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Thermo-environmental evaluation of traditional cogenerative and fuel cell plants
Applied Energy 71 (2002) 127–146 www.elsevier.com/locate/apenergy
Thermo-environmental evaluation of traditional cogenerative and fuel cell plants Petronilla Fragiacomo*, Davide Gambarotti Department of Mechanical Engineering, University of Calabria, Arcavacata di Rende, 87030 Cosenza, Italy Received 18 June 2001; received in revised form 31 October 2001; accepted 10 November 2001
Abstract A model is proposed that can contemporaneously determine the optimum techno-economic working trajectory of any cogenerative plant and achieve the successive thermodynamic and environmental comparison. By means of the introduction of suitable coefficients, based on aspects of an energy and environmental nature, an engineering approach to the concept of sustainable development is provided. Moreover, the model enables the recording, for every technological solution, in optimum running and planning conditions, of the working moments and the load diagrams of the primary engine and of the possible auxiliary boiler. From a study of the results obtained from the application of the proposed procedure to a real case, using plant solutions with differing degrees of technological maturity, it emerged that the analysis of economic convenience, despite often being a decisive factor in the choice of a cogenerative system, does not necessarily provide a complete evaluation of the said system. # 2002 Published by Elsevier Science Ltd. All rights reserved. Keywords: Energy; Exergy; Cogenerative plants; Fuel cells; Techno-economic; Thermo-environmental
1. Introduction At any given time, such as the present, in which engineering activities in the energy field are orientated towards the control and containment of energy degradation (principle II) and the reduction of irreversibility is considered a crucial point in the theme of control and rational use of energy resources, the use of classic technoeconomic mathematical simulation models, orientated exclusively towards energy ‘‘lost’’ (within the framework of principle I), appears to be insufficient, above all if
* Corresponding author. Tel.: +39-0984-494615; fax: +39-0984-494673. E-mail address: [email protected] (P. Fragiacomo). 0306-2619/02/$ - see front matter # 2002 Published by Elsevier Science Ltd. All rights reserved. PII: S0306-2619(01)00048-4
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Nomenclature Symbols Electric coefficient Fi Difference between OF1i, and OF2i cc Conventional boiler (%) el Electric efficiency (%) ex Exergetic efficiency (%) HRSG Heat Recovery System Generator efficiency (%) ma Alternative motor efficiency (%) t Thermal efficiency (%) Updating coefficient to the half hour (1800) l Thermal coefficient ’ Significant time span Exergy (kW) f Exergy of the fuel (kW) p Exergy of the derived products (kW) Hazard index attributed to compound i E Euros ( 0.9 $) ACF Annual cash flow (E/years) Amm Economic amortisement (E/years) C Cost (E/years) CEX Unitary exergetic coefficient cf Fuel cost (E/kJ) ci Irreversibility cost (E/kJ) CVIA Environmental impact evaluation coefficient ENEL Ente Nazionale Energia Elettrica (Italian electric company) ER Relevant polluting emissions G Mass flow (kg/s) GT Gas Turbine Hi Low heat value (kJ/kg) I Taxes (E/years) ICE Internal combustion engine IN Economic investment in plants (E) IRR Internal rate of return K Power unit price (E/kW) LM Limits of polluting emissions Lm Losses due to irradiation and convection (%) Lm Transf. losses from mechanical to electric power (%) Lmix Losses from steam mixing in the combust. chamber (%) NAG Net annual gain (E/years) NPV Net present value OF Objective function P Power (kW)
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PAFC PI R SOFC Ta To Y Z
Phosphoric acid fuel cell Profitability index Gains or costs avoided (E/years) Solid oxide fuel cell Environmental temperature (K) Reference temperature (K) Taxes per power unit (E/kW) Cost of plant components (E/years)
Subscripts cc cg dis diss e ea eau ec ei er f ipe j k m max n p pc s sc t tr
Function of the month considered Conventional boiler With co-generation Dissipated post-combustor Dissipated auxiliary boiler Electricity Electricity withdrawn Self-produced electricity Electricity yielded Maximum electric power used Electric demand fuel Commitment of electric power with the supplier Index of day Index of month Maintenance Maximum Number of years Evoluted market value Post-combustor Current market value Without co-generation Thermal power Thermal demand
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these models are used for a comparative study of energy plants with differing technological maturity. Therefore, a study is believed to be fundamental, covering both a techno-economic feasibility analysis outlining technologically adequate solutions while evaluating the pay back period of the extra costs linked to the energy plant, together with a thermal-economic and environmental analysis capable of a wide-ranging evaluation of the practicability of the plant solution.
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To achieve optimisation of co-generative plants based on the above-mentioned considerations, this paper puts forward an evaluation procedure, successively using two different refinements of the model realised in [1,2], thereby allowing the determination, for every possible technological solution, of design and optimum working mode and successively, the evaluation of the cost in thermo-environmental terms of opting for one technological alternative rather than for another.
2. Current situation All this, however, would pre-suppose the appearance of a norm-tariff incentive framework and a knowledge of plant practicability sufficient to enable an effective economic saving for the producer (not just in the planning phase), effective energy saving for the company and a real environmental saving for society in general. Whichever method is proposed, establishing the prevalence or otherwise of benefits achievable, essentially consists in a comparison between: money spent to carry out the investment; benefits that are supposed to be generated by the investment itself during useful plant life [3]. Concentrating attention on the formulation of the objective function, the following kinds of simulation model can be characterised: . Classic. In this type, the most used objective function (O.F.) consists, as exemplified in expression (1), in minimising the summation of the annual costs relative to the various components (amortisation, depreciation, maintenance), Zi, and the running costs, often limited just to fuel cf, expressed as the product of the cost of the same, of the mass flow Gf and of the low heat value Hi [4]. F1 ðxÞ ¼ min Zi þ cf Gf Hi ð1Þ . Thermo-dynamic. This model is based essentially on the second principle of thermodynamics in which the aim is to minimise energy inefficiency and is completely detached from investment costs. It can be observed that, also associating a monetary value to the exergy produced owing to irreversibility, ci, as pointed out in expression (2), is not a very interesting evaluation from an economic point of view, since a net dissociation occurs between the efficiency and the costs required to obtain it.
F2 ðxÞ ¼ min ci ci ðxÞ
ð2Þ
. Thermo-economic. Specifically, the objective function that ensues from the former is written as the ratio of annual running cost and the flow of exergy produced by the system [4,5].
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According to this formulation, the OF is founded on methods like the theory of energy cost (TEC) [5,6] or the theory of functional analysis (TFA) [7,8], which share out the running costs among the various components as a function of the inefficient energy flow, ci(x), generated by each one of them, defined by the difference between the incoming inefficient energy flow, relative to the fuel and the outgoing inefficient energy flow relative to the energy products obtained by each single component ‘‘i’’ [9–11]. F3 ðxÞ ¼ min ðZi þ cfi i ðxÞ
ð3Þ
3. Working considerations In current market conditions it is difficult, in the area of techno-economic analysis and of acquisition evaluation, to use two openly contrasting and not easily reconciled requirements, such as: economic savings; energy and environmental savings. In fact, the potential purchaser pays attention exclusively to evaluation of economic profitability and only through legislative imposition will he consider other aspects not strictly economic. Furthermore, from the study of evaluation methods, available in the wealth of literature on the subject, it can be deduced that both the thermal-economic analysis methods and the techno-economic analysis methods, although effectively adapting themselves to the optimisation of individual plants, cannot, however, be used as such for the comparative study of plant solutions having differing technological maturity. This is because the economic examination of plant alternatives, at parity of efficiency in energy terms, often leads back to the following schematisation [10]: case 1—contained fixed costs but high variable costs; case 2—considerable fixed costs but moderate variable costs. This implies that the alternatives referring to the first case (commercially established technologies) tend, in an energy raw materials market undervalued with respect to the real scarcity of availability, to prevail over those assimilable to the second case (of a technological innovative character), which while appreciable from a efficiency and/or environmental aspect, have high investment costs [11].
4. Working hypothesis To this purpose the aim of this paper is to evaluate and illustrate the techno-economic feasibility of the installation of a cogeneration group without neglecting the thermodynamic and environmental aspects.
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By means of the definition of a mathematical model, below denominated technoeconomic, inspired by the one realised in [1,2,12] the optimum plant in terms of size and running mode is defined each usable technology. Moreover, to obtain more accurate and efficient running, this model was constructed in such a way as to be able to provide functional diagrams of the co-generative plants in the time span relative to the tariff rates (laid out below). Successively reformulating the model in a framework to evaluate the thermodynamic and environmental aspects, precisely denominated thermo-environmental, the previously obtained results are estimated so as to be able to evaluate the requirements (efficiency, emissions etc.) and/or specific situations, to supply a possible objective approach to the concept of ‘‘externality assessment’’. 5. Structure of the model and evaluation procedure With the purpose of achieving consistent savings, in energy and economic terms, control of the evolving working conditions of the plant itself over a period of time is fundamental. Taking what was achieved in [1,12] as a starting point the proposed evaluation model is completely defined once established: 1. decisional variables; 2. the constraint functions: efficiency constraints; energy balance constraints; 3. the techno-economic objective function; 4. the thermo-environmental objective function. The optimal running point is obtained by determining the value that the decisional variables have to assume, shown in Table 1. To determine the region of the admissible decisional variable values suitable constraint functions are used, identified as follows: 5.1. Efficiency constraints In the sphere of normal working both the primary engine and the auxiliary boiler have to respect the nominal maximum power defined in the planning phase. 5.2. Energy balance constraints In this case three groups of equations can be identified, that is: 5.2.1. Electric balance constraints Pe;cg kj ð’Þ þ Pea;kj ð’Þ ¼ Per;kj ð’Þ þ Pec;kj ð’Þ
ð4Þ
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Table 1 Decisional variables Thermal power supplied by fuel to the co-generative group (kw) Power supplied by the fuel to the conventional boiler (kw) Thermal power supplied by the fuel al post-combustor (kw) Co-generated electric power (kWe) Electric power yielded to the electric grid (kWe) Electric power withdrawn from the electric grid (kWe) Maximum power used with ENEL (Kwe) Co-generated thermal power (kWt) Thermal power supplied by the conventiona; auxiliary boiler (kWt) Thermal power dissipated into the environment (kWt)
Pf,cg Pf,cc Pf,pc Pe,cg Pec,cg Pea,cg Pei Pt,cg Pt,cc Pt,dis+Pt,diss
where the indexes take account that, in the case of electric energy, the moment of time when the purchase or sale takes place is significant. More precisely, with ‘‘k=1. . .12’’ the month is defined, with ‘‘j=1. . .(k)’’ the day (with (k) the function of the month is considered) and with ‘‘’=1. . .48’’ the significant time span, which in the current electric tariff regime corresponds to half an hour. Assuming that the primary engine always runs at the nominal maximum power, the coefficient kj(’) only takes on the values 1 and 0, respectively indicating whether the primary engine in the time span ’ on day j in the month k has to work or not [13]. 5.2.2. Thermal balance constraints Pt;cg kj ð’Þ þ Pt;cc lk ljð’Þ þ Pt;pc kj ð’Þ 5 Ptr;kj ð’Þ
ð5Þ
In this case the introduction of the coefficients and l are not imputable to the cost factor but exclusively serve to obtain the running moments respectively of the primary engine with possible post-combustor and of the auxiliary boiler, from which to extrapolate the load diagrams. 5.2.3. Capacity constraints Pei 5 Pea;kj ð’Þ Pe;cg 5 Pec;kj ð’Þ
ð6Þ
That represent the obvious capacity constraints, inherent in the maximum power used and that yielded by the supplying company. 5.3. System variably constraints Pt;x 5 0
Pe;y 5 0 Pf;z 5 0
8x; y; z
that is all the system variables must be non negative.
ð7Þ
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6. ‘‘Techno-economic’’ objective function To represent the co-generative theory, with reference to the movement of money generated, the investment is defined as a series of expenditures and incomes. In the formulation of the objective function proposed it was decided to maximise the Net Annual Gain, NAG, which leads back to evaluating the residual incomes after covering the amortisement rate [5,14,15]. This with the precise intention of the benefit that can be gained in the light of the costs needed to realise it: annual cash flow; annual amortisation rate. The annual cash flow, ACF, is expressed as the difference between running income and expenditure. The incomes correspond both to effective money transfers and to costs avoided compared to conventional solutions. The expenses correspond to the extra running costs sustained for the realisation of the co-generative solution [15]. The annual amortisement rate, represents the fixed amount of capital investment imputable to the working year [16]. The various costs and gains entries of the ACF are laid out in detail both in the absence, Table 2, as well as in the presence of cogeneration, Tables 3, 4 and 5. The objective function obtained from them is the following: OF1 ¼ maxNAG ¼ maxðACF AmmÞ ¼ n max Rea;sc þ Rt;sc þ Iea;sc þ Ripe;sc þ If; sc Cea;cg Iea;cg Cipe;cg o
Ieau;cg Cf;cg If; cg Cf;cc If;cc Cm;cg þ Rec Amm
ð8Þ
7. Thermo-environmental objective function In this phase the aim is to evaluate the thermo-environmental impact of the previously optimised plants. Therefore the sizes and the running modes obtained from the previous simulation are imposed and two appropriate coefficients are introduced. Table 2 Annual cost obtained in absence of co-generation Electricity Aquisition of electric energy from the ENEL grid Electric energy taxes Use of electric energy power
Rea,sc=k j j Kea,sc,kjj.Per,kjj.y Iea,sc=Yea,sc.k Per,sc,k Ripe,sc=Kipe.k Per,sc,k
2.1 2.2 2.3
Fuel Acquisition of thermal energy required Taxes on fuel
Rt,sc=Kf,sc.k (Ptr,sc,k /cc) If,sc=Yf,sc.k (Ptr,sc,k/cc)
2.4 2.5
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Table 3 Annual costs sustained in the co-generative setup Electricity Cea,cg=k j ’ Kea,cg,kj’.Pea,cg,kj’. Iea,cg=Yea,cg.k Pea,cg,k
3.1 3.2
Cipe,cg=Kipe,cg.k Pea,cg,max,k Ieau,cg=Yeau,cg.k Pe,cg,k
3.3 3.4
Cf,cg=Kf,cg.k Pf,cg,k If,cg=Yf,cg. k [Pf,cg,k-%x.Pe,cg,k] %x: tax-exempted fuel [kWhexempted fuel/kWhe] [18]
3.5 3.6
Fuel for the conventional boiler Taxes on the aquisition of fuel for the boiler
Cf,cc=Kf,cc.k Pf,cc,k If,cc=Yf,cc.k Pf,cc,k
3.7 3.8
Maintenance Additional maintenance costs
Cm,cg=Km,cg.k Pe,cg,k
3.9
Acquisition of electric energy from the ENEL grid. Taxes relative to the withdrawal of electric energy from the ENEL grid Power used relative to the aquisition of electric energy Taxes on self-produced electric energy. Fuel Fuel for co-generation Taxes on aquisition of fuel for co-generation
Table 4 Annual gains obtained through co-generation Gains from electricity yield Yielding to grid
Rec=k j ’ Kec,cg,kj’.Pec,cg,kj’.
4.1
Table 5 Annual amortisement through co-generation Amortisement Investment for co-generation
Amm=(INcg INsc)/n
5.1
A thermodynamic coefficient that evaluates the thermodynamic aspects—this approach requires the detailed knowledge of the energy flows for every component and the energy interactions present among the various components. This translates into a considerable mass of data to elaborate according to one of the methods available in the specialist bibliography [7,8,17]. To slim down the model the determination of exergetic efficiency was employed, by means of what is defined as the direct method, which enables the exergetic efficiency to be obtained through the electric and thermal efficiencies, as expressed in the following relation: ex ¼ ½el þ "t ð1 Ta=ToÞ where " is the possible deviation between heat available and heat exploited.
ð9Þ
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Once the exergetic efficiency ex is determined for the individual plant, the most efficient plant is identified as the reference plant and then the (unitary exergetic coefficient) CEX is identified [4,6], as the ratio of the exergetic efficiency of the reference plant, ex,r, and the efficiency of the plant examined ex,i, that is: CEX;i ¼
f = p r=
f=
p i¼
ex;r =ex;i 5 1
ð10Þ
This coefficient, which is greater than unity relative to the greater inefficiency of the tested plant compared to the reference plant, will be used directly in Table 3 in expressions 3.5–3.9, with the aim of penalising the less efficient solutions and at the same time keeping the weight of irreversibility high, obtaining the expressions shown in Table 6. An environmental coefficient estimating environmental impact and penalising the less efficient plants—unfortunately, despite the existence of European and international directives in this respect, only few States have introduced, into their norms, adequate limits for the needs encountered. It follows that respect of the norms aimed at safeguarding the environment, does not in reality guarantee eco-compatible plants. In this regard an ad hoc coefficient, CVIATOT, is defined, equal to 1+CVIAi, which cuts into fuel costs in the form of tax increases as shown in Table 7, in the expressions 7.1 and 7.2. The coefficient CVIAi (environmental impact evaluation coefficient), calculated as a function of the limits of polluting emissions (LM) and of the entity of relevant polluting emissions (ER), for each component ‘‘i’’ to be kept under control, therefore can be defined according to the following expression:
LM ER CVIAi ¼ 1
ð11Þ LM Table 6 Annual costs sustained introducing the coefficient Cex Annual costs ‘‘exergonomic’’ Fuel for co-generation Taxes on co-generation fuel
C*f,cg=Kf,cg.k Pf,cg,k.CEX I*f,cg=Yf,cg.k [Pf,cg,k %x.Pe,cg,k].CEX %x: tax-exempted fuel [kWhexempted fuel/kWhe] [19]
6.1 6.2
Fuel for the boiler Taxes on boiler fuel
C*f,cc=Kf,cc.k Pf,cc,k.CEX I*f,cc=Yf,cc.k Pf,cc,k.CEX
6.3 6.4
Table 7 Annual costs sustained introducing the coefficient CVIAi Annual costs ‘‘environmental’’ Taxes on primary motor fuel Taxes on boiler fuel
I**f,cg=k I*f,cg,k.CVIATOT I**f,cc=kI*f,cc,k.CVIATOT
7.1 7.2
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where, is the hazard index attributed to compound ‘‘i’’. In this paper for ease of calculation this index was set equal to unity. Tables 6 and 7 show the modified cost entries (indicated by * and **), used to obtain the objective function of the optimised model proposed in the formulation denominated thermo-environmental, giving: n OF2 ¼ max NAG ¼ maxfACF Ammg ¼ max ½Rea;sc þ Rt;sc þ Iea;sc þ Ripe;sc þ If ;sc o
Cea ;cg Iea ;cg Cipe ;cg þ Ieau;cg Cf ;cg If ;cg
Cf;cc Cm ; cg þ Re ; c Amm ð12Þ
The result obtained will be used to quantify the cost, in thermo-environmental terms, relative to one certain technology, ‘‘i’’, rather than to another [4,17], by means of the difference indicated by Fi, between the result of the first simulation, distinguished by OF1i, and the result of the second simulation OF2i: Fi ¼ OF1i OF2i
ð13Þ
8. Application and analysis of the results Imagining, in a not too distant future, the diffusion of a relevant number of high efficiency cogeneration power stations and attributing a much less marginal role than at present to electricity and heat generation spread over the area, a real case test was performed on a Calabrian food conservation company ‘‘Giacinto Callipo conserve alimentari srl’’, for the following list of reasons: size being such that its energy needs can be covered by small to medium capacity plants; working that necessitates thermal and electric demand at the same time; location of industrial activity not far from urban settlement. This company, fitted with a conventional boiler and a co-generative endothermic plant currently in the testing phase, works on the preparation and processing of tuna fish. By means of a series of visits on the spot, a study of the working cycle was carried out, producing the thermo-electric data illustrated in Fig. 1, relative to the threeyear period from 1995 to 1997, so as to arrive to the discrete distribution in hourly bands of the energy requirements of a typical working day, as summarised in Tables 8 and 9. Three endothermic and two fuel cell plants, of a power compatible with the requirements obtained, were used for the economic analysis, their purchase and maintenance costs, supposing the use of the same fuel in the company, are summarised in Table 10.
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Fig. 1. Thermal and electric demand prevision for the years after 1997. Table 8 Balance of annual electric consumption in the three-year period 1995/1997 Years
kWh expended
Cost kWh (E)
Total cost kWh +employed power (E)
1995 1996 1997
684 575 563 700 660 900
45 726 40 364 49 224
64 035 58 674 67 533
Table 9 Balance of annual thermal consumption in the three-year period 1995/1997 Years
Kg expended
Annual cost (E)
1995 1996 1997
128.900 163.600 181.680
33.855 38.512 41.390
Table 10 Comparative energy costs of co-generative systems Plant
Plant cost (E/kWe)
Maintenance cost (E/kWh)
ICE 330 kW ICE 279 kW ICE 200 kW PAFCpa (SOFC+GT)pa PAFCsa (SOFC+GT)sa
619.75 790.18 764.68 1.342.78 1.962.53 981.26 1.084.56
0.01239 0.01136 0.01239 0.01183 0.01547 0.01033 0.01291
a
p=Market price of initial trading; s=market price of established trading.
It should be pointed out that a PAFC (phosforic acid fuel cell) cell was chosen for the fuel cell technologies, being the most available commercially and the best documented, and an SOFC (solid oxide fuel cell) combined with a gas turbine, GT, which is the most efficient solution for this technology in terms of electric efficiency. In
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addition, two different cost hypotheses were elaborated for the latter technology, cautiously, with respect to the excessively optimistic indications provided by the manufacturers. In the first hypothesis reference is made to prices in the initial phase of commercialisation, indicated by PAFCP and (SOFC+GT)P, in the second to prices presumed in the commercial development phase, PAFCS and (SOFC+GT)S. In the financial reference scenario, in which special attention has been paid to the economic variability reported in Table 11, the application of the optimised technoeconomic model enabled the determination, for the various plant solutions examined, of optimum sizing and running mode, with the aim of maximising the economic payback of the investment. From evaluation of the results obtained testing the ICE (Internal Combustion Engine) in the production cycle under examination, Table 12, the best result in terms of net annual gain is obtained from the 330 kW group. In detail the optimal functional trend of this group shown in Table 13 and in Fig. 2, provides for: Table 11 Values of the main economic variables Discount rate on money Annual inflation rate Bank loan rate Tax burdens Percentage of own capital
5% 2.5% 12% 30% 100%
Table 12 Balance of techno-economic simulation of plants with alternative engine Plant type Economic parameters
ICE 330 kW
ICE 200 kW
ICE 279 kW
Investment (E) Annual cash flow (E/years) Plant working life (years) Amortisement (E/years) Net annual gain (E/years)
231.372.70 47.528.50 13 17.792.46 29.730.87
142.025.60 34.263.82 13 10.924.61 23.338.69
219.019.00 56.088.25 8 27.377.38 28.710.87
Fig. 2. Trend of 330 kW thermo-electric cogenerator supply.
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running only in company working hours, 2700 h/year; yield to grid of about 100 kWe from 7.30 am to 19.30; withdrawal from the grid in non-working hours of about 80 kWh for about 3850 h/year. As far as the other groups are concerned, it should be pointed out that the 279 kW ICE group, in which the trend of the coefficients kj’ and lkj’ is reported in Table 14, gives an economic result slightly inferior to the former, but is characterised for optimal running, Fig. 3, providing for continuous activation throughout the whole day, which however means a consistent reduction in its working life. While it can be inferred from analysis of the economic results of the techno-economic simulation on two innovative co-generative plants, shown in Table 15, that the solutions, in terms of net annual Gains, under both cost hypotheses, provide poorly competitive results, however, examination of the NAG in the light of the cash flow generated, it can be deduced that the gap is reduced as was presumed, almost exclusively to the differing purchase cost of traditional compared to innovative plants, while the other factors are sufficiently comparable. From the functional diagrams, Figs. 4 and 5, poor efficiency of the SOFC+GT is found from the thermal aspect, largely compensated by the greater and economically more significant electrical efficiency, together with a useful lifespan comparable to the 330 kW ICE plant for both of the two cells used. Moreover, from a sensibility analysis carried out on some economic indexes, thoroughly documented in literature, NPV (net present value), IRR (internal rate of return) and PI (profitability index), shown in Figs. 6, 8 and 10, the great competitiveness of the endothermic compared to the fuel cell motor, can be inferred. Only under the developed market cost hypothesis can a comparison between a plant with ICE and one with fuel cells be made. It should be pointed out, however, under this hypothesis, despite a positive NPV index the cells allow a maximum IRR of 10% without going beyond the limit of useful lifespan. In the thermo-environmental simulation, Figs. 7, 9 and 11, there is a trend inversion in which the endothermic group, while presenting a positive NPV both for 10 and 13 years, does not enable the capital to be recouped, without going beyond the limit of useful plant life with an IRR of 5%. While both the PAFCS and the SOFC+GTscontinue to show a positive NPV index in all the referenced years and an updated payback rate of at most 10%, sufficient to remunerate the capital invested exhibiting a profitability index greater than 0.5 in both cases. Finally, from the analysis of Table 16 in which the values shown by the indexes CEX (unitary exergetic coefficient) and CVIATOT (environmental impact evaluation coefficient) it is pointed out how great differences exist in the exergetic sphere among the co-generative motors examined, with deviations greater than 20–25%. All of this translates into a waste of energy resources that in the specific case is equal to about 650,000 kWh for a year. To gather the potentiality of the proposed evaluation procedure and to avoid the analysis of solutions in themselves not economically acceptable, the thermo-environmental simulation, its data summarised in Table 17, was limited to the innovative
Table 13 Coefficient kj’ e lkj’ trend for the 330 kW endothermic engine
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Table 14 Coefficient kj’ e lkj’ trend for the 279 kW endothermic engine
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Table 15 Balance of techno-economic simulation of cell fuel plants Plant type Economic parameters
PAFCP
PAFCS
(SOFC+GT)P
(SOFC+GT)S
Investment (E) Annual cash flow (E/years) Working life of plant (years) Amortisation (E/years) Net annual gain (E/years)
335.697.00 36.647.27 12 25.822.84 10 824 42
245.317.00 36.647.27 12 18.870.30 17 776 45
508.296.90 42.085.56 12 39.099.40 2 930 89
280.900.90 43.836.35 12 21.607.52 22 228 82
Fig. 3. Trend of 279 kW thermo-electric cogenerator supply.
Fig. 4. Trend of optimal thermo-electric fuel cell PAFC supply.
technologies and to the more advantageous groups among the endothermic systems examined. From analysis of data obtained from the simulations, determining the value of the coefficient Fi (difference between the result of the first simulation, OF1i, and the result of the second simulation OF2i) shown in Table 18, it is pointed out that the
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Fig. 5. Trend of optimal thermo-electric cycle SOFC+GT supply.
Fig. 6. Net present value—techno-economic data simulation.
Fig.7. Net present value—thermo-environmental data simulation.
Fig. 8. Internal rate of return—techno-economic data simulation.
greater penalisation occurs precisely with the plants which are less efficient from the thermo-environmental point of view. It follows that the thermo-environmental simulation makes the fuel cell competitive in virtue of their greater thermodynamic efficiency. Indeed under the hypothesis of consolidated prices, the (SOFC+GT)s plant thanks to its high electrical efficiency,
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Fig. 9. Internal rate of return—thermo-environmental data simulation.
Fig. 10. Profitability index—techno-economic data simulation.
Fig. 11. Profitability index—thermo-environmental data simulation. Table 16 Thermo/environmental coefficients for compared co-generative plants Plant type Coefficients CEX (unitary exergetic coefficient) CVIATOT (environmental impact evaluation coefficient)
ICE 279 kW
ICE 330 kW
ICE 200 kW
PAFC
(SOFC+GT)
1.189 1.190
1.268 1.165
1.373 1.193
1.115 1.009
1.000 1.012
Table 17 Balance of the thermo-environmental simulation Plant type Economic parameters
ICE 330 kW
PAFCP
PAFCS
(SOFC+GT)P
(SOFC+GT)S
Investment (E) Annual cash flow (E/years) Working life of plant (years) Amortisation (E/years) Net annual gain (E/years)
231.372.70 28.979.43 13 17.797.62 11 181 29
335.697.00 36.647.27 12 25.822.84 10 824 42
245.317.00 36.647.27 12 18.870.30 17 776 45
508.296.90 42.085.56 12 39.099.40 2 930 893
280.900.90 43.836.35 12 21.607.52 22 228 82
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OF1i (E)
OF2i (E)
Fi=OF1-OF2 (E)
Fi/ OF1i
ICE 330 kW PAFCp PAFCs (SOFC+GT)p (SOFC+GT)s
23.338.69 17.611.70 24.516.73 2.930.89 22 640 44
11.181.29 10.824.42 17.776.45 2.930.38 22 050 64
12.156.88 6.786.76 6.739.76 202.451.10 589.79
0.520 0.385 0.270 0.068 0.030
(about 60%) and to its low thermo-environmental penalisation (Fi/ OF1i=3%), achieves a result in terms of NAG double that achieved by the 330 kW ICE group, which instead is greatly penalised from the thermo-environmental point of view (Fi/ OF1i=52%).
9. Conclusions In this paper, considering the current trends in the subject of energy rationalization, in terms of use and environmental compatibility a process of evaluation for traditional and innovative co-generation energy systems was created. The trend of optimal technical-economic use was determined from the application of this process to an actual case. A comparison and evaluation of exergy and considerations of environmental characteristics led to optimal thermo-environmental system results. From the results of the study it was determined that the economic convenience analysis even though, it is often a decisive factor in the choice of a cogenerative system, does not necessarily supply a complete evaluation.
References [1] Arcuri P, Florio G, Fragiacomo P. Impiego della cogenerazione nel comparto industriale. La Termotecnica, dicembre 1996. [2] Arcuri P, Belli M, Florio G, Fragiacomo P. Optimal design of small size cogeneration plants with particular reference to quality of thermal regeneration. In: Proceedings of TAIES ’97 thermodynamic analysis and improvement of energy system. Pechino, Cina, 10–13 June 1997. p. 277. [3] http://www.antares.it/ndenardi. [4] Santarelli M, Borchiellini R, Calı` M. Considerazioni sull’ottimizzazione termoeconomica di impianti energetici. 53 Congresso Nazionale Ati, Firenze, 1998. [5] Arena AP, Calı` M, Santarelli M. Confronto di metodi di analisi termoeconomica applicati ad un sistema termodinamico classico di cogeneration. Atti del IX Congresso ‘‘S. STECCO’’. Milano: Tecnologie e Sistemi Energetici Complessi; 26/27 giugno 1997. [6] Arena PA, Calı` M, Santarelli M, Borchiellini R. Un esempio di applicazione termoeconomica a un caso reale di centrale termoelettrica a ciclo combinato. 51 Congresso Nazionale ATI. Udine; 1996.
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[7] Frangopoulos CA. Thermoeconomic functional analysis: an innovative approach to optimal design of thermal systems. Second Law Aspects of Thermal Design. ASME; 1984. [8] Frangopoulos CA. Optimal synthesis and operation of thermal systems by the thermoeconomic functional approach. Journal of Engineering for Gas Turbines and Power 1992;114. [9] Silvestrini M. Energia degli impianti, Energia ed economia, Politecnico di Milano. Corso Energia; 1991. [10] Baccarini C, Benedetti M, Borghesi A, Bortoli G. Calcoli di convenienza economica: casi e problemi. Padova: CEDAM; 1984. [11] Salvi D. Una metodologia semplificata di analisi di impianti cogenerativi a metano di piccola e media taglia. Atti del Convegno Nazionale Gruppi Combinati Prospettive Tecniche ed Economiche; 1993. [12] Arcuri P, Florio G, Fragiacomo P. Valutazioni Energetiche di Impianti Cogenerativi alimentati a Metano. CH4 Energia e Metano; 1996;(3/4):24, Maggio-Agosto. [13] Arcuri P, Florio G, Gagliardi M, Scornaienchi NM. Dimensionamento ottimale di impianti cogenerativi con accumulo termico. Atti del 6 Convegno Nazionale ATIG. Bari; Novembre 1997. p. 211. [14] Florio G, Fragiacomo P. Confronto Tecnico Economico fra una Cella a Combustibile (PAFC) ed un Motore a C.I. dotato di Convertitore Catalitico per la Generazione di Elettricita` e Calore. Atti del 5 Convegno ATIG, vol. V. Rimini; 14–16 Novembre 1995. p. 145. [15] Consonni S, Macchi E. Rassegna critica dello stato dell’arte dei sistemi cogenerativi alimentati a gas naturale. Libro Bianco sulla Cogeneration, volume terzo, 11; 1997. [16] Panati G, Golinelli GM. Tecnica economica industriale e commerciale, vol. 4. Roma: La nuova scientifica; 1991. [17] Stoppato AL. The Exergetic Analysis for Energy System Diagnosis in Proceedings of ESDA, Montpellier; 1–4 July 1996. [18] Petrecca G. Approfondimento dei temi della cogenerazione CSE Tecnosud srl, Roma; 13–14 maggio 1998.
Thermo-environmental evaluation of traditional cogenerative and fuel cell plants Petronilla Fragiacomo*, Davide Gambarotti Department of Mechanical Engineering, University of Calabria, Arcavacata di Rende, 87030 Cosenza, Italy Received 18 June 2001; received in revised form 31 October 2001; accepted 10 November 2001
Abstract A model is proposed that can contemporaneously determine the optimum techno-economic working trajectory of any cogenerative plant and achieve the successive thermodynamic and environmental comparison. By means of the introduction of suitable coefficients, based on aspects of an energy and environmental nature, an engineering approach to the concept of sustainable development is provided. Moreover, the model enables the recording, for every technological solution, in optimum running and planning conditions, of the working moments and the load diagrams of the primary engine and of the possible auxiliary boiler. From a study of the results obtained from the application of the proposed procedure to a real case, using plant solutions with differing degrees of technological maturity, it emerged that the analysis of economic convenience, despite often being a decisive factor in the choice of a cogenerative system, does not necessarily provide a complete evaluation of the said system. # 2002 Published by Elsevier Science Ltd. All rights reserved. Keywords: Energy; Exergy; Cogenerative plants; Fuel cells; Techno-economic; Thermo-environmental
1. Introduction At any given time, such as the present, in which engineering activities in the energy field are orientated towards the control and containment of energy degradation (principle II) and the reduction of irreversibility is considered a crucial point in the theme of control and rational use of energy resources, the use of classic technoeconomic mathematical simulation models, orientated exclusively towards energy ‘‘lost’’ (within the framework of principle I), appears to be insufficient, above all if
* Corresponding author. Tel.: +39-0984-494615; fax: +39-0984-494673. E-mail address: [email protected] (P. Fragiacomo). 0306-2619/02/$ - see front matter # 2002 Published by Elsevier Science Ltd. All rights reserved. PII: S0306-2619(01)00048-4
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Nomenclature Symbols Electric coefficient Fi Difference between OF1i, and OF2i cc Conventional boiler (%) el Electric efficiency (%) ex Exergetic efficiency (%) HRSG Heat Recovery System Generator efficiency (%) ma Alternative motor efficiency (%) t Thermal efficiency (%) Updating coefficient to the half hour (1800) l Thermal coefficient ’ Significant time span Exergy (kW) f Exergy of the fuel (kW) p Exergy of the derived products (kW) Hazard index attributed to compound i E Euros ( 0.9 $) ACF Annual cash flow (E/years) Amm Economic amortisement (E/years) C Cost (E/years) CEX Unitary exergetic coefficient cf Fuel cost (E/kJ) ci Irreversibility cost (E/kJ) CVIA Environmental impact evaluation coefficient ENEL Ente Nazionale Energia Elettrica (Italian electric company) ER Relevant polluting emissions G Mass flow (kg/s) GT Gas Turbine Hi Low heat value (kJ/kg) I Taxes (E/years) ICE Internal combustion engine IN Economic investment in plants (E) IRR Internal rate of return K Power unit price (E/kW) LM Limits of polluting emissions Lm Losses due to irradiation and convection (%) Lm Transf. losses from mechanical to electric power (%) Lmix Losses from steam mixing in the combust. chamber (%) NAG Net annual gain (E/years) NPV Net present value OF Objective function P Power (kW)
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PAFC PI R SOFC Ta To Y Z
Phosphoric acid fuel cell Profitability index Gains or costs avoided (E/years) Solid oxide fuel cell Environmental temperature (K) Reference temperature (K) Taxes per power unit (E/kW) Cost of plant components (E/years)
Subscripts cc cg dis diss e ea eau ec ei er f ipe j k m max n p pc s sc t tr
Function of the month considered Conventional boiler With co-generation Dissipated post-combustor Dissipated auxiliary boiler Electricity Electricity withdrawn Self-produced electricity Electricity yielded Maximum electric power used Electric demand fuel Commitment of electric power with the supplier Index of day Index of month Maintenance Maximum Number of years Evoluted market value Post-combustor Current market value Without co-generation Thermal power Thermal demand
129
these models are used for a comparative study of energy plants with differing technological maturity. Therefore, a study is believed to be fundamental, covering both a techno-economic feasibility analysis outlining technologically adequate solutions while evaluating the pay back period of the extra costs linked to the energy plant, together with a thermal-economic and environmental analysis capable of a wide-ranging evaluation of the practicability of the plant solution.
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To achieve optimisation of co-generative plants based on the above-mentioned considerations, this paper puts forward an evaluation procedure, successively using two different refinements of the model realised in [1,2], thereby allowing the determination, for every possible technological solution, of design and optimum working mode and successively, the evaluation of the cost in thermo-environmental terms of opting for one technological alternative rather than for another.
2. Current situation All this, however, would pre-suppose the appearance of a norm-tariff incentive framework and a knowledge of plant practicability sufficient to enable an effective economic saving for the producer (not just in the planning phase), effective energy saving for the company and a real environmental saving for society in general. Whichever method is proposed, establishing the prevalence or otherwise of benefits achievable, essentially consists in a comparison between: money spent to carry out the investment; benefits that are supposed to be generated by the investment itself during useful plant life [3]. Concentrating attention on the formulation of the objective function, the following kinds of simulation model can be characterised: . Classic. In this type, the most used objective function (O.F.) consists, as exemplified in expression (1), in minimising the summation of the annual costs relative to the various components (amortisation, depreciation, maintenance), Zi, and the running costs, often limited just to fuel cf, expressed as the product of the cost of the same, of the mass flow Gf and of the low heat value Hi [4]. F1 ðxÞ ¼ min Zi þ cf Gf Hi ð1Þ . Thermo-dynamic. This model is based essentially on the second principle of thermodynamics in which the aim is to minimise energy inefficiency and is completely detached from investment costs. It can be observed that, also associating a monetary value to the exergy produced owing to irreversibility, ci, as pointed out in expression (2), is not a very interesting evaluation from an economic point of view, since a net dissociation occurs between the efficiency and the costs required to obtain it.
F2 ðxÞ ¼ min ci ci ðxÞ
ð2Þ
. Thermo-economic. Specifically, the objective function that ensues from the former is written as the ratio of annual running cost and the flow of exergy produced by the system [4,5].
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According to this formulation, the OF is founded on methods like the theory of energy cost (TEC) [5,6] or the theory of functional analysis (TFA) [7,8], which share out the running costs among the various components as a function of the inefficient energy flow, ci(x), generated by each one of them, defined by the difference between the incoming inefficient energy flow, relative to the fuel and the outgoing inefficient energy flow relative to the energy products obtained by each single component ‘‘i’’ [9–11]. F3 ðxÞ ¼ min ðZi þ cfi i ðxÞ
ð3Þ
3. Working considerations In current market conditions it is difficult, in the area of techno-economic analysis and of acquisition evaluation, to use two openly contrasting and not easily reconciled requirements, such as: economic savings; energy and environmental savings. In fact, the potential purchaser pays attention exclusively to evaluation of economic profitability and only through legislative imposition will he consider other aspects not strictly economic. Furthermore, from the study of evaluation methods, available in the wealth of literature on the subject, it can be deduced that both the thermal-economic analysis methods and the techno-economic analysis methods, although effectively adapting themselves to the optimisation of individual plants, cannot, however, be used as such for the comparative study of plant solutions having differing technological maturity. This is because the economic examination of plant alternatives, at parity of efficiency in energy terms, often leads back to the following schematisation [10]: case 1—contained fixed costs but high variable costs; case 2—considerable fixed costs but moderate variable costs. This implies that the alternatives referring to the first case (commercially established technologies) tend, in an energy raw materials market undervalued with respect to the real scarcity of availability, to prevail over those assimilable to the second case (of a technological innovative character), which while appreciable from a efficiency and/or environmental aspect, have high investment costs [11].
4. Working hypothesis To this purpose the aim of this paper is to evaluate and illustrate the techno-economic feasibility of the installation of a cogeneration group without neglecting the thermodynamic and environmental aspects.
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By means of the definition of a mathematical model, below denominated technoeconomic, inspired by the one realised in [1,2,12] the optimum plant in terms of size and running mode is defined each usable technology. Moreover, to obtain more accurate and efficient running, this model was constructed in such a way as to be able to provide functional diagrams of the co-generative plants in the time span relative to the tariff rates (laid out below). Successively reformulating the model in a framework to evaluate the thermodynamic and environmental aspects, precisely denominated thermo-environmental, the previously obtained results are estimated so as to be able to evaluate the requirements (efficiency, emissions etc.) and/or specific situations, to supply a possible objective approach to the concept of ‘‘externality assessment’’. 5. Structure of the model and evaluation procedure With the purpose of achieving consistent savings, in energy and economic terms, control of the evolving working conditions of the plant itself over a period of time is fundamental. Taking what was achieved in [1,12] as a starting point the proposed evaluation model is completely defined once established: 1. decisional variables; 2. the constraint functions: efficiency constraints; energy balance constraints; 3. the techno-economic objective function; 4. the thermo-environmental objective function. The optimal running point is obtained by determining the value that the decisional variables have to assume, shown in Table 1. To determine the region of the admissible decisional variable values suitable constraint functions are used, identified as follows: 5.1. Efficiency constraints In the sphere of normal working both the primary engine and the auxiliary boiler have to respect the nominal maximum power defined in the planning phase. 5.2. Energy balance constraints In this case three groups of equations can be identified, that is: 5.2.1. Electric balance constraints Pe;cg kj ð’Þ þ Pea;kj ð’Þ ¼ Per;kj ð’Þ þ Pec;kj ð’Þ
ð4Þ
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Table 1 Decisional variables Thermal power supplied by fuel to the co-generative group (kw) Power supplied by the fuel to the conventional boiler (kw) Thermal power supplied by the fuel al post-combustor (kw) Co-generated electric power (kWe) Electric power yielded to the electric grid (kWe) Electric power withdrawn from the electric grid (kWe) Maximum power used with ENEL (Kwe) Co-generated thermal power (kWt) Thermal power supplied by the conventiona; auxiliary boiler (kWt) Thermal power dissipated into the environment (kWt)
Pf,cg Pf,cc Pf,pc Pe,cg Pec,cg Pea,cg Pei Pt,cg Pt,cc Pt,dis+Pt,diss
where the indexes take account that, in the case of electric energy, the moment of time when the purchase or sale takes place is significant. More precisely, with ‘‘k=1. . .12’’ the month is defined, with ‘‘j=1. . .(k)’’ the day (with (k) the function of the month is considered) and with ‘‘’=1. . .48’’ the significant time span, which in the current electric tariff regime corresponds to half an hour. Assuming that the primary engine always runs at the nominal maximum power, the coefficient kj(’) only takes on the values 1 and 0, respectively indicating whether the primary engine in the time span ’ on day j in the month k has to work or not [13]. 5.2.2. Thermal balance constraints Pt;cg kj ð’Þ þ Pt;cc lk ljð’Þ þ Pt;pc kj ð’Þ 5 Ptr;kj ð’Þ
ð5Þ
In this case the introduction of the coefficients and l are not imputable to the cost factor but exclusively serve to obtain the running moments respectively of the primary engine with possible post-combustor and of the auxiliary boiler, from which to extrapolate the load diagrams. 5.2.3. Capacity constraints Pei 5 Pea;kj ð’Þ Pe;cg 5 Pec;kj ð’Þ
ð6Þ
That represent the obvious capacity constraints, inherent in the maximum power used and that yielded by the supplying company. 5.3. System variably constraints Pt;x 5 0
Pe;y 5 0 Pf;z 5 0
8x; y; z
that is all the system variables must be non negative.
ð7Þ
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6. ‘‘Techno-economic’’ objective function To represent the co-generative theory, with reference to the movement of money generated, the investment is defined as a series of expenditures and incomes. In the formulation of the objective function proposed it was decided to maximise the Net Annual Gain, NAG, which leads back to evaluating the residual incomes after covering the amortisement rate [5,14,15]. This with the precise intention of the benefit that can be gained in the light of the costs needed to realise it: annual cash flow; annual amortisation rate. The annual cash flow, ACF, is expressed as the difference between running income and expenditure. The incomes correspond both to effective money transfers and to costs avoided compared to conventional solutions. The expenses correspond to the extra running costs sustained for the realisation of the co-generative solution [15]. The annual amortisement rate, represents the fixed amount of capital investment imputable to the working year [16]. The various costs and gains entries of the ACF are laid out in detail both in the absence, Table 2, as well as in the presence of cogeneration, Tables 3, 4 and 5. The objective function obtained from them is the following: OF1 ¼ maxNAG ¼ maxðACF AmmÞ ¼ n max Rea;sc þ Rt;sc þ Iea;sc þ Ripe;sc þ If; sc Cea;cg Iea;cg Cipe;cg o
Ieau;cg Cf;cg If; cg Cf;cc If;cc Cm;cg þ Rec Amm
ð8Þ
7. Thermo-environmental objective function In this phase the aim is to evaluate the thermo-environmental impact of the previously optimised plants. Therefore the sizes and the running modes obtained from the previous simulation are imposed and two appropriate coefficients are introduced. Table 2 Annual cost obtained in absence of co-generation Electricity Aquisition of electric energy from the ENEL grid Electric energy taxes Use of electric energy power
Rea,sc=k j j Kea,sc,kjj.Per,kjj.y Iea,sc=Yea,sc.k Per,sc,k Ripe,sc=Kipe.k Per,sc,k
2.1 2.2 2.3
Fuel Acquisition of thermal energy required Taxes on fuel
Rt,sc=Kf,sc.k (Ptr,sc,k /cc) If,sc=Yf,sc.k (Ptr,sc,k/cc)
2.4 2.5
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Table 3 Annual costs sustained in the co-generative setup Electricity Cea,cg=k j ’ Kea,cg,kj’.Pea,cg,kj’. Iea,cg=Yea,cg.k Pea,cg,k
3.1 3.2
Cipe,cg=Kipe,cg.k Pea,cg,max,k Ieau,cg=Yeau,cg.k Pe,cg,k
3.3 3.4
Cf,cg=Kf,cg.k Pf,cg,k If,cg=Yf,cg. k [Pf,cg,k-%x.Pe,cg,k] %x: tax-exempted fuel [kWhexempted fuel/kWhe] [18]
3.5 3.6
Fuel for the conventional boiler Taxes on the aquisition of fuel for the boiler
Cf,cc=Kf,cc.k Pf,cc,k If,cc=Yf,cc.k Pf,cc,k
3.7 3.8
Maintenance Additional maintenance costs
Cm,cg=Km,cg.k Pe,cg,k
3.9
Acquisition of electric energy from the ENEL grid. Taxes relative to the withdrawal of electric energy from the ENEL grid Power used relative to the aquisition of electric energy Taxes on self-produced electric energy. Fuel Fuel for co-generation Taxes on aquisition of fuel for co-generation
Table 4 Annual gains obtained through co-generation Gains from electricity yield Yielding to grid
Rec=k j ’ Kec,cg,kj’.Pec,cg,kj’.
4.1
Table 5 Annual amortisement through co-generation Amortisement Investment for co-generation
Amm=(INcg INsc)/n
5.1
A thermodynamic coefficient that evaluates the thermodynamic aspects—this approach requires the detailed knowledge of the energy flows for every component and the energy interactions present among the various components. This translates into a considerable mass of data to elaborate according to one of the methods available in the specialist bibliography [7,8,17]. To slim down the model the determination of exergetic efficiency was employed, by means of what is defined as the direct method, which enables the exergetic efficiency to be obtained through the electric and thermal efficiencies, as expressed in the following relation: ex ¼ ½el þ "t ð1 Ta=ToÞ where " is the possible deviation between heat available and heat exploited.
ð9Þ
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Once the exergetic efficiency ex is determined for the individual plant, the most efficient plant is identified as the reference plant and then the (unitary exergetic coefficient) CEX is identified [4,6], as the ratio of the exergetic efficiency of the reference plant, ex,r, and the efficiency of the plant examined ex,i, that is: CEX;i ¼
f = p r=
f=
p i¼
ex;r =ex;i 5 1
ð10Þ
This coefficient, which is greater than unity relative to the greater inefficiency of the tested plant compared to the reference plant, will be used directly in Table 3 in expressions 3.5–3.9, with the aim of penalising the less efficient solutions and at the same time keeping the weight of irreversibility high, obtaining the expressions shown in Table 6. An environmental coefficient estimating environmental impact and penalising the less efficient plants—unfortunately, despite the existence of European and international directives in this respect, only few States have introduced, into their norms, adequate limits for the needs encountered. It follows that respect of the norms aimed at safeguarding the environment, does not in reality guarantee eco-compatible plants. In this regard an ad hoc coefficient, CVIATOT, is defined, equal to 1+CVIAi, which cuts into fuel costs in the form of tax increases as shown in Table 7, in the expressions 7.1 and 7.2. The coefficient CVIAi (environmental impact evaluation coefficient), calculated as a function of the limits of polluting emissions (LM) and of the entity of relevant polluting emissions (ER), for each component ‘‘i’’ to be kept under control, therefore can be defined according to the following expression:
LM ER CVIAi ¼ 1
ð11Þ LM Table 6 Annual costs sustained introducing the coefficient Cex Annual costs ‘‘exergonomic’’ Fuel for co-generation Taxes on co-generation fuel
C*f,cg=Kf,cg.k Pf,cg,k.CEX I*f,cg=Yf,cg.k [Pf,cg,k %x.Pe,cg,k].CEX %x: tax-exempted fuel [kWhexempted fuel/kWhe] [19]
6.1 6.2
Fuel for the boiler Taxes on boiler fuel
C*f,cc=Kf,cc.k Pf,cc,k.CEX I*f,cc=Yf,cc.k Pf,cc,k.CEX
6.3 6.4
Table 7 Annual costs sustained introducing the coefficient CVIAi Annual costs ‘‘environmental’’ Taxes on primary motor fuel Taxes on boiler fuel
I**f,cg=k I*f,cg,k.CVIATOT I**f,cc=kI*f,cc,k.CVIATOT
7.1 7.2
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where, is the hazard index attributed to compound ‘‘i’’. In this paper for ease of calculation this index was set equal to unity. Tables 6 and 7 show the modified cost entries (indicated by * and **), used to obtain the objective function of the optimised model proposed in the formulation denominated thermo-environmental, giving: n OF2 ¼ max NAG ¼ maxfACF Ammg ¼ max ½Rea;sc þ Rt;sc þ Iea;sc þ Ripe;sc þ If ;sc o
Cea ;cg Iea ;cg Cipe ;cg þ Ieau;cg Cf ;cg If ;cg
Cf;cc Cm ; cg þ Re ; c Amm ð12Þ
The result obtained will be used to quantify the cost, in thermo-environmental terms, relative to one certain technology, ‘‘i’’, rather than to another [4,17], by means of the difference indicated by Fi, between the result of the first simulation, distinguished by OF1i, and the result of the second simulation OF2i: Fi ¼ OF1i OF2i
ð13Þ
8. Application and analysis of the results Imagining, in a not too distant future, the diffusion of a relevant number of high efficiency cogeneration power stations and attributing a much less marginal role than at present to electricity and heat generation spread over the area, a real case test was performed on a Calabrian food conservation company ‘‘Giacinto Callipo conserve alimentari srl’’, for the following list of reasons: size being such that its energy needs can be covered by small to medium capacity plants; working that necessitates thermal and electric demand at the same time; location of industrial activity not far from urban settlement. This company, fitted with a conventional boiler and a co-generative endothermic plant currently in the testing phase, works on the preparation and processing of tuna fish. By means of a series of visits on the spot, a study of the working cycle was carried out, producing the thermo-electric data illustrated in Fig. 1, relative to the threeyear period from 1995 to 1997, so as to arrive to the discrete distribution in hourly bands of the energy requirements of a typical working day, as summarised in Tables 8 and 9. Three endothermic and two fuel cell plants, of a power compatible with the requirements obtained, were used for the economic analysis, their purchase and maintenance costs, supposing the use of the same fuel in the company, are summarised in Table 10.
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Fig. 1. Thermal and electric demand prevision for the years after 1997. Table 8 Balance of annual electric consumption in the three-year period 1995/1997 Years
kWh expended
Cost kWh (E)
Total cost kWh +employed power (E)
1995 1996 1997
684 575 563 700 660 900
45 726 40 364 49 224
64 035 58 674 67 533
Table 9 Balance of annual thermal consumption in the three-year period 1995/1997 Years
Kg expended
Annual cost (E)
1995 1996 1997
128.900 163.600 181.680
33.855 38.512 41.390
Table 10 Comparative energy costs of co-generative systems Plant
Plant cost (E/kWe)
Maintenance cost (E/kWh)
ICE 330 kW ICE 279 kW ICE 200 kW PAFCpa (SOFC+GT)pa PAFCsa (SOFC+GT)sa
619.75 790.18 764.68 1.342.78 1.962.53 981.26 1.084.56
0.01239 0.01136 0.01239 0.01183 0.01547 0.01033 0.01291
a
p=Market price of initial trading; s=market price of established trading.
It should be pointed out that a PAFC (phosforic acid fuel cell) cell was chosen for the fuel cell technologies, being the most available commercially and the best documented, and an SOFC (solid oxide fuel cell) combined with a gas turbine, GT, which is the most efficient solution for this technology in terms of electric efficiency. In
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addition, two different cost hypotheses were elaborated for the latter technology, cautiously, with respect to the excessively optimistic indications provided by the manufacturers. In the first hypothesis reference is made to prices in the initial phase of commercialisation, indicated by PAFCP and (SOFC+GT)P, in the second to prices presumed in the commercial development phase, PAFCS and (SOFC+GT)S. In the financial reference scenario, in which special attention has been paid to the economic variability reported in Table 11, the application of the optimised technoeconomic model enabled the determination, for the various plant solutions examined, of optimum sizing and running mode, with the aim of maximising the economic payback of the investment. From evaluation of the results obtained testing the ICE (Internal Combustion Engine) in the production cycle under examination, Table 12, the best result in terms of net annual gain is obtained from the 330 kW group. In detail the optimal functional trend of this group shown in Table 13 and in Fig. 2, provides for: Table 11 Values of the main economic variables Discount rate on money Annual inflation rate Bank loan rate Tax burdens Percentage of own capital
5% 2.5% 12% 30% 100%
Table 12 Balance of techno-economic simulation of plants with alternative engine Plant type Economic parameters
ICE 330 kW
ICE 200 kW
ICE 279 kW
Investment (E) Annual cash flow (E/years) Plant working life (years) Amortisement (E/years) Net annual gain (E/years)
231.372.70 47.528.50 13 17.792.46 29.730.87
142.025.60 34.263.82 13 10.924.61 23.338.69
219.019.00 56.088.25 8 27.377.38 28.710.87
Fig. 2. Trend of 330 kW thermo-electric cogenerator supply.
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running only in company working hours, 2700 h/year; yield to grid of about 100 kWe from 7.30 am to 19.30; withdrawal from the grid in non-working hours of about 80 kWh for about 3850 h/year. As far as the other groups are concerned, it should be pointed out that the 279 kW ICE group, in which the trend of the coefficients kj’ and lkj’ is reported in Table 14, gives an economic result slightly inferior to the former, but is characterised for optimal running, Fig. 3, providing for continuous activation throughout the whole day, which however means a consistent reduction in its working life. While it can be inferred from analysis of the economic results of the techno-economic simulation on two innovative co-generative plants, shown in Table 15, that the solutions, in terms of net annual Gains, under both cost hypotheses, provide poorly competitive results, however, examination of the NAG in the light of the cash flow generated, it can be deduced that the gap is reduced as was presumed, almost exclusively to the differing purchase cost of traditional compared to innovative plants, while the other factors are sufficiently comparable. From the functional diagrams, Figs. 4 and 5, poor efficiency of the SOFC+GT is found from the thermal aspect, largely compensated by the greater and economically more significant electrical efficiency, together with a useful lifespan comparable to the 330 kW ICE plant for both of the two cells used. Moreover, from a sensibility analysis carried out on some economic indexes, thoroughly documented in literature, NPV (net present value), IRR (internal rate of return) and PI (profitability index), shown in Figs. 6, 8 and 10, the great competitiveness of the endothermic compared to the fuel cell motor, can be inferred. Only under the developed market cost hypothesis can a comparison between a plant with ICE and one with fuel cells be made. It should be pointed out, however, under this hypothesis, despite a positive NPV index the cells allow a maximum IRR of 10% without going beyond the limit of useful lifespan. In the thermo-environmental simulation, Figs. 7, 9 and 11, there is a trend inversion in which the endothermic group, while presenting a positive NPV both for 10 and 13 years, does not enable the capital to be recouped, without going beyond the limit of useful plant life with an IRR of 5%. While both the PAFCS and the SOFC+GTscontinue to show a positive NPV index in all the referenced years and an updated payback rate of at most 10%, sufficient to remunerate the capital invested exhibiting a profitability index greater than 0.5 in both cases. Finally, from the analysis of Table 16 in which the values shown by the indexes CEX (unitary exergetic coefficient) and CVIATOT (environmental impact evaluation coefficient) it is pointed out how great differences exist in the exergetic sphere among the co-generative motors examined, with deviations greater than 20–25%. All of this translates into a waste of energy resources that in the specific case is equal to about 650,000 kWh for a year. To gather the potentiality of the proposed evaluation procedure and to avoid the analysis of solutions in themselves not economically acceptable, the thermo-environmental simulation, its data summarised in Table 17, was limited to the innovative
Table 13 Coefficient kj’ e lkj’ trend for the 330 kW endothermic engine
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Table 14 Coefficient kj’ e lkj’ trend for the 279 kW endothermic engine
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Table 15 Balance of techno-economic simulation of cell fuel plants Plant type Economic parameters
PAFCP
PAFCS
(SOFC+GT)P
(SOFC+GT)S
Investment (E) Annual cash flow (E/years) Working life of plant (years) Amortisation (E/years) Net annual gain (E/years)
335.697.00 36.647.27 12 25.822.84 10 824 42
245.317.00 36.647.27 12 18.870.30 17 776 45
508.296.90 42.085.56 12 39.099.40 2 930 89
280.900.90 43.836.35 12 21.607.52 22 228 82
Fig. 3. Trend of 279 kW thermo-electric cogenerator supply.
Fig. 4. Trend of optimal thermo-electric fuel cell PAFC supply.
technologies and to the more advantageous groups among the endothermic systems examined. From analysis of data obtained from the simulations, determining the value of the coefficient Fi (difference between the result of the first simulation, OF1i, and the result of the second simulation OF2i) shown in Table 18, it is pointed out that the
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Fig. 5. Trend of optimal thermo-electric cycle SOFC+GT supply.
Fig. 6. Net present value—techno-economic data simulation.
Fig.7. Net present value—thermo-environmental data simulation.
Fig. 8. Internal rate of return—techno-economic data simulation.
greater penalisation occurs precisely with the plants which are less efficient from the thermo-environmental point of view. It follows that the thermo-environmental simulation makes the fuel cell competitive in virtue of their greater thermodynamic efficiency. Indeed under the hypothesis of consolidated prices, the (SOFC+GT)s plant thanks to its high electrical efficiency,
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Fig. 9. Internal rate of return—thermo-environmental data simulation.
Fig. 10. Profitability index—techno-economic data simulation.
Fig. 11. Profitability index—thermo-environmental data simulation. Table 16 Thermo/environmental coefficients for compared co-generative plants Plant type Coefficients CEX (unitary exergetic coefficient) CVIATOT (environmental impact evaluation coefficient)
ICE 279 kW
ICE 330 kW
ICE 200 kW
PAFC
(SOFC+GT)
1.189 1.190
1.268 1.165
1.373 1.193
1.115 1.009
1.000 1.012
Table 17 Balance of the thermo-environmental simulation Plant type Economic parameters
ICE 330 kW
PAFCP
PAFCS
(SOFC+GT)P
(SOFC+GT)S
Investment (E) Annual cash flow (E/years) Working life of plant (years) Amortisation (E/years) Net annual gain (E/years)
231.372.70 28.979.43 13 17.797.62 11 181 29
335.697.00 36.647.27 12 25.822.84 10 824 42
245.317.00 36.647.27 12 18.870.30 17 776 45
508.296.90 42.085.56 12 39.099.40 2 930 893
280.900.90 43.836.35 12 21.607.52 22 228 82
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P. Fragiacomo, D. Gambarotti / Applied Energy 71 (2002) 127–146 Table 18 Comparison of techno-economic and thermo-environmental results Objective functions Plant type
OF1i (E)
OF2i (E)
Fi=OF1-OF2 (E)
Fi/ OF1i
ICE 330 kW PAFCp PAFCs (SOFC+GT)p (SOFC+GT)s
23.338.69 17.611.70 24.516.73 2.930.89 22 640 44
11.181.29 10.824.42 17.776.45 2.930.38 22 050 64
12.156.88 6.786.76 6.739.76 202.451.10 589.79
0.520 0.385 0.270 0.068 0.030
(about 60%) and to its low thermo-environmental penalisation (Fi/ OF1i=3%), achieves a result in terms of NAG double that achieved by the 330 kW ICE group, which instead is greatly penalised from the thermo-environmental point of view (Fi/ OF1i=52%).
9. Conclusions In this paper, considering the current trends in the subject of energy rationalization, in terms of use and environmental compatibility a process of evaluation for traditional and innovative co-generation energy systems was created. The trend of optimal technical-economic use was determined from the application of this process to an actual case. A comparison and evaluation of exergy and considerations of environmental characteristics led to optimal thermo-environmental system results. From the results of the study it was determined that the economic convenience analysis even though, it is often a decisive factor in the choice of a cogenerative system, does not necessarily supply a complete evaluation.
References [1] Arcuri P, Florio G, Fragiacomo P. Impiego della cogenerazione nel comparto industriale. La Termotecnica, dicembre 1996. [2] Arcuri P, Belli M, Florio G, Fragiacomo P. Optimal design of small size cogeneration plants with particular reference to quality of thermal regeneration. In: Proceedings of TAIES ’97 thermodynamic analysis and improvement of energy system. Pechino, Cina, 10–13 June 1997. p. 277. [3] http://www.antares.it/ndenardi. [4] Santarelli M, Borchiellini R, Calı` M. Considerazioni sull’ottimizzazione termoeconomica di impianti energetici. 53 Congresso Nazionale Ati, Firenze, 1998. [5] Arena AP, Calı` M, Santarelli M. Confronto di metodi di analisi termoeconomica applicati ad un sistema termodinamico classico di cogeneration. Atti del IX Congresso ‘‘S. STECCO’’. Milano: Tecnologie e Sistemi Energetici Complessi; 26/27 giugno 1997. [6] Arena PA, Calı` M, Santarelli M, Borchiellini R. Un esempio di applicazione termoeconomica a un caso reale di centrale termoelettrica a ciclo combinato. 51 Congresso Nazionale ATI. Udine; 1996.
146
P. Fragiacomo, D. Gambarotti / Applied Energy 71 (2002) 127–146
[7] Frangopoulos CA. Thermoeconomic functional analysis: an innovative approach to optimal design of thermal systems. Second Law Aspects of Thermal Design. ASME; 1984. [8] Frangopoulos CA. Optimal synthesis and operation of thermal systems by the thermoeconomic functional approach. Journal of Engineering for Gas Turbines and Power 1992;114. [9] Silvestrini M. Energia degli impianti, Energia ed economia, Politecnico di Milano. Corso Energia; 1991. [10] Baccarini C, Benedetti M, Borghesi A, Bortoli G. Calcoli di convenienza economica: casi e problemi. Padova: CEDAM; 1984. [11] Salvi D. Una metodologia semplificata di analisi di impianti cogenerativi a metano di piccola e media taglia. Atti del Convegno Nazionale Gruppi Combinati Prospettive Tecniche ed Economiche; 1993. [12] Arcuri P, Florio G, Fragiacomo P. Valutazioni Energetiche di Impianti Cogenerativi alimentati a Metano. CH4 Energia e Metano; 1996;(3/4):24, Maggio-Agosto. [13] Arcuri P, Florio G, Gagliardi M, Scornaienchi NM. Dimensionamento ottimale di impianti cogenerativi con accumulo termico. Atti del 6 Convegno Nazionale ATIG. Bari; Novembre 1997. p. 211. [14] Florio G, Fragiacomo P. Confronto Tecnico Economico fra una Cella a Combustibile (PAFC) ed un Motore a C.I. dotato di Convertitore Catalitico per la Generazione di Elettricita` e Calore. Atti del 5 Convegno ATIG, vol. V. Rimini; 14–16 Novembre 1995. p. 145. [15] Consonni S, Macchi E. Rassegna critica dello stato dell’arte dei sistemi cogenerativi alimentati a gas naturale. Libro Bianco sulla Cogeneration, volume terzo, 11; 1997. [16] Panati G, Golinelli GM. Tecnica economica industriale e commerciale, vol. 4. Roma: La nuova scientifica; 1991. [17] Stoppato AL. The Exergetic Analysis for Energy System Diagnosis in Proceedings of ESDA, Montpellier; 1–4 July 1996. [18] Petrecca G. Approfondimento dei temi della cogenerazione CSE Tecnosud srl, Roma; 13–14 maggio 1998.