Optimization of energy sources structure to minimize environment pollution

. The paper gives a general statement of the problem of choosing the structure of energy sources of urban heat supply systems to meet technical, economic and environmental constraints. One of the effective approaches to solve such a problem is the construction and optimization of redundant schemes of technological structures of energy sources. A model based on the theory of energy hubs is presented as one of the methods for constructing the redundant scheme. The application of the theory of energy hubs for selecting the types of energy sources allows, in an enlarged form, selecting the main equipment of energy sources, and evaluating technical and economic indices, and the degree of negative impact on the environment (at the level of gross emissions of harmful substances into the atmosphere). A case study of modeling a redundant system for selecting the optimal structure of energy sources, considering the minimum atmospheric pollution, is illustrated.


Introduction
A significant adverse impact of energy facilities on the environment is the pollution of atmosphere. In Russia, power plants and boiler houses burn about 390 million tons of fuel equivalent a year, throwing into the atmosphere about 3.67 million tons of pollutants, which is 21% of the total volume (17.35 million tons) of atmospheric emissions for all stationary sources of the Russian Federation as of 2016 [1,2].
One of the key mechanisms of environmental protection in our country is the assessment of the caused damage and the corresponding payment for emissions of air pollutants. However, as practice shows, the existing algorithm for calculating damage from environmental pollution [3] leads to inadequate compensation for the damage. The operating costs of existing plants for complex chemical purification reach 10% of the company's annual income, and relative size of penalties is 0.05%. As a result, domestic polluting enterprises do not have effective economic incentives to implement environmental protection measures. To change the situation, it is necessary to clarify the concept of environmental damage, as well as penalties for it. It is important that effective measures for the prevention of harmful emissions are justified and taken into account already in the design stage.
An analysis of the domestic scientific and methodological literature, as well as the available methodological tools for the influence of heat supply systems on air pollution, allows us to draw a number of conclusions. The proposed approaches to solve the problems of reconstruction and development of heat supply systems are mainly focused on improving their reliability, controllability and economy. Normally, in these approaches, the activities aimed at reducing the negative impact on the environment are determined for already selected options of the system development, which is not always the best solution [4][5][6][7][8]. The greatest effect on reducing emissions can be achieved when the measures are considered for all compared options [9].
The search for the most profitable composition of energy sources in the urban heat supply systems is a complex problem of scheme-and-structure optimization. Under energy source structure optimization we understand the optimal choice of its type, location and configuration of equipment. The problem has a nonlinear character and is difficult to formalize for practical implementation. The objective is to determine the energy source types, location and configuration of its equipment, including a variety of technical and economic conditions, environmental and territorial restrictions. Solution to such a problem depends on a large number of external and internal factors, such as compliance with the heat and electricity balance conditions; reliability, environmental and other constraints. The environmental constraints that stand out in terms of the degree of impact are the requirements of reducing harmful emissions of pollutants into the atmosphere. Heat power industry is one of the industries that most negatively affect the surface layers of the atmosphere.
A methodological approach based on the construction of redundant schemes, developed both in Russia and other countries, proved rather effective in the optimization of structure of energy sources in urban heat supply systems [10,11].
The methodological approach to the construction of redundant schemes is also developed at Melentiev Energy Systems Institute SB RAS. It implies that a researcher constructs a redundant design calculated scheme of a heat supply system as a set of all admissible configurations of the heat network and the location of heat sources, considering constraints related to obstacles on the terrain and sites chosen for placement of the sources [12]. The idea of the approach is that when choosing the heat sources, the redundant scheme is supplemented by a fictitious node and a subset of fictitious links connecting it with those nodes where the optimal heat power of a source is selected. The number of fictitious links for each source node depends on how many alternatives of source types are considered at a given node. The local optimization of various trees of initial approximation is carried out by the directional enumeration of trees. This allows obtaining solutions close to optimal ones. The redundant scheme when prepared includes all possible alternatives, which eliminates the risk of excluding an optimal solution from consideration.
The authors of [13,14] propose such an approach to construct a structural scheme of an energy source based on a redundant scheme. According to this approach, various options of energy source equipment are considered in a single scheme, which contains a finite number of components with their possible interrelationships.

The mathematical statement of the problem
The mathematical statement of the problem of selecting the structure of energy sources of urban heat supply systems considering technical, economic and environmental constraints can be presented as follows. The objective function is the sum of costs determined by the composition, type and performance of the system components, USD: In this case, the following constraints are met: Urban heat balance, Gcal/year: (3) The condition for competition in options for the reconstruction and/or modernization of existing energy source 1 I i ∈ is as follows: the competition condition in the options for each new energy Heat generation by the i -th energy source, Gcal: power generation by source i , MWh: dependence of heat output on the fuel type: dependence of electricity output on heat output: dependence of electricity output on installed capacity: dependence of gross emissions of harmful substance k on the fuel type: constraints on the amount of fuel used: gross emissions of harmful substance k from the i -th energy source, t/year: urban heat supply system should meet the standards of the protection of the atmosphere: -the maximum permissible emissions (MPE) of harmful substances, t/year: -the maximum permissible concentrations (MPC) for the dispersion of these emissions, mg/m 3 : (    Dotted lines in Figure 1 show possible competing options … for each energy source. The above mathematical formulation is a mixed integer nonlinear programming (MINLP) problem. It is nonlinear, which in particular is explained by the presence of integer variables m i V , and nonlinear dependences (8)- (11). Therefore, to solve it, we propose decomposing it into simpler subproblems that are solved in stages. In the first stage, subproblem (1)- (14) is solved, where the types of energy sources are determined, the composition of the main equipment is selected, and the negative impact on the environment is assessed (at the level of gross emissions).
In the subsequent stages, equations (15)- (17) are taken into account, that is, for the energy sources chosen in the first stage, the equipment is determined, given the MPC of harmful substances in the surface layer of the atmosphere.

Modelling of redundant scheme of energy source structure
Optimization of a structure of energy sources as the first stage problem can be solved using the theory of energy hubs [15], which is widely used in modern practice [16].
The energy hub is an intermediate link between energy producers and the transport infrastructure, on the one hand, and consumers, on the other. It ensures the transfer, conversion, production and storage of various types of energy carriers. The energy hub transforms the energy carrier, changing its potential, which allows integrating any consumer into the system.
The technological model of the hub includes four structural components [17]: 1. Input flows of energy carriers supplied directly from producers or from the system of energy transport infrastructure (fuel supply systems, from renewable energy sources (wind and solar energy), for example, electricity from centralized electricity supply system or heat from district heating system, etc.
2. Energy converters ensure the conversion of some types of energy carriers into their other types (boiler room, chiller, heat pump, etc.), or responsible for a change in physical parameters of energy carriers (electrical transformer, network pump, pressure regulator, etc.).
4. Output flows of energy carriers sent to consumers loads (heat, cooling, power consumption, etc.).
The energy carriers in the energy hub can be transferred from the input to the output with changing parameters (for example, electric voltage) or with a significant transformation changing the form of the energy carrier (for example, the cogeneration unit can convert gas into electricity and heat).
The modeling of hubs is based on three assumptions [18]: 1. There are no losses in the hubs, except for conversion and storage losses; 2. The simulated system is in a stable, steady state; 3. The energy flow is always directed from input to outputs of the hub.
, z is the number of converters, ω is the number of inputs, µ is the number of outputs. The energy flows going through converters γ R can be described in a vector form: where L -the vector of outputs, i.e. energy supply (heat and electricity production), harmful emissions, etc.; P -vector of inputs, i.e. consumption of primary energy (fuel, electricity); C -input-to-output coupling matrix.
where α , β are the input and output energy carriers, respectively.
The coupling coefficient αβ c of converters characterizes the efficiency of conversion of fuel α into energy β and depends on the fuel type (coal, gas, etc.), equipment types and capacities (boiler, turbine, etc.) and its operating conditions. If α P is common for several converters, then αβ c will also depend on the distribution of the input energy flows, which is described by the distribution coefficients (20) The following conditions are imposed on the distribution of energy carriers between converters in the energy source structure: The outputs of the energy source structure, in addition to energy flows, can be the amounts of harmful emissions produced by the combustion of organic fuels (for example, Let us consider, for example, an option of an energy source to be designed. Its scheme is shown in Figure 3. The structure of the energy source includes three converters: an electrical transformer, a gas turbine and a gas boiler. According to (18), the relation between its inputs and outputs is described by equation: where C is input-to-output coupling matrix; converters e L , h L , NO L are output flows of electricity, heat and NO emissions, respectively; e P , g P are input electricity and gas flows, respectively.
Matrix C of the energy source whose model is demonstrated in Figure 3 is written in the following form: where, GT g ν , bo g ν are the distribution coefficients of gas for the gas turbine and the gas boiler, respectively. According to (21)-(22), the following conditions should be met: where, To simplify the modeling of transformation processes, the authors of [19] propose using a piecewise linear approximation of the efficiency functions of converters and dependencies of pollutant emissions on fuel consumption. Expression (28) represents technical capabilities of the converters (their minimum and maximum load) [19].
Expression (29) imposes a constraint on the output flows. In the case that the environmental factor should be considered, it will characterize the MPE of harmful substances in the atmosphere.
Thus, the considered options of energy source structures in the form of energy hubs form a redundant scheme ( Figure  1) [20].

Case study of selecting an optimal structure of energy source
The construction of a redundant scheme of an energy source begins with selection of options for the equipment configuration. The optimal structure choice the is made for a redundant set of single energy source equipment, that has an industrial heat load of 1.32 Gcal/h. Technical, economic and cost indices for the options of energy source equipment are given in Table 1. The cost of laying a gas pipeline, thousand USD -9 9 Option 1 suggests the installation of oil fuel-fired boilers E-1/9-1M. Option 2 suggests the installation of a Mini-CHP based on low-power gas-fired plants SITA54 manufactured in France. Option 3 includes a Mini-CHP based on gas plants DG98M with a low-power gas-fired waste heat boiler KUV-30. All the options have equal heat and electricity output. To this end, when the energy source equipment does not produce electricity, it is purchased from an external electric power system (Table 1, Option 1). Figure 4 demonstrates the gross emissions of harmful substances by energy source option.  Table 2 indicates the sizes of penalties for harmful substance emission, taken according to [21].  Figure 5 shows the models of power plants in the form of hubs created according to the options of equipment presented in Table 1.
The outputs of hubs, in addition to heat and electricity are the annual emissions of harmful substances.
Comparison of the considered options of the energy source structure in terms of technical and economic indices, as well as emissions of harmful substances into the atmosphere with the help of the method proposed above, made it possible to obtain the optimal solution, which corresponds to option 2 ( Figure 5, hub 2). This option of the structure suggests installing a natural gasfired Mini CHP of type 3512HR SITA54 with a heat capacity of 1.64 Gcal/h and a maximum electric power providing the needs of an industrial enterprise of 2.06 MW. The gross emissions of harmful substances when operating at the design heat load in this option of the energy source structure are minimal and will be: NO x -12.92 t/year, CO -14.82 t/year, benzopyrene -8.27E-9 t/year.

Conclusions
The choice of the energy sources optimal structure is a complex nonlinear problem due to the presence of discrete variables, non-linear functions, for example, power generation, dependence of pollutant emissions on fuel consumption, etc. We propose solving this problem in stages. In the first stage, the types of energy sources are determined, the composition of the main equipment is selected, the negative impact of energy sources on the environment is assessed (at the level of gross emissions). In the second stage, for the selected areas of energy sources development, the equipment composition is specified considering the MPC of harmful substances in the surface layer of the atmosphere.
The problem of the first stage can be solved by constructing redundant schemes of energy source structures by the methodology of energy hubs. This provides the following advantages: − the flexibility of the model as a result of considering more connections and types of equipment for energy supply to consumers; − the opportunity to optimize the types of power plants, the cost of generated energy, levels of environmental pollution and tackle other problems by selecting different combinations of input vectors; − the relative ease to take into account environmental constraints, because gross emissions of harmful substances as well as technological indices are considered as output parameters.
The considered case study demonstrates that, in the first stage of optimizing the energy sources structure, the equipment characteristics can be linearized, which allows solving the problem of choosing the directions of energy sources development as a linear programming problem with integer variables.