Decision Matrix in an Autonomous Power System for Agro-Industrial Complexes with Renewable Energy Sources

Abstract

The article focuses on systems analysis in identifying optimal areas for using distributed energy sources in the agro-industrial complex. Applying a systems approach enables a comprehensive assessment of various aspects of solar energy, wind energy, hydropower systems and integrated power plants that provide autonomous energy supplies. The research methodology includes a functional–structural approach that helps to assess the internal characteristics of systems, allowing for a deeper understanding of their structure and functions. This, in turn, leads to the creation of different models reflecting specific elements and relationships in energy systems. The main point is to take into account the level of functional and structural perfection, which helps to more accurately determine the areas where the introduction of renewable energy sources will be most effective, taking into account the specifics and needs of the agro-industrial complex. This approach not only contributes to a more optimal allocation of resources but also improves the sustainability and efficiency of energy systems in the face of a changing climate and the growing demand for environmental technologies.

1. Introduction

The electricity demand is increasing due to the exponential growth of consumption in the residential, industrial and other economic sectors [1,2], and means are constantly being sought to optimize the consumption of resources against the criteria of sustainable development [1]. The depletion of fossil fuels and growing concerns about global warming have stimulated the use of renewable energy [3]. Electricity can be obtained from various sources, such as waste processing and biogas recovery [2], wind turbines, solar panels, and small hydroelectric plants (HPP) [4]. Despite the good knowledge of these technologies and the factors affecting their operation, this cannot guarantee a continuous and reliable electricity supply due to their strong dependence on climatic conditions, consumer needs and the differences between the produced and the consumed energy [5]. However, the use of only sustainable energy resources cannot guarantee a continuous energy supply due to their unpredictability and strong dependence on environmental conditions, as well as load fluctuations [6,7]. Due to the importance of environmental aspects, modeling of such renewable energy source (RES) systems should be carried out at the lowest cost and with the least amount of environmental pollution possible [8]. When choosing RES systems, consumers are faced with the issue of efficiency of use, and, after examining the criteria for evaluating their types, consumers often do not choose the most profitable types of RES systems or their combinations. A promising area for the use of RES is agriculture, particularly in off-grid areas where most of the electricity is still generated by diesel generators, which are expensive to operate and are responsible for significant carbon emissions [9]. They integrate multiple power sources to supply electricity to consumers and allow different resources to aggregate the generated power, which is similar to a system of distributed energy resources [10]. To ensure the power supply of remote and isolated areas, it is appropriate to use distributed power systems with integrated renewable sources. Some authors recommend the use of hybrid systems, such as, for example, combining solar energy with wind sources, thus increasing the amount of electricity produced and thereby better satisfying the end users’ needs [11]. This necessitates looking for algorithms and technical solutions to support the mutual work of different energy sources, i.e., an optimization task must be solved for a given part of the electrical network—production should be as close as possible to consumption and correspond to its needs. Mandatory conditions for solving these tasks include identifying the models of work and production for the autonomous energy supply of agricultural facilities based on renewable energy sources and, as a result, increasing their energy efficiency [9,12]. When choosing a technology for the production of electrical energy from renewable energy sources, many random, stochastic, and periodic factors depending on the geographical location and climatic conditions, time of day, month, etc. must be taken into account [13]. After the identification of the main factors, they must be taken into account when choosing the appropriate technology for the production of electrical energy. The main factor is the amount and type of local natural resources—energy potential from solar, wind, water energy, etc. To compare the individual energy sources, and to be able to make an appropriate choice, specific indicators must be used. In this way, the different energy sources are placed under the same conditions and the decision is made based on expert judgment and the application possibilities of a given technology. For example, the random nature of the sunshine during the day leads to fluctuations in the operation of the photovoltaic panels and, hence, a change and inconsistency in the generated power and a decrease in the harvested electrical energy. When choosing a power supply from wind turbines, in addition to the availability of sufficient energy potential, the appropriate technology, type of turbine, components, etc., must be selected [14,15]. In addition, economic factors must also be taken into account—the price of electricity, purchase period, life cycle, and even the possibility of disposal after decommissioning. All this shows that the problem of choosing and making a decision to provide electricity with the help of renewable energy sources makes the optimization problem extremely important and complex. This can be achieved through a preliminary thorough study and familiarization with the available energy resources from renewable sources and the possibility of their joint work and complementation in a common power system based on distributed resources, thus creating prerequisites for optimal use of different types of RES; from there we can increase the reliability of the power supply system and establish better technical and economic indicators [16,17,18]. That is why the issues related to the design, optimization, and modeling of renewable energy sources working together and forming the so-called virtual power plants are of great interest in the literature [18,19].

The simultaneous use of several renewable energy sources is a prerequisite for increasing the reliability of the power supply system and significantly reducing investment and operating costs [20]. Some authors pay special attention to the fact that investment costs and reliability of electricity supply have a strong positive correlation [21]. Others derive as an objective function the optimal configuration of the power system to minimize costs [22]. All this shows that no universal solution for the selection and optimal use of RESs is currently known. It is necessary to look for a comprehensive system approach that allows for a thorough analysis of the site, taking into account the essential factors influencing both the operation of energy production and the consumption of electrical energy. The goal is to optimize the operation of the power system with full use of the available energy resources for a given region, climatic conditions, etc.

2. Materials and Methods

The systematic approach to justifying the areas for efficient use of different types of renewable energy sources includes the key categories of continuity, complexity and organization, which are the main principles of this approach.

The principle of unification of the system implies a specific study of an object, taking into account its connections with other ones. According to the principle of complexity, the internal processes of a system can never be fully determined because they depend on several external internal factors. In this aspect, it is assumed that the processes have a certain potential which can be used under specific conditions with a given probability. One of the essential advantages of the systems approach is its ability not only to analyze objects but also to carry out a synthesis that allows for finding the optimal solution for given conditions. The energy supply system based on renewable energy sources is a rather complex structure composed of expected and artificial elements which is integrated by performing many tasks. According to the principle of integrity, the object boundaries are determined by dividing it into 3 components, namely transform electrical energy, energy storage, and supply and distribution of electricity to the user; this system itself can be considered as an autonomous RES (RESS), while other RESs and technical devices (TD consumers) are representatives of the external environment. Taken together, they form a “meta renewable energy source” (MRES) [9].

The main task of this system is to convert renewable energy into electrical energy and transmit it to the end users. Following the goal hierarchy, this task is minor in regard to the MRES. The main goal of the MRES is to provide consumers with electricity with a minimal impact on the environment. Our investigation refers to autonomous power systems with RESs for supplying Agro-Industrial Complexes with installed power that reaches up to 100 kW.

Figure 1 shows the block diagram of the MRES and the connections between its main elements.

The composition of the system is as follows: (1) a converter (REC) for converting the incoming energy from the RES; (2) a Battery Energy Storage System (BESS) for storing electrical energy; (3) an electricity quality device (EQD); and (4) a power supply unit (PS) to provide the connection to the electrical network. The selected parts of the MRES have all the characteristics inherent to classical power systems with renewable energy sources. The main task of the MRES is the determination of all elements as well as the internal and external interactions and limitations in their operation and parameters of change. In this way, maximum efficiency is guaranteed in their optimization and finding of the objective function [9].

It is also appropriate when designing systems to provide opportunities for adaptive management of energy flows, as indicated in [23]. In this way, the system operation is optimized through cascade management of electrical energy and at a sufficiently high level of energy security.

An MRES must be analyzed both in terms of the technical devices and facility and during its operation. In the process of spatial analysis, its boundary conditions and external factors are established; the time analysis process assumes the use of a common life cycle period. The life cycle of a system is considered as a sequence of processes that reflect its state from the stage of defining technical requirements to the stage of decommissioning. The life cycle period will include the intended operation, consisting of stages such as construction, implementation, maintenance, operation as planned, as well as regular operation, storage, and reconstruction [9].

The main period of the life cycle is the operation stage, as it is at this stage that the obtained economic efficiency is the highest. In this regard, to solve the problem, it is recommended to compare different types of energy transfer systems in the time corresponding to the operational period [9].

From all that has been said so far, it can be assumed that the search for the optimal application of a relevant technology from renewable energy sources and their optimal utilization is based on the following principles and assumptions:

• Choice of the configuration of the MRES—identifying the main elements according to your needs;
• Determination of the purpose of the MRES—for supplying one or a group of users or for parallel operation with the power network;
• Assessment of the produced power over time and its compliance with the needs of the consumers.

The optimal structure of the MRES depends on the field of application and the place of installation of the power source. In this regard, the technical building and conceptual design with a preliminary assessment of energy resources and choice of power system is essential. At this stage, all possible factors must be taken into account, such as internal factors, which are directly related to the system and can have an impact on its operation, and external factors, which characterize the environment and limitations of the MRES.

The operating properties of the system S expressed by the quality vector $\overrightarrow{K}=f\left(K_e, C\right)$, where $K_e$ is the efficiency of the system and $C$ is the economic costs spent to fulfill the goal.

The system efficiency is a function of system quality indicators:

$$K_e=f\left(K_r,K_T, K_{ei}, K_{ep}\right),$$

(1)

where $K_r$ is the reliability; $K_T$ are the technical indicators; $K_{ei}$ are the energy indicators; $K_{ep}$ are the environmental performance/parameters.

The probability of non-failure operation is represented by $p \left(t\right)$; technical indicator—standard size series ${\mathrm{T}}_{\mathrm{s}}$, which depends on the power of the installed furniture and its energy efficiency class $\eta$; environmental indicators include harmlessness $H$ and safety $Hs$. ${ K}_r=\left\{\left.p \left(t\right)\right\}\right.,K_T=\left\{\left.{\mathrm{T}}_{\mathrm{s}}\right\}\right.,$ $K_{ei}=\left\{\eta \right.\},$ $K_{ec}=\left\{\left.H, Hs\right\}\right.$.

The analysis shows that the MRES reliability can be represented by the indicator $p\left(t\right)$. The remaining indicators depend on the energy performance of the power equipment and its compliance with environmental requirements for harmlessness $H$ and safety $H_s$. $K_{\mathrm{H}}=\left\{\left.p \left(t\right)\right\}\right.,{ K}_T=\left\{\left.T_s\right\}\right.,$ $K_{en}=\left\{\eta \right.\},$ $K_{ec}=\left\{\left.H,H_s\right\}\right.$.

The economic indicator $C$ of the MRES depends on the depreciation costs $D$ and the costs of acquiring and building the system $P_r$ [9]:

$$C=D+P_r.$$

(2)

To analyze and simplify the calculation procedures and reduce the internal interactions between the individual indicators of the study, only the complex indicators of reliability, efficiency, and price are analyzed [24,25]. The main problem in the construction of virtual power plants is the planning of energy flows. A self-scheduling Virtual Energy Hub (VEH) is proposed in the research [26], taking into account the uncertainties associated with renewable resources.

Fluctuations in the power produced by the MRES and the presence of maximum peak power in consumption are a prerequisite for resizing the power of the power supply system; this is followed by higher investment and operating costs and incomplete utilization of the produced electrical energy. In addition, some individual indicators of the selected technology and the type of primary source (RES) are taken into account, such as the absence of waste products in the production of electrical energy, noise, etc., which affect the effectiveness of the system as a whole [27,28,29]. Comprehensive indicators of reliability, efficiency, and price combine the main 6 indicators. Then, the efficiency can be represented as:

$$K_e=f\left(p\left(t\right), \eta \right).$$

(3)

External operating factors affecting the quality of the system are:

$$Y=\left\{Y_u,Y_d,Y_m\right\},$$

(4)

where $Y_u$ is the working conditions; $Y_d$ is the destabilizing influences; $Y_m$ is the working mode.

The working conditions are defined by the MRES factors that determine the consumed electricity by the technological process P. Hence $Y_u=f\left(P\right)$.

The climatic conditions are one of the major external factors influencing the work of the MRES. The changes in this external factor can lead to deviations in the operation of the main elements of the system and, from there, to the failure of some elements, reducing the trouble-free operation and reliability of the MRES. Another major factor is the user’s mode of operation. It is characterized by its load schedule—a change in the power consumed in the cycle. The last important factor involves the $R_S$ limits imposed on the structure and parameters of the systems. For the study, the following restrictions on the structure of the MRES are accepted: Discrete restriction $R_{SM}$ of the set $M_{CA}$ of strictly admissible systems. Renewable systems using solar $S_S$, wind $S_W$, and water flow energy $S_{Wat}$. Restriction $R_{Sk}$, which only allows the use of serial equipment and devices in systems; restriction $R_{SP}$ on the system’s peak power and the power grid length $O_{S\mathrm{P}}=\left\{\left.\mathrm{P}\le { \mathrm{P}}_{max}; L\le { L}_{max}\right\}\right.$.

Then

$$R_S=\left\{R_{SM},R_{SK},R_{SP}\right\}.$$

(5)

The initial data set can be written as a function $D=\left\{{CK}_E, Y,R_s\right\}$. Symbol ${CK}_E$ means that we are talking about the composition of the vector $K$.

In the case under consideration, it is not possible to introduce the resulting performance indicator $K_E$, which is the function $f\left(k\right)$ of quality indicators. Therefore, Equation (3) is synthesized using the following heuristic method based on expert assessments (10 scientists with Ph.D. degrees with specialization in the field of energy management):

$$\left.\begin{array}{c}\begin{array}{c}{K}_E={\displaystyle \sum _{i=1}^{i=m}}{C}_{Wi}{K}_i;\\ K_i=1-{\displaystyle \frac{K_i}{K_{ib}}}, i=1,m;\end{array}\\ {\displaystyle \sum _{i=1}^{i=m}}{C}_{Wi}=1,{ C}_{Wi}>0,i=1,m.\end{array}\right\},$$

(6)

where $K_i$ is the quality indicator; $K_i$ and $K_{ib}$ are the base value of the numerical indicator; $C_{Wi}$ are the weighting factors or “weights” of single indicators.

Table 1. Performance indicators of the MRES.

Index	System Reliability, %	$\mathit{\eta }$
Rank	100	2
Weight	70–510	0.2–49

shows data from the processing of the results.

Then, target (6) will be written as

$$K_E=C_{W1}P\left(t\right)+C_{W2}\eta =0.751p\left(t\right)+0.249\eta .$$

(7)

The analysis of the results shows that the reliability indicator of the MRES has a higher significance than the efficiency indicator. This is explained by the fact that reliability evaluates how often errors and/or interruptions occur in the system operation for a certain time and efficiency evaluates the degree of use of the technical capabilities of the available equipment for the specific conditions at the given time.

Performance properties are the output parameters of the MRES. During the analysis, it is necessary to take into account the structure of the system and the technical requirements of the user when evaluating the internal characteristics of the systems themselves by using a functional–structural approach. With the functional–structural approach, the object is considered not in its specific form but as a set of functions. Since the functions are implemented only in the structure, abstracting from the connections of the system with the external environment, the structure of the system is studied, i.e., elements and their relationships within the system.

To conduct a functional–structural analysis of systems, in accordance with the restriction ${\mathrm{O}}_{S\mathrm{M}}$ on their structure, the structure of the systems under consideration is analyzed [30,31,32].

System $S_S$ is a set of devices for converting solar energy and transferring the received energy to the consumer with a given quality. It consists of solar cells (SC), storage batteries (GB) with a charge controller, a DC/AC inverter, electrical protection equipment, a cable line (CL), and circuit breakers QF1–QF5 (Figure 2a).

System ${\mathrm{S}}_{\mathrm{w}}$ is a set of devices for converting the kinetic energy of the wind flow into the mechanical energy of a rotating rotor with its subsequent conversion into electrical energy and the transfer of the resulting energy to the consumer with a given quality. It consists of rechargeable batteries AB; a wind generator G; a short-circuit charge controller; an electric brake designed to slow down the blades in case of strong wind gusts TE; a mechanical brake TB is designed to brake and/or stop the wind turbine during installation or maintenance; circuit breakers QF1–QF5 to protect the circuit from overloads and short circuits; the IT inverter, which is protected by the FU fuse; and an electricity meter Wh (Figure 2b).

The system ${\mathrm{S}}_{\mathrm{W}\mathrm{a}\mathrm{t}}$ is a set of devices for converting the kinetic energy of water and transferring the energy received to the consumer with a given quality. It consists of a device for supplying water to the HP turbine, which directs the flow of water to the GT hydraulic turbine. In this case, the kinetic energy of the water flow is converted into the rotational motion of the hydro turbine shaft, which is connected to the shaft of generator G. A three-phase electric motor is used as a generator.

The generator produces a three-phase alternating current. The excitation system (ES) is designed to power the excitation winding of the generator as well as to maintain voltage at the generator outputs. The circuit breaker QF1 is designed to protect the generator from short circuit currents and overload. The Wh electricity meter is used to account for electricity and the QF2 circuit breaker is designed to protect against short-circuit currents and overload (Figure 2c).

In addition to the listed elements, the systems contain fenced platforms or a mast with braces for installing equipment, racks for instruments and equipment, devices that increase the safety of systems, and some other elements.

3. Results

A comprehensive analysis of the above energy transmission systems and the study of their structure and functions are carried out by representing them with models obtained using various description methods. Let us use the functional–structural descriptions of the MRES, each generating the corresponding model types. A structural description of the system focused on the material structure of the object can be carried out using a graphical structural model—an ordered image of the elements of the system and the relationships among them—giving an idea of the material components of the object, their main relationships and levels of hierarchy. The structural model of the RES system using solar energy, wind energy, and water flow energy is compiled based on their schematic diagrams. The structural model has the form of a connected tree-type graph, the basis of which is the complexes of a converter, for example, solar energy into electrical energy, an electric energy accumulator, a DC-to-AC inverter, electrical equipment protection equipment, and a cable line. The complexes, in turn, contain sets of photovoltaic modules and batteries. Kits unequivocally break down into assembly units or elements such as solar cells, trackers, metal frames, etc.

The model does not contain contours and cross-links among elements of different levels, and it is a “skeleton” of the system, with a strict and unambiguous subordination of material elements arranged by hierarchy levels (complexes—kits—assembly units).

Quantitatively, in the RES system, using solar energy consists of 14 elements, using wind energy consists of 18, and using the energy of the water flow consists of 11 elements.

Additional information about the properties of the system can be obtained through dynamic connections that occur during the system operation. The possibility of studying these properties appears in the functional description of the system, i.e., logical formulation and definition of interrelations of functions. In our case, for the most complete functional description of the system, it is advisable to use the logical chain method, based on the gradual disclosure of the entire chain of sequentially connected functions that characterize the structure of the analyzed object. At the same time, the logical description and systematization of the object functions were performed based on a diagram of functions, the construction procedure of which is generalized in the FAST (Functional Analysis System Technique) methodology.

A practical tool for determining the relationship of functions is the repeated posing of two basic questions, “Why?” and “How?”, which determine the immediately preceding and immediately subsequent function, as follows:—It is necessary to provide the consumer with electricity.—How?—Transmit AC electrical energy to it.—How?—Invert DC to AC.—How?—Convert solar energy into direct current energy.—How?—Remove the energy of the sun.

We check the correctness of the location of the critical path functions by asking the question “Why?” and moving at the same time in the reverse order, as follows:—Remove the energy of the Sun.—Why?—To convert solar energy into DC energy.—Why?—To invert DC to AC, etc.?—The “When” question allows you to identify auxiliary functions that are performed simultaneously with one or another function of the critical path or which are due to it.

3.1. Functional Models of Systems

So, in addition to performing the basic functions, the system along the entire critical path must ensure safety and ease of maintenance; to obtain electrical energy it is necessary to install a converter and ensure its rotation to follow the Sun, and to continuously obtain an alternating current, it is necessary to ensure the accumulation of electricity and protection of electrical equipment, etc. Based on structural models and diagrams of functions, we build a functional model of the RES system—a logical-graphic representation of the composition and interrelations of the object’s functions.

Functional models of systems are given in Figure 3, Figure 4 and Figure 5.

On the first level of the model, the main function of the system is shown. It supplies the consumer with electrical energy, and the secondary functions accompanying it, to ensure the reliability of the power supply and operational safety. The last one is external.

The functions that characterize the sequence of transformations and correspond to the operating principle of the system determine the composition of the main functions included in the II levels of the model. Differentiation of the main functions into auxiliary functions occurs at levels III and IV.

3.2. Decision Matrixes for the Use RES in an Autonomous Power System

The identification of links among the elements of the system is carried out according to the matrices of the “element-element” links for solar, wind, and waterpower systems shown, respectively, in Figure 6, Figure 7 and Figure 8. The explicit contact (physical contact) links are marked with the letter “Φ” and the implicit correlations (indirect effects) are marked with “k”. Within each type of relationship, we single out harmful (−), neutral (±), and useful (+), as well as direct “_Π”, reverse “_O”, and the performance of the coordination function “_C”.

Links inside the frames circled with a thick line are internal, relating to this set of equipment (subsystem), links outside the frames are external, showing links with other sets.

The functionality of the autonomous power system also depends on the need for updating, flexibility, mobility, elements, hybrid operation, connection and cogeneration. The determination of their coefficients is carried out based on the functional–structural models and the correlation matrix.

The coefficients of actualization $K_{\mathrm{а}F}$, elements $K_{\mathrm{а}N}$ and connections $K_{\mathrm{а}C}$ are defined as follows:

$$K_{\mathrm{а}F}={\displaystyle \frac{F_p}{F_{tn}}};$$

(8)

$${ K}_{\mathrm{а}N}={\displaystyle \frac{N_u}{N_{tn}}};$$

(9)

$$K_{\mathrm{а}C}={\displaystyle \frac{C_u}{C_{tn}}},$$

(10)

where $F_p$ is the necessary (positive) functions; $F_{tn}$ is the total number; $N_u$ is the number of useful elements; $N_{tn}$ is the total number of elements; $C_u$ is the number of useful connections; $C_{tn}$ is the total number of connections.

The coefficients of functional embodiment $K_{\mathrm{K}F}$, elements $K_{\mathrm{K}N}$, and connections $K_{\mathrm{K}\mathrm{C}}$ are defined as follows:

$$K_{\mathrm{K}F}={\displaystyle \frac{F_{bf}}{F_{tn}}};$$

(11)

$$K_{\mathrm{K}N}={\displaystyle \frac{N_{bf}}{N_{tn}}};$$

(12)

$$K_{\mathrm{K}C}={\displaystyle \frac{C_{ExL}}{C_{ExL}+C_{InL}}},$$

(13)

where $F_{bf}$ is the number of basic functions; $N_{bf}$ is the number of material carriers; $C_{ExL}$ and ${ C}_{InL}$ are the link numbers (internal and external).

Using the compatibility coefficients for functions $K_{\mathrm{c}F}$, material elements for $K_{\mathrm{c}N}$ and connections for $K_{\mathrm{c}\mathrm{C}},$ we obtain:

$$K_{\mathrm{c}F}=1-{\displaystyle \frac{F_c}{F_{tn}}};$$

(14)

$${ K}_{\mathrm{c}N}=1-{\displaystyle \frac{N_c}{N_{tn}}};$$

(15)

$${ K}_{\mathrm{c}C}=1-{\displaystyle \frac{C_c}{C_{tn}}},$$

(16)

where $F_{\mathrm{c}}$ is the matching functions and $N_{\mathrm{c}}$ and C_c are, respectively, the number of the functional elements.

The functionality factor of breadth can be calculated by

$$K_{br}={\displaystyle \frac{F_{tn}+F_{\mathrm{p}}}{F_{tn}}},$$

(17)

where $F_{\mathrm{p}}$—the number of potential features.

The results of calculations according to (8)–(17), as well as the values of the coefficient of functional organization, found as an average of the four previous ones, for the systems under consideration are shown in

Table 2. Coefficients of functional and structural perfection of power transmission systems.

Type of RES	Coefficients
	Actualization/ Updates				Concentration				Compatibility				${\mathit{K}}_{\mathit{b}\mathit{r}}$	${\mathit{K}}_{\mathit{o}\mathit{r}\mathit{g}}$
	${\mathit{K}}_{\mathbf{а}\mathit{F}}$	${\mathit{K}}_{\mathbf{а}\mathit{N}}$	${\mathit{K}}_{\mathbf{а}\mathit{C}}$	$\overline{{\mathit{K}}_{\mathit{a}}}$	${\mathit{K}}_{\mathbf{к}\mathit{F}}$	${\mathit{K}}_{\mathbf{к}\mathit{N}}$	${\mathit{K}}_{\mathbf{к}\mathit{C}}$	$\overline{{\mathit{K}}_{\mathit{k}}}$	${\mathit{K}}_{\mathit{c}\mathit{F}}$	${\mathit{K}}_{\mathit{c}\mathit{N}}$	${\mathit{K}}_{\mathit{c}\mathit{C}}$	$\overline{{\mathit{K}}_{\mathit{c}}}$
${\mathrm{S}}_{\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$	1	1	0.68	0.89	0.63	0.46	0.60	0.57	0.74	0.85	0.95	0.84	1	0.77
${\mathrm{S}}_{wind}$	1	1	0.52	0.84	0.13	0.71	0.48	0.44	0.82	0.82	0.82	0.82	1	0.70
${\mathrm{S}}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{r}}$	1	1	0.61	0.87	0.62	0.54	0.61	0.59	0.85	1	1	0.95	1	0.85

. At the same time, the values included in the formulas, respectively, for the systems $S_{\mathrm{C}}$, $S_{\mathrm{B}} \mathrm{and}$ $S_{\mathrm{Г}}$ have amounted to =19, =19, =13, =13, =26, =38, =12, =6, =23, =15, =5, =2, =2, =0, =23, =23, =17, =17, =30, =58, =3, =12, =28, =30, =5, =3, =2, =0, =13, =13, =11, =11, =11, =18, =8, =6, =11, =7, =2, =0, =0, =0.

Knowing the coefficient $k_{org}$, the corrected system efficiency indicator ${K^{\prime }}_{Eff}$ is found though the following:

$${K^{\prime }}_{Eff}={\displaystyle \frac{K_{br}}{k_{org}}}.$$

(18)

The coefficient of functional organization $k_{org}$ of every system under consideration, we find as the average of the four above [32]. The obtained results (Table 2) and the calculated efficiency according to (18) shows that the maximum is obtained when using autonomous systems with wind and solar energy—${K^{\prime }}_{Eff}=$ 1.29 and 1.43 pu, respectively.

Knowing the $k_{org}$, the system efficiency indicator $K_{Eff}$ from (6) is found as

$$K_{Eff}=k_{org}{\sum }_{i=1}^{i=m}{C}_{Wi}{K}_i.$$

(19)

Taking into account the weighting factor depending on the efficiency, reliability and cost criteria, it turns out that $K_{EffSolar}=12.1$, $K_{EffWind}=10.4$ and $K_{EffWatter}=8.7$ pu, respectively. The highest efficiency and reliability of the power supply are obtained when using hybrid power supply systems with a combination of the three main energy sources.

According to the proposed method, it is possible to evaluate a preliminary calculation for the most suitable form of energy supply with the help of renewable energy sources depending on the functional organization of the power supply system.

4. Conclusions

In the article, a systematic approach is used, which makes it possible to determine the most suitable power system, fully utilizing renewable energy sources for given geographical conditions.

Models of the distribution of zones for optimal use of renewable energy sources (RES) and the applicability of the system analysis method in determining the zones for optimal use of photovoltaic, wind, hydraulic and integrated power plants for autonomous power supply of a remote agricultural site have been synthesized.

Evaluation indicators are proposed and a methodology for choosing the type of the most suitable energy source is developed using matrices, taking into account the functional–structural relationships of the burial system, obtained by evaluating their internal characteristics using an approach and a functional–structural description of the MRES, each of which generates the corresponding models depending on the type of primary source, the local geographical conditions and climatic conditions, and the consumption needs. According to the obtained results (shown in Table 2), the calculated efficiency according to (18) shows that the maximum is achieved when using autonomous systems with wind and solar energy of 1.29 and 1.43 units, respectively. The highest efficiency and reliability of the power supply are obtained when using hybrid power supply systems with a combination of the three main energy sources.

To determine the areas of optimal use of different types of RES, the system analysis method was chosen. The spatial and temporal limits of the studied object are defined.

The main factors influencing the possibility of application of the starting system using renewable sources are the climatic conditions and the available energy potential, the installed power and the mode of operation, the probability of trouble-free operation and efficiency and exploitation.