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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.19 No.1 pp.3-13
DOI : https://doi.org/10.7232/iems.2020.19.1.003

# Low-Carbon Economy as the Main Factor of Sustainable Development of Energy Security

Ivan A. Kapitonov*
Higher School of Tariff Regulation, Plekhanov Russian University of Economics, Moscow, Russian Federation
Department of Energy Policy, Institute of Economics of the Russian Academy of Sciences, Moscow, Russian Federation
*Corresponding Author, E-mail: k4pitonovi@yandex.ru
February 11, 2020 February 25, 2020 February 29, 2020

## ABSTRACT

The concept of low-carbon development involves several interrelated tasks: improving energy efficiency, using renewable energy, protecting and improving the quality of greenhouse gas sinks, limiting or reducing emissions, developing greenhouse gas absorption technologies, eliminating subsidies, and other methods of promoting environmentally destructive activities. The implementation of the principle of low-carbon development is in line with the gradual transformation of the world energy – the transition from fossil fuels as the main source of primary energy resources to other sources of energy. The relevance of the study is determined by the fact that the most important element of development is the possibility of consumption of energy resources and, accordingly, the possibility of their production in the context of economic changes. The methods of statistical analysis, mathematical modelling, the method of criteria estimates were used in the work. Based on the developed mathematical model of behavior of the control object, it is possible to predict the state of stable equilibrium of the energy security territory. The novelty of the article is that the issue of the sustainable development structure of energy security is raised for the first time.

## 1. INTRODUCTION

Today, the security issue reverberates and the reason for its appearance is very transparent – the growing threat to humanity and its multi-vectority. Among threats there are the following: destabilization of the system of international economic relations, high degree of uncertainty of the participants’ actions in the economic space, disintegration tendencies, escalation of international tension, permanent occurrence of global and local crises, limited world resources and their high cost. Recently, the security of the state, the security of the territory and the security of the individual are not considered separately – they are interconnected and interdependent. If any objective or subjective reason (for example, war) represents a threat to national security, it represents a threat both to the enterprise and to the private individual. All this determines the relevance of the study of world experience in solving complex problems of economic security of any subject of management and its institutionalization (the historical process of transition from the phenomenon, which is self-governing and self-organized to managed and organized).

Contributes to the preservation of economy and the use of alternative energy. Low-carbon economy – in the simplest interpretation of the term – is an economy based on energy efficiency, reducing greenhouse gas emissions, and increasing the share of renewable energy sources (Rosa et al., 2018). Therefore, the development of such an economy will contribute to reducing the negative impact on the components of the environment. Combining the desire to improve energy efficiency, to increase the share of renewable energy sources and thus to reduce greenhouse gas emissions, the low-carbon economy is recognized by everybody as a way to implement the concept of sustainable development – a development in which the impact on the environment remains within the economic capacity of the biosphere, so that the natural basis for the reproduction of human life – a source of economic and social well-being – is not destroyed (Buyankin, 2018;Atanelishvili and Silagadze, 2018).

The actions to reduce carbon dioxide emissions into the atmosphere should not only slow down the pace of climate change. This, in its turn, will affect economic and social systems. In the industrial structure, low-carbon agriculture reduces dependence on oil and gas energy and creates an organic, ecological and highly efficient way of development (De Boni, 2017). Low-carbon energy with low carbon emissions creates favorable conditions for the rapid development of low-carbon industry, as a result of which the industry with high carbon emissions will gradually be replaced and its development will slow down. The development of low-carbon logistics will help to improve efficiency and create more efficient logistics lines and routes. Low-carbon services market expects more rapid development.

The most famous foreign scientists, supporters of green economy define a green economy as an economy that is a dependent component of the natural environment within which it exists and is a part of the global ecosystem (Karazijienė and Jurgelevicius, 2017). Since 2009, in the OECD and UN documents, the term “green economy” and its derivatives has become key in determining the directions of sustainable development.

The integrity and sustainability of the state historically depends not only on the effective functioning of the triad of its main systems: political, military and economic, but also from the security system, which unites international, regional, public and state institutions (organizations, structures, authorities) and economic entities, which protect the state from the negative influence of internal and external threats on the basis of the development of norms and laws to ensure the vital interests of citizens, as well as exclusion of the possibility of causing damage to the economy.

## 2. LITERATURE REVIEW

The influence of political, economic, ecological and spiritual crises, the lack of resources and ideas, and the arbitrary nature of aggressive processes necessitate a revision of existing approaches to the issue of ensuring economic security of the country (Hameiri and Jones, 2015;Pirogov and Cherentsov, 2018). Since the regions are the locomotives of the economy of any state, of course they feel this influence (Kosai and Unesaki, 2016). Therefore, the cornerstone of the question is the development of the theoretical and methodological foundations of the synergetic management of economic security in particular of regions or other forms of territories in general (Bialasiewicz et al., 2005).

There are several reasons, which, in fact, concern not so much the general understanding of the economic security of the territory, but it just as a control object, which makes it possible to assume that such specificity exists (Levy, 2009). Therefore, before examining the economic security of the territory as a managed system, it is necessary to study its subject field, that is, territories in terms of a systematic approach (Kononov and Kononov, 2016;Santos et al., 2018). According to the terms of the general theory of systems (systemology), any territory is a system in which the set of inputs into production resources – labor costs (labor items, labor means, labor fources) are transformed into finished products and services (Feng, 2016; Karazijienė and Jurgelevicius, 2017). And the territory also operates within a large system – the foreign policy, economic, social and technical environment with which it con-stantly has complex relationship (Russett, 1979).

In cybernetics the territory can be represented as the intersection of two higher-level systems: the supersystem “society” and the supersystem “resources” (Ivanov, 2016). According to the terms of cybernetics, the founder, the sociotechnical system consists of two subsystems: managed and managing (Treu, 2018). A managed system or managed object is determinant, since it is a set of elements for which control relationships arise (Lappalainen, 2007). That is, the management system of the territory relates to its organizational management structure (Fischhendler and Katz, 2013).

Economic security of the territory as a managed system inherited almost all the properties of the system, as well as its inherent systemic principles: openness, nonlinearity, dynamism, dissipativeness, emergence, homeostaticity, attraction, bifurcation, fractality (Matúš, 2015). In it, processes of self-organization and self-deorganization with such characteristics (according to the scientific content of the synergetics), described by G. Hacken, namely (Froestad and Shearing, 2017), can take place:

• – intensive exchange of energy, information or other resources of the system with the environ-ment, and it is completely chaotic;

• –the behavior of the system is characterized by spontaneity and is described by several values – parameters of order and control parameters (information overload of the system disappears);

• –the presence of a critical value of the control parameter (associated with the arrival of energy, information, knowledge or other re-sources), in which the system is able to lose the state of stable equilibrium (homeostasis); the quantitative accumulation of certain deformations of vital parameters leads to qualitative changes;

• –the new state is due to the harmonious (coherent) behavior of the elements of the system;

• –a new state exists only with a continuous nonstop flow of energy, information, knowledge or other resources (in the presence of internal and external sources of oscillations (fluctuations) of the system). The increase in the intensity of the exchange leads to the critical transitions of the system, resulting in its structure becoming complicated up to the occurrence of turbulent chaos.

## 3. MATERIALS AND METHODS

A significant number of scientific papers became the basis for understanding the economic security of the territory as a managed system (Kazantsev, 2012). But quite often security in the economy is considered chaotically and haphazardly, from which comes the relevance of its research on the part of the system approach, as well as in-depth study of its structure, functions, processes, and goals with the help of iterative analysis.

The article uses the method of comparative statistical analysis, which makes it possible to analyze the energy structure of the states and individual territories. In the framework of the analysis, the statistical method is used to obtain statistical data. The method of criteria assessments is mainly used to form a scale that assesses the adequacy of the efforts made and forms a general framework for understanding how progress in achieving socio-economic parameters is determined. It is also worth noting that the method of mathematical modeling, which is used to build a model of forecasting energy sustainable development of territories, and in a local format, as the model does not consider the context of globalization.

## 4. RESULTS AND DISCUSSION

On the basis of the analysis of the current state and trends of alternative energy development, the criteria were defined for assessing the interaction of the market environment indicators, state regulation of investment and innovation activities, which will reflect the complete set of interdependencies for assessing the development of renewable energy in the countries (Mažylis and Pikšrytė, 2013).

For further research and calculations, a sample of 18 countries has been formed that represent and as a whole characterize most regions of the world, including the USA and Canada, China, India and Brazil, the most developed countries of Europe – France, Norway, Italy, Spain, Germany, Great Britain, countries Eastern Eu-rope – Hungary, Poland, Czech Republic, Slovenia and Slovakia, as well as the Baltic countries – Lithuania and Latvia.

The sample obtained represents 32% of world GDP and 21% of the world population. Therefore, it is sufficiently indicative of the quantitative and qualitative composition in the context of the analysis of the development of renewable energy. It has been decided to collect data for the 10 years (2008-2017) (Asan et al., 2016).

As a result of the statistical data collection, 14 tables with initial values of indicators for the further analysis and calculation of the integral indicator of the effectiveness of the alternative energy development have been formed. Data for the analysis of state support are based on the quantitative assessment of incentives for the development of alternative energy in the state through the following factors:

• - special “green” tariff;

• - investment or tax privileges;

• - reduction of income taxes, energy taxes, VAT, etc.;

• - subsidies for electricity producers;

• - public investment, loans, grants, capital subsidies.

If a country uses one of the given incentives, we assign it a value of 1, if it does not use – 0. In the end, the corresponding parameter will be from 0 to 5, where zero will characterize the lack of state support, and five – maximum state support. The expert estimation method has assigned weight coefficients to the lower-level parameters in such a way that, within each of the criteria, the sum of the coefficients equals one (Table 1).

By analogy, we define the corresponding values for the second level indicators. We determine that the estimation of the market environment will have a coefficient of 0.45, that is, the most will affect the value of the final integral indicator, the state regulation – 0.3 and the investment and innovation environment – 0.25. According to the results of the calculations we have the dynamics of the integral values of the market environment criteria, state regulation of the investment and innovation environment of renewable energy sources (Table 2).

The priority feature in the growth of the “green” economy is a radical increase in energy efficiency, so the term “low-carbon” economy is widely used. It is seen as the basis of the green economy and a model of the economy of the future. Implementation of low-carbon development involves the solution of several interrelated objectives: improving energy efficiency, using renewable energy, protecting and enhancing sinks of greenhouse gases, limitation or reduction of emissions, development of technologies for sequestration of greenhouse gases, phasing out subsidies and other methods of encouraging environmentally destructive activities.

The implementation of the concept of low-carbon development is in line with the gradual transformation of world energy – the transition from fossil fuels as the main source of primary energy resources to other sources of energy. In accordance with the highly probable scenario of human civilization, the structure of energy production and consumption with the absolute predominance of hydrocarbons at the present time (Figure 1) will change in the direction of increasing the share of renewable energy sources in the structure of energy consumption (Figure 2).

In recent decades, the low-carbon economy has become a priority of a number of political programs: the European Union Development Strategy 2020 “Europe 2020”, which includes a number of mandatory targets for the low-carbon economy; the Road Map of the European Commission to move towards a low-carbon economy until 2050 with decarbonization priorities for the energy and transport sectors, etc.

We see that according to the integral estimation of the market environment (Figure 3) Norway has the best characteristics, and the corresponding dynamics is maintained throughout the analyzed period, the values fluctuate within the range of 0.45-0.47. The overall dynamics of development is indicative, as the positive dynamics for the period 2008-2017 is observed in relation to absolutely all the countries being analyzed, which indicates the global tendencies of growth of qualitative market characteristics of the renewable energy sources development (Strielkowski and Lisin, 2016). The leaders are also Spain, Germany, Italy, Latvia, Brazil and the United Kingdom. As could have been predicted, the Czech Republic, Slovakia and Slovenia have the worst performance, ranging from 0.007 to 0.025, which is more than 15 times less than in Norway. It should be noted that in the period from 2008 to 2014, the Czech Republic had the lowest rating, but starting from 2015, the integrated assessment of the market environment outstripped the respective values of Slovakia and Slovenia (Mohapatra, 2017).

Figure 3 shows that Canada has the best integrated assessment of government regulation, showing a value greater than 0.8 within the entire analyzed period. Leaders are also Norway, Great Britain, Germany, the USA and Lithuania. The dynamics of Poland and Slovakia are interesting as they showed the greatest increase of the corresponding estimate for 2008-2017, as well as Slovenia, although it is characterized by the lowest values within the range of 0.28-0.48, also had a significant growth, coming up close to 0.5 in 2017.

According to the calculation of the integral indicator which characterizes the investment and innovation activity in the country, we have two obvious leaders – the USA and China, with the United States characterized by rather stable dynamics at the level of values of 0.68-0.77, while for the analyzed 10 years, the PRC has significantly improved its position by increasing the volume of patents in the field of RES, as well as by reducing the amount of CO2 emissions into the atmosphere. Among the lowest values, we have indicators of such countries as Brazil, Czech Republic, India, Slovakia and Slovenia. Most of the sample is in the middle range, characterizing the investment and innovation environment of the integral estimate from 0.4 to 0.6.

In reality, however, member states do not share the pan-European vision of how the EU energy market should be organized and are making every effort to implement their own national energy policy. Thus, on the development of RES in the EU for the period up to 2030:

• – Denmark supports the targets for 2030;

• – Lithuania believes that RES development targets should be set after a thorough assessment of the impact on industries and specific member states;

• – Austria is strongly in favor of ensuring the safety of the energy system and considering the social consequences;

• – Finland calls for an indicative or moderately binding target;

• – France calls for the consolidation of renewable energy development targets at a later stage, after partial harmonization of the renewable energy support system and approval of the renewable energy integration program in the energy system;

• – Portugal is ready to achieve this goal only in cooperation with other states;

• – Estonia is ready to support renewable energy development targets if the EU's proposed support mechanisms ensure that the country receives a significant economic impact;

• – Romania supports renewable energy development targets to be set by member states.

According to the world economic forum, in 2016, renewable energy became cheaper or equal in price with fossil energy in more than 30 countries. Australia, Brazil, Mexico, Chile, Germany, Israel, New Zealand, Turkey, Japan, etc. are among these states. These reports noted that solar and wind energy have now become quite competitive in many regions. Over the past five to seven years, solar technologies have demonstrated a unique growth rate for the energy sector of installed capacity – at the level of 30-40% per year. According to this indicator, solar energy is confidently ahead of all other energy technologies. Such high rates of development are determined by a significant reduction in the cost of the main technological equipment of solar power plants and, first of all, photovoltaic modules (PVM) for direct conversion of solar radiation into electrical energy.

According to the forecasts of the largest UBS Bank, the rejection of the construction of traditional thermal and nuclear power plants in Europe will occur within the next ten years. In Asian countries, investment in the construction of solar photovoltaic plants (PVP), as noted by General Electric Co., also become more profitable than in projects with traditional thermal power plants. In Russia, according to the calculations produced by LLC “Aliansi”, cost-effective photovoltaic power station may be currently constructed without government subsidies in the South of the European part of Russia, in Altai, in Southern Siberia, the Far East, on Sakhalin. In 2014, the cost of electricity from solar and wind power plants was equal (Figure 4). After 2015, there is already a lower cost of “solar” energy in comparison with the “wind” one. This becomes the basis for the advanced development of solar energy in the future. According to estimates made by analysts in 2011, large-scale development of solar energy was predicted by 2035-2040.

The expected seven- and eight-fold increase in electricity production over the ten-year period (2015-2025) should bring solar energy to the first place among all renewable energy generation technologies. These circumstances are caused by a combination of the following favorable factors: a significant reduction in the cost of basic solar equipment, growing progress in the field of accumulation of large amounts of electricity and the emergence of highly efficient storage devices based on fundamentally new technical solutions, and state support.

Geothermal energy is the fourth largest and fastest among other types of renewable energy. Installed capacity of geothermal power plants increased from 5.83 GW in 1990, 7.97 in 2000 to 10.72 GW in 2018. Average annual growth between 2000 and 2018 was 3.1%. The installed capacity of geothermal plants in the leading countries in 2018: US to 3.09, Philippines – 1.9, Indonesia 1.197, Mexico – 0.958, Italy – 0.843, New Zealand – 0.628 and Japan – 0.536 GW (Sakulyeva and Kseniia, 2019).

In fact, energy security is now defined as the elimination of the threat that the energy aspect will be-come a potential obstacle to the economic growth of states in the long term. While for large net importing countries, lack of energy can be an obstacle to maintaining sufficient growth rates, for a country the development and economic growth of which are significantly tied to energy exports, these are the factors limiting production and exports. High prices, the uncertainty of the forecast for the duration of the period of high prices, the reliability and sufficiency of the energy delivery infrastructure, the reliability of suppliers – all these issues are of great importance for world energy security.

So, according to the results of the integrated assessment of the economic support for the development of alternative energy (Figure 5), Norway is of paramount importance, while the lowest is the Czech Republic, Slovakia and Slovenia. Also, Canada, Germany and the USA have a high level of RES output. China has one of the fastest paces of renewable energy development, which at the beginning of the analyzed period had an integral estimate of 0.32 and increased it by almost 60% – up to the leaders of the sample (0.52). In general, we have global positive dynamics in the period 2008-2017 in the field of alternative energy and stimulating its development through state regulation of the industry and improving the investment and innovation climate of the states as a whole, therefore, we can conclude that in the near future trends will be maintained. Particular attention should be paid to India and China, since, according to many forecasts, these two countries will show the highest growth rates of renewable energy use, as they have significant potential.

The study of economic support for the development of alternative energy as part of the energy security of the territory makes it possible to single out the following points: over the past few years the dynamics of generation and consumption of energy from renewable sources have been steadily growing, the share of alternative energy sources has been increasing, among which water energy dominates and the proportion of solar energy has also been rapidly increasing. At the highest state level, an action plan is being developed to improve the energy efficiency of the economy, in particular, strategies for the development of renewable energy have been developed, and a bilateral dialogue is underway with international agencies on the development of alternative energy, in particular the International Renewable Energy Agency. Also, one of the highest “green” tariffs is currently in force, which remains a powerful incentive for the development of domestic renewable energy, but at the same time there is an imperfection of the legislative base re-garding some aspects of its use, in particular, by house-holds.

In 2004, for the first time, a synergetic model of the stability of an average firm was offered, in which the important role of the control parameters that they play while choosing the path to one or another steady state was revealed. Synergetic modeling of economic processes and phenomena is based on two main points:

• – the choice of order parameters, that is, macroscopic variables, quantitatively characterizing the main connections in the system and control parameters, that is, external conditions in which the system cannot change, and therefore, has to adjust to them.

• – making up the main proportions, which states that the rate of change of the order parameters with the influence of time is proportional to their growth minus their loss. The ratio of proportions is formed on the basis of experience.

Mathematical modeling of the territory sustainability provides the ability to predict the state of stable equilibrium, which allows us to develop appropriate measures to manage the economic security of the territory. The sustainability of the industrial activity of a territory is determined by such parameters as: the number of highly organized personnel, the availability of equity capital and the volume of investments (credit). That is, in this case, the concept of sustainability of a territory is essentially equivalent to the concept of sustainability of a company, since with sustainable development of a territory; there is a consolidation of social and economic policies and a process of structuring the economy of a territory as a corporate structure. The mathematical model of the stability of the territory is presented in the form of a system of three differential equations (Eq. 1):

${ Y ˙ 1 = – γ Y 1 + α Y 2 + α Y 2 Y 3 ≡ f 1 ( Y 1 , Y 2 , Y 3 ) Y ˙ 2 = μ Y 2 – β Y 1 + μ Y 3 – β Y 1 Y 3 ≡ f 2 ( Y 1 , Y 2 , Y 3 ) , Y ˙ 3 = – ω Y 3 + δ Y 2 ≡ ( Y 1 , Y 2 , Y 3 )$
(1)

where $Y 1 = Y 1 ( t )$ – the number of employees at the time, people; $Y 2 = Y 2 ( t )$ – the amount of personal capital at the time t, rub.; $Y 3 = Y 3 ( t )$ – the amount of borrowed capital, i.e. the loan at the time, rub; $Y ˙ 1 , Y ˙ 2 , Y ˙ 3$ – derivatives with respect to the independent variable .

The values of the coefficients are as follows:

• α: the proportionality coefficient, showing how much of its capital a territory can allocate to attract new employees. Namely, promotional costs (including the Internet), informing about the prospects for expanding the scope of activity of the territory, about the well-organized work of employees, about the cohesion of the team, as well as the respectability of external and internal design offices. In short, these are the costs to form a reputation on the labor market. However, from a mathematical point of view, this coefficient does not greatly influence the type of sustainability of the system: it is important that it is not close to zero.

• γ: proportionality coefficient, which summarizes the various reasons as a result of which an employee may be dismissed or he/she quits himself/herself. Employees’ turnover threatens to lose accumulated experience, skills, and competencies, which in turn affects the increase in the cost of finding, selecting and training new employees with lower productivity.

• μ: proportionality coefficient, which shows the effectiveness of capital investments in the territory (taking into account the influence of various taxes, payments, fees – they carry a dissipative effect on the “energy” of the territory and threaten with a decrease in profitability).

• β:proportionality coefficient characterizing the amount of territory expenses per employee. This includes the costs of wages, deductions for social events and the cost of the territory for the maintenance of labor; except for those included in the wage fund (these include expenses of the territory for social security of workers, their cultural and everyday services, for their housing, on vocational training and other labor costs).

• δ:proportionality coefficient, which affects the availability of equity capital. Its sufficient share testifies to a high level of financial health of the territory, solvency in the long term. If the share of own capital is low, then the company faces bankruptcy.

• ω:proportionality ratio indicating the difficulty to obtain a loan. For example, a high interest loan increases the risk of non-repayment, which threatens with bankruptcy.

For an average firm, the coefficients α and β should be relatively large, since both relate to expenses for employees, and the coefficient μ and γ, on the contrary, should not be large because, firstly (in the case of μ), the profit from operations on the market is not too high, otherwise the company would be big, not medium; and secondly (in the case of γ), in a civilized society in the territory, the employee turnover rate is low.

In the model $Y 1 , Y 2 , Y 3$ , variable factors or in the synergetics thesaurus they are called order parameters; α, γ, μ, β, δ, ω are constant factors (proportionality coefficients) or control parameters. We clarified the model of sustainability of the territory as a social structure. The second and third components of the right side of the first equation of the mathematical model (1) indicate that the increase in new employees is proportional to the availability of equity capital and the use of credit for its intended purpose (capital meeting $− α Y 2 Y 3$ ) (people prefer working in a large company, which, in turn, more invests in the formation of its attractive image), and the first member indicates a reduction in the number of employees in the enterprise, mainly due to the lack of funding and due to other, less important reasons .

The members of the right-hand side of the second equation of the mathematical model (2) indicate that the rate of growth of equity is determined in proportion to its value, which is obtained by investing the amount of capital and credit (terms) minus the costs associated with salaries and loan maintenance (summands $μ Y 2 и μ Y 3$ ). The coefficients µ and β of the equation reflect the share of the use of equity and credit for the salary of employees and credit resources.

The third equation of system (2) reflects the fact that the rate of turnover of the credit volume (the possibility of additional lending) is positively affected by the availability of equity capital (the larger the capital of the territory is, the more willingly they are given a loan) and in a negative way – already existing credit obligations $( δ Y 2 )$ . We have also proposed “soft modeling” or a technique for qualitative analysis of a mathematical model (1) first, stationary relation is found, and equating the derivatives to zero, namely, a nonlinear system of algebraic equations (Eq. 2) is considered:

${ − γ Y 1 + α Y 2 + α Y 2 Y 3 = 0 μ Y 2 + μ Y 3 − β Y 1 − β Y 1 Y 3 = 0 , δ Y 2 − ω Y 3 = 0$
(2)

From the third equation it follows: $Y 2 = ω δ Y 3$ , while from the first – $Y 1 = 1 γ ( α ω δ Y 3 + α ω δ Y 3 2 )$ . By substituting these expressions into the second equation of an algebraic system, we get (Eq. 3):

$Y 3 [ Y 3 2 + 2 Y 3 + ( 1 − μ γ β α − μ γ δ β α ω ) ] = 0$
(3)
after obvious transformations. So, the first radical is $Y 3 ( 1 ) = 0$ and we have a trivial singular point (0, 0, 0). Two other radicals are written as follows (Eq. 4):
$Y 3 ( 2 , 3 ) = − 1 ± μ γ β α + μ γ δ β α ω$
(4)

Since the desired stationary outcomes must be in the first quadrant, the relations between the coefficients of the mathematical model (2) are easily established, namely:

$μ γ > β α$
(5)

At the same moment the numerical parameters ω and δ acquire arbitrary positive values, following the economic content:

$μ γ β α ω ω + δ > 1$
(6)

Equities (5, 6) are derived from the requirement that one of the radicals $Y s ( 2 , 3 )$ must be positive, that is not limited only with the trivial stationery solution. For this purpose the condition $μ γ β α ( 1 + δ ω ) > 1$ must be met, the realization of which can be in two ways. The stability of stationary solutions is estimated knowing the radicals of the characteristic equation (Eq. 7).

$[ ( ∂ f 1 ( * ) ∂ Y 1 − λ ) ∂ f 1 ( * ) ∂ Y 2 ∂ f 1 ( * ) ∂ Y 3 ∂ f 2 ( * ) ∂ Y 1 ( ∂ f 2 ( * ) ∂ Y 2 − λ ) ∂ f 2 ( * ) ∂ Y 3 ∂ f 3 ( * ) ∂ Y 1 ∂ f 3 ( * ) ∂ Y 2 ( ∂ f 3 ( * ) ∂ Y 3 − λ ) ] Y 1 = Y 1 s Y 2 = Y 2 s Y 3 = Y 3 s = 0$
(7)

here (Eq. 8):

$λ 3 + α 1 λ 2 + α 2 λ + α 3 = 0$
(8)
Or (Eq. 9, 10, 11):
$α 1 = − ( ∂ f 1 ( * ) ∂ Y 1 + ∂ f 2 ( * ) ∂ Y 2 + ∂ f 3 ( * ) ∂ Y 3 )$
(9)
$α 2 = | ∂ f 1 ( * ) ∂ Y 1 ∂ f 1 ( * ) ∂ Y 2 ∂ f 2 ( * ) ∂ Y 1 ∂ f 2 ( * ) ∂ Y 2 | + | ∂ f 1 ( * ) ∂ Y 1 ∂ f 1 ( * ) ∂ Y 3 ∂ f 3 ( * ) ∂ Y 1 ∂ f 3 ( * ) ∂ Y 3 | + | ∂ f 2 ( * ) ∂ Y 2 ∂ f 2 ( * ) ∂ Y 3 ∂ f 3 ( * ) ∂ Y 2 ∂ f 3 ( * ) ∂ Y 3 |$
(10)
$α 3 = − [ ∂ f 1 ( * ) ∂ Y 1 ∂ f 1 ( * ) ∂ Y 2 ∂ f 1 ( * ) ∂ Y 3 ∂ f 2 ( * ) ∂ Y 1 ∂ f 2 ( * ) ∂ Y 2 ∂ f 2 ( * ) ∂ Y 3 ∂ f 3 ( * ) ∂ Y 1 ∂ f 3 ( * ) ∂ Y 2 ∂ f 3 ( * ) ∂ Y 3 ]$
(11)
where equations $∂ f i ( L ) ∂ Y j ( i , j = 1 , 2 , 3 ; f i ( L )$ – correspondingly the right parts of the equation of the mathematical model (1), representing partial derivatives; designation |•| corresponds to the second order determinant in finding the coefficient $α 2$ and the third order determinant in the case of the coefficient $α 3$ .

If $λ 1 , λ 2 , λ 3$ are the required radicals of the (Eq. 6), then the following equation is satisfied (Eq. 12):

$α 1 = − ( λ 1 + λ 2 + λ 3 ) ; α 2 = λ 1 λ 2 + λ 2 λ 3 ; α 3 = λ 1 λ 2 λ 3$
(12)

Specifically, in our case, the determinant (7) takes the form (Eq. 13):

$[ ( − γ − λ ) α α Y 2 − β − β Y 3 μ − λ μ − β Y 1 0 δ − ω − λ ] = 0$
(13)

This is calculated at the stationary point. It should be noted that the radicals of the characteristic equation can be: real (negative and positive), complex (with negative real parts and positive real parts), and also pure imaginary. To study the nature of the equation radiradicals (6) and their signs, the discriminant of the equation is used (Eq. 14):

(14)

Hurwitz conditions $− α 1 > 0 , α 3 > 0 , α 1 α 2 − α 3 > 0$ ; Descartes’ theorem: the number of positive radicals of an algebraic equation is equal or less by an even number of the number of sign changes in the sequence of coefficients $1 , α 1 , α 2 , α 3$ . The same theorem is applied to the number of negative radicals of the equation and changes in the signs of the sequence, that is, to the radicals of the equation (Eq. 15):

$− λ 3 + α 1 λ 2 − α 2 λ + α 3 = 0$
(15)

Specifically, for the trivial singular point of the mathematical model (2), the determinant is written (Eq. 16):

$[ ( − γ + λ ) λ 0 − β μ − λ μ 0 δ − ( ω + λ ) ] = 0$
(16)

And characteristic (Eq. 17):

$λ 3 + ( γ − μ + ω ) λ 2 + ( − μ γ + ω γ − μ ω − δ μ + β α ) λ − γ μ ω − δ μ γ + β α ω = 0.$
(17)

Based on the developed mathematical model of the control object behavior, it becomes possible to predict the state of stable equilibrium of the territory. There are several types of prediction that requires an understanding of the laws of development:

• – Inertial forecasting or extrapolation is that the process continues the trajectory that was before it began, that is, the future parameters of the system are determined on the basis of previous development trends.

• – Scenario design is to determine the likelihood of possible alternatives for development or the desired state in the future turbulent macroenvironment. Scripts depend on the resources invested in the future.

• – Design management is to predict the impact of decisions. It refers to the structuralist approach, in which there is no dynamic prehistory. In the future, this type of forecasting is applied. As noted above, nonlinear dynamics studies the properties of dynamic systems, which are systems that describe a process in time, namely, the transition from a state of stable equilibrium to unstable and vice versa. The main tasks are: first, the search and classification of a particular equilibrium point, and secondly, the identification of sets that either attract (attractors) or repel (repellers).

## 5. CONCLUSIONS

For the qualitative analysis of the dynamic system, which is the territory, the phase space method is used. It is based on the geometry of time and allows you to visualize the behavior of the territory. A significant simplification of the description of the dynamic system state belongs to the advantages. The phase system space is an abstract multidimensional space in which the change in the coordinates of a point (that is, its movement) forms curves (phase trajectories) over time, which vividly describes the evolution of a non-linear, “chaotic” system in a geometric form (phase portrait). The main characteristic of space is its dimension, i.e. the number of parameters that must be set to determine the state of the system. A phase portrait is a collection of all phase paths describing all possible modes. On its basis, it is possible to determine the particular equilibrium point of the system as a guideline to which it will come with time.

In the economic context, the phase trajectories are the trajectories of the economic development of a business entity, or the trajectories of individual business processes (core and supportive) and interests of stake-holders. If all of them are in the area of attraction of the attractor, then there is no need to make quick management decisions to change the situation. On the contrary, if they are not within the domain of attractor’s attraction, then there is a need to make quick management decisions.

The advantages of introducing green energy are obvious. After all, coal, gas, oil, converted by combustion into electricity are an exhausted resource and can be used only once, each kilogram, liter or barrel. Then they will turn into greenhouse gases and other toxic emissions and will never be available to us again. In the case of renewable energy stations, they only capture and convert the energy around them. Of course, their existence has an impact on the environment: photo panels cast a shadow, and wind turbines create aerodynamic resistance to wind and turbulence. Not all the RES are equally environmentally safe. Some can cause environmental damage. In particular, we are talking about hydroelectric power plants (HPP). Many floodplain ecosystems were destroyed due to hydroelectric power plants, which led to a decrease in species diversity. However, in recent years, hydropower has given way to new types of generation: solar and wind power. According to experts, their share of generation will be equal to the share of hydropower plants by 2030.

The current stage of energy development in the European Union is characterized by the following factors: high dependence on energy imports in a limited number of large energy suppliers; high instability of energy prices; increased risk of energy security coming from the producer states and energy transit countries; increasing threat of climate change, insufficient level of links between the energy systems of the EU countries. The use of renewable energy sources (RES) largely provides a solution to all of the above problems. The achievement of the goals set by the European Union in the field of renewable energy development is based on a system of effective tools and mechanisms to stimulate and support this process.

## Figure

Structure of the World Energy Consumption, 2014.

Structure of the World Energy Consumption, 2050.

Integral figures of the market environment criteria.

Forecast of comparative changes in the cost of electrical energy.

Value of the economic support effectiveness index for the development of RES in 2008-2017.

## Table

Figures of weight coefficients of parameters

Integral values of the economic support criteria for the development of alternative energy of the countries in 2008-2017

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