Short-term forecasting of electricity generation by HPP's of power system of Uzbekistan

. The article describes the possibility of using the method of least squares (LSM) to predict the production of electricity per day by hydroelectric power plants in the energy system of Uzbekistan. There are obtained predictive equations and the coefficients of the approximating functions necessary for forming these equations by using the LSM. There are presented forecasting analyses by comparing polynomial functions of the highest degree using the LSM.


Introduction
Currently, all hydraulic power plants operating in Uzbekistan's power system, except Charvak and Khodjikent HPPs, operate based on the amount of water flow in the basic part of the load schedule.The role of hydropower engineering in ensuring a balance between the generation and consumption of electric energy in the power system of the Republic of Uzbekistan is determined by the availability of hydraulic and fuel resources, the degree of their development, and economic indicators.Considering this factor, the problem of forecasting electric energy generation at hydraulic power plants to ensure a balance is relevant.

About the short-term forecasting of electricity generation by hydropower plants
The prospects for developing the electric power industry in Uzbekistan are considered for the long term.The demand for electricity in the sectors of the economy and the population is determined by the level of economic development, the efficiency of energy use, and energy saving.These factors are interrelated and jointly form possible scenarios for the socioeconomic development of the Republic.However, under any development scenario, the most important objective, as well as in the electric power systems (EPS) of developed countries, is the formation of optimal proportions and structure for the development of the electric power industry, ensuring a complete and reliable power supply of the country's economic sectors and population [1,[6][7][8][9][10].
Given the fact that today the share of 90% of electricity generation in the energy system of Uzbekistan accounts for the thermal power plants and in the long term, it is necessary to provide a reorientation of electrical engineering to a more economical using of fuel resources, especially gas, and expanding up to share 20-25% of renewable natural energy resources, which are traditional hydropower resources of the country.
Hydropower resources are one of the oldest, continuously renewable sources of energy, which continues to have a significant role in the energy system of the Republic of Uzbekistan.
The role of hydro engineering in the energy balance of the Republic of Uzbekistan is determined by the availability of hydraulic and fuel resources, the degree of their development, and economic indicators [3][4].
It should be noted that hydraulic power plants (HPP) are simultaneously the most important element of the water management complex of the region and ensure the integrated use of water resources in the interests of various sectors of the economy, which significantly increases the total economic efficiency of their creation for the country's economy.
The total gross theoretical hydro-energetic potential of the river flow of Uzbekistan is composed of 88,5 billion kW•h per year.From the technical hydro energy potential of the Republic, which consists of 27,4 billion kW•h per year, about 7 billion kW•h have already been mastered by now.The technically possible for further use of Uzbekistan's energetic hydro resources is the amount of 20,4 billion kW•h per year.In this regard, the concept of electricity generation provides in this area [1]: -the reconstruction and modernization of existing HPP; -the restoration on a new technical basis of decommissioned mothballed and decommissioned small HPP; -the construction of HPP on the drops of irrigation canals; -the construction of HPP on unused areas of natural watercourses.The further development of hydro engineering in Uzbekistan presupposes the full use of the potential of natural and artificial watercourses of the Republic through the construction of new and modernization of existing HPP with a phased implementation of the tasks.
At the same time in this studying, the development of the electric power industry is considered in terms of the use of hydropower resources and the development of hydro engineering of Uzbekistan, in particular, the forecasting of electricity which is generated by HPP of Uzbekistan.
Reliable fuel and energy supply are needed to plan for electricity generation by HPP and the cascades of HPP with a maximum lead time.At the same time, the methods of planning HPP power generation are based on data about the volume of water inflow into river basins, as well as HPP power generation for previous periods, and are short-term forecasts, since the values of the inflow volume make sense with little advance time [2].
Hydrological forecasts, in their most general sense, are the definition of various elements of the hydrological mode with a certain advanced time, based on the knowledge of the laws of the development of natural processes that determine the corresponding phenomena in specific physical and geographical conditions.The nature of the hydrological mode and the variability of its elements are directly related to the climate and the variability of weather conditions on the territory of the river and basins.The main meteorological elements, such as precipitation and air temperature, have the character of stochastic variables at certain time scales and determine the similar nature of the hydrological elements that depend on them.Therefore, the practical possibilities of long-term forecasts of runoff and other elements of the water mode, as well as other characteristics that depend on these elements, are significantly different in different climatic conditions and depend on the degree of influence of meteorological conditions on the runoff during the forecast period.The smaller the influence of unknown factors at the time of issuing the forecast, the less the uncertainty caused by them and the greater the possibility for hydrological forecasts and vice versa.The frequent incompleteness of hydrological information, the randomness and multifactorial nature of hydrological processes, the degree of influence of each of which on the formation of the phenomenon under consideration is not possible to take into account fully, as well as the inability to represent them in the form of a certain dependence, forces the use of statistical methods.The particular importance of the issues of statistical estimates of sample distribution parameters, an artificial increase of information, and selection of the most suitable mathematical model, that is, in the general case, the method of hydrological forecasts is a quantitative relationship between the predicted value as a function and the underlying factors.Therefore, the elucidation of the regularities inherent in the totality of phenomena formed as a result of multifactorial relationships is possible only by statistical methods.
In forecasting based on statistical methods, retrospective statistical information on the parameters and load modes of the EPS is used.It is based on the apparatus of statistical analysis and forecasting of time series.It should also be noted that in the process of shortterm planning of electrical modes, the results obtained during their long-term planning are used.At the same time, the solutions are adjusted, taking into account the specified circuitmode conditions.The results of solving the problems of short-term planning of electrical modes are transmitted to the level of long-term control of modes as planned values [5].

The results of calculation experiments
We will analyze the results of forecasting the daily electricity generation at hydroelectric power stations in Uzbekistan's electric power system for June and July 2019 using the least squares method (LSM) and compare its computational efficiency.To determine the approximating coefficients of predictive equations, the LSM analysis is performed for the following functions: -the linear function (LSM-1), -the quadratic function (LSM-2), -the cubic function (LSM-3), -the biquadratic function (LSM-4) -the 5th degree polynomial function (LSM-5).We will perform the necessary calculations and, according to the criterion of the least squares method (1), we will determine the approximating function whose value of the sum of squared deviations (SSD) is the smallest [6][7][8]: Moreover, in practice, well-known forecasting models that do not consider the market, random nature of relationships are often unsuitable for planning and managing EPS modes.In such a situation, for the analysis, modeling, and forecasting of operating parameters and characteristics of the electrical system, it is advisable to apply methods of direct construction of models from observational data (statistics).Such methods make it possible to identify implicit cause-effect relationships and patterns hidden in retrospective data and present them explicitly in mathematical models [3][4][10][11][12].
As we know, the management of EPS based on planning (forecasting) is divided into four-time levels: long-term (prospective), short-term planning (forecasting), and operational To obtain the approximating function, the data of daily electricity generation by hydroelectric power plants in June was used, forming a training sample.The electricity generation values of the first four days of July 2019 formed a control sample.The control sample data is necessary to determine the accuracy of the forecast of the operating parameters of the EPS.
With justification on the training sample data, the LSM is applied for the above functions of the polynomials of the highest degree, the prognostic functions (2-6) LSM-1, LSM-2, LSM-3, LSM-4, and LSM-5 are formed, respectively.y=f(x)=0.0729x+25.65 (2) 2 -0.5038x+28.73 (3) y=f(x)= 0.0006х 3 -0.0093х 2 -0.1524x+27.748(4) y=f(x)= -0.0002х 4 +0.0141х 3 -0.2811x 2 +1.7935х+24.29 (5) y=f(x)= -0.000009х 5 +0.0005х 4 -0.0054х 3 -0.0488x 2 +0.6941х+25.687(6) We will make the necessary calculations and, according to the criterion of the least squares method (LSM) (1), we determine an approximating function whose sum of the squared deviations is the smallest [20]: Мn(хn,yn) tend to be in a straight line, and there is every reason to believe the presence of a linear relationship: Find the coefficients a and b so that the sum of the squared deviations was the smallest.To do this, we find partial derivatives of the first order.According to the rule of linearity, you can differentiate directly under the sum icon: )) ( ( )] [( 2 (9) We compose a standard system of equations: After simplification, the system of equations will have the following form: We rewrite the system in the "applied" form: To determine the coefficients of the approximating functions of a polynomial of the second degree, it is necessary to use the following system of equations: To determine the coefficients of approximating functions of a polynomial of high degree, it is necessary to create a system of equations similarly and solve it.With justification on the obtained predictive equations, we will use a control sample to predict the daily generated electricity (GW•h) by HPP in the power system of Uzbekistan and determine the error by extrapolation.By according to the LSM criterion, the smallest SSD was obtained when predicting by using the 3rd-degree polynomial function (LSM-3), and the largest by the 4th-degree polynomial function (LSM-4): From the numerical inequality, it can be seen that the SSD systems of LSM-2 and LSM-3 are approximately equal.In this regard, the test results for the accuracy of the forecast of the LSM-2 and LSM-3 functions, shown in Table 1, should be compared.

Conclusion
Thus, in conclusion, it should be noted that based on the results of the calculation of the analyzed functions, according to the LSM criterion, the most accurate forecast of daily electricity generation at HPPs was obtained by forecasting with the use of a quadratic function (LSM-2).

Table 1 .
The results of the calculation and verification of the forecast accuracy