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Article

Technical and Economic Analysis of Low-Emissions Modernization of Existing Heating Plants in Poland

by
Anna Hnydiuk-Stefan
1,
Aleksandra Otawa
1,*,
Krzysztof Stefan
2 and
Dariusz Zmarzły
2
1
Faculty of Production Engineering and Logistics, Opole University of Technology, 45-758 Opole, Poland
2
Faculty of Electrical Engineering Automatic Control and Informatics, Opole University of Technology, 45-758 Opole, Poland
*
Author to whom correspondence should be addressed.
Energies 2021, 14(21), 7426; https://doi.org/10.3390/en14217426
Submission received: 7 October 2021 / Revised: 25 October 2021 / Accepted: 4 November 2021 / Published: 8 November 2021
Browse Figures
Versions Notes

Abstract

:
An analysis is performed with regards to technologically outdated heating plants operating in many areas where fossil fuels such as coal and gas are utilized, in order to consider the alternatives of their modernization. By application of a chart using a variety of alternatives, the economic feasibility of executing two types of modernization of heating plants are explored: a single-fuel gas–steam CHP plant and a coal-fired heating plant to a coal-fired CHP plant with a condensing turbine. This study demonstrates how the selection of modernization technology is affected, in terms of profitability, by the value and variability in time of the price relationships between energy carriers, rapidly growing charges related to CO2 emission allowances, and costs depending on other pollutant emissions that originate from the operation of electricity and heat sources powered by fossil fuels. In both technical cases of modernization, lower prices of energy carriers coupled with CO2 emissions allowances lead to higher prices of electricity that can be sold as additional products following this modernization, and consequently, the specific cost of heat production in the repowered heat sources is lowered. The calculations were performed by the application of models of heating plant modernization applying continuous time notations, which offer the determination of the most suitable time of initiation of this modernization. Such relationships would be difficult to describe in the case of the use of traditional discrete models. In the case of a simultaneous increase in the prices of all main factors affecting the cost of heat generation, such as the price of gas, electricity and CO2 emissions, the fastest modernization of the heating plant to single-fuel gas–steam CHP provides the possibility of the best economic performance.

1. Introduction

The energy policy of the European Union has for many years emphasized the importance of district heating in improving energy efficiency and reducing CO2 emissions. The current system promotes heating systems, but by imposing strict regulations it clearly emphasizes that only heating systems that ensure high efficacy can receive support [1]. Meanwhile, many heat sources are already outdated and are often characterized by low efficiency of heat production. The existing heating sector requires intensive modernization processes [2]. This means that adequate investment in restoring old, local heat sources, and repairs and modernizations of heat-generating units are becoming a necessity [3] and such processes need to be accompanied by taking into account new technical, legal, economic and environmental aspects [4].
The repowering of heating plants to combined power generators that operate according to the demand for district heating plays a particularly important role in this respect [5]. The support for the development of combined heat and power production has been the goal of the European Union’s energy policy for several years [6]. One example of this is EC Directive 2004/8. Extensive deployment of cogeneration solutions can play an important role in decarbonizing Europe and achieving its energy targets [7]. Combined heat and power (CHP) reduces the cost of the energy system, as it uses less primary energy from fossil fuels. Quite evidently, lower consumption of fossil fuels also means lower carbon dioxide emissions and the costs related to this [8].
For the reasons outlined above, thermodynamic and economic analysis of such solutions forms a current necessity. The results of such analysis may offer grounds for performing rational investment processes in heating plants and combined heat and power plants. This article presents an analysis of economic effectiveness of two modernization options—heating plants repowered to single-fuel gas–steam CHP plants, and heating plants repowered to coal-fired CHP plants including a condensing turbine.
The article shows how individual price factors related to fuel, electricity and heat sales, as well as the level of CO2 emission prices and environmental fees affect the profitability of modernized heat plants, taking into account the current and possible future price conditions, assuming different times to start modernization by using a novelty methodology based on mathematical models with continuous time.

2. Mathematical Models Applying Continuous Time Notation in Technical and Economic Effectiveness of Heating Plants and CHP Plants

Continuous-time mathematical models offer an innovative approach to the technical and economic analysis of investment processes in enterprises forming heat sources [9]. Continuous time notations have a considerable advantage over discrete records [10]. They make it possible to easily and quickly analyze variations in, for example, the value of NPV (net present value) in order to find its optimal value [11]. In addition, these notations provide means for the analysis of variations in this value depending on changes in time, among others in energy prices and environmental charges [12].
In the analysis that was carried out for the purpose of this article, a record applying continuous time was used that was developed and described in detail in the publication [10]. Figure 1 shows a time diagram that was utilized to develop universal mathematical models with continuous time which were used to analyze the modernization of existing heating plants and CHP plants.
The intervals ❬0,t1❭, ❬t1,t2❭, ❬t2,T❭ in Figure 1 represent the successive years of operation of the heating plant and CHP plant before, during and following their repowering. When the value equal to zero is substituted for the production of electricity in the interval expressed by ❬0,t1❭ in these models, they apply to the repowered heating plant.
The basic relationship used to determine the technical and economic effectiveness of modernization of power plants, heating plants and combined heat and power plants, taking into account the investment incurred in this modernization, is formed by the equation for the total NPV that is obtained from their operation throughout an interval in time T. In a continuous record, the value of NPV is expressed in the following manner [13]:
N P V = ∫ 0 t 1 F + A + S − K e − F − A 1 − p e − r t d t + + ∫ t 1 t 2 F + A + F M + A M + S M − K e M − F − A − F M − A M 1 − p e − r t d t + + ∫ t 2 T F + A + F M + A M + S mod − K e mod − F − A − F M − A M 1 − p e − r t d t + − ∫ 0 T F + R e − r t d t − ∫ t 1 T F M + R M e − r t d t → max
The criterion expressed by gaining a minimum, mean, specific cost of heat production kh,av in heat sources over the T years of their operation is equivalent to the criterion expressed by NPV, as they aim at the maximum value of searching for an effective technology for the modernization of heat and power plants and heating plants [14]. The rational approach in the operation of a heating plant is manifested by its ability to generate heat at the lowest possible cost [10]. The projected economic effects cannot be achieved in the absence of a prior analysis concerned with the costs of heat generation and without appropriate steps designed to control this cost [15,16]. The methodology for determining the formula for the mean specific cost, kh,av, of heat generation in a modernized heat source in a notation of continuous time was developed and discussed in detail in the study reported in [15]. This formula takes the following form [15]:
k h , a v = − σ A e e l t = 0 a e l − r e a e l − r t 1 − 1 + σ A + 1 η h 1 + x s w , m , w a s e f u e l t = 0 a f u e l − r e a f u e l − r t 1 − 1 + + σ A + 1 η h ρ C O 2 p C O 2 t = 0 a C O 2 − r e a C O 2 − r t 1 − 1 + σ A + 1 η h p CO     p CO t = 0 a C O − r e a C O − r t 1 − 1 + + σ A + 1 η h ρ N O X p N O X t = 0 a N O X − r e a N O X − r t 1 − 1 + σ A + 1 η h ρ S O 2 p S O 2 t = 0 a S O 2 − r e a S O 2 − r t 1 − 1 + + σ A + 1 η h ρ d u s t p d u s t t = 0 a d u s t − r e a d u s t − r t 1 − 1 + σ A + 1 η h 1 − u ρ C O 2 e C O 2 t = 0 b C O 2 − r e b C O 2 − r t 1 − 1 + + 1 + x s a l , t , i n s δ s e r v i τ s r 1 − e − r t 1 + z i τ s 1 + 1 T − 1 + 1 T − t 1 T e − r t 1 + − σ A M e e l M , t = t 1 a e l M − r e a e l M − r t 2 − e a e l M − r t 1 + + σ A M + 1 η h M 1 + x s w , m , w a s e f u e l M , t = t 1 a f u e l M − r e a f u e l M − r t 2 − e a f u e l M − r t 1 + + σ A M + 1 η h M ρ C O 2 p C O 2 M , t = t 1 a C O 2 M − r e a C O 2 M − r t 2 − e a C O 2 M − r t 1 + σ A M + 1 η h M ρ C O p C O M , t = t 1 a C O M − r e a C O M − r t 2 − e a C O M − r t 1 + + σ A M + 1 η h M ρ N O X p N O X M , t = t 1 a N O X M − r e a N O X M − r t 2 − e a N O X M − r t 1 + σ A M + 1 η h M ρ S O 2 p S O 2 M , t = t 1 a S O 2 M − r e a S O 2 M − r t 2 − e a S O 2 M − r t 1 + + σ A M + 1 η h M ρ d u s t p d u s t M , t = t 1 a d u s t M − r e a d u s t M − r t 2 − e a d u s t M − r t 1 + σ A M + 1 η h M 1 − u M ρ C O 2 e C O 2 M , t = t 1 b C O 2 M − r e b C O 2 M − r t 2 − e b C O 2 M − r t 1 + + i + i M 1 + x s a l , t , i n s δ s e r v M τ s r e − r t 1 − e − r t 2 + z i τ s 1 + 1 T − t 1 T e − r t 1 − 1 + 1 T − t 2 T e − r t 2 + + i M τ s 1 + 1 T − t 1 − t 1 T − t 1 e − r t 1 − 1 + 1 T − t 1 − t 2 T − t 1 e − r t 2 + − σ A mod e e l mod , t = t 2 a e l mod − r e a e l mod − r T − e a e l mod − r t 2 + σ A mod + 1 η h mod 1 + x s w , m , w a s e f u e l mod , t = t 2 a f u e l mod − r e a f u e l mod − r T − e a p a l mod − r t 2 + + σ A mod + 1 η h mod ρ C O 2 p C O 2 mod , t = t 2 a C O 2 mod − r e a C O 2 mod − r T − e a C O 2 mod − r t 2 + σ A mod + 1 η h mod ρ C O p C O mod , t = t 2 a C O mod − r e a C O mod − r T − e a C O mod − r t 2 + + σ A mod + 1 η h mod ρ N O X p N O X mod , t = t 2 a N O X mod − r e a N O X mod − r T − e a N O X mod − r t 2 + σ A mod + 1 η h mod ρ S O 2 p S O 2 mod , t = t 2 a S O 2 mod − r e a S O 2 mod − r T − e a S O 2 mod − r t 2 + + σ A mod + 1 η h mod ρ d u s t p d u s t mod , t = t 2 a d u s t mod − r e a d u s t mod − r T − e a d u s t mod − r t 2 + + σ A mod + 1 η h mod 1 − u mod ρ C O 2 e C O 2 mod , t = t 2 b C O 2 mod − r e b C O 2 mod − r T − e b C O 2 mod − r t 2 + + i + i M 1 + x s a l , t , i n s δ s e r v mod τ s r e − r t 2 − e − r T + z i τ s 1 + 1 T − t 2 T e − r t 2 − 1 T e − r T + + i M τ s 1 + 1 T − t 1 − t 2 T − t 1 e − r t 2 − 1 + 1 T − t 1 − T T − t 1 e − r T r 1 − e − r T
For the case when modernization includes a heating plant, the value of zero is substituted in the place of the annual cogeneration factor σA in the interval denoted by ⟨ 0 , t 1 ⟩ .
Using Equation (2), an analysis of the economic viability of modernization of the heating plant was performed in the later sections of in the article with regard to two possible alternatives of this modernization—a heating plant using a single-fuel gas–steam CHP plant and a coal-fired CHP plant including a condensing turbine. The results of the analysis are presented in charts in Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30 and Figure 31 for several selected probable scenarios of variations in fuel prices, electricity and emissions per CO2 tonne. The calculations were performed by application of multiple scenarios, i.e., for different mean values of fuel, electricity and CO2 emission allowances over the entire time interval ⟨ 0 , T ⟩ , for T = 20 years of projected exploitation. The prices of energy carriers and environmental charges form integral means, as they vary exponentially over the entire range of time T. The variations in the value of prices applied in the calculations assume very wide ranges and include current and possible variations in the prices in the future. The calculations were carried out depending on the year t1 of the initiation of this modernization (t1 = 0), i.e., when the repowering takes place immediately/at the time of purchase, and when we intend to consider a modernization that can be initiated at a later time, i.e., after 5, 10 or 15 years (when t1 = 5, 10 and 15 years).

3. Analysis of Economic Feasibility of Modernizing a Heating Plant to a Single-Fuel Gas-Steam CHP Plant

One of the possible courses of modernization of heating plants that can play a very important role in terms of low-emission development involves the development of a gas-based system [9]. The constantly growing energy consumption, resulting from rapid economic development, population growth and technological progress, has led to the consideration of the application of natural gas as a fuel offering relatively low CO2 emissions, and hence, it has gained an increasingly popular role in the energy sector and forms a very important raw material for the global economy [17]. One of the ways of increasing the consumption of natural gas involves its application in the existing coal-fired power plants and combined heat and power plants [18,19]. More and more commonly, views are expressed that natural gas should be considered primarily as fuel when the modernization of existing coal-fired CHP plants and construction of new cogeneration power units are taken into account [20].
When the application of gas is considered, the key issue is related to the profitability of this process [21]. This condition is related to an economically viable ratio of electricity price to the price of natural gas and coal. Natural gas forms an expensive fuel, and in the places where expensive fuel is utilized, the product derived from it needs to be offered at a sufficiently high price. As a result of decreasing gas prices and the reducing ratio of gas price to coal price and under the condition that electricity prices are sufficiently high, the profitability of repowering using gas technologies can be a feasible option [10].
Despite the awareness of the high price of gas, we can note that the modernization potential using technologies based on gas turbines forms a promising direction and forms a very important study aspect for environmental reasons, as it is related to lower emissions of carbon dioxide and other pollutants into the environment [9]. It is worth noting that the use of the gas–steam system leads to a decrease in CO2 emissions, as CO2 emission from natural gas combustion is about two times lower per unit of chemical energy of the fuel combustion compared with emission from coal combustion (for hard coal, CO2 is equal to ρ C O 2 c o a l ≈ 95 kgCO2/GJ, and for natural gas ρ C O 2 g a s ≈ 55 kgCO2/GJ). These technologies are also characterized by relatively high energy efficiency [17,22].

3.1. Assumptions Adopted in the First Option of Modernization

The zero values of the exponents a c o a l , a e l , b C O 2 , correspond to the respective coal prices e c o a l = 11.4 PLN/GJ, electricity e e l = 180 PLN/MWh and prices of purchasing carbon dioxide emission allowances e C O 2 = 29.4 PLN/Mgco2. The price of gas e g a s m o d in the period following modernization was taken to be equal to 32 PLN/GJ. The selling price of electricity is constant and is equal to the price prior to this modernization. The following input data was adopted in the current analysis: specific investment for the modernization equal to iM = 2.5 million/MW (gas and steam systems are much cheaper in terms of investments than coal-based systems); cogeneration factor σ A and σ A M equal to 0, since the projected modernization involves a heating plant, and in the period following the modernization the CHP plant with a hierarchical gas–steam system was equal to σ A m o d = 4; construction period of CH Plant b = 2 years; efficiency of heating plant ηc = 0.85 and the same value was adopted with regard to the period throughout modernization as well as following it, i.e., η h M = η h m o d = 0.85; fixed cost rate related to investment equal to δserv = 0.03 as well as an assumption that δ s e r v = δ s e r v M = δ s e r v m o d ; discounting rate r = 7%; annual period corresponding to the utilization of maximum (rated) capacity equal to τs = 2900 h/a.

3.2. Results of Analysis

In the first alternative that was analysed, the calculations assumed an increase in gas price (Figure 2) combined with rising purchase prices of CO2 emission allowances (Figure 3). The curves in Figure 2 and Figure 3, which contain the calculation results, have an increasing tendency. The increase in gas prices and purchase prices of CO2 emission allowances lead to an increase in the cost of heat production, kh,av, regardless of the year, t1, corresponding to the initiation of this modernization. The lower the fuel or environmental costs, the lower the cost, kh,av.
When we take on an analysis of the effect of the instant of initiation of modernization on its economic effectiveness, we can see that the more distant in time the year t1 is, the lower the specific cost of heat generation, kh,av. However, it does not mean that the modernization is unprofitable, as the specific cost of heat generation in the modernized heat source becomes smaller with a longer time that elapses from the instant t1 when this modernization is initiated, i.e., when the modernization will take place as late as possible, and preferably not at all. The curve developed for t1 = 15 years demonstrates that specific cost, kh,av, is the lowest in this case. This is due to the fact in the annual costs of the operation of the modernized heat source, there is again a capital cost (the depreciation rate of the investment expenditure JM along with the interest on it), the cost of which does not occur in the depreciated heat source. Consequently, the annual cost of heat generation is low, as its production is only determined by the exploitation cost. However, we need to remember that if the heat source is not modernized, its further operation may be impossible in the future, as it will have to be shut down due to technical wear. Therefore, the most rational strategy in terms of the stability and safety of heat source operation is related to its modernization as soon as possible [10]. Modernization with the use of gas systems is very dependent on the competitiveness of gas price in relation to other energy carriers (primarily compared to hard coal). In Figure 2, it can also be observed that the lower ratio of the gas price to the prices of energy carriers and lower environmental fees provide a more beneficial process of the fastest feasible repowering to a gas and steam system. The faster the modernization, the lower the cost of heat generation that can be obtained in this case.
In subsequent calculations, the calculations assume an increase in the price of electricity eel (Figure 4), coupled with an increase in gas and electricity prices as well as purchase prices of CO2 emission allowances (Figure 5).
The curves in Figure 4 and Figure 5 assume decreasing characteristics. The conducted analysis demonstrates that the price of electricity eel forms the decisive parameter—the higher it is, the lower the cost of heat generation. The revenues from the sales of electricity exceed the costs, which leads to a decrease in the specific cost kh,av and thus improves the economic effectiveness of this modernization. The faster the modernization, the more profitable it is due to the lower cost of heat production. In Figure 4 and Figure 5, it can also be seen that the cost of heat generation kh,av takes on negative values, which means that there is a so-called avoided cost of heat production in the modernized CHP plant. When this negative value is lower, the profit generated by the CHP plant is greater [10,23]. On the curves presented in Figure 4 and Figure 5, we can also see that the sooner the time t1, corresponding to initiation of the modernization, the smaller the specific cost of heat generation that can be derived in this case. During the modernization to the gas–steam system, the increase in the electricity price considerably and beneficially affects the profitability of this process. However, in order to ensure that the modernization applying gas–steam systems is economically viable, the price of electricity needs to be at adequately high levels in relation to the price of natural gas that is applied in the repowered systems plus the price of CO2 emission allowances.
The universal, mathematical models applying continuous time notations presented in this paper provide tools for the comprehensive assessment of the effect of various parameters on the economic effectiveness of modernization of heat sources.
The charts that follow (Figure 6, Figure 7 and Figure 8) contain the results of the calculations performed for three selected combinations of parameters that play a decisive role on the values of the specific cost of heat generation kh,av in a heating plant repowered to a gas–steam CHP plant. In the analysis presented in Figure 6, an assumption was made regarding an increase in the gas price egas, whereas the price of CO2 emission allowances was adopted as t1 for the year of initiation of the modernization. The lowest specific cost is in this case achieved for the case of the fastest executed repowering process (curves 1,2,3,4) combined with the condition regarding the lowest possible prices of purchasing CO2 emission allowances.
In the following figure (Figure 7), which originated as a consequence of the conducted calculations, the adopted parameter involved the prices of electricity eel. The lowest specific cost was recorded for the case of the fastest modernization, (curve 3) combined with the highest adopted price of electricity.
Figure 8 contains a curve generated on the basis of the calculations, in which an increase in the tariff eCO2 was adopted in the analysed range of gas prices. The increasing cost of purchasing emission allowances generates an increase in the cost of heat production. As we can see on the basis of the analysis of these curves, the most beneficial process involves a modernization that is coupled with the lowest adopted price of natural gas (curve 1).
The subsequent stages in the analysis of the specific cost of heat production in a heating plant repowered to a gas–steam combined heat and power plant was also performed with regard to various scenarios of variations in the prices of fuel, electricity and CO2 emission allowances, but the calculations assumed variations in their values only in a specific range ⟨ t 2 , T ⟩ following the modernization. In the period before and during the modernization, i.e., in time intervals given by ⟨ 0 , t 1 ⟩ , ⟨ t 1 , t 2 ⟩ (Figure 1), a constant value of prices of energy carriers and environmental charges was adopted. The applied universal mathematical formulae applying continuous time notations make it possible to conveniently control the variations of prices in the selected period. The results of the analysis are presented in Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16.
Within the intervals marked by ⟨ 0 , t 1 ⟩ , ⟨ t 1 , t 2 ⟩ (Figure 1), an assumption was made regarding the adoption of constant values of energy carriers and environmental charges. The zero values of the exponents: a g a s m o d ,   a c o a l ,   a c o a l M ,   a e l ,   a e l M ,   a e l m o d , b C O 2 ,   b C O 2 M ,   b C O 2 m o d correspond to the following prices in the intervals ⟨ 0 , t 1 ⟩ and ⟨ t 1 , t 2 ⟩ : e g a s m o d = 20 PLN/GJ; e c o a l = 8 PLN/GJ; e e l = 180 PLN/MWh oraz e C O 2 = 29.4 PLN/Mgco2. These calculations were performed for T = 30 years of exploitation, and for t1 = 0 as well as t1 = 3.
In Figure 9 and Figure 10, the plots representing the functions are rising since they have been developed under the assumption of an increase in gas prices. The faster the modernization, the more profitable it is due to the lower costs of heat production. The same is the case with the curves in Figure 11 and Figure 12, calculated for rising carbon dioxide permit allowances. Moreover, as mentioned earlier, gas combustion contributes to lower CO2 emissions, and in the case of lower gas prices and lower CO2-related charges, the cost of heat production may even be negative. If we assume an increase in the price of electricity (Figure 13, Figure 14, Figure 15 and Figure 16), we will see that with the resulting relationship between this price and the gas prices and environmental costs assumed in this scenario, the cost of heat generation significantly decreases and assumes negative values for the CHP plant following its repowering.

4. Analysis of Economic Effectiveness of Repowering a Heating Plant to Coal-Fired CHP Plant Comprising a Condensing Turbine

The second possible course of modernization involves the repowering of a heating plant to a coal-fired CHP plant comprising a condensing turbine [3].
Currently, around 75% of thermal power in the European Union is generated on the basis of fossil fuels, and the rest is generated using biomass, heat pumps, geothermal energy, solar radiation and nuclear energy [2].
Coal forms the largest source of solid fuel in the world and is one of the most important sources of electricity. Coal has also taken on the role as the most cost-competitive source of energy [24]. In order to rationally use coal, it is necessary to develop, and above all, implement, highly efficient technologies so that the use of coal for energy purposes is as low as possible for the environment, and so that it could become an ever cleaner source of energy [25].
Contrary to its condemnation, it can be forecasted that in the coming years the power system will continue to be mainly based on carbon sources, therefore considering the modernization options, leaving coal as the basic fuel forms the most feasible option [26].

4.1. Assumptions Adopted in the Second Alternative of Modernization

The zero values of the exponents a c o a l , a g a s , a e l , b C O 2 correspond to the following prices of coal equal to e c o a l = PLN 8; gas e g a s = 32 PLN/GJ; electricity e e l = 180 PLN/MWh and purchase prices of carbon dioxide emission allowances equal to e C O 2 = 29.4 PLN/Mgco2.
The following input data were adopted in the calculations performed by application of the formula in (2): specific expenditure for a coal-fired heating plant i = 1.5 million PLN/MW; specific investment in the repowering of the heating plant iM = 4 million PLN/MW; efficiency ratio of heating plant ηh = 0.85, with a remark that the same value was adopted throughout the modernization process as well as following it, i.e., η h M = η h m o d = 0.85; rate of fixed cost that is independent of the investment δserv = 0.03 as well as an assumption that δ s e r v = δ s e r v M = δ s e r v m o d ; period of construction of CHP plant equal to b = 3 years; discounting rate r = 7%; annual period corresponding to the use of maximum (rated) capacity τs = 2900 h/a; cogeneration factor σ A and σ A M equal to 0, since the modernization involves a heating plant, and in the period following the modernization, the following value was adopted for CHP plant σ A m o d = 0.6.

4.2. Results of Analysis

The curves in Figure 17 and Figure 18 assume increasing characteristics. The increase in coal prices and the purchase prices of CO2 emission allowances adopted in the calculations leads to the increase in the cost of heat production kh,av, irrespective of the year t1 related to the initiation of the modernization. It is very important to take into account the impact of purchase prices of CO2 emission permits on the economic effectiveness of modernization, and this subject forms a very important consideration in this analysis since these issues are valid now and they are attracting significant interest in the European Union’s energy sector. Due to the current and future legal regulations providing restrictions on CO2 emissions, the purchase of CO2 emission permits will result in an increase in overall costs for countries whose energy sector is based on coal.
On the basis of a comparison of Figure 3 and Figure 18, we can see that along with the adopted increase in CO2 emission prices, the cost of heat generation in a gas–steam CHP plant is similar to the same amounts generated in a modernized coal-fired CHP plant with a condensing turbine. The costs for the gas–steam system are even slightly lower at earlier times, t1, in comparison to the costs of the coal-fired CHP plant.
Just as in the case of the previously considered alternative of modernization, it can also be observed here that the more distant the year t1, the lower the specific cost of heat generation kh,av.
The curves in Figure 19 assume a decreasing course. This is due to the adopted assumption regarding an increase in the electricity price eel. The price of electricity eel forms an important parameter—when it gets higher, the cost of generating heat is lower. In this case, the lowest specific cost kh,av is achieved for t1 = 5 coupled with the highest level of analysed electricity price eel. As a result, the relationship between electricity prices and coal prices and purchase prices of CO2 emission allowances assumed in this case are very favourable. The revenues from the sales of electricity exceed the costs, and the specific cost kh,av decreases, which improves the economic efficiency of the modernization.
However, on the basis of the calculations performed under the assumption of increasing coal prices and rising cost of CO2 emission allowances coupled with increase in electricity prices, we can see that the curves in Figure 20 assume rising courses in this case, and the revenues from the sales of electricity in such a relationship do not compensate for the increase in the specific cost kh,av.
Figure 21, Figure 22 and Figure 23 contain the results of calculations carried out for various examples consisting of sets of parameters that have an effect on the value of specific costs of heat generation kh,av in a heating plant repowered to a coal-fired CHP plant. In Figure 21, the values of the curves are calculated for increasing coal prices ecoal, and the adopted parameters include the purchase prices of CO2 emission allowances and the year t1, corresponding to the initiation of modernization. On the basis of the analogy to the previous calculations, the cost kh,av is rising and assumes the lowest values for t1 = 15, as presented in curves 1″, 2″, 3″ as well as 4″. Apart from that, these curves practically overlap and the assumed differences in the price eCO2 for t1 = 15 do not cause an increase in the value of cost kh,av. The remaining curves also demonstrate that the differences in the cost kh,av for the same year t1, characterized by various rates of CO2 emission allowances, are in this case only small. On the basis of the analysis of the curves calculated for the earliest adopted year of initiation of the modernization, t1 = 5, we can see that the higher purchase prices of CO2 emission allowances lead to the higher cost of heat production. In the subsequent series of analysis presented in Figure 22, the analysed parameter includes the price of electricity eel. The curves in this figure are similar in characteristics to the curves in Figure 21; however, in the case of the higher electricity prices eel, we can see that a lower cost of heat production is achieved. In turn, in Figure 23, the calculations adopt rising values of eCO2 and a fixed cost ecoal. The increase in the cost of purchasing carbon dioxide emission permits leads to an increase in the cost of heat production in the repowered heat sources in which coal combustion will take place.
In the subsequent datasets applied for the analysis presented in Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30 and Figure 31, the specific cost of electricity production is investigated for various scenarios of variations in the prices of coal, electricity and CO2 emission allowances, but the calculations include the ranges of the variations in their values only in the time period from t2 to T, i.e., in the period after modernization. Throughout the periods prior to and during modernization, that is, over the intervals ⟨ 0 , t 1 ⟩ , ⟨ t 1 , t 2 ⟩ (Figure 1), an assumption was made regarding constant prices of energy carriers and environmental charges. Zero values of exponents a c o a l , a c o a l M , a e l , a e l M , b C O 2 , b C O 2 M correspond to the following fixed prices in the range ⟨ 0 , t 1 ⟩ and ⟨ t 1 , t 2 ⟩ : e c o a l = 8 PLN/GJ; e e l = 180 PLN/MWh as well as e C O 2 = 29.4 PLN/Mgco2. The calculations were performed for T = 30 years of exploitation and for t1 = 0 as well as t1 = 3.
In Figure 24, Figure 25, Figure 26 and Figure 27, the curves assume ascending characteristics since they were developed for the case when an assumption is made regarding rising coal prices as well as carbon dioxide emission charges. At the beginning of the modernization at t1 = 0 (Figure 24 and Figure 26), the cost of heat production is slightly lower compared to the case at the beginning of the modernization, i.e., for t1 = 3 (Figure 25 and Figure 27). On the other hand, in Figure 28, Figure 29, Figure 30 and Figure 31 the courses of the functions are decreasing, as they were compiled for the rising electricity price. The cost of heat production decreases depending on the ratio of electricity price to coal price and CO2 emission charges. The adoption of adequately high prices of electricity e e l in relation to fuel prices and environmental costs leads to negative values of the cost of heat production (Figure 28, Figure 29, Figure 30 and Figure 31).

5. Conclusions

The article reported the results of a study using universal mathematical models, applying methodology with continuous time notations with the purposes of defining a functional space of technical and economic phenomena accompanying processes of heat and electricity generation, which offer an analysis of repowered heat sources. On their basis, calculations were performed with the purpose of analysing how the cost of heat production is affected by the values and changes in price relationships between energy carriers and the purchase prices of CO2 emission permits in the conditions of varied modernization technologies. The use of models in a continuous notation over time forms an innovative approach to performing detailed technical and economic effectiveness of modernization processes in heating plants and combined heat and power plants.
Two alternatives of modernization were applied for an economic analysis. One involved the repowering of an existing heating plant into a single-fuel gas–steam combined heat and power plant, and the other involved the repowering of a coal-fired CHP plant with a condensing turbine.
The decisive quantities that significantly affect the economic effectiveness of modernization include the prices of fuels, electricity and the cost of emission per one CO2 tonne.
The lower the prices of energy carriers and charges for CO2 emissions, and the higher the price of electricity, the lower the unit cost of heat production in the repowered heat sources. For example, on the basis of a comparison of Figure 3 and Figure 18, we can see that along with the adopted increase in CO2 emission prices, the cost of heat generation in a gas–steam CHP plant is similar to the same amounts generated in a modernized coal-fired CHP plant with a condensing turbine. When an analysis is performed with regard to the modernization of the heating plant immediately at the time of its purchase (t = 0), we can observe that with the price of emission allowances around 100 PLN/Mg in the alternative in which the modernization applies a gas–steam CHP plant, the cost of heat production will be equal to about 72 PLN/GJ. In the alternative where we consider the modernization to a coal-fired CHP plant with a condensing turbine, the cost of heat production will be equal to around 82 PLN/GJ.
The results of this research demonstrate that in the case of an increase in the prices of individual factors analysed at work, such as gas or coal, the cost of investment may reduce the potential profits to such an extent that, taking into account the profitability of the investment, it would be better to delay it for as long a time as possible. However, in the case of a simultaneous increase in the prices of all main factors affecting the cost of heat generation, such as the price of gas, electricity and CO2 emissions, the fastest possible modernization of the heating plant to single-fuel gas–steam CHP would be better, as it forms the most beneficial alternative for the investor, and can significantly reduce the cost of heat generation compared with the case of when such a repowering process does not take place at all.
An investor can make a decision regarding the modernization of the heat source immediately at the time of its purchase (since at this point the relationships between fuel, electricity and CO2 emission allowance prices is the most favourable), or if it is feasible, continue the operation of the heating plant, because the relationships between the decisive parameters affecting the cost of heat production could be more beneficial in the future.

Author Contributions

Conceptualization, A.H.-S. and A.O; software, A.O.; validation, A.H.-S., A.O., K.S. and D.Z.; formal analysis, A.H.-S., A.O. and D.Z.; writing—original draft preparation, A.H.-S. and A.O.; writing—review and editing, A.H.-S., K.S. and D.Z.; visualization, A.O.; data curation, K.S., supervision, A.H.-S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Acknowledgments

We would like to thank Ryszard Bartnik for his valuable support.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

Adepreciation rate, %
Finterest on investment resources, PLN
Keannual exploitation cost, PLN
NPVnet present value, PLN
prate of income tax, %
Rinstalment on debt repayment, PLN
rdiscounting rate, %
Sannual revenue, PLN
ttime, year
Texploitation cost of CHP plant, PLN
ispecific investment in a power plant or CHP plant; PLN/MW
iMspecific investment in the modernization of a power plant or CHP plant; PLN/MW
ael, afuel, ah, aCO2, aCO, aSO2, aNOX, adust, bCO2exponents; -
ηhenergy efficiency of heat and electricity generation; %
uratio of chemical energy in total annual fuel consumption, for which the purchase of CO2 emission permits is not required; %
σAannual cogeneration factor; -
pCO2, pCO, pNO, pSO2, pdustspecific charges on emissions of CO2, CO, NOx, SO2, particulate matter; PLN/kg
xsw,m,wascoefficient representing the costs of supplementing water, auxiliary materials, sewage disposal, slag storage, waste; %
xsal,t,inscoefficient representing the cost of remuneration, taxes, insurance; %
δservcost of maintenance and overhaul of equipment; %
zdiscounting coefficient (freezing coefficient) on capital investment J at the instant represented by the construction of the investment, z > 1;
τ s annual period when the maximum rated capacity is achieved in the CHP plant; -
ρ CO 2 , ρ CO , ρ NO x , ρ SO 2 , ρ d u s t CO2, CO, NOx, SO2, particulate matter emission per unit of chemical energy of fuel, kg/GJ.

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Figure 1. Diagram of operation of repowered power plant, CHP plant and heating plant [10].
Figure 1. Diagram of operation of repowered power plant, CHP plant and heating plant [10].
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Figure 2. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the mean gas price ( e g a s m o d ) m e a n and value of the exponent a g a s 0 − T depending on the year t1, corresponding to the initiation of the modernization.
Figure 2. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the mean gas price ( e g a s m o d ) m e a n and value of the exponent a g a s 0 − T depending on the year t1, corresponding to the initiation of the modernization.
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Figure 3. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the mean price of CO2 emissions ( e C O 2 m o d ) m e a n and value of the exponent b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
Figure 3. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the mean price of CO2 emissions ( e C O 2 m o d ) m e a n and value of the exponent b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
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Figure 4. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the mean price of electricity ( e e l m o d ) m e a n and value of the exponent a e l 0 − T depending on the year t1, corresponding to the initiation of the modernization.
Figure 4. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the mean price of electricity ( e e l m o d ) m e a n and value of the exponent a e l 0 − T depending on the year t1, corresponding to the initiation of the modernization.
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Figure 5. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the value of the exponent a g a s 0 − T   a e l 0 − T b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
Figure 5. Specific cost of heat production in a heating plant repowered to a single-fuel gas–steam CHP plant in the function of the value of the exponent a g a s 0 − T   a e l 0 − T b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
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Figure 6. Specific cost of heat production in the heating plant repowered to gas–steam CHP plant in the function of the mean fuel price ( e g a s m o d ) m e a n and value of exponent a g a s 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1 applies to t1 = 5 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1′—applies to t1 = 10 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1″—applies to t1 = 15 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 2—applies to t1 = 5 years, e C O 2 m o d = 60 PLN/Mgco2; 2′—applies to t1 = 10 years, e C O 2 m o d = 60 PLN/Mgco2; 2″—applies to t1 = 15 years, e C O 2 m o d = 60 PLN/Mgco2; 3—applies to t1 = 5 years, e C O 2 m o d = 90 PLN/Mgco2; 3′—applies to t1 = 10 years, e C O 2 m o d = 90 PLN/Mgco2; 3″—applies to t1 = 15 years, e C O 2 m o d = 90 PLN/Mgco2; 4—applies to t1 = 5 years, e C O 2 m o d = 110 PLN/Mgco2; 4′—applies to t1 = 10 years, e C O 2 m o d = 110 PLN/Mgco2; 4″—applies to t1 = 15 years, e C O 2 m o d = 110 PLN/Mgco2.
Figure 6. Specific cost of heat production in the heating plant repowered to gas–steam CHP plant in the function of the mean fuel price ( e g a s m o d ) m e a n and value of exponent a g a s 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1 applies to t1 = 5 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1′—applies to t1 = 10 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1″—applies to t1 = 15 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 2—applies to t1 = 5 years, e C O 2 m o d = 60 PLN/Mgco2; 2′—applies to t1 = 10 years, e C O 2 m o d = 60 PLN/Mgco2; 2″—applies to t1 = 15 years, e C O 2 m o d = 60 PLN/Mgco2; 3—applies to t1 = 5 years, e C O 2 m o d = 90 PLN/Mgco2; 3′—applies to t1 = 10 years, e C O 2 m o d = 90 PLN/Mgco2; 3″—applies to t1 = 15 years, e C O 2 m o d = 90 PLN/Mgco2; 4—applies to t1 = 5 years, e C O 2 m o d = 110 PLN/Mgco2; 4′—applies to t1 = 10 years, e C O 2 m o d = 110 PLN/Mgco2; 4″—applies to t1 = 15 years, e C O 2 m o d = 110 PLN/Mgco2.
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Figure 7. Specific cost of heat production in the heating plant repowered to gas–steam CHP plant in the function of the mean fuel price ( e g a s m o d ) m e a n and value of exponent a g a s 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e e l m o d ) 150 PLN/MWh; 1′—applies to t1 = 10 years, e e l m o d = 150 PLN/MWh; 1″—applies to t1 = 15 years, ( e e l m o d ) 150 PLN/MWh; 2—applies to t1 = 5 years, e e l m o d = 200 PLN/MWh; 2′—applies to t1 = 10 years, e e l m o d = 200 PLN/MWh; 2″—applies to t1 = 15 years, ( e e l m o d ) 200 PLN/MWh; 3—applies to t1 = 5 years, ( e e l m o d ) 250 PLN/MWh; 3′—applies to t1 = 10 years, ( e e l m o d ) 250 PLN/MWh; 3″—applies to t1 = 15 years, ( e e l m o d ) = 250 PLN/MWh.
Figure 7. Specific cost of heat production in the heating plant repowered to gas–steam CHP plant in the function of the mean fuel price ( e g a s m o d ) m e a n and value of exponent a g a s 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e e l m o d ) 150 PLN/MWh; 1′—applies to t1 = 10 years, e e l m o d = 150 PLN/MWh; 1″—applies to t1 = 15 years, ( e e l m o d ) 150 PLN/MWh; 2—applies to t1 = 5 years, e e l m o d = 200 PLN/MWh; 2′—applies to t1 = 10 years, e e l m o d = 200 PLN/MWh; 2″—applies to t1 = 15 years, ( e e l m o d ) 200 PLN/MWh; 3—applies to t1 = 5 years, ( e e l m o d ) 250 PLN/MWh; 3′—applies to t1 = 10 years, ( e e l m o d ) 250 PLN/MWh; 3″—applies to t1 = 15 years, ( e e l m o d ) = 250 PLN/MWh.
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Figure 8. Specific cost of heat production in the heating plant repowered to gas–steam CHP plant in the function of the mean price ( e C O 2 m o d ) m e a n and value of exponent b C O 2 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years ( e g a s m o d ) = 8 PLN/GJ; 1′—applies to t1 = 10 years, ( e g a s m o d ) = 8 PLN/GJ; 1″—applies to t1 = 15 years, e g a s m o d = 8 PLN/GJ; 2—applies to t1 = 5 years, e g a s m o d = 16 PLN/GJ; 2′—applies to t1 = 10 years, ( e g a s m o d ) = 16 PLN/GJ; 2″—applies to t1 = 15 years, ( e g a s m o d ) = 16 PLN/GJ; 3—applies to t1 = 5 years, ( e g a s m o d ) = 32 PLN/GJ; 2′—applies to t1 = 10 years, ( e g a s m o d ) = 32 PLN/GJ; 2″—applies to t1 = 15 years, ( e g a s m o d ) = 32 PLN/GJ.
Figure 8. Specific cost of heat production in the heating plant repowered to gas–steam CHP plant in the function of the mean price ( e C O 2 m o d ) m e a n and value of exponent b C O 2 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years ( e g a s m o d ) = 8 PLN/GJ; 1′—applies to t1 = 10 years, ( e g a s m o d ) = 8 PLN/GJ; 1″—applies to t1 = 15 years, e g a s m o d = 8 PLN/GJ; 2—applies to t1 = 5 years, e g a s m o d = 16 PLN/GJ; 2′—applies to t1 = 10 years, ( e g a s m o d ) = 16 PLN/GJ; 2″—applies to t1 = 15 years, ( e g a s m o d ) = 16 PLN/GJ; 3—applies to t1 = 5 years, ( e g a s m o d ) = 32 PLN/GJ; 2′—applies to t1 = 10 years, ( e g a s m o d ) = 32 PLN/GJ; 2″—applies to t1 = 15 years, ( e g a s m o d ) = 32 PLN/GJ.
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Figure 9. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean gas price as well as value of the exponent a g a s m o d for t1 = 0.
Figure 9. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean gas price as well as value of the exponent a g a s m o d for t1 = 0.
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Figure 10. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean gas price as well as value of the exponent a g a s m o d for t1 = 3.
Figure 10. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean gas price as well as value of the exponent a g a s m o d for t1 = 3.
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Figure 11. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 0.
Figure 11. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 0.
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Figure 12. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 3.
Figure 12. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 3.
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Figure 13. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean electricity price as well as value of the exponent a e l m o d for t1 = 0.
Figure 13. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean electricity price as well as value of the exponent a e l m o d for t1 = 0.
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Figure 14. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean electricity price as well as value of the exponent a e l m o d for t1 = 3.
Figure 14. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the mean electricity price as well as value of the exponent a e l m o d for t1 = 3.
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Figure 15. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 0.
Figure 15. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 0.
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Figure 16. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 3.
Figure 16. Specific cost of heat generation in the heating plant repowered to a gas–steam CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 3.
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Figure 17. (a) Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of the mean fuel price ( e c o a l m o d ) m e a n   as well as value of the exponent a c o a l 0 − T depending on the year t1, corresponding to the initiation of the modernization. (b) Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of value of the exponent a c o a l 0 − T and price relations ( e c o a l ) t = T / e c o a l t = 0   depending on the year t1, corresponding to the initiation of the modernization.
Figure 17. (a) Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of the mean fuel price ( e c o a l m o d ) m e a n   as well as value of the exponent a c o a l 0 − T depending on the year t1, corresponding to the initiation of the modernization. (b) Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of value of the exponent a c o a l 0 − T and price relations ( e c o a l ) t = T / e c o a l t = 0   depending on the year t1, corresponding to the initiation of the modernization.
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Energies 14 07426 g018 550
Figure 18. Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of the mean price ( e C O 2 m o d ) m e a n   as well as value of the exponent b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
Figure 18. Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of the mean price ( e C O 2 m o d ) m e a n   as well as value of the exponent b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
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Energies 14 07426 g019 550
Figure 19. Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of the mean electricity price ( e e l m o d ) m e a n   as well as value of the exponent a e l 0 − T depending on the year t1, corresponding to the initiation of the modernization.
Figure 19. Specific cost of heat production in heating plant repowered to coal-fired CHP plant in the function of the mean electricity price ( e e l m o d ) m e a n   as well as value of the exponent a e l 0 − T depending on the year t1, corresponding to the initiation of the modernization.
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Energies 14 07426 g020 550
Figure 20. Specific cost of heat production in a heating plant repowered to coal-fired CHP plant in the function of the value of the exponent a c o a l 0 − T   a e l 0 − T b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
Figure 20. Specific cost of heat production in a heating plant repowered to coal-fired CHP plant in the function of the value of the exponent a c o a l 0 − T   a e l 0 − T b C O 2 0 − T depending on the year t1, corresponding to the initiation of the modernization.
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Energies 14 07426 g021 550
Figure 21. Specific cost of heat production in the heating plant repowered to coal-fired CHP plant in the function of the mean fuel price ( e c o a l m o d ) m e a n and value of exponent a c o a l 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1′—applies to t1 = 10 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1″—applies to t1 = 15 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 2—applies to t1 = 5 years, ( e C O 2 m o d ) = 60 PLN/Mgco2; 2′—applies to t1 = 10 years, e C O 2 m o d = 60 PLN/Mgco2; 2″—applies to t1 = 15 years, ( e C O 2 m o d ) = 60 PLN/Mgco2; 3—applies to t1 = 5 years, e C O 2 m o d = 90 PLN/Mgco2; 3′—applies to t1 = 10 years, ( e C O 2 m o d ) = 90 PLN/Mgco2; 3″—applies to t1 = 15 years, e C O 2 m o d = 90 PLN/Mgco2; 4—applies to t1 = 5 years, e C O 2 m o d = 110 PLN/Mgco2; 4′—applies to t1 = 10 years, e C O 2 m o d = 110 PLN/Mgco2; 4″—applies to t1 = 15 years, e C O 2 m o d = 110 PLN/Mgco2.
Figure 21. Specific cost of heat production in the heating plant repowered to coal-fired CHP plant in the function of the mean fuel price ( e c o a l m o d ) m e a n and value of exponent a c o a l 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1′—applies to t1 = 10 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 1″—applies to t1 = 15 years, ( e C O 2 m o d ) = 30 PLN/Mgco2; 2—applies to t1 = 5 years, ( e C O 2 m o d ) = 60 PLN/Mgco2; 2′—applies to t1 = 10 years, e C O 2 m o d = 60 PLN/Mgco2; 2″—applies to t1 = 15 years, ( e C O 2 m o d ) = 60 PLN/Mgco2; 3—applies to t1 = 5 years, e C O 2 m o d = 90 PLN/Mgco2; 3′—applies to t1 = 10 years, ( e C O 2 m o d ) = 90 PLN/Mgco2; 3″—applies to t1 = 15 years, e C O 2 m o d = 90 PLN/Mgco2; 4—applies to t1 = 5 years, e C O 2 m o d = 110 PLN/Mgco2; 4′—applies to t1 = 10 years, e C O 2 m o d = 110 PLN/Mgco2; 4″—applies to t1 = 15 years, e C O 2 m o d = 110 PLN/Mgco2.
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Energies 14 07426 g022 550
Figure 22. Specific cost of heat production in the heating plant repowered to coal-fired CHP plant in the function of the mean fuel price ( e c o a l m o d ) m e a n and value of exponent a c o a l 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e e l m o d ) = 150 PLN/MWh; 1′—applies to t1 = 10 years, ( e e l m o d ) = 150 PLN/MWh; 1″—applies to t1 = 15 years, ( e e l m o d ) = 150 PLN/MWh; 2—applies to t1 = 5 years, e e l m o d = 200 PLN/MWh; 2′—applies to t1 = 10 years, ( e e l m o d ) = 200 PLN/MWh; 2″—applies to t1 = 15 years, e e l m o d = 200 PLN/MWh; 3—applies to t1 = 5 years, ( e e l m o d ) = 250 PLN/MWh; 3′—applies to t1 = 10 years, ( e e l m o d ) = 250 PLN/MWh; 3″—applies to t1 = 15 years, ( e e l m o d ) = 250 PLN/MWh.
Figure 22. Specific cost of heat production in the heating plant repowered to coal-fired CHP plant in the function of the mean fuel price ( e c o a l m o d ) m e a n and value of exponent a c o a l 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e e l m o d ) = 150 PLN/MWh; 1′—applies to t1 = 10 years, ( e e l m o d ) = 150 PLN/MWh; 1″—applies to t1 = 15 years, ( e e l m o d ) = 150 PLN/MWh; 2—applies to t1 = 5 years, e e l m o d = 200 PLN/MWh; 2′—applies to t1 = 10 years, ( e e l m o d ) = 200 PLN/MWh; 2″—applies to t1 = 15 years, e e l m o d = 200 PLN/MWh; 3—applies to t1 = 5 years, ( e e l m o d ) = 250 PLN/MWh; 3′—applies to t1 = 10 years, ( e e l m o d ) = 250 PLN/MWh; 3″—applies to t1 = 15 years, ( e e l m o d ) = 250 PLN/MWh.
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Energies 14 07426 g023 550
Figure 23. Specific cost of heat production in the heating plant repowered to coal-fired CHP plant in the function of the mean price ( e C O 2 m o d ) m e a n and value of exponent b C O 2 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e c o a l m o d ) = 8 PLN/GJ; 1′—applies to t1 = 10 years, ( e c o a l m o d ) = 8 PLN/GJ; 1″—applies to t1 = 15 years, ( e c o a l m o d ) = 8 PLN/GJ; 2—applies to t1 = 5 years, ( e c o a l m o d ) = 16 PLN/GJ; 2′—applies to t1 = 10 years, ( e c o a l m o d ) = 16 PLN/GJ; 2″—applies to t1 = 15 years, ( e c o a l m o d ) = 16 PLN/GJ; 3—applies to t1 = 5 years, ( e c o a l m o d ) = 32 PLN/GJ; 2′—applies to t1 = 10 years, ( e c o a l m o d ) = 32 PLN/GJ; 2″—applies to t1 = 15 years, ( e c o a l m o d ) = 32 PLN/GJ.
Figure 23. Specific cost of heat production in the heating plant repowered to coal-fired CHP plant in the function of the mean price ( e C O 2 m o d ) m e a n and value of exponent b C O 2 0 − T depending on the year t1, corresponding to initiation of modernization, where: 1—applies to t1 = 5 years, ( e c o a l m o d ) = 8 PLN/GJ; 1′—applies to t1 = 10 years, ( e c o a l m o d ) = 8 PLN/GJ; 1″—applies to t1 = 15 years, ( e c o a l m o d ) = 8 PLN/GJ; 2—applies to t1 = 5 years, ( e c o a l m o d ) = 16 PLN/GJ; 2′—applies to t1 = 10 years, ( e c o a l m o d ) = 16 PLN/GJ; 2″—applies to t1 = 15 years, ( e c o a l m o d ) = 16 PLN/GJ; 3—applies to t1 = 5 years, ( e c o a l m o d ) = 32 PLN/GJ; 2′—applies to t1 = 10 years, ( e c o a l m o d ) = 32 PLN/GJ; 2″—applies to t1 = 15 years, ( e c o a l m o d ) = 32 PLN/GJ.
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Figure 24. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean fuel price as well as value of the exponent a c o a l m o d for t1 = 0.
Figure 24. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean fuel price as well as value of the exponent a c o a l m o d for t1 = 0.
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Energies 14 07426 g025 550
Figure 25. Specific cost of heat generation in the heating plant repowered to a coal-fired CHP plant in the function of the mean fuel price as well as value of the exponent a c o a l m o d for t1 = 3.
Figure 25. Specific cost of heat generation in the heating plant repowered to a coal-fired CHP plant in the function of the mean fuel price as well as value of the exponent a c o a l m o d for t1 = 3.
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Energies 14 07426 g026 550
Figure 26. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 0.
Figure 26. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 0.
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Energies 14 07426 g027 550
Figure 27. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 3.
Figure 27. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean price as well as value of the exponent b C O 2 m o d for t1 = 3.
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Energies 14 07426 g028 550
Figure 28. Specific cost of heat generation in the heating plant repowered to a coal-fired CHP plant in the function of the mean price as well as value of the exponent a e l m o d for t1 = 0.
Figure 28. Specific cost of heat generation in the heating plant repowered to a coal-fired CHP plant in the function of the mean price as well as value of the exponent a e l m o d for t1 = 0.
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Energies 14 07426 g029 550
Figure 29. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean price as well as value of the exponent a e l m o d for t1 = 3.
Figure 29. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the mean price as well as value of the exponent a e l m o d for t1 = 3.
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Energies 14 07426 g030 550
Figure 30. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 0.
Figure 30. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 0.
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Energies 14 07426 g031 550
Figure 31. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 3.
Figure 31. Specific cost of heat generation in the heating plant repowered to coal-fired CHP plant in the function of the of the exponent a g a s m o d   a e l m o d   b C O 2 m o d for t1 = 3.
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Hnydiuk-Stefan, A.; Otawa, A.; Stefan, K.; Zmarzły, D. Technical and Economic Analysis of Low-Emissions Modernization of Existing Heating Plants in Poland. Energies 2021, 14, 7426. https://doi.org/10.3390/en14217426

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Hnydiuk-Stefan A, Otawa A, Stefan K, Zmarzły D. Technical and Economic Analysis of Low-Emissions Modernization of Existing Heating Plants in Poland. Energies. 2021; 14(21):7426. https://doi.org/10.3390/en14217426

Chicago/Turabian Style

Hnydiuk-Stefan, Anna, Aleksandra Otawa, Krzysztof Stefan, and Dariusz Zmarzły. 2021. "Technical and Economic Analysis of Low-Emissions Modernization of Existing Heating Plants in Poland" Energies 14, no. 21: 7426. https://doi.org/10.3390/en14217426

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