Upgrading EU Directive with rational exergy model.

INTRODUCTION

According to projection data published by the International Energy Agency (OECD/IEA 2006a), cogeneration, or combined heat and power (CHP), systems may reduce [CO.sub.2] emissions by 0.3 Gt/yr by the year 2050 and may increase to 1.4 Gt/yr if distributed CHP systems penetrate the HVAC market (EU 2006a). When rational exergy benefits are factored in, the actual carbon wedge may in fact increase to 3 Gt/yr in 2050 (Kilkis 2007a). In order to quantify the energy benefits of CHP systems, the European Union has issued Directive 2004/8/EC (EU 2004) and CEN/CENELEC Workshop Agreement CWA 45547 (CEN 2005). CWA 45547 provides default values for the analysis and rating of CHP systems in terms of primary energy savings. This agreement (CWA 45547) emphasizes that a combined-cycle thermodynamic process, whether central or distributed, may only qualify for CHP status if it provides both heat and electric (or mechanical) power to consumers outside the CHP site boundary. Therefore, combined-cycle electric power plants (single-fuel input, single output--electric power to the consumer), condensing boilers, or combined systems (single-fuel input, single output--heat only to the consumer) are not eligible for CHP incentives. In this respect, CWA 45547 describes the site-consumer boundary at the energy meters (Figure 1). This is also important because the rationale of the exergy supply and demand, thus environmental sustainability, must also be metered (Figure 2).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

This paper shows that measuring temperatures on the boundary, within the plant site, and in the consumer area is equally important if a comprehensive sustainability analysis is to be carried out by a rational exergy analysis. The importance of temperatures and the quality of the energy supply is emphasized; for example, if the site generates, supplies, and meters cold water to the consumers through an absorption chiller at the site, not only may the site become a trigeneration (power, heat, and cold) system, but also the exergy rationale is different than if the absorption chiller belongs to the consumer area and the site remains a cogeneration system. In any case, conventional energy metering cannot rate the exergy in the cold water supply and exergy used in the consumer area unless all the temperatures involved in the exergy analysis are metered. In this study, Figure 2 was taken from CWA 45547 and then modified to factor in the rational exergy management model by defining the essential temperature measuring points and the environment reference temperature. This figure shows a CHP site with a cascaded electric power generator, or polygenerator, exemplified by the HEGEL project (EU 2006b). This polygenerator has two stages of power generation. The first stage is an internal combustion engine (ICE). In the second stage, part of the ICE waste heat is utilized in a bottoming steam engine (SE) or a micro steam turbine (ST), which is located in the CHP site. Because, the HEGEL polygenerator delivers heat to the consumer area, it is a CHP system.

This paper explains that because Directive 2004/8/EC (EU 2004) is based only on the first law of thermodynamics, it does not recognize the importance of site-consumer boundaries and essential temperatures, which are important for rational exergy management, to achieve a wider perspective for sustainable designs and applications. This is especially important when the rationale in matching the exergy (quality) of energy resources with the exergy required by different applications in the built environment has to be granted. For example, the HEGEL polygenerator may establish a better exergy rationale, but this added benefit cannot be recognized by Directive 2004/8/EC without the exergy rationale. To achieve this goal, a new model is needed, which should also be suitable to be adopted for the Directive. The rational exergy management model (REMM), which was recently developed by Kilkis (2007b), can upgrade and enable the Directive to reveal and quantify hidden sustainability benefits of CHP systems and empower it with optimization algorithms. REMM accommodates both the CHP plant boundary and the users within a given built environment and enables optimum rationale between the supply and demand exergies; i.e., it shows how an optimum exergy balance can be achieved in the exergy mix of the built environment.

ANALYSIS

Summary of EU Directive 2004/8/EC

With the best available technology, conventional electric power generation efficiency is about 60%. Directive 2004/8/EC is a response to the European Parliament resolution of November 15, 2001, for developing a green paper for incentives to encourage more efficient power plants, including CHP systems (EU 2004). Its quantitative Annexes I and II cover the following technologies and follow a two-phase approach:

a. Combined-cycle gas turbine with heat recovery (must be supplied to external consumers)

b. Steam back-pressure turbine

c. Steam condensing extraction turbine

d. Gas turbine with heat recovery

e. Internal combustion engine

f. Microturbines

g. Stirling engines 

h. Fuel cells

i. Steam engines

j. Organic Rankine cycles 

k. Any other technology or combination under the definition "cogeneration" shall mean the simultaneous generation in one process of thermal energy and electrical and/or mechanical energy.

According to Phase 1, generated electrical energy is considered to be produced from cogeneration when an overall (heat and power) annual efficiency of 75% is reached (80% in types (a) and (c) above). These percentages also represent threshold values for CHP incentives and status, provided that useful net heat (and/or cold) is simultaneously provided to the customer area. Below these values, electricity produced is subject to the power-to-heat ratio, C, which is defined in Equation 1. The term C may also be written in terms of heat and power generation efficiencies, namely, CHPH and CHPE (EU 2004). If C is not known, the default values in Table 1 may be used for types (a), (b), (c), (d), and (e).

Table 1. Default Power-to-Heat Ratio C (EU 2004)

Type of CHP System                   Default Power to Heat Ratio C

Combined cycle with heat recovery                             0.95
Steam back-pressure turbine                                   0.45
Steam condensing extraction turbine                           0.45
Gas turbine with heat recovery                                0.55
Internal combustion engine                                    0.75

[E.sub.CHP] = C*[H.sub.CHP] {[H.sub.CHP]>0} (1)

[[CHPE.sub.[eta]]] = C.[[CHPH.sub.[eta]]] {[H.sub.CHP]>0} (2)

According to Phase 2, "high-efficiency cogeneration" must fulfill the following criteria:

* Production from cogeneration units shall provide primary energy savings calculated according to Equation 3 of at least 10% compared with the references for separate production of heat and electric power.

* Production from small-scale and microcogeneration units providing primary energy savings may qualify as high-efficiency cogeneration.

Percent primary energy savings, PES, is calculated from Equation 3, whose derivation is explained in Appendix A with an analog model developed in this study. Equation 3 can be simplified by introducing C from Equation 2. The result is shown in Equation 4.

PES = [1-/[[[CHPH[eta]]/[RefH[eta]]]+[[CHPE[eta]]/[RefE[eta]]]]] X 100 (3)

PES = [1 - 1/[CHPH[eta]](1/[RefH[eta]] + C/[RefE[eta]])]] X 100 (4)

The Council of the European Union has set a target for establishing harmonized efficiency reference values before February 21, 2006. However, there are ongoing debates without any final consensus, and harmonization is incomplete (CEFIC 2005). Some progress was made in 2006, when a comprehensive table was prepared for harmonized efficiency reference values, which were put into a matrix showing year of system and year of construction (DG TREN 2006, Table 7.1). Harmonized values are necessary to factor in the year of plant construction, type of fuel, fuel mix, climate conditions, and realistic data that are important for rating and classification of heat and power generating units, whether they are combined or separated. In this study, a sample table was prepared after reviewing actual field data available in the literature (OECD/IEA 2006a, 2006b; Badami et al. 2006). Individual EU member states such as Portugal have also taken their own steps of transposition of the Directive (Nuno et al. 2007).

Critique of the Directive Using REMM

Although Equation 4 includes C, Directive 2004/8/EC cannot optimize C for maximum PES for given applications and other sustainability conditions; a simple differentiation of Equation 4 to seek for an optimum C yields a trivial solution, C [right arrow] [infinity] which represents an infinite energy efficiency that is not admissible. If a CHP system is operating with a thermal efficiency CHPH of 0.55 and C is then 0.6 from Equation 2, CHPE is 0.33. According to Equation 3 or Equation 4, PES

PES = [1 - 1/[[0.55/0.90] + [0.33/0.52]]] X 100 = 19.7%.

According to the Directive, this system qualifies for CHP because PES is greater than 10%. However, Equation 4 neither shows how the system may be improved by utilizing the exergy of the input fuel better nor does it ask for the type of fuel. In other words, another CHP unit with the identical efficiencies given above but using a different type of fuel having a different exergy cannot be differentiated from the above example. By the same token, the temperature of waste heat provided to the consumers and the minimum exergy required to satisfy those consumers do not make any difference according to Equations 3 and 4. That is why it is so important to know, adjust, and optimize these temperatures for a better exergy efficiency and rationale for utilizing energy resources for sustainability.

Another point of concern is the insensitivity of Equation 3 to the quality of services provided. For example, consider another CHP unit with a thermal efficiency [CHPH[eta]]. of 0.40, which generates electric power with [CHPE[eta]]. of 0.42 by using part of the waste heat to generate additional electric power. Obviously, this unit delivers a higher energy quality because it provides more electricity, which has a higher exergy than the waste heat. But according to Equation 3, this unit has almost the same PES (20.1%), yet its exergy benefits, thus the opportunity of doing more useful work(ASHRAE 2004); the second law of thermodynamics enables, remain missing. The same argument is also present in the 2004 ASHRAE Handbook--HVAC Systems and Equipment one to see that the two different energy streams in CHP have different energy values, that heat and electricity are not interchangeable, and electrical energy is generally of higher value. Beyond the interchangeability, how missed opportunities can be captured may only become visible by a rational exergy analysis that should definitely be incorporated into the Directive. Furthermore, Equation 3 does not recognize the fact that line transmission losses for a central CHP plant may become substantial if the site and consumer area are far from each other (Equation 12). In summary, the Directive completely ignores the exergetic aspects of CHP.

REMM Upgrades 2004/8/CE Directive

When sustainability, carbon emissions, and global warming become important issues of concern, the balance among the qualities of energy supply and demand points in the built environment become very important. The common metric of the exergy balance rationale is provided by rational exergy efficiency, [[PSI].sub.R] (Kilkis 2007a, 2007b). Equation 5 is a scale about how rational is the match between the supply and demand exergies. If these do not match, harmful emissions, such as [CO.sub.2], caused by fossil fuel use increase. Because PES is related, by definition, to fossil fuels and the directive aims to lower the harmful emissions, the potential positive impact of CHP systems on the environment must be re-described, not only in terms of energy efficiency, but also rational exergy efficiency.

[[PSI].sub.R] = [[[epsilon].sub.min]/[[epsilon].sub.max]] = Minimum exergy that can satisfy an application/Actual exergy supplied (5)

For a thermal energy conversion application like the one shown in Figure 2, [[epsilon].sub.max] may be indexed to the flame temperature [T.sub.f] of the fuel and the temperature of the environment so that the application may come into thermal equilibrium [T.sub.ref]. Variable [T.sub.ref] may be selected to be the temperature of the ground, sea, or lake but preferably in close vicinity of the applications. Because outdoor air temperature is quite variable, even hourly, it should be the last option. Variable [[epsilon].sub.min] is the minimum amount of exergy that could satisfy the same task. For chemical or mechanical systems, an equivalent flame temperature may be defined (Kilkis 2007a, 2007b). Then the exergy balance may be calculated from the temperatures involved, based on the ideal Carnot cycle applied to both the supply and demand sides. According to the sign convention, for exergy to be positive both in heating and cooling processes, there are two distinct cases:

[[PSI].sub.R] = [(1 - [T.sub.ref]/[T.sub.app])/(1 - [T.sub.ref]/[T.sub.f])] {[T.sub.app] > [T.sub.ref]} (6a)

[[psi].sub.R] = [(1 - [T.sub.app]/[T.sub.ref])/(1 - [T.sub.ref]/[T.sub.f])] {[T.sub.app] < [T.sub.ref]} (6b)

For the special case, [T.sub.app] = [T.sub.ref], [T.sub.ref] may be selected in order to satisfy one of the above inequality conditions. This seemingly arbitrary selection does not affect the overall rationality of the exergy balance because all temperatures are referenced to the same [T.sub.ref] (Figure 3). Variable [[PSI].sub.R] also depends upon the kind of application that utilizes the thermal energy supplied from the system at temperature [T.sub.app]. Because Equations 3 and 4 do not incorporate the exergy component, a new [PES.sub.RCHP] equation was derived, whose details are given in Appendix A. First, Equation 6 needs to be modified for a CHP system because there are two different kinds of energy outputs, namely, electrical and thermal. According to the principal temperatures defined in Figure 3 for a CHP system, Equation 5 can be written in the following format, where exergy values for unit energy are given in Equations 8 through 11. In Equation 11, the minimum exergy demand is for space heating at a comfort indoor air temperature of [T.sub.a]. A low .[[PSI].sub.RCHP] means that most of the exergy of the fuel input ([FC.sub.1]) to the system (Plant 1) per unit energy is destroyed and opportunities of deriving more useful work from the same amount of fuel are missed. Therefore, additional fuel, [FC.sub.2] is required to make up this destruction by another plant ( Plant 2).

[FIGURE 3 OMITTED]

[[PSI].sub.RCHP] = [[[[epsilon].sub.Hmin] + C X [[epsilon].sub.Emin]]/[[[epsilon].sub.Hmax] + C X [[epsilon].sub.Emax]]] (7)

[[epsilon].sub.Emax] = (1[T.sub.ref]/[T.sub.f]) (8)

[[epsilon].sub.Emin] = (1[T.sub.ref]/[T.sub.E]) (9)

[[epsilon].sub.Hmax] = (1-[T.sub.ref]/[T.sub.app]) (10)

[[epsilon].sub.Hmin] = (1-[T.sub.ref]/[T.sub.a]) or [[epsilon].sub.Emin] = (1-[T.sub.a]/[T.sub.ref]) {[T.sub.a] < [T.sub.ref]} (11)

The first term in Equation 12 is the direct fuel spending in Plant 1) with efficiency [[eta].sub.1]. The second term is a result of compounded fuel spending in Plant 2 with efficiency [[eta].sub.2] If [[PSI].sub.RCHP] was high, the second term could be greatly avoided. If the consumer area and Plant 2 are close or integrated as in a CHP system, [[eta].sub.T] may be assumed unity. Then, Equation 12 may be simplified, if [[eta].sub.1] and [[eta].sub.2] are close to each other.

[[summation].sup.FC] = [FC.sub.1] + [FC.sub.2] = (1/[[eta].sub.1]) + (1/[[[eta].sub.2] X [[eta].sub.T]])(1-[[psi].sub.RCHP]) (12)

[[summation].sup.FC] = F[C.sub.1] + F[C.sub.2] = (1/[eta]) (2[[PSI].sub.RCHP]) {[[eta].sub.T] = 1} (13)

Because the energy efficiency terms are already included in Equation 3, the exergy efficiency component may be easily incorporated in the form of a multiplier. Details of this derivation are given in Appendix A. The new rational energyexergy savings factor [PES.sub.RCHP] becomes:

[PES.sub.RCHP] = [1 - 1/[([CHPH[eta]]/[RefH[eta]] + [CHPE [eta]]/[RefE[eta]]) X [(2[Ref[PSI].sub.RCHP])/(2[[psi].sub.RCHP])]]] X 100 (14)

[PES.sub.RCHP] = [1 - 1/[CHPH[eta](1/[RefH[eta]] + C/[RefH[eta]]) X [(2[Ref[PSI].sub.RCHP])/(2[[PSI].sub.RCHP])]]] X 100 (15)

In Equation 14, if [[PSI].sub.RCHP] is equal to [Ref[PSI].sub.R](no rational exergy improvement), then [PES.sub.R] will be equal to PES. Variables [Ref[PSI].sub.RCHP] and [[PSI].sub.RCHP] are calculated according to Equations A-6 and A-7 in Appendix A. Because all equations are based on unit exergies and unit energy and unit power, Equations 14 and 15 may be directly used to calculate compound reduction in carbon emissions if the fuel type is known.

CASE STUDIES

Parametric Analysis with REMM and Its Optimization Benefits

Equations 14 and 15 include the effects of the type of application(s), C, fuel type, fuel exergy, and exergy used (and destroyed) at the site and consumer area in calculating the primary energy savings from both the exergy and energy efficiency points of view. Therefore, Equations 14 and 15 do not only bring the desired harmonization but also the necessary comprehension to the directive. Second, this model shows that it is important to know the application(s) that are tied to the CHP system downstream and the temperatures of the input and output at the site-consumer boundaries and within the tied-in applications in order to optimize the system, including the allocation of exergy among alternative applications for maximizing the primary energy savings.

This model makes it more precise and accurate to rate different CHP systems and designs in terms of sustainability and reducing harmful emissions. The reference rational exergy efficiency value is also a function of the type or types of applications in the consumer area. This seems to make it difficult to assign a unique [PES.sub.RCHP] value to a CHP unit before it is shipped to the market. However, this is, in fact, another advantage of [PES.sub.RCHP]; if the manufacturer and consumer want to maximize the [PES.sub.RCHP] in order to increase their benefits from related private or government incentives, they need to work together in sizing and optimizing the CHP in order to achieve maximum [PES.sub.RCHP] on a case-by-case participatory approach. This policy steers both the consumer and the manufacturer away from off-the-shelf solutions toward greener and more sustainable solutions every time. If, for example, the application is indoor space heating, the reference rational exergy efficiency of the heating system, based on a ground-source heat pump (GSHP) using grid electricity, may be chosen as 0.10 (API 1975), and for the CHP plant, a typical exergy value of 0.3 may be chosen (Sugimoto et al. 2006). If the CHP unit is a high-efficiency polygenerator unit with a steam-electric bottoming cycle, such that C is 1.05 and [[eta].sub.T] is 1, then from Equation A-6, [Ref[PSI].sub.R] is 0.2024.

[Ref[PSI].sub.RCHP] = [[0.1 + 1.05 + 0.3]/[1 + 1.05]] = 0.2024

If input fuel, which is natural gas, combustion temperature [T.sub.f] is 2000 K (3140.6[degrees]F), waste heat temperature [T.sub.app] is 330 K (134.6[degrees]F) for minimum exergy use, and if electricity could alternatively be generated in a binary cycle with waste heat at a minimum temperature for electricity production [T.sub.E] of 500 K (440.6[degrees]F) and for indoor comfort heating [T.sub.a] is 293 K (68[degrees]F), then for a reference (ground) temperature [T.sub.ref] of 283 K (50[degrees]F), Equations 8 through 11 give the unit exergy terms for Equation 7: [[epsilon].sub. Emin] = (1 - 283 / 500) = 0.434, [[epsilon].sub. Emax] = (1 - 283 / 2000) = 0.858, [[epsilon].sub.Hmin]= (1 - 283 / 293) = 0.034, [[epsilon].sub.Hmax] = (1 - 283 / 330) = 0.142.

From Equation 14,

[[PSI].sub.RCHP] = [[0.034 + 1.04 + 0.434]/[0.142 + 1.04 + 0.858]] = 0.469.

If CHPH[eta] is 0.403 and CHPE[eta] is 0.423, then [PES.sub.R] from Equation 15 and Table 2 for the reference values for steam generation is

[PHS.sub.RCHP] = [1 - 1/[(0.403/0.90 + 0.423/0.52) X ([2 - 0.2024]/[2 - 0.469])]] X 100 = 32.5%

Table 2. Preliminary Reference Values

System        RefH  RefE

Steam         0.90  0.52
Process heat  0.85  0.52

The compound fuel savings according to REMM is 12.4 percentage points more (32.5%-20.1%) than what Equation 3 gives. In reality, this is 62% more fuel savings rating. Table 3 shows the difference between Equations 3 and 15 for typical CHP cases. For example, [PES.sub.RCHP] for a simple CHP is calculated by changing [T.sub.app] from 330 K (134.6[degrees]F) to 450 K (350.6[degrees]F) in the above example and C is taken as 0.6 for the calculations shown above, where CHPH[eta] is 0.55 and CHPE[eta] is 0.33. Figure 4 shows the impact of REMM in achieving an accurate rating of the attributes of CHP systems. In this analysis, [Ref[PSI].sub.R] is kept fixed at 0.198 (C = 0.97). CHPH[eta] and CHPE[eta] are also kept fixed at 0.47 and 0.46, respectively. According to Equation 3, PES is 30.4%, and it is constant, irrespective of the exergy benefits. When Equation 15 is used, [PES.sub.RCHP], which includes both energy and exergy benefits, is higher than PES. It is now also possible to optimize a CHP system. For example, the impact of C is important. If C changes from 0.97 to 0.6 (more heat output, CHPH[eta] = 0.6; less electric power, CHPE[eta] = 0.36; [Ref[PSI].sub.R] = 0.175; [T.sub.app] = 450 K; [[episilon].sub.Hmax] = 0.37), fuel savings decrease, which is shown by the broken line. This is because electric power has a higher exergy and by reducing that output of CHP, the overall benefits decrease. In contrary, according to Equation 3, PES reduces by only two percentage points (dotted line). This is an interesting case result; according to the Directive, it makes almost no difference to reduce the electric output substantially and increase the waste heat output.

Table 3. Comparison of Equations 3 and 15

         System        Directive 2004/8/EC  Corrected Directive
                         (Equation 3) PES        (Equation 15)
                                                [PES.sub.RCHP]

1  Simple CHP                        19.7%                26.6%

2  Polygeneration (EU                20.1%                32.5%
   2006b)

3  Trigeneration with                40.8%                52.6%
   heat pump

[FIGURE 4 OMITTED]

In CHP systems, Equation 7 can accommodate the special case when [T.sub.a] equals [T.sub.ref]'. Then, although [[episilon].sub.Hmin] in the above example approaches zero, [[PSI].sub.RCHP] remains a positive number but decreases to 0.436. This is because although the indoor air temperature is decreased from 293 to 283 K, which requires less exergy input, [[episilon].sub.Hmax] remains the same. In an indoor cooling application with an absorption system using heat at the same [T.sub.app] as the example given above, and if [T.sub.a] is 275 K (41[degrees]F), typical for a cold storage warehouse, then the rule governing Equation 6b applies to Equation 11, such that [[episilon].sub.Hmin] is 0.028 and [[PSI].sub.RCHP] is 0.463.

Optimization

A polygeneration system may be combined with a GSHP such that additional heat can be provided to the consumer simply by allocating part of the electrical (or mechanical) power produced by CHP to drive the heat pump. If the average heating COP is 4, and one-third of the electricity produced is consumed by the heat pump motor (X = 1/3), then CHPH[eta] is 0.967 and CHPE[eta] is 0.282, and C drops to 0.292. In this case, [[PSI].sub.CHP] slightly increases from 0.47 to 0.5, in spite of the fact that less electric power is output to consumers. [PES.sub.RCHP] increases from 32.5% to 50%. Calculations show that in allocating part of the electric power output to a GSHP has special benefits as long as there is more heat demand than electricity in the consumer area. In this case, [PES.sub.RCHP] may be maximized in terms of C by varying the amount of electric power output allocated to the GSHP. Figure 5 gives these results. Table 4 shows the numerical data prepared for Figure 5. It is interesting that while the part of the electric power allocated to the heat pump increases, the thermal efficiency exceeds one. This is an expected result because additional heat is provided from the ground through the GSHP. Both Table 4 and Figure 5 show that a GSHP trigenerator saves more fuel when more electric power is allocated to the GSHP. Yet, there must be enough electric power to drive the GSHP and the polygenerator must at least provide that much power--while C increases, the size of GSHP increases and, thus, its power demand increases. Therefore, optimization is subjected to the following constraints, namely

CHPE[eta] > [1/[COP]] (16)

CHPE[eta] [greater than or equal to] (1/[COP] + Cmin). (17)

Table 4. Effect of GSHP Size on the Performance of the Trigenerator

X     [CHPH.sub.[eta]]  [CHPE.sub.[eta]]   PES     C    [PSI]RCHP

0          0.403           0.423          20.7   1.049    0.470

0.1        0.573           0.381          26.9   0.665    0.475

0.18       0.708           0.347          31.2   0.490    0.481

0.2        0.742           0.338          32.2   0.456    0.483

0.3        0.911           0.296          36.8   0.325    0.495

1/3        0.967           0.282          38.2   0.292    0.500

0.4        1.080           0.254          40.8   0.235    0.511

0.5        1.249           0.211          44.3   0.169    0.532

0.6        1.418           0.169          47.4   0.119    0.560

0.7        1.588           0.127          50.2   0.080    0.601

X     [Ref[PSI].sub.RCHP]    [PES.sub.RCHP],      Remarks
                                         %

0         0.202              32.5            Polygeneration

0.1       0.180              38.7            Trigeneration

0.18      0.166              43.0            Optimal 1

0.2       0.163              44.0            Trigeneration

0.3       0.149              48.6            Trigeneration

1/3       0.145              50.0            Trigeneration

0.4       0.138              52.6            Optimal 2

0.5       0.129              56.3            Unfeasible

0.6       0.121              59.7            Unfeasible

0.7       0.115              63.0            Unfeasible

[FIGURE 5 OMITTED]

Equation 16 depicts the constraint that stands for the fact that the polygenerator must produce at least 1/COP unit amount of electricity in order to drive the GSHP. Equation 17 stands for the fact that the polygenerator must generate more electric power that can be delivered to the consumers in addition to what is spent by the GSHP. This is necessary to retain the CHP status of the system. However, the importance of the boundary is obvious--according to Figure 2, it is essential to know who owns the GSHP. Here, two optimality cases arise.

Optimal Case 1. If GSHP belongs to the consumer(s), then Constraint 17 is not applicable because the polygenerator provides useful heat to the consumer, including power to drive the GSHP. If, however, the polygenerator is packaged with a GSHP and marketed as a trigenerator by itself, then because the GSHP will consume electricity within the CHP boundary, the polygenerator must satisfy Equation 17, too, by providing a minimum sustainable amount of electric power to the consumer. In this case, if [C.sub.min] is taken as 0.1 (C > 1/4 + 0.1), then the optimal solution from REMM calculations, will be

X = 0.18, CHPH[eta] = 0.708, CHPE[eta] = 0.347 (rounded to 0.35), C = 0.490, [[PSI].sub.RCHP] = 0.481, [PES.sub.RCHP] = 43%.

Optimal Case 2. If the GSHP belongs to the consumer(s), then the optimal point will be determined by Equation 17, namely, C[greater than are equal to]= 1 / 4. Then the optimal solution will be

X = 0.4, CHPH = 1.080, CHPE = 0.254, C = 0.235, [[PSI].sub.RCHP] = 0.511, [PES.sub.RCHP] = 52.6%.

The trigeneration system may be used for all seasons because the GSHP may also be used for summer indoor comfort cooling and air conditioning. Figure 6 shows the schematic of the trigeneration system that can be built above HEGEL system. Here the GSHP is driven with part of the CHP power output. The remaining electricity is provided to the consumers. Cold and hot storage tanks shave off the peak loads. On the consumer site, part of the heat delivered may be used for absorption and/or liquid desiccant cooling.

[FIGURE 6 OMITTED]

RESULTS AND DISCUSSION

This paper has introduced a more comprehensive definition of fuel savings for rating and evaluating CHP systems in terms of both energy and exergy. The importance of both the quality and the quantity of the energy source used is acknowledged. It has been shown that exergy is an important metric to reveal, understand, and appreciate the real advantages of CHP systems and optimize them to minimize their environmental footprint and harmful emissions, maximize their fuel savings, and, thus, to accomplish an optimum sustainability among the conflicting factors of environment, energy, human needs, and economics. A sustainable CHP may mean an integration of several green components, which can now be optimized using REMM. On the other hand, alternative types of energy conversion and use components need to be compared and optimized, not only from the economic point of view but also from the environmental point of view. For example, the impact of using natural gas in an external combustion engine such as a steam boiler rather than an internal combustion engine such as a modified diesel engine in the HEGEL polygenerator must be speculated both from exergy and energy points of view, which cumulatively affect the emissions as given in Equation 12. An internal combustion engine-based CHP system is boosted to have little carbon emissions by using a three-way catalyst (Badami et al. 2006; OECD/IEA 2006b). In fact, the catalyst converts carbon monoxide in the exhaust to [CO.sub.2], which is actually of great concern for global warming. A typical highefficiency steam boiler, when connected to a low-efficiency steam engine, may prove to be more environmentally friendly when detailed calculations are carried out, mainly through Equation 12 and [PES.sub.RCHP] calculations.

CONCLUDING REMARKS

Table 4 reminds us that in addition to the 10% minimum PES that is required by the Directive, a minimum rational exergy efficiency standard may also be established. For example, [[PSI].sub.RCHP] could be required to be at least 0.25 greater than [Ref[PSI].sub.RCHP] . All cases in Table 4 satisfy such a condition, especially when X increases above 0 (trigeneration). Because Equations 14 and 15 are an embodiment of Equation 3, they already factor in the rational exergy efficiency to minimum fuel savings requirement of the Directive. Therefore, addition of a new minimum rational exergy efficiency standard, especially for trigeneration, seems to be trivial. However, this issue needs further discussion and probably a separate study in the future.

This paper addresses the fact that rational exergy analysis calculations depend on the selection of [T.sub.ref] Because all associated temperatures in the rational exergy analysis, which are shown in Figure 3, are referenced to the same [T.sub.ref], the final rational decisions about exergy balances, which are derived from the rational exergy analysis, are not altered. After all, according to the sample (Figure 7), which was prepared for the optimal trigeneration solution given in Table 3, column 3 (X = 0.4 in Table 4), the sensitivity of final [PES.sub.RCHP] results is small. [PES.sub.RCHP] changes 1 percentage point for every 1.5[degrees] Directive might need a default [T.sub.ref] value in the near future for C (2.7[degrees]F) change in [T.sub.ref] . Yet, one can argue that the a complete harmonization of the Directive. Without overcomplicating the current Directive, this goal may be simply accomplished by assigning a default value that is described in terms of a minimum absolute temperature difference between the [T.sub.ref] to be selected and the nearest application temperature for a given CHP case.

[FIGURE 7 OMITTED]

This issue. In the field, both thermal and electric generation efficiencies continuously change is a matter for further discussion and is an important milestone for complete harmonization of the directive depending on the application demand and, consequently, the C value changes at different part loads. Results obtained in this study are equally applicable to a daily or hourly dynamic batch analysis in order to factor in the load changes and the resulting batch performances of the CHP system. A control algorithm may be developed to optimize instantaneous performance of the CHP system, which seems to be the next step to be achieved. This study has shown that there are important issues that have not been addressed yet in Directive 2004/8/EC. Most importantly, the PES equation must accommodate the rational exergy term, which is given in this paper. Precise definition of the site-user boundary, measuring essential temperatures, and diversifying the exergy-balanced applications on the consumer side must also be emphasized. In this respect, integration of CHP with suitable heat pumps and other alternative energy systems must also be preferred and the entire energy mix in the built environment must be optimized by using REMM.

NOMENCLATURE 

C = power-to-heat ratio, dimensionless (Equation 1)

[C.sub.min] = minimum acceptable power-to-heat ratio for CHP status, dimensionless

CHPE[eta] = electrical efficiency of CHP, defined as annual electricity from CHP divided by the fuel input used to produce the sum of useful heat output and electricity from CHP, dimensionless

CHPH[eta] = thermal efficiency of CHP, defined as annual useful heat output divided by the fuel input used to produce the sum of useful heat output and electricity from CHP, dimensionless

COP = heat pump coefficient of performance, dimensionless

E = electrical energy, or power (taken unity), kWh (Btu) or kW ([Btu*h.sup.-1])

[E.sub.CHP] = useful electric output of CHP system to the consumer, kWh (Btu) or kW ([Btu*h.sup.-1])

[f.sub.c] = calorific value of fuel, kg [(kWh).sup.-1] ([lb*Btu.sup.-1])

[sigma]FC = compound fuel spending that a CHP system is responsible for unit energy or power output, kg (lb) or [kg*h.sup.-1] ([lbh.sup.-1])

[FC.sub.1] = direct fuel spending in the CHP system, kg (lb) or [kg*h.sup.-1] [lb*h.sup.-1])

[FC.sub.2] = indirect fuel spending attributable to the exergy destruction in CHP, kg or [kg*h.sup.-1] ([lb*h.sup.-1])

H = thermal energy (heat) or thermal power, kWh (Btu) or kW ([Btu*h.sup.-1])

FS = fuel savings ratio, dimensionless

[H.sub.CHP] = heat output of CHP to the consumer, kWh (Btu) or kW ([Btu*h.sup.-1])

PES = percent primary energy savings (according to Directive 2004/8/EC, Equation 3), dimensionless

[PES.sub.RCHP] = percent primary energy-exergy savings of CHP (Equation 14), dimensionless

RefFC = fuel spending at reference conditions for unit energy or power output, kg (lb) or [kg*h.sup.-1] ([lb*h.sup.-1])

R = demand resistance to fuel (analogy to electric resistance), (kWh)/kg (Btu/lb)

RefH[eta] = efficiency reference value for separate heat production, dimensionless

RefE[eta] = efficiency reference value for separate electricity production, dimensionless

[Ref[PSI].sub.R] = reference rational exergy efficiency, dimensionless

T = temperature, K ([degrees]F)

[T.sub.a] = indoor dry-bulb air temperature, K ([degrees]F)

[T.sub.app] = application inlet temperature, K ([degrees]F)

[T.sub.E] = minimum source temperature that electricity can be generated, K ([degrees]F)

[T.sub.f] = flame temperature of the fuel spent in System (i), K ([degrees]F)

[T.sub.ref] = reference temperature of the environment that any process tends to become in equilibrium, K ([degrees]F)

X = ratio of the power allocated to a heat pump motor to the power generated by CHP, dimensionless

Greek Symbols

[eta] = energy efficiency, dimensionless

[[eta].sub.T] = line transmission and parasitic losses attributable to a power plant, dimensionless

[[psi].sub.R] = rational exergy efficiency, dimensionless

[[psi].sub.RE] = rational exergy efficiency of electrical energy generation of CHP, dimensionless

[[psi].sub.RH] = rational exergy efficiency of thermal energy generation of CHP, dimensionless

[[psi].sub.RCHP] = overall rational exergy efficiency of the CHP system, dimensionless

[episilon] = useful work (exergy) that a unit thermal energy flow (fuel) can accomplish, dimensionless

[[episilon].sub.max]= unit exergy of the fuel input ([[episilon].sub.max] = [[episilon].sub.Emax] + [[episilon].sub.Hmax]) to CHP, dimensionless

[[episilon].sub.min] = minimum exergy that satisfies a given task (application) that requires unit energy, dimensionless

[[episilon].sub.Emax] = unit exergy spent in providing electricity from CHP, dimensionless

[[episilon].sub.Emin] = minimum unit exergy that could provide the same electricity, dimensionless

[[episilon].sub.Hmax] = unit exergy spent in providing heat from CHP, dimensionless

[[episilon].sub.Hmin] = minimum unit exergy that could provide the same heat for a given application, dimensionless

Acronyms

FP6 = Sixth EU Framework Programme (for research and technology development)

HEGEL= high-efficiency combined-cycle gas polygenerator for ecological local generation

REFERENCES

API. 1975. Efficient Use of Energy, pp. 49-50. New York: American Institute of Physics.

ASHRAE. 2004. 2004 ASHRAE Handbook--HVAC Systems and Equipment, Chapter 7, Cogeneration systems and engine and turbine drives. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Badami, M., A. Casetti, P. Campanile, and F. Anzioso. 2006. Performance of an innovative 120 kWe natural gas cogeneration system. Energy, August. Elsevier Science Direct.

CEFIC. 2005. Joint Statement on EU Directive. European Chemical Industries Association.

CEN. 2005. Workshop agreement, Manual for determination of combined heat and power (CHP), CEN/CENELEC Workshop Agreement (CWA) 45547. European Committee for Standardization/European Committee for Electrotechnical Standardization.

DG TREN. 2006. Guidelines for the Implementation of the CHP Directive 2004/8/EC. Guidelines for Implementation of Annex II and Annex III, draft, Council of the European Union, Directorate-General for Energy and Transport, Brussels, Belgium, June.

EU. 2005. Green Paper on energy efficiency or doing more with less. Brussels, Belgium: European Union.

EU. 2004. Directive 2004/8/EC on the promotion of cogeneration based on useful heat demand in the internal energy market and amending Directive 92/42/EEC. European Union.

EU. 2006a. HEGEL Project responds to universal need for sustainability when integrated with building HVAC. Executive Committee meeting report, October 20. Brussels, Belgium: European Union.

EU. 2006b. HEGEL: High-efficiency combined-cycle gas polygenerator for ecological local generation, Project Agreement Document, Project No. 20153. Brussels, Belgium: European Union.

OECD/IEA. 2006a. Energy technology perspectives: Scenarios & strategies to 2050 in support of the G8 plan of action. Organization for Economic Co-operartion and Development/International Energy Agency. Paris: Organization for Economic Co-operation and Development/ International Energy Association.

OECD/IEA. 2006b. World Energy Outlook 2006. Paris: Organization for Economic Co-operation and Development/ International Energy Association.

Kilkis, S. 2007a. Development of a rational exergy management model to reduce [CO.sub.2] emissions with global exergy matches, Honors thesis, Georgetown University, Washington, DC.

Kilkis, S. 2007b. A rational exergy management model for curbing CO2 emissions. ASHRAE Transactions. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Nuno, A.M., M. Eliseu, and M. Salvador. 2007. Portuguese Start-transposition of the EU cogeneration directive. Cogeneration and On-Site Power Production, January- February, pp. 45-51.

Sugimoto, S., T. Fujii, and J. Ohta. 2006. An appraisal method of exergy cost minimization for co-generation systems. Int. J. Exergy 3(3):255-71.

APPENDIX A

Derivation of Equations 3 and 14 with REMM

According to the electrical analogy shown in Figure A-1, the total flow of the fuel supply RefFC in terms of [kg*h.sup.-1] on Branch 1 at reference conditions is the sum of the fuel flows (currents) at Branches 2 and 3. Branch 2 depicts the fuel flow (in analogy to electric current) demanded by a separate thermal system at reference conditions in order to satisfy a unit heat load (H = 1 kW or 1 [Btu*h.sup.-1]). This branch spends a certain type of fuel, which has a calorific value [f.sub.c]. In analogy to electrical resistance, [R.sub.H] represents the resistance of the thermal system to fuel supply, i.e., the higher the efficiency, the less is the fuel demand and less is the fuel flow (in analogy to electric current). Branch 3 depicts the flow of the same type of fuel (same [f.sub.c]) that is necessary for a separate electric power generation system with a reference efficiency of RefE[eta] in order to satisfy an electric load identical to the output that an equivalent CHP system would provide beside the unit H (E = CH = C kW or C [Btu*h.sup.-1]). An equivalent resistance R to fuel supply flow can be defined similarly to two parallel resistances in an electrical circuit over the same unit potential difference, in analogy to H. Using the same analogy for the actual conditions for a CHP system operating at efficiencies [CHPH.sub.[eta]] and [CHPE.sub.[eta]], the incremental fuel savings in Branches 2 and 3, namely, [delta][FS.sub.2] and [delta][FS.sub.3] can be written in Equations A-1 and A-2, assuming that the same type of fuel is used.

[FIGURE A-1 OMITTED]

In Branch 2:

[DELTA][FS.sub.2] = [(1/[RefH[eta]/[f.sub.c]])/(1/(CHPH[eta]/[f.sub.c]))] = [(1/[RefH[eta]])/(1/[CHPH[eta]])] (A-1)

In Branch (3):

[DELTA][FS.sub.3] = [(1/[RefE[eta]/[Cf.sub.c]])/(1/(CHPE[eta]/[Cf.sub.c]))] = [(1/[RefE[eta]])/(1/[CHPE[eta]])] (A-2)

Then, fuel savings on Branch 1 with respect to RefFC can be calculated with the same analogy. In a ratio format, this saving is the term PES, defined in the Directive as:

PES = 1 - [1/[(1/[[DELTA][FS.sub.2]]) + (1/[[DELTA][FS.sub.3]])]] = 1 - [1/[([CHPH[eta]]/[RefH[eta]]) + ([CHPE[eta]]/[RefE[eta]])]] (A-3)

Correction for Secondary Fuel Consumption

According to REMM, Figure A-1 needs to take into account additional fuel consumption required to offset the exergy destroyed in Branches 2 and 3. In other words, because the processes in Branches 2 and 3 destroy exergy, lost opportunities for additional useful work need to be offset by some other processes in the built environment at an expense of additional fuel spending, which is given in Equations 12 and 13. See Figure A-2. Therefore, each of the Branches 2 and 3 is responsible from two stages of fuel consumption. For example, [R.sub.H] must be rewritten in the following form:

[summation][R.sub.H] = [c.sub.f][1/[RefH[eta]] + [1/[RefH[eta]]](1 - [[PSI].sub.RH])] = [c.sub.f][1/[RefH[eta]]](2 - [[PSI].sub.RH]) (A-4)

Therefore, REMM introduces a multiplier at a magnitude of (2 -[[PSI].sub.RH]) to Branch 2 and (2 - [[PSI].sub.RE]) to Branch 3. Then, the corrected Equation 3 becomes

[PES.sub.R] = [1 - 1/[([CHPH[eta]]/[RefH[eta]]) X [[2 - [Ref[PSI].sub.RH]]/[2 - [[PSI].sub.RH]]] + ([CHPE[eta]]/[RefE[eta]]) X ([2 - Ref[[PSI].sub.RE]]/[2 - [[PSI].sub.RE]])]] X 100. (A-5)

If the rational exergy terms related to heat and power are combined for CHP according to the following equations (see also Equation 1),

[Ref[PSI].sub.RCHP] = [[[H.sub.CHP] X [Ref[PSI].sub.RH] + [E.sub.CHP] X [Ref[PSI].sub.RE]]/[[H.sub.CHP] + [E.sub.CHP]]]

= [[Ref[[PSI].sub.RH] + C X Ref[[PSI].sub.RE]]/[1 + C]] (A-6)

[[psi].sub.RCHP] = [[[[epsilon].sub.Hmin] X [H.sub.CHP] + [[epsilon].sub.Emin] X [E.sub.CHP]]/[[[epsilon].sub.Hmax] X [H.sub.CHP] + [[epsilon].sub.Emax] X [E.sub.CHP]]]

= [[[[epsilon].sub.Hmin] + C X [[epsilon].sub.Emin]]/[[[epsilon].sub.Hmin] + C X [[epsilon].sub.Emax]]] (A-7)

then Equation A-5 may be simplified in the following format:

[PES.sub.RCHP] = [1 - 1/[[([CHPH[eta]]/[RefH[eta]]) + ([CHPE[eta]]/[RefE[eta]])] X ([2 - [Ref[PSI].sub.RCHP]]/[2 - [[PSI].sub.RCHP]])]] X 100 (A-8)

[FIGURE A-2 OMITTED]

Birol I. Kilkis, PhD

Fellow ASHRAE

Siir Kilkis

Student Member ASHRAE

Birol I. Kilkis is an external consultant to Watts Radiant, Springfield, MO. Siir Kilkis is a graduate researcher at Georgetown University, Washington, DC.