Search

Relevance. Today, there are many methodologies for predicting power consumption of various objects. However, there is no a general methodology that is suitable for all types of energy systems, including the sectoral characteristics of small northern settlements and other objects with the stochastic nature of electricity consumption schedules. At the same time, during the development of problem-oriented forecasting methods, it is necessary to take into account computational and statistical features of forecasted time series to the maximum and apply them adequately. The mentioned circumstance prompts the creation of criteria-indicators that allow evaluating the quality of the applied model for solving the forecasting problem, correctness of its construction and correctness of applying a priori information about the object and its physical properties.Aim. Develop and apply the criteria-indicators, which allow evaluating the quality of the forecast regression model and the influence of the dimensionality of such model base on a forecasting error. Methods. The choice of rational dimensionality of the regression model basis for the adaptive forecasting problem is based on the known and developed criteria-indicators. The main provisions of such criteria-indicators were formulated, which provide an assessment of the quality of conditioning of an equivalent square matrix, the presence of uninformative elements of the matrix, and linear dependence of the columns. Results. Based on the analysis of criteria-indicators, the authors selected a rational dimension of the regression model basis for the problem of adaptive short-term forecasting of the state of discrete non-stationary dynamic systems. Conclusions. The authors have previously selected the most promising criteria-indicators and developed a normalized difference factor of diagonal predominance. This allows us to evaluate the influence of the basis size change on the regression model quality when building an approach of adaptive short-term forecasting of electricity consumption by autonomous power systems of small northern settlements on the basis of regression analysis methods. Based on the analysis of criteria-indicators the authors obtained information about the influence of the regression model basis dimension on the forecasting problem solution error. The authors stated the further stages of research to reduce this error. The paper introduces and describes one of the ways to improve the forecasting model quality. The dependence of the forecasting error on the size of the regression model basis were revealed; the criteria-indicators considered in the article were successfully applied. It is confirmed that the pre-selected and developed criteria-indicators make it possible, at the stage of compiling an equivalent square matrix and performing preliminary actions on it, to track changes within the matrix. The changes will lead to improvement in the solution of the problem of adaptive short-term forecasting.

The relevance. The construction of a problem-oriented tool for forecasting electricity consumption in small northern settlements is of paramount importance for the implementation of development plans for Arctic and Far North regions. At present, a large number of varieties of electricity consumption forecasting methods are used, including expert, statistical, artificial intelligence methods, hybrid methods, and others. As a rule, there is no universal method, equally effective (by the criterion "counting time - counting accuracy" for the main types of problems of electricity consumption forecasting. The noted circumstance requires research in the direction of creating a computational complex: identification of computational properties of electricity consumption model - construction of an adequate method of information extraction. The purpose: Development of an approach based on a retrospective regression analysis, which allows to make adaptive short-term forecasting of electricity consumption of regional isolated electrical complexes (RIEC). Methods: The approach to obtain short-term forecasts of electricity consumption of regional isolated electrical complexes is based on a retrospective regression analysis. The predictive model based on the QRETC responses is presented in the form of a linear regression with an internal set of functions forming an orthogonal and orthonormalized basis. At the same time the preliminary information received from the object - RIEC's responses, is written in the form of a system of linear algebraic equations presented in matrix form. Finding of coefficients at basis functions is carried out taking into account the method of least squares, and the solution of the received equations on the basis of Kaczmarz method. Verification of performance of the developed approach was carried out by means of the analysis of regression residuals of forecasting. Results. With the help of аdaptive short-term forecasting of electric power consumption by autonomous power systems of small northern settlements based on the methods of retrospective regression analysis the short-term forecast for the prediction interval of 30 minutes was obtained. Conclusions. The approach of adaptive short-term forecasting of power consumption by autonomous power systems of small northern settlements on the basis of regression analysis methods, which allows obtaining a short-term forecast of power consumption for the preemptive interval of 30 minutes, has been developed. Substantial advantage of the developed approach is demonstrated by the fact that when building a procedure of adaptive short-term forecasting of energy consumption on the basis of retrospective regression analysis it is rational to combine the processes of identification of coefficients at basic functions and tunability of mathematical model of non-stationary discrete stochastic process at each step. The analysis of regression residuals of ROETC response forecasting has been carried out and the performance of the developed algorithm of electricity forecasting and the adequacy of the accepted provisions in forming a priori information when implementing the approach to short-term forecasting of a stochastic process based on retrospective regression analysis has been confirmed.

One of the main problems in building energy-efficient and non-resource-intensive decentralized power supply systems in the Arctic zone and regions of the Far North is forecasting the consumption of electrical energy by small northern settlements. Among the existing methods that give an acceptable result in terms of accuracy, one can single out approaches based on the ARIMA econometric method. A method based on the Wold decomposition and correlation functions of the stochastic process is considered, an adaptive model of the difference equation is constructed, which makes it possible to predict energy consumption of the active power of autonomous systems of a small settlement in the interval of 0–4 hours, by reducing the stochastic process to a stationary Markov process with short memory. The purpose of the work is to build a methodology for short-term forecasting of electric energy consumption by autonomous energy systems of small northern settlements, taking into account the specifics of energy consumption in the conditions of the Arctic zone and the Far North, based on a stochastic series of data on electric energy consumed by the settlement over the previous period. Methods: approach to obtaining a short-term forecast of electricity consumption by autonomous energy systems of small northern settlements based on the ARIMA econometric method. In this case, a difference equation is constructed for the deterministic and random components of the available stochastic series of energy consumption; Wold decomposition and correlation functions of the energy consumption are used. To adapt the model, the studied stochastic process is reduced to a Markov process with a short memory. To do this, it is necessary to use a difference operator, which reduces the relative contribution of consumption deterministic component. Results. Based on Wold decomposition and correlation functions, it was possible to obtain a model that gives a short-term forecast of active power consumption for a lead time of 4 hours. Conclusions. Based on the Wold decomposition and the correlation functions of the stochastic process, the authors of the work managed to obtain an adaptive model of the difference equation, which makes it possible to predict active power consumption of autonomous systems of a small settlement with a lead time of 4 hours. The stationarity of the random process was carried out by introducing a difference operator of the first order, which makes it possible to reduce the relative contribution of the deterministic component of the stochastic series. The authors managed to reduce the process to a stationary Markov process with a short memory. The expansion coefficients of the difference equation were estimated by solving a nonlinear equation, which consists in finding the global maximum of the likelihood function. The constructed 90 % probabilistic boundaries allow us to talk about a satisfactory adjustment of the adaptive parameters of the difference equation for predicting the system. The result of forecast modeling with four-hour lead time shows good agreement with experiment.

The relevance of the is caused by the need to bridge the gap between the existing approaches to modeling isolated systems of power supply considering dynamic processes in their physically diverse subsystems, in the presence of weak communications and weak interactions between single systems. The aim of the research is to design the problem-oriented numerical method directly applicable to initial mathematical models of the isolated systems of power supply, and having advantage by criterion «counting duration – account accuracy» in relation to universal numerical methods. Object: electrotechnical complex consisting of set of the isolated systems of power supply united by weak communications and weak interactions. Methods. When analyzing a form and structure of initial mathematical model of set of the electrotechnical complexes consisting of the isolated systems of power supply united by weak communications and weak interactions, and when designing a problem-oriented numerical method the authors have used: power approach to mathematical modeling of electrotechnical complexes and systems, provision of theoretical bases of electrical equipment, theory of numerical methods of solution of rigid systems of the differential equations, correct assumptions by drawing up mathematical models and computer modeling. Results. The paper introduces the concept «Regionally isolated electrotechnical complex» and the authors determine its characteristic signs. The article considers the possibility of developing new algorithms for controlling the «Regionally isolated electrotechnical complex» to decrease the possible ecological damage and average settlement cost of electric power production by the power plants included in «Regionally isolated electrotechnical complex». The authors determined the initial structure of the mathematical model of «Regionally isolated electrotechnical complex». The paper demonstrates the fundamental difference between the structure of the given model and the model in a normal form of Cauchy. Вasic presence of properties of rigidity and superrigidity at the analyzed class of models is given. The authors designed and realized in the BKM-3 program the focused three-step numerical method applicable to the initial mathematical model of «Regionally isolated electrotechnical complex». The authors carried out the numerical experiment which shown the essential advantage of the BKM-3 program, by criterion «counting duration – account accuracy» in the field of applicability, on the idealized mathematical models of «Regionally isolated electrotechnical complex».