by binary series or other insufficient limited-data variables, which are inadequate in a problem representation. Most AI computing techniques can adapt this strategy to improve their adaptive learning and model performance.Web of Science121art. no. 1902

Photovoltaic energy all-day and intra-day forecasting using node by node developed polynomial networks forming PDE models based on the L-transformation

Forecasting Photovoltaic (PV) energy production, based on the last weather and power data only, can obtain acceptable prediction accuracy in short-time horizons. Numerical Weather Prediction (NWP) systems usually produce free forecasts of the local cloud amount each 6 h. These are considerably delayed by several hours and do not provide sufficient quality. A Differential Polynomial Neural Network (D-PNN) is a recent unconventional soft-computing technique that can model complex weather patterns. D-PNN expands the n-variable k(th) order Partial Differential Equation (PDE) into selected two-variable node PDEs of the first or second order. Their derivatives are easy to convert into the Laplace transforms and substitute using Operator Calculus (OC). D-PNN proves two-input nodes to insert their PDE components into its gradually expanded sum model. Its PDE representation allows for the variability and uncertainty of specific patterns in the surface layer. The proposed all-day single-model and intra-day several-step PV prediction schemes are compared and interpreted with differential and stochastic machine learning. The statistical models are evolved for the specific data time delay to predict the PV output in complete day sequences or specific hours. Spatial data from a larger territory and the initially recognized daily periods enable models to compute accurate predictions each day and compensate for unexpected pattern variations and different initial conditions. The optimal data samples, determined by the particular time shifts between the model inputs and output, are trained to predict the Clear Sky Index in the defined horizon.Web of Science1422art. no. 758

A substitution of the general partial differential equation with extended polynomial networks

General partial differential equations, which can describe any complex functions, may be solved by means of the dimensional similarity analysis to model polynomial data relations of discrete data observations. Designed new differential polynomial networks define and substitute for a selective form of the general partial differential equation using fraction derivative units to model an unknown system or pattern. Convergent series of relative derivative substitution terms, produced in all network layers describe partial derivative changes of some combinations of input variables to generalize elementary polynomial data relations. The general differential equation is decomposed into polynomial network backward structure, which defines simple and composite sum derivative terms in respect of previous layers variables. The proposed method enables to form more complex and varied derivative selective series models than standard soft computing techniques allow. The sigmoidal function, commonly employed as an activation function in artificial neurons, may improve the polynomial and substituting derivative term abilities to approximate complicated periodic multi-variable or time-series functions in a system model

Uncertain natural frequency analysis of composite plates including effect of noise – A polynomial neural network approach

Acknowledgement SN and SS gratefully acknowledge the financial support from Lloyd’s Register Foundation Centre during this work.Peer reviewedPostprin

Power quality multi-step predictions with the gradually increasing selected input parameters using machine-learning and regression

Autonomous off-grid systems dependent upon Renewable Energy (RE) sources are characterized by stochastic supplies of the fluctuating low short-circuit power. Power Quality (PQ) standards define load characteristics in electric power systems and their ability to function properly without failures. Monitoring, prediction and optimization of PQ parameters are necessary to maintain their alterations steady within the prescribed range, which allow fault-tolerant operation of various electrical devices. It is not possible to measure complete PQ data for all possible combinations of dozens of grid-connected appliances, whose load specifics and collisions primarily determine the course of PQ parameters and their eventual disturbances. Self-adapting PQ prediction models based on Artificial Intelligence (AI) are required as induced power is influenced particularly by changeable weather conditions in real off-grid operation mode of systems using RE. A novel multi-step PQ prediction algorithm is proposed, which develops AI models with the gradually increasing number of selected input PQ-parameters. In each next step a more complex model is formed, using an additional co-related PQ-input to calculate its target PQ-output with a better accuracy. PQ-models with the progressively growing PQ-inputs, using their data predicted in the previous step, can better approximate and estimate the target quantity. The presented results show this training and feature selection procedure can step by step improve accuracy of PQ-models for unknown combinations of off-grid connected household appliances.Web of Science26art. no. 10044