Economic analysis of heat production in existing medium size combined heat and power plant, with respect to the CO2 allowances purchasing cost

Energy Conversion and Management 171 (2018) 110–125

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Economic analysis of heat production in existing medium size combined heat and power plant, with respect to the CO2 allowances purchasing cost Jarosław Król, Paweł Ocłoń

T

⁎

Cracow University of Technology, Faculty of Mechanical Engineering, Institute of Thermal Power Engineering, Al. Jana Pawła II 37, 31-435 Cracow, Poland

A R T I C LE I N FO

A B S T R A C T

Keywords: Combined heat and power Modeling of energy systems Economic analysis

This paper presents mathematical modeling and economic analysis of a medium size combined heat and power (CHP) operation, installed in Poland. The plant is equipped with steam boilers, extraction condensing turbine, and the grade type water boilers. The paper determines the most efficient mode of CHP operations. The economic efficiency analysis is performed for transient seasons, characterized by low demands for heating, which obliged production units to operate out of its nominal conditions at a lower efficiency. The developed method is also suitable for analyzing complex power plants, with a few energy equipments. The developed mathematical model for simulating CHP performance gives the possibility to select the boiler type, and assess the probability and efficiency of each configuration. The dedicated tool calculates the selected operation mode, heating power demand, and enables models comparison. The algorithm includes real equipment operational parameters, technical limitations, actual energy prices and costs regarding energy law acts. The performed analysis is up-to-date, due to a few aspects: permanently increased fossil fuels costs, low electric energy prices, growing costs of CO2 emission allowances, and high electricity production cost on turbine’s condensing section at steam parameters of T = 435 °C and p = 34 bar. A detailed cost analysis is performed on each product separately: thermal energy, electric energy from cogeneration and electric energy from condensation, during every hour, frequently. The calculation is carried every an hour for a period of 24 h, the energy balance is ensured during the calculation. The most important result of this study is a comparison of CHP to water boiler operation profitability, also including the net profit comparison. Furthermore, the cost of the CO2 emission is studied, for the production profitability in two scenarios, as the price increases from 7 EUR/tone to 15 EUR/tone and 30 EUR/tone.

1. Introduction The thermal energy is used for many different applications and purposes, such as in residential and industrial buildings, workshops, and in production processes, which requires certain temperature conditions. Each application has different nature of consumption and requires different production units. A particular example covers both, production for district heating grid and thermal energy needed in the industry. In the countries with a comparable climate to Poland, which characterize long winter season, a significant part of the heat is produced in Combined Heat and Power plants (CHP). The CHP technology is known for decades, and so far was well examined and developed. Karlson et al. [1] studied CHP plant owned and operated by Karlskoga Energi och Miljö AB in Sweden. The life-cycles of the fuels used by the CHP – household/industrial waste, bio-oil, light fuel oil, wood waste, wood chips, a slaughterhouse-waste-derived product and peat to generate ⁎

Corresponding author. E-mail address: [email protected] (P. Ocłoń).

https://doi.org/10.1016/j.enconman.2018.05.054 Received 16 April 2018; Received in revised form 12 May 2018; Accepted 16 May 2018 0196-8904/ © 2018 Published by Elsevier Ltd.

202,222 MWh of heat, 119,234 MWh of steam and 28,220 MWh of electricity have been studied. Also, the carbon footprint of the plant was calculated for year-2016. Havukainen et al. [2] conducted life cycle analysis (LCA) for energy production from forest biomass in small scale CHP plant. Their study used the LCA for two purposes. The first aim was to quantify the environmental impacts of the energy production of a small-scale, combined heat and power production plant utilizing different forest biomasses. The second aim was to estimate the changes in the environmental impacts on the district heat production from natural gas when partially replacing it by heat from the Combined Heat and Power plant. Havukainen et al. [2] results indicated that by using forest biomass instead of natural gas in energy production, the global climate impacts are reduced when biogenic carbon is excluded, while the local effects are higher (acidification potential and eutrophication potential). Hu et al. [3] studied a phase-change heat storage facility in CHP integrated with renewable energy sources, wind energy. They analyzed an integrated thermal and power system with phase-change heat

Energy Conversion and Management 171 (2018) 110–125

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η Q̇ Q ̇ QChem5

Nomenclature cp E5̇ E6̇ E h ṁ T p Ḟ Cf CCHP CCond

specific heat capacity, kJ/(kg·K) electric power in co-generation mode, MW electric power in condensation mode, MW energy, MWh enthalpy, kJ/kg mass flow rate, t/h temperature, °C pressure, bar mass flow rate of fuel, t/h chemical energy cost, EUR/GJ chemical energy cost for electricity production in co-generation, EUR chemical energy cost for electricity production in condensation, EUR

NCV xCHP xCond uCCHP uCCond CHeat5

storage (HS) facility to improve the flexibility of the system, where the heat released from the extraction steam does not match the heat load. They used thermal resistance in modeling the heat storage system. The operation plan of the integrated system is optimized by the linear programming (LP) method to minimize the wind energy loss. Zhang and Kang [4] studied the effects of the distribution density of a biomass combined heat and power plant network on heat utilization efficiency in village–town systems. They obtained an optimal biomass CHP plant network using geographical information system (GIS) tools. They calculated the optimal value of the heat transmission threshold through a multi-scheme comparison. Wang et al. [5] by using the EES (Engineering equation solver) and Ebsilon Professional 13, studied the direct air-cooled, high-pressure heat supply power units. The characteristics of heat transfer and supply of cold-end between typical temperature range in winter time was analysed. In quality and quantity regulations, the cold-end heat transfer characteristics with different fans in isolation, the coal consumption, and the net power were investigated. The authors determined the optimal operation mode and energy saving effect of heating and air-cooled systems. Haakana et al. [6] presented a methodology to promote the operation of CHP plant in the liberalized energy markets. The methodology considered a combination of marketplaces available to the power plant for its end products heat and electrical power, with a particular reference to electricity reserve market opportunities. The methodology proposed by the authors was tested with price data of the respective energy and power markets between years 2013 and 2015. Guo et al. [7] assessed the eco-efficiency of coal-fired CHP plants in Chinese eco-industrial parks. By a sensitivity analysis, they indicated that consideration of freshwater consumption and capital depreciation would have a significant impact on eco-efficiency. Zhao et al. [8] proposed a flue gas recovery system for natural gas CHP plant with distributed peak-shaving heat pumps. The system has many benefits, such as improve network transmission and distribution capacity, provide energy savings, and reduce the emission. Vögelin et al. [9] performed economic optimization of CHP plant. The proposed optimization algorithm is robust. It has the ability to optimize at different power, storage and operational systems. Also, Vögelin et al. [10] performed a design analysis of gas engine CHP for building and industrial heat demand with varying price structures. They conducted optimization of plant power, heat storage size and operating strategy. Kalina [11] studied alternative configurations of heat recovery process in small and medium scale combined gas and steam cycle power plants. He considered the combined the CHP with Organic Rankine Cycle (ORC) and performed the energy and exergy efficiency analysis of the heat recovery process. Gustavsson and Hulteberg [12] studied the coproduction of gasification-based biofuels in existing CHP. They analyzed the production capacity and integration potential of those CHPs.

energy efficiency heat flow rate, GJ/h thermal energy, GJ chemical energy stream for heat production in co-generation, GJ/h net calorific value, GJ/t chemical energy ratio on 1 MWh production in co-generation, GJ/MWh chemical energy ratio on 1 MWh production in condensation, GJ/MWh unit cost of 1 MWh production in co-generation, EUR/ MWh unit cost of 1 MWh production in condensation, EUR/ MWh cost of thermal energy production in co-generation, EUR/ GJ

They found that there is a significant potential for biofuel production by utilizing existing Fluidized Bed Boilers as well as the utilization of waste heat and tail gases enable high overall efficiency. The results of Gustavsson and Hulteberg [12] revealed that integrated biofuel production decreases power generation from a CHP plant. Nelson et al. [13] modeled a solarized 100 kWe/165 kWt microturbine for CHP application. They found that the fuel use is reduced by 26.0% compared to the traditional microturbine at maximum power output. Salman et al. [14] studied the impact of retrofitting existing CHP with polygeneration of biomethane. The authors performed a comparative techno-economic analysis of integrating three different gasifiers and evaluated the operational limits of CHP by process integration with gasification. Salman et al. [14] compared technical performance of integrated gasifiers with CHP and performed economic analysis and sensitivity analysis by varying various parameters of the power plant. Kim and Edgar [15] used mixed-integer nonlinear programming to determine the optimal scheduling of combined heat and power plants in the wholesale energy market. The authors optimized the power production and maximized it during on-peak hours. The maximum profit was realized by committing more efficient generating units. The authors found that the less efficient generating units can be brought online due to operating constraints. Oreggioni et al. [16] assessed of biomass gasification CHPs with absorptive and adsorptive carbon capture units in Norway. The authors used LCA analysis of gasification CHP plants with absorptive and adsorptive CCS technologies. They found that CHP with pressure-vacuum swing adsorption (PVSA) cycles exhibit better environmental performance than CHP with installed MEA unit. Lee et al. [17] conducted modeling and optimization of an integrated wastewater treatment plant with a combined heat and power generation system. Thermal, environmental and economic aspects were considered. The proposed system was optimized (using the non-dominant sorting genetic algorithm-II (NSGA-II)) via the thermo-environ-economic method. Authors found that the total cost rate and environmental impact decreased by 16.9% and 5.3%, respectively. Also, the total required heat and 47% of electricity demand were covered after optimization. Zhong et al. [18] performed an optimization of solar aided coal-fired CHP based on changeable integrate mode under different solar irradiance. The authors optimized the operation strategy and used MINLP model to optimize the heat exchanger area and the integrated mode. Ziębik et al. [19] performed a thermodynamic evaluation of CHP integrated with installation of coal gasification. They found that the relative energy savings of IGCC-CHP are near the result of a gas and steam CHP and that the COHP (coefficient of heat performance) can help to divide fuel between heat fluxes. The higher COHP values in the case of heat recovery, the lower thermal parameters are obtained. Amirante et al. [20] proposed a novel, cost-effective configurations of CHPs for a small-scale cogeneration from biomass. The authors proposed a novel approach in 111

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mathematical modeling of thermodynamic processes of power stations enables in simulating the energy balance and calculate the economic efficiency of the heat and electricity production processes. Having such knowledge, the management has a reliable tool to control the production costs, and consciously undertake the decisions about the most economically and efficient mode of operation. The developed tool can be used for forecasting, production cost control, and efficiency monitoring, to support the right decision makings.

designing the gas to the gas heat exchanger. The heat exchanger is suitable to externally fired combined plants using carbon-neutral biomass. The heat exchanger is small in size and has low pressure drop. Thus the energy losses are negligible. Based on the performed literature survey, it is found that there is a possibility to improve the CHP performance. The primary goal of the CHP units design improvement is efficient energy usage by end-users and maximize the effectiveness of production units. The developed

Fig. 1. Online scheme of simulated CHP unit. 112

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2.2. Water boilers WR-25 characteristic

From the economic point of view on the thermal production, the primary objective is to maximize the income concerning all environmental requirements. That direction is not always coherent with the highest possible energy usage from fossil fuels. The unusual situation appears, when the complex CHP is considered. For example, when the CHP unit consists of traditional water boilers and steam boilers connected with extraction condensing turbine (Fig. 1). In particular, the problem facing the state, when the extraction-condensing turbine is not more profitable in comparison to traditional industrial water boiler. To better understand this unusual situation, it should be mentioned about a few technical and energy market aspects:

All-water boilers are of grate type water-tube boilers. The nominal heating power is 25 MW. Cumulated heating power of two water boilers WR-25 is rated on 50 MW and 492 t/h of hot water. The water boilers were built in the 1980 year and did not have any refurbishment since then. 2.3. Turbine VE40 description The main turbine is extraction condensing type turbine manufactured by Alstom (Table 3). The turbine is equipped with two lowpressure extractions. One outlet is regulated and is a source of thermal energy for the low-pressure steam collector, using heat exchangers for the district heating grid. The second outlet is without any regulation. Nonregulated extraction outlet is providing the secondary stream of low-pressure steam to condensate regeneration. At the end of the turbine, the condensing outlet is located. The condenser is operating at the pressure of 5 kPa and is coupled with cooling tower water circulation. The mentioned description is presenting only main components and technical parameters of examined CHP plant, which is required as input data of the developed mathematical models. To better understand and visualize the installation, the scheme of studied CHP unit is presented in Fig. 1.

• Steam boiler efficiency at low capacity; • Technological minimum of a steam boiler; • Technological minimum of the turbine on condensation; • Cold start/stop time of steam boiler; • Low-efficiency electricity production at steam parameters T = 435 °C, p = 34 bar; • High electricity production cost in condensation mode; • Low prices of electric energy; • Variable demand for thermal energy in time. If all the abovementioned parameters are considered at low and variable demands for thermal energy, production on industrial water boiler can provide a higher profit in comparison to production in cogeneration. To prove that statement, a mathematical model of existing medium size CHP plant in Poland is developed. The model calculates 24 h economic yield in function of heat power demand. The developed mathematical model is a practical case study, which is based on actual data and installation parameters. What is important to mention, the presented tool described in this paper was tested on a real object and is used in every day of operation for cost assessment and operation mode selection. The detailed technical parameters are presented in the following sections of this paper.

3. Analyzed model The developed model of CHP allows one to compare the costs of heat production in the two different units, co-generation system, and industrial water boiler. Energy system 1 covers the heat production on the steam boiler and extraction condensation turbine, with a parallel production of electricity. Energy system 2 includes heat production in industrial water boiler of WR25 type. The algorithm developed in this study is calculating the energy flows and economic yield for 24 h operation, as the function of heat power demand from district heating grid. For this analysis, the heat power demand at the turn of the seasons is chosen, which occurs during autumn-winter and winter-spring periods. At that period, the need for thermal energy is at quite low levels, with considerable fluctuations between day and night. Such situation creates severe conditions for production in industrial equipment, which are usually designed to work under nominal load. If the situation is explored in detail considering more technical parameters, the calculations reveal unexpected results. The main observation is that heat production in co-generation at low levels is more expensive than production in water boiler. That statement is delivering the idea of considerable capability to optimization working modes. To perform the optimization, it is required an adequately developed mathematical algorithm. The proposed model shall enable a calculation of energy balance for different operating conditions, i.e., heat demands and modes, with the parallel calculation of the costs. The significant advantage of the presented approach is to improve the CHP efficiency, with the zero capital expenditures. In the calculation, the following assumptions are made:

2. Installation description The exemplary CHP plant (Fig. 1) produces the heating power of 127.1 MW and electric power of 32.86 MWe. The power plan is quite complex, which provides heat to the city, and consist of following equipment: three steam boilers of OR-64 type produced by Rafako company, which deliver steam at the temperature of 435 °C and pressure of 34 bar for two turbines. One turbine is extraction-condensing turbine (Alstom VE40 type) with the nominal electric power of 20.44 MWe. The second turbine is old generation extraction-backpressure turbine AR4 with an electrical output of 4 MWe. The CHP power production is also realized on two gas engines GE Jenbacher J624 GS-H02 linked to two electrical energy generators of 4.2 MWe output. The system also contains two water boilers (WR-25 type) manufactured by Sefako company. In the following section, the production unit technical specification is given. 2.1. Steam boilers OR-64 characteristic All steam boilers are of grate type with the three-way draft channel of exhaust fumes. The first draft is traditional evaporator screen in the combustion chamber. Between the first and second draft, the second stage steam superheater is located. Whereas in the second draft channel, the first stage steam superheater exists. In the second draft, the second and the third water preheater is installed. The first stage water preheater and combustion air preheater is on the third draft channel, before exhaust fans. The steam production units are quite venerable but had revamping in years 2000–2003, that is why represents an acceptable level of efficiency. Total heating power of three boilers OR-64 is rated on 1125 MW and 150 t/h of superheated steam. (See Tables 1 and 2).

Table 1 Technical parameters of OR-64 steam boiler.

113

Year of construction

1962–1965 r.

Nominal heating power QN Minimum power MW Allowable pressure pmax Nominal pressure pN Maximum steam temperature Tmax Nominal temperature TN Nominal steam flow rate VN Minimum technical steam performance Vmin

37.5 MW 16 MW 4.0 MPa 3.8 MPa 450 °C 435 °C 50 t/h 20 t/h

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to develop the formulas of energy balance at indicated components of CHP. In line with the mass flow diagram, the boiler OR-64 is producing superheated steam at the parameters of 435 °C and 34 bar, to feed turbine VE40 accordingly to nominal parameters. The superheated steam is produced by the stream of hard coal, which delivers the chemical energy to the boiler. The formula on the chemical energy supplied is given by Eq. (1)

Table 2 Technical parameters of water boilers WR-25. Year of construction

1980

Nominal heating power QN Allowable pressure pmax Nominal pressure pN Inlet water temperature Tmax Maximum outlet water temperature Tmax Nominal hot water flow rate VN Minimum technical water flow rate Vmin

25 MW 2.0 MPa 1.1 MPa 80 °C 150 °C 246 t/h 37 t/h

Q1̇ = F1̇ NCV

Demand for chemical energy is related to the current demand for thermal energy, delivered by the regulated outlet in the turbine. At the same time, the electrical energy production is realized on the co-generation section, as well as the condensation part of the turbogenerator. In result, the general requirement for chemical energy in Energy system 1 is related to the amount of the thermal and electrical energy (cogeneration), also to the electric energy produced on the condensation end. This situation occurs because condensation section cannot be switched off. It can be only regulated from 6.5 t/h to 35 t/h mass flow rate, to influence the electric energy output. The boiler efficiency, for chemical energy conversion to the thermal energy included in superheated steam, is expressed by the Eq. (2). Following formula is achieved from the boiler efficiency assessment as the function of steam production. The installation operator ordered such study in the past. The study was performed by the external company. The documentation with the details of the study, is not provided by the CHP owner. The same formula is used for all steam boilers. The function on boiler efficiency is given as follows

Table 3 Technical parameters of VE40 steam turbine. Year of construction

2003

Type Nominal electric power output pN Maximum pressure pmax Nominal inlet pressure pN Nominal outlet pressure p4 Nominal outlet pressure p6 Nominal outlet pressure p17 Inlet water temperature TN Inlet maximum water temperature Tmax Nominal steam flow rate VN Maximum steam flow Vmax Extraction regulated flow rate VN Extraction nonregulated flow rate VN Minimum condensing outlet flow rate Vmin Maximum condensing outlet flow rate Vmax

Extraction - condensing 20.44 MWe 3.9 MPa 3.4 MPa 0.3 MPa 0.005 MPa 0.05 MPa 435 °C 450 °C 115 t/h 123.5 t/h 102 t/h 9.25 t/h 6.5 t/h 35 t/h

ηOR64 =

• Net Calorific Value of the hard coal – 22.5 GJ/t • Cost of energy from coal with transport and pollution emission = 3.83 EUR/GJ • Air and water physical properties used in the calculation were appropriately assigned to the parameters in each point on the diagram • The boilers efficiency as a function of the output • Other equipment efficiency is taken from technical documentation • Electric energy prices for different time zones: Z0 = 35.29 EUR/ MWh Z1 = 47.06 EUR/MWh; Z2 = 44.71 EUR/MWh • Thermal energy price 7.06 EUR/GJ • The cost of CO emission = 7 EUR/t CO is included • Water price = 0.82 EUR/m . Water price included in the cost of GJ. • Owners demand 2

(1)

0.0001ṁ 33−0.0357ṁ 32 + 2.7904ṁ 3 + 20.604 99

(2)

The total amount of thermal energy from the hard coal, converted in the boiler to the superheated steam, can be calculated from the formula

Q1̇ = F1̇ NCVηOR64

(3)

Indeed, it is equal to the energy contained in the superheated steam

Q3̇ = ṁ 3 (h3−h2)

(4)

The model of Energy system 1 is taking every hour heating power demand listed in Table 4, and accordingly calculates mass and energy balance for 24 h operation of the examined CHP plant. To calculate the required steam mass flow rate to the heat exchanger Eq. (5) is used:

2

3

ṁ 18 =

̇ 3.6Q15 (h5−h16 ) η18

(5)

The steam mass flow rate is proportional to the thermal energy demand and includes the efficiency of heat exchangers η18. The equation for temperature T5 is determined by the historical relation of T5, to the actual steam production.

3.1. Calculation methodology 3.1.1. Energy system 1 The general idea of the model is to control the production cost of the heating plant, so the functionality of the mathematical algorithm is designed to treat heating power demand as a leading factor. Therefore, hourly heating power demand is an initial point for the calculation. The required power for the district heating grid is calculated, as a function of forecasted ambient temperature. A mathematical formula is derived from the historical data of relation the outside temperature vs. heating power delivery. Energy system 1 model describes the production of the steam boiler OR-64 and the heat and electricity production in extraction condensation turbine VE40. Fig. 1. presents the numbered points, which are used

T5 = 1.03(0.000007ṁ 34−0.0023ṁ 33 + 0.2804ṁ 32−15.174ṁ 3 + 503.46)

(6)

Whereas the temperature T16 is calculated in the relation to the heating power demand by using the Eq. (7): 2

̇ + 0.7323Q15 ̇ + 51.189 T16 = −0.0036Q15

(7)

For the empirical formulas (6) and (7) the least square method was used to approximate temperatures T5 and T16 based on the historical data of system operation. From the regulated outlet (ṁ 4 ) is taken the stream, to supply the

Table 4 Heating power demand for 24 h used in mathematical models: Energy system 1 and Energy system 2. Hour Heating power demand (MW) Hour Heating power demand (MW)

00:00 20.3 12:00 6.0

01:00 21.7 13:00 6.3

02:00 23.2 14:00 6.7

03:00 24.6 15:00 7.1

04:00 24.6 16:00 10.6

114

05:00 24.6 17:00 11.9

06:00 24.6 18:00 13.3

07:00 23.2 19:00 14.7

08:00 21.7 20:00 16.1

09:00 18.9 21:00 17.5

10:00 16.1 22:00 18.9

11:00 10.6 23:00 20.3

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Table 5 Main energy distribution in co-generation production process.

Fig. 2. Boiler power vs heating power demand including technical min.

degasser (ṁ 19 ). The ṁ 19 mass flow rate is used to supply energy for degasification process and keep minimum water temperature before boiler. It is related to the mass flow rate delivered to the degasser, which means, condensate from the heat exchangers, condensate from the turbine condensation section and demineralized water (with mass flow rate of ṁ demi ) to cover the loss. The mass flow rate to the degasser can be calculated from the equation

h −h ṁ 19 = (ṁ 18 + ṁ 8 + ṁ demi ) ⎛ 2 21 ⎞ ⎝ h4−h2 ⎠ ⎜

⎟

(8)

Time

Total Q3 [GJ]

Heating Q18 [GJ]

Q5 [GJ] for E5 [MWh]

Q6 [GJ] for E6 [MWh]

E5 [MWh]

E6 [MWh]

E5 + E6 [MWh]

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

107 114 120 126 126 126 126 120 114 101 89 65 57 57 57 57 65 70 77 83 89 95 101 107

73 78 84 89 89 89 89 84 78 68 58 38 22 23 24 26 38 43 48 53 58 63 68 73

11 12 14 15 15 15 15 14 12 10 8 4 2 2 2 2 4 5 6 7 8 9 10 11

22 22 22 22 22 22 22 22 22 22 22 22 33 32 31 29 22 22 22 22 22 22 22 22

3.0 3.3 3.6 3.9 3.9 3.9 3.9 3.6 3.3 2.7 2.1 1.0 0.5 0.5 0.6 0.6 1.0 1.3 1.5 1.8 2.1 2.4 2.7 3.0

1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 2.5 2.4 2.3 2.1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7

4.7 5.0 5.3 5.6 5.6 5.6 5.6 5.3 5.0 4.3 3.8 2.7 3.0 2.9 2.9 2.7 2.7 3.0 3.2 3.5 3.8 4.1 4.4 4.7

where: regeneration, the part of the steam used in co-generation is calculated as

h21 – the weighted enthalpy of the streams to the degasser: ṁ 18 + ṁ 8 + ṁ demi

ṁ 19CHP = ṁ 19−ṁ 19Cond

Having the energy and mass flow of ṁ 5 and ṁ 19 , it is possible to calculate the mass and energy flow through the regulated, heating turbine exit ṁ 4

Based on the mass flow in the points 5, 12 (Fig. 1) and the steam parameters, it is possible to calculate the electricity production on the co-generation section using the Eq. (12). The equation includes overall efficiency of the generator unit.

(9)

ṁ 4 = ṁ 5 + ṁ 19

The stream ṁ 19 delivered to the degasser has to be split between cogeneration and condensation part, because the mentioned stream is used for condensate regeneration from both parts. It creates the situation, that allocation to only one part, does not represents the real costs, that is why energy is dynamically divided to the current demand. The stream allocation to the condensation part is given by the formula

h −h ṁ 19Cond = (ṁ 6 + ṁ 17 ) ⎛ 2 6 ⎞ ⎝ h19−h2 ⎠ ⎜

(11)

E5̇ =

(ṁ 18 (h3−h5) + ṁ 19CHP (h3−h5 )) ηel 3.6

(12)

At the actual stage, the mathematical model calculates the possible electrical output on the co-generation unit. The algorithm is designed in the way, to deliver information about the two essential factors. The first one is the chemical energy effort required to produce 1 MWh of electric energy (GJ/MWh). The second is the cost of electrical energy production (EUR/MWh). Expenses input in formula includes the cost of transport, environment protection, CO2 emission and water. Mentioned parameters are given by Eqs. (13) and (14).

⎟

(10)

Having the steam flow rate for the condensation section

Fig. 3. Energy delivered and produced in the steam boiler. 115

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Fig. 4. Thermal energy usage.

Fig. 5. Electrical energy generation for 24 h operation.

Fig. 6. Chemical energy input comparison to produce 1 MWh of electric energy in co-generation and condensation mode. 116

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Fig. 7. Chemical energy allocation for heat and electricity production.

Fig. 8. Thermal energy income vs cost.

Fig. 9. Electricity from co-generation income vs cost.

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Fig. 10. Electricity from condensation income vs cost.

Fig. 11. Cumulated CHP profitability of 24 h operation.

continuous operation needs to be supplied by the 6.5 t/h of steam as a minimum. It leads to the situation, where the advantage of higher flexibility presented equipment becomes its disadvantage. It occurs mainly when electric energy prices are low and steam overproduction due to the boiler technical minimum. To examine this situation in details the analogical energy and cost evaluation, as for co-generation part, is done. The steam flow rate through the condensation outlet is related to three parameters:

Chemical energy effort (GJ) to produce 1 MWh of electric energy in co-generation is given as

x CHP =

ṁ 18 (h3−h5) + ṁ 19CHP (h3−h5 ) E5̇ ηOR64

(13)

Chemical energy cost in (EUR/MWh) is calculated as

uCCHP = x CHP Cf

(14)

The total chemical energy cost required for electricity production in cogeneration is given by Eq. (15)

CCHP =

• Decision making to maximize or minimize the electricity production which depends on electricity price, • Boiler technical minimum. Surplus steam production is worked out in condensation section, • Boiler technical maximum. All produced steam is used in-cogen-

Cf (ṁ 18 (h3−h5) + ṁ 19CHP (h3−h5))·1[h] ηOR64

(15)

Eq. (15) calculates the energy cost related to one-hour operation in CHP mode. The presented algorithm is concentrated on the electricity production in co-generation. To close the energy balance required for the total electricity production the formulas associated with the electricity come out from the condensation exit are developed. Turbine VE40 has regulated mass flow rate through the back outlet in the range from 6.5 t/h up to 35 t/h. It enables to control the electric power output irrelevantly to the heating power demand from the district heating grid. It means that turbine construction enables increase electrical power, when the price on the energy stock exchange is high. From the other hand, the condensation outlet cannot be switched off, and for

eration, except 6.5 t/h of turbine technological minimum.

Hence, there is a need to develop an algorithm, which undertakes all these technical aspects to reflect the real working conditions. Based on the stream passing the condensation outlet, The electric power performance is calculated by the Eq. (16)

E6̇ Cond =

118

ṁ 6 (h3−h6 ) ηel 3.6

(16)

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Table 6 Thermal energy and electricity production income and costs during the 24 h operation. Time

Thermal energy income [EUR]

Electricity form cogen. income [EUR]

Electricity from cond. income [EUR]

Thermal energy production - cost [EUR]

Electricity production cost in cogen. [EUR]

Electricity production cost in cond. [EUR]

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

515.91 551.49 589.61 625.19 625.19 625.19 625.19 589.61 551.49 480.33 409.17 269.39 152.49 160.11 170.28 180.44 269.39 302.43 338.01 373.59 409.17 444.75 480.33 515.91

104.86 115.46 126.75 137.19 137.19 137.19 137.19 169.00 153.95 125.69 97.82 48.01 23.67 18.62 19.78 20.93 45.61 55.92 67.72 80.10 92.93 83.74 94.27 104.86

59.21 59.28 59.35 59.41 59.41 59.41 59.41 79.14 79.04 78.83 78.55 77.80 115.7 83.76 79.72 75.68 73.91 74.10 74.29 74.47 74.62 59.02 59.12 59.21

−352.78 −372.21 −393.67 −414.39 −414.39 −414.39 −414.39 −393.67 −372.21 −333.78 −296.58 −209.03 −118.32 −124.24 −132.12 −140.01 −209.03 −234.67 −259.39 −278.07 −296.58 −315.09 −333.78 −352.78

−55.40 −60.22 −65.41 −70.29 −70.29 −70.29 −70.29 −65.41 −60.22 −50.59 −41.04 −21.54 −10.62 −11.14 −11.83 −12.52 −21.54 −26.40 −31.63 −36.31 −41.04 −45.80 −50.59 −55.40

−108.15 −106.73 −105.55 −104.76 −104.76 −104.76 −104.76 −105.55 −106.73 −109.93 −114.73 −123.24 −185.18 −178.65 −169.95 −161.26 −123.24 −123.04 −121.54 −117.85 −114.73 −112.11 −109.93 −108.15

complete view on the energy used in the condensation section, it is ̇ Cond needed to add the energy allocated in the stream E19

Table 7 Cumulated CHP profitability of 24 h operation. Time

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Thermal energy - profitability [EUR]

Electricity in cogen. profitability [EUR]

Electricity in cond. profitability [EUR]

Total CHP unit profitability [EUR]

163.13 179.28 195.95 210.80 210.80 210.80 210.80 195.95 179.28 146.55 112.59 60.36 34.17 35.87 38.15 40.43 60.36 67.76 78.62 95.52 112.59 129.66 146.55 163.13

49.47 55.24 61.34 66.90 66.90 66.90 66.90 103.59 93.73 75.10 56.78 26.47 13.05 7.48 7.95 8.41 24.07 29.51 36.09 43.79 51.89 37.94 43.67 49.47

−48.95 −47.44 −46.20 −45.35 −45.35 −45.35 −45.35 −26.42 −27.68 −31.11 −36.18 −45.43 −69.46 −94.89 −90.23 −85.58 −49.32 −48.94 −47.25 −43.38 −40.11 −53.09 −50.81 −48.95 Sum

148.67 171.61 195.11 215.88 215.88 215.88 215.88 251.81 224.70 171.22 115.16 25.86 −37.86 −63.19 −55.69 −48.20 20.34 33.02 51.54 79.40 107.24 100.49 124.92 148.67 2 628.35

̇ Cond = E19

̇ + E19 ̇ Cond E6̇ = E6̇ Cond + E17 For the defined streams, the chemical energy demand, to produce electricity in condensation part, is calculated by Eq. (21)

x Cond =

uCCond = x Cond Cf

(21)

(22)

Based on the Eq. (22) and chemical energy price, it is possible to determine the total chemical energy cost used for electricity production in condensation

CCHP =

Cf (ṁ 6 + ṁ 17 + ṁ 19Cond )(h3−h2)·1[h] ηOR64

(23)

The mentioned equations are closing the energy balance for the turbogenerator, realized for the electric energy production. To obtain the energy flow passed through the turbine, the stream used for heating power is needed to be calculated. As aforementioned, a stream of energy passing the regulated exit is not at fully used for the thermal energy supply to district heating grid. A small part of the steam is re-used to sustain the steam production process in boilers. In other words, the part of the steam has to be reversed to the production cycle. Literally to the degasser tanks to realize the degasification process and to uphold minimum water temperature entering the boiler, which is designed to ∼105 °C. To get the real results about the energy used for heating, above assumption mentioned is taken into consideration in formulas. It allows to more precisely construct the thermal energy balance used for district heating grid, and asses the right costs of production.

(17)

Enthalpy h17 is calculated from the historical data based on the relation of the temperature T17 to the flow rateṁ 17

T17 = 13.734ṁ 17 + 43.763

(ṁ 6 + ṁ 17 + ṁ 19Cond )(h3−h2 ) E6̇ ηOR64

The unit chemical energy cost (EUR/MWh) for production in condensation part is calculated using the formula

ṁ 17 (h3−h17 ) ηel 3.6

(19)

3.6

Enthalpy h19 is equal to the enthalpy h4 and h5: h4 = h5 = h19 Total electric power produced in the condensation section is calculated as

For the condensation generation is also included the electric power produced on non-regulated stream ṁ 17 used for the first condensate regeneration

̇ = E17

ṁ 19Cond (h3−h19 ) ηel

(18)

As a function of the temperature T17 and pressure p17. To have the 119

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Fig. 12. Heating power demand vs technical boiler WR25 min.

Fig. 13. Water boiler WR25 operation parameters.

Fig. 14. Water boiler WR25 heat production profitability.

The steam mass flow rate for heating energy (ṁ 18) is calculated from Eq. (5). To calculate the heating energy in the stream, the Eq. (24) is used

̇ = ṁ 18 (h5−h16) Q18

(24)

Based on the Eq. (5), is possible to evaluate the chemical energy requirement, to produce the relevant heating energy. The chemical energy is strictly correlated with the boiler OR64 efficiency given by Eq. 120

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Fig. 15. Cumulated water boiler WR25 profitability.

balance.

Table 8 Water boiler WR25 production summary. Time

Thermal energy income [EUR]

Thermal energy production - cost [EUR]

Thermal energy profitability [EUR]

Total WR25 unit profitability [EUR]

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

515.91 551.49 589.61 625.19 625.19 625.19 625.19 589.61 551.49 480.33 409.17 269.39 152.49 160.11 170.28 180.44 269.39 302.43 338.01 373.59 409.17 444.75 480.33 515.91

−359.16 −381.47 −406.15 −430.24 −430.24 −430.24 −430.24 −406.15 −381.47 −337.28 −293.82 −204.57 −121.22 −126.94 −134.51 −142.01 −204.57 −226.50 −249.45 −271.84 −293.82 −315.57 −337.28 −359.16

156.75 170.02 183.46 194.95 194.95 194.95 194.95 183.46 170.02 143.05 115.35 64.83 31.27 33.17 35.77 38.43 64.83 75.93 88.56 101.75 115.35 129.18 143.05 156.75 Sum

148.22 161.18 174.30 185.49 185.49 185.49 185.49 171.25 158.24 132.09 105.19 56.25 24.02 27.67 30.18 32.76 56.68 67.43 79.67 92.48 105.70 121.26 134.83 148.22 2 769.59

3.1.2. Energy system 2 The second mathematical model is developed to calculate the energy balance cost and production efficiency on the water boilers of WR25 type. System complexity is much less than Energy system 1. The calculations are carried out for the nominal parameters of the water boiler; it means inlet temperature of 80 °C and outlet temperature 150 °C. The computations of water boiler energy balance use the same thermal power demand from district heating grid. Based on that, the energy needed to cover requirement for heating power is calculated as

̇ = 3.6Q15 ̇ / η20 Q11

From the production needs, the model calculates the chemical energy input to the water boiler. It is computed on the nearly the same way, as for steam boiler. Installation operator provided a formula for the boiler efficiency calculation, as a function of produced power. The mentioned relation is given by

ηWR25 =

̇ 3 + 0.0594Q11 ̇ 2 + 0.06159Q11 ̇ + 66.17858 −0.00166Q11 100

(28)

The empirical formula (28) is obtained from the examination of the boiler’s by external company. This examination was ordered by the system operator, and formula (28) is used in evaluation of heating energy output as well as profits and costs in real operational mode of the studied installation. By dividing energy production through the water boiler efficiency, the chemical energy is calculated as

(2) at actual load of production

̇ QChem 18 = ṁ 18 (h5−h16)/ ηOR64

(27)

(25)

̇ ̇ QChem 9 = Q11/ ηWR25

(29)

Knowing the amount of chemical energy and the chemical energy unit cost, the cost of heat production in the extraction-condensing turbine is calculated as:

Knowing the actual chemical energy requirement, as well as the chemical energy cost, it is possible to evaluate the production cost

̇ CHeat18 = QChem 18 Cf

̇ CHeat11 = QChem 9 Cf

(26)

(30)

The cost of chemical energy for water boiler is the same as for steam boiler OR64. Analogically to the Energy system 1, the algorithm is computing the production cost for every hour of operation. Energy system 1 despite the heat production cost, also considers production costs of electrical energy. It is necessary to calculate total operating costs in the used models, to assess which is more profitable for the operator.

At this stage, it can be assumed that energy balance occurred between the steam boiler and turbogenerator is finalized. This part presents the general formulas of energy balance. The written algorithm includes the functionality of every hour calculation and contains formulas and logical conditions, which considers technical parameters and production limits. The idea is to reflect as closely as possible the 1 h operation of the unit above, to precisely calculate 24 h energy and cost 121

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Fig. 16. CHP and WR25 profitability comparison.

Fig. 17. Comparison of 1 h operation profitability for listed scenarios.

4. Results and discussion

Furthermore, heating power demand during the day is going far below the steam boiler technical minimum. It creates the situation, that boiler has to produce more steam than the district heating grid demand. The surplus power production has to be worked out somewhere in the system. To utilize the higher steam production, there are two possible ways; one is to release the superheated steam to the environment, what is pure energy waste, and significantly reduces financial results. The second way is to increase the electric power production in the condensation section. Fig. 3 presents the boiler thermal power output, chemical energy delivered and occurring efficiency, at every hour of production. Taking the assumption for the calculation purposes, that power production is constant in the hourly operation; power is recalculated to the thermal energy output. Based on that, for the turbine and generator five main energy streams are used to cost calculation. Considering the Q3̇ as energy introduced to the turbogenerator, supplied energy is transformed in the three main energy product:

Based on the two mathematical models of heat and electricity production, described in Section 3.1, the cost analysis is performed. The calculation is made on the exemplary heating curve shown in Table 4. The heating curve, typical for transitional seasons is presented in this study. Power demand range presented in Table 4, is characteristic due to relatively low levels of heat demands and high differences between day and night. Energy system 1 model calculates the superheated steam production requirement, to cover needs of heating power and electricity production. Computations are carried out regarding boiler’s technical minimum output, turbine’s condensation minimum flow rate, and other technical equipment aspects. To generate steam for combined production on the turbine of VE40 type, a single steam boiler is sufficient, what is presented in Fig. 2. Fig. 2 delivers a few critical information about the system operation. To cover heating demand in the system, extra power for the electricity production, roughly about 30% more, should be provided.

Q18 – thermal energy used for heating 122

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Fig. 18. Comparison of 24 h operation profitability for listed scenarios.

E5– electric energy produced in co-generation E6– electric energy produced in condensation

Fig. 7 displays where is used the chemical energy delivered to the system. The most fuel is used for heating energy, electricity produced in condensation and the less is used for electricity in co-generation. Based on the derived formulas and assumed price of chemical energy, the production costs for each product are achieved. To visualize the profits/cost relation, the comparison charts are made, to show the thermal energy production profitability (Fig. 8). Fig. 8 shows the profit from thermal energy sold to the district heating grid, with a comparison to the appropriate production cost. The profitability is kept within all range of thermal load. For the electricity produced in co-generation situation looks similar (Fig. 9). The Fig. 9 displays, that electricity production in co-generation brings profit at every hour of operation. The situation starts to be completely different, where the profitability of production in condensation is analyzed (Fig. 10). Due to the high energy input for electricity production in condensation, the profitability is permanently below zero. It means, that production of every MWh in condensation mode at current level of chemical energy price, creates a loss for the company. The cumulated financial profit/loss 24 h operation summary, contains Fig. 11 and Tables 6 and 7. To clarify the obtained results, the sum of columns contain Profitability production of each product, is not precisely equal to the column Total CHP profitability. It is not because of errors in calculations, but the mathematical algorithm includes owner electrical demand considered in the calculation. Data presented in Fig. 11 and Table 6, provided a few significant conclusions. The most important is the economic yield, and the components influence on the final result. The detailed computation indicates the scale of the relation of costs and profits on production, for each product separately. In result, it builds the awareness and supports the conscious decision making, concerning energy market actual conditions. For example the extremely high electricity production cost in condensation mode, needs to be considered in the operation modes schedule and future approach to investment activity. The following section will explain the results of Energy system 2. Energy system 2 model analogically to Energy system 1, calculates the operation of water boiler WR25, which is an alternative source of thermal energy for district heating grid. The Energy system 2 used the same heating power demand (Table 4), to reflect the similar working conditions and make the analysis comparable. In this case, the heating power demand is equal to the boiler thermal power generated Fig. 12. By knowing the heating power demand, the algorithm computed the required chemical energy for heat production accordingly to Eq. (29), and displayed in Fig. 13. A critical remark is the

Between the energy supplied and the final product, appears intermediate energy product, which is thermal energy used for E ̇ 5 and E ̇ 6 generation: Q5 for E5 – cumulated (in one hour period) thermal energy used for production in co-generation (including allocations for condensate regeneration)

Q5 = (ṁ 18 + ṁ 19CHP )(h3−h5)·1[h]

(31)

Q6 for E6 – thermal energy used for production in condensation (including allocations for condensate regeneration). The formula on Q6 is

Q6 = (ṁ 6 + ṁ 17 + ṁ 19Cond )(h3−h2)·1[h]

(32)

It is the cumulated (in one hour period) thermal energy used for production of 1 MWh in condensation from the streams: ṁ 6 , ṁ 17 andṁ 19Cond Table 5 presents the primary energy flows for every hour of operation during 24 h period. As total thermal energy delivered to process is considered the energy delivered in Q3, which is the total amount of energy allocated in the superheated steam. From the energy delivered, the energy is separated for heating and electricity production. Fig. 4 presents the thermal energy usage. Fig. 4 indicates that the surplus production of steam, during the low heating power demand, is delivered into condensation section, which is used in electricity production. Fig. 5 displays the hourly total electrical energy generation, with a partition on production in cogeneration section as well condensation section. Knowing the part shares in total electricity production, the energy input based on the formulas (12) and (20) is calculated. Fig. 6 shows the comparison between co-generation and condensation modes. The chemical energy has to be supplied to produce 1 MWh of electric energy during the 24 h period in co-generation and condensation modes. Fig. 6 presents a considerable difference for energy input ratio between co-generation and condensation mode. The cogeneration part requires about 3 times less energy, to produce the same amount of electrical energy. Knowing the electricity production for the chemical energy input required, and thermal quantity produced at the appropriate boiler efficiency, total chemical energy usage can be calculated. It is a crucial factor, relevant to calculate production profitability. 123

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business activity. The analysis was performed on existing installation and robust data provided by the operator. Two dedicated mathematical algorithms were developed. The Energy system 1 describes the production in the CHP part of the installation, whereas Energy system 2 is dedicated to production in water boiler. The examined case is up-todate, due to the complexity of the installation. Another issue is, the particular study reflects the situation occurred in many similar (comparable design parameters) power plants under operation in Poland and Eastern Europe. From the presented detailed study, the following conclusions can be drawn:

water boiler technical minimum, which is at the much lower level and does not create overproduction. Accordingly to the water boiler efficiency formula, the chemical energy requirement for Energy system 2 is calculated. From the comparison of Fig. 13 with Fig. 3, it is clear that the amount of chemical energy is significantly smaller, due to no energy required for electricity production. In the final settlement Energy system 2 is less energyconsuming, but without profits from the production of electricity. Fig. 14 shows profits and costs for thermal energy production in water boiler. Fig. 14 displays that at every heating power demand within 24 h operation installation generates a positive economic result. The cumulated profitability for every hour operation is shown in the Fig. 15. A detailed summary is provided in Table 8. The results displayed in last column Total WR25 unit - profitability (Table 8) are not equal to the sum of first three columns, because also in the Energy system’s 2 algorithm, installation owner demands are deducted from the total profitability. Below is presented the summary of production profitability studied in models for thermal energy production in CHP installation (Energy system 1) and a traditional water boiler (Energy system 2). It was proven, that under specific conditions the CHP is not the most economically efficient way of heat production. The difference at 24 h operation is not huge (∼140 EUR for a particular example). In the long-term activity, it can bring significant cumulative adding value; especially it is zero investment optimization. This situation is clearly shown in the Fig. 16. Profit form electric energy production on the extraction-condensing turbine is alternating. At high thermal demands generates higher income from operation, whereas, at low thermal demand, electricity production causes a loss from the activity. Operation profitability differs much considerably, if the higher price for CO2 emission or a significant increase in the chemical energy, is considered. Currently, the top subject considered in EU is the price of CO2 emission and the activity to limit the available emission rights on the market. In the time that free allocations for CO2 emission will be shrinking, that is why the vision of substantial price increase for CO2 emission allocation is authentic, and up to date subject. Due to that, this paper includes the analysis of CO2 emission price change, on the production profitability at current prices for electric and thermal energy. For the calculation purposes, the CO2 price increase in three scenarios is assumed: actual 7 EUR/tone, the second up to 15 EUR/tone and the third 30 EUR/tone, other economic parameters remain the same. Fig. 17 displays the results of the analysis. Fig. 17 presents the one-hour operation profitability of the CHP installation which is strongly affected by the increase of the CO2 allowances. At price of 15 EUR for one tone of emission, almost 1/3 of operation period generates a loss, whereas at price of 30 EUR/tone, which was the EU assumption of the initial price for the emission, induce permanent loss. For the water boiler, WR25 the situation is a bit better: at 15 EUR/tone is still remunerative, but at 30 EUR/tone also generates a loss. To compare the 24 h profitability for listed scenarios, Fig. 18 is shown. From Fig. 18 one can deduce, that the CO2 emission cost has a tremendous influence on the installations profit. If the price of the CO2 emission would achieve 15 EUR/tone, the production profitability becomes questionable. Assuming, that power plant has to buy one hundred percent of allowances for CO2 emission for 30 EUR/tone at current energy price; it would cause business for heat production completely uneconomical. In result, the old units have to be modernized or replaced by new and more efficient.

• The mathematical models for simulation of power plant operation,

•

•

with parallel cost analysis, is a valuable tool for business management and production forecasting. The utility of the properly designed and tested system is indisputable. The crucial factor is that such kind of tools can be developed with no or minimal capital expenditures. The only requirement is appropriately measured installation, data acquisition, and equipment’s actual technical specifications. It was proved, that production on CHP equipped in the extractioncondensing turbine is less profitable in comparison to the traditional water boiler. The situation occurs under specific conditions, especially at low heating power demand. Deliberately, for the current case study, was chosen demand from transient seasons. It reveals the “weakness” of the production on the extraction-condensing turbogenerator set. Future CO2 emission price increase has a considerable impact on thermal and electrical energy production activity. The statement is especially significant for installations, equipped with extractioncondensing turbines. The performed scenarios show, that production on water boilers at a higher price for CO2 emission (the increase from 7 EUR/tone to 30 EUR/tone), generates three times lower loss to production in CHP.

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