Research of the variable natural potential of the wind and energy energy in the northern strip of the ukrainian carpathians

. The expediency of studying the varying potential of wind and solar energy in the northern strip of the Ukrainian Carpathians is substantiated. The technique of conducting experiments to determine the natural potential of wind and solar energy is proposed and a model for determining the relative volumes of electricity generation by wind farms and solar electrical installations is developed. Based on the conducted research, according to the Drohobych meteorological station, an energy assessment of wind and solar energy resources in the northern strip of the Ukrainian Carpathians was performed. It is substantiated that the theoretical curves of distribution of wind velocity in separate quarters of the year in the territory of the northern strip of the Ukrainian Carpathians are described by the Weibull distributions. Based on the calculations, it is established that the highest total daily solar radiation is in the summer months. Daily graphs of the relative generation of electricity by wind farms and solar electric installations have been constructed. The expediency of formation of combined systems of energy supply of objects from wind and solar energy in the northern strip of the Ukrainian Carpathians has been established. The substantiated patterns of change in the natural potential of wind and solar energy, as well as the graphs of the relative generation of electricity from them, will significantly speed up managerial decisions and improve their quality.


Introduction
The relevance of the problem of efficient energy supply of objects from renewable sources of wind and solar energy is confirmed by the fact that individual territories have considerable uneven supply of this energy in different seasons of the calendar year, as well as with respect to their individual species [1][2][3][4][5][6][7][8][9][10][11]. In addition, the creation of energy systems for renewable energy sources and wind to meet consumer needs is a pressing issue, given the recent trends in fossil fuel prices. The peculiarity of creating small energy systems using renewable wind and solar energy is that individual installations do not operate on a single grid, but individually, ie provide electricity to a limited number of consumers. That is why an adequate assessment of their potential is possible if appropriate research is carried out taking into account specific natural production conditions [12][13][14][15][16][17][18][19][20][21].
Conducted scientific studies by Ukrainian and foreign scientists have made it possible to solve many problems of efficient use of non-traditional and renewable energy sources [5][6][7][8][9]. Among these are studies related to the creation of efficient energy systems based on the use of renewable wind and solar energy, operating in deterministic or stochastic conditions [10][11]. At the same time, it has been proved that there is a need to substantiate mathematical models of the changing potential of wind and solar energy in different regions of the world [1][2][3][4]. They are at the heart of the modeling and optimization of energy systems for wind and solar energy.
According to this, the substantiation of mathematical models of natural potential and the possibility of wind and sun energy production in the northern lane of the Ukrainian Carpathians has important scientific and practical value.
The purpose of this work is to substantiate mathematical models of natural potential and to simulate the production of wind and solar energy in the northern lane of the Ukrainian Carpathians.

Theoretical backgrounds
The energy characteristics of solar and wind resources have a significant impact on the functional performance of renewable energy systems. The analysis of literature sources suggests that to account for the characteristics of solar radiation and wind resources in different energy supply projects, two methods are used: 1) generate retrospective meteorological data for previous years; 2) create models of meteorological conditions. We used the first method of energy estimation of solar radiation and wind energy resources.
To study the random flow, one must be able to estimate the random deviations (fluctuations) of the intensity of the solar radiation and wind. Statistical processing is carried out equally for stationary and non-stationary processes, with the only difference being that the non-stationary flow is investigated not by absolute value but by relative or absolute deviation.
During mathematical processing of a given parameter by experimental (empirical) data, which is limited in number, it is impossible to determine the true values of the distribution characteristics, and therefore determine the so-called estimates of mathematical expectation, variance, root mean square deviation and coefficient of variation. These estimates are called statistical characteristics.
The empirical distributions are consistent with the theoretical criteria specially developed in theory [13]. Arrange the data of the empirical series in ascending order and thus form a variational series: The variational series is divided into k intervals. The number of intervals is determined by the formula: The results of the calculations are recorded in Table 1. ...
The frequency is then determined i m by a random variable at each interval, and an empirical frequency is calculated The following are the statistical characteristics (estimates): mathematical expectation Dispersion: standard deviation: where зм Y -displacement of the scatter zone of random magnitude Y relative to zero. The estimate of the coefficient of variation according to the formula is calculated if the scatter zone of the exponent Y has a displacement relative to zero. Provided that Y 1 of variation series is correct (is included in the sample ), it is considered that: зм YY = 1 . Checking the extreme values of the variation series for their sampling.
where t -quantile of normal distribution.
Compare the calculated value d N with an actual one and make a conclusion about expediency of carrying out additional experiments. Construction of a histogram (polygon) of the distribution of the studied indicator and hypothesis about the theoretical pattern of distribution. According to the variation series, plot the relationship between the investigated value and the empirical frequency. For this purpose, the upper, lower and average values of the intervals Y are determined by a certain measure on the abscissa axis. The y-axis defines the empirical frequency.
On the appearance of the histogram, as well as on the value of the coefficient of variation, put forward a hypothesis regarding the theoretical pattern of distribution.
Calculation of theoretical frequency. Calculate the density of the distribution function ( ( )) i fY for each partial interval. For Weibull's theoretical distribution, we first need to find the parameters a і b [15]. For each partial interval, the theoretical frequency is calculated: where Y D -interval step. Checking the proximity of empirical and theoretical distributions. The proximity between empirical and theoretical distribution is verified by criterion 2  [15]. To this end, it is necessary to calculate a product for each partial interval - Express the criterion by the formula: where k˘ -the number of intervals to match them. Determine the number of degrees of freedom by the formula then the theoretical distribution reflects the empirical data. Otherwise, the proximity between empirical and theoretical distribution is absent.
Production and computer experiments were conducted to achieve the stated purpose and to fulfill the tasks of the work. During the study of the potential of the region and the processes of electricity production from wind and solar energy, the methods of passive production observations, statistical data processing, simulation modeling, etc. were used.
The essence of production experiments is to create an information base on the main characteristics of the design objects and the design environment. Synthesis of theoretical studies and results of production experiments allows us to build the necessary model for estimating electricity production from wind and solar energy.
Determining the distribution of average power consumption of objects and seasonal irregularity is based on the analysis of retrospective data of electricity consumption of enterprises of Stryi district of Lviv region. In order to expand the sample needed to build the trend of seasonality of energy consumption, data from different farms should be normalized -leading to a unit of average monthly energy consumption: The main parameter characterizing wind potential is the dynamics of wind speed change. Wind velocity and solar radiation distributions are constructed for each month of the year by processing an array of retrospective data from weather station observation logs.

Research results and discussion
Each of the periods of the year for a given region is characterized by the speed of wind flow, on which the choice of type of wind installation depends and the total amount of solar energy that influences the calculation and choice of solar photomodules [5,9].
Statistical analysis of the obtained data on wind speed in the territory of Stryi district of Lviv region (northern strip of Ukrainian Carpathians) allowed to determine their numerical characteristics and to substantiate theoretical distribution laws, which are Weibull distributions (Fig. 1-4)  The estimation of the mathematical expectation of wind speed in the territory of a given region for the first quarter is -4,88m/s, the estimate of the standard deviation -3,32 m/s., The coefficient of variation -0,68. (Fig. 1). For the second quarter, the estimation of the mathematical expectation of wind speed on the territory of agricultural enterprises is 4.07 m/s, the estimate of the standard deviation is 3.2 m/s, the coefficient of variation is 0.78. (Fig.2).

Fig. 2. Wind velocity distribution in the northern strip of the Ukrainian Carpathians (2rd quarter)
For the third quarter, the estimation of the mathematical expectation of wind speed on the territory of agricultural enterprises is 4.09 m/s, the estimate of the standard deviation is 3.13 m/s, the coefficient of variation is 0.76. (Fig.3). For the fourth quarter, the estimation of the mathematical expectation of wind speed on the territory of agricultural enterprises is 4.36 m/s, the estimate of the standard deviation is 3.21 m/s, the coefficient of variation is 0.73. (Fig. 4).

Fig. 4. Wind velocity distribution in the northern strip of the Ukrainian Carpathians (4th quarter)
Similarly, the statistical analysis of the received data on the total solar energy supply in the territory of the northern strip of the Ukrainian Carpathians was carried out, and the results are presented in Table. 2. Subsequently, the simulation of electricity production was performed on the basis of the developed simulation model. In modeling the production of energy resources from solar and wind energy, the wind and solar potentials of the northern strip of the Ukrainian Carpathians were taken into account, which made it possible to construct appropriate daily schedules ( Fig.  5 and 6). https://doi.org/10.1051/e3sconf/202015406002 energy in the northern strip of the Ukrainian Carpathians, combined systems should be formed. At the same time, their components will be both wind power plants and solar electric collectors, which will replace about 27% of electricity. The conducted research will be useful for the managers of projects of energy supply of objects from wind and solar energy in the northern strip of the Ukrainian Carpathians. They can also be used when designing such systems. The substantiated patterns of change in the natural potential of wind and solar energy, as well as the graphs of the relative generation of electricity from them, will significantly speed up managerial decisions and improve their quality.

Conclusion
Based on the conducted research, according to the Drohobych meteorological station, an energy assessment of wind and solar energy resources in the northern strip of the Ukrainian Carpathians was performed. It is substantiated that theoretical curves of distribution of wind speed in separate quarters of the year in the territory of the northern strip of the Ukrainian Carpathians are described by Weibull distributions with mathematical expectation, which fluctuates within 3.21..4.09 m/s. It is established that the highest amount of total daily solar radiation occurs in the summer months ( Table 1). The performed researches made it possible to build daily schedules of relative generation of electricity by wind installations (Fig. 5) and solar electric installations (Fig. 6). Combined systems should be designed to provide efficient energy supply for wind and solar energy in the northern strip of the Ukrainian Carpathians. At the same time, their components will be both wind power plants and solar electric collectors, which will replace about 27% of electricity