6.3.1. Horizontal Design (Horizontal-MRM)

In this design method, which is very similar to that presented by [1], the full load operation of the prime mover extends until the yearly PES becomes greater than a minimum PES, instead of being positive (Figure 6.5). The prime mover size remains the same as the prime mover size recommended by the classic MRM.

Deriving the equation for the above condition results in the constraint presented in Eq. (6-10):

$PES=\frac{\sum _{yearly}{F}_{pp}+\sum _{yearly}{F}_b-\sum _{yearly}{F}_{CCHP}}{\sum _{yearly}{F}_{pp}+\sum _{yearly}{F}_b}\ge PE{S}_{\min }$

(6-8)

$(1-PE{S}_{\min })\sum _{yearly}\frac{{\eta }_{e,CCHP}{F}_{CCHP}}{{\eta }_{e,pp}{\eta }_g}-\sum _{yearly}{F}_{CCHP}+(1-PE{S}_{\min })\sum _{yearly}\frac{\zeta }{{\eta }_b}\ge 0$

(6-9)

and finally

$\sum _{yearly}{F}_{CCHP}\le \frac{1-PE{S}_{\min }}{{\eta }_b\left[1-(1-PE{S}_{\min })\frac{{\eta }_{e,CCHP}}{{\eta }_{e,pp}{\eta }_g}\right]}\sum _{yearly}\zeta$

(6-10)

The FLO and PLO efficiency of components is assumed to be equal in Eqs. (6-8) to (6-10).

The yearly fuel consumption of the CCHP system $\sum _{yearly}{F}_{CCHP}$ is dependent on the operation mode of the prime mover. When the prime mover operates in full load it consumes fuel according to the nominal efficiency, but when it operates in partial load it consumes more fuel and follows its partial load efficiency. Hence

$\sum _{yearly}{F}_{CCHP}=\sum _{FLO}{F}_{CCHP}+\sum _{PLO}{F}_{CCHP}=\sum _{FLO}\frac{E_{nom}}{{\eta }_{e,CCHP}^{FLO}}+\sum _{PLO}\frac{E_{PM}}{{\eta }_{e,CCHP}^{PLO}}$

(6-11)

$E_{PM}=\left\{\begin{array}{cc}\hfill E_{dem}\hfill & \hfill E_{dem}\le E_{nom}\hfill \\ \hfill E_{nom}\hfill & \hfill E_{dem}>E_{nom}\hfill \end{array}\right.$

(6-12)

Depending on the type of prime mover, its electrical efficiency in FLO and PLO conditions ( ${\eta }_{e,CCHP}^{FLO}$, ${\eta }_{e,CCHP}^{PLO}$) can be found from the data presented in Chapters 1 and 2.

6.3.2. Vertical Design (Vertical-MRM)

In vertical-MRM, the full load operation time of the prime mover is the same as that recommended by the classic MRM, but the prime mover size becomes greater until the PES remains greater than a minimum PES. Figure 6.5 depicts a graphical explanation of this method.

The equation that can be derived for the vertical-MRM is similar to that derived for the horizontal-MRM in Eqs. (6-10) to (6-12).

In the MRM methods the length of full load operation time may be known (the classic MRM) or unknown (the horizontal-MRM) but the problem is determining the time when the prime mover is supposed to operate in full load or partial load. To determine the time when the prime mover should be programmed for FLO or PLO another constraint should be introduced. This constraint can be based on the cooling, heating, or electrical loads of the consumer. The constraint can also be expressed based on different economic criteria. Moreover, the ability to sell electricity to the grid has an impact on the time for FLO and PLO. In addition, different fuel and electricity tariffs in peak demand and nonpeak demand times can change the constraint. Specifying the constraint depends on the decision-making of the designer. The decision should be made based on evaluations and calculations such as those mentioned in this paragraph.

6.3.3. High-level Analysis

While energy has different aspects such as thermodynamic (energy and exergy), economic, and environmental, both the vertical- and horizontal-MRM sizing methods use only the energy criterion to size the prime mover. The high-level MRM uses the economic criterion of net present value (NPV) after applying the PES constraint. In this method, by changing the prime mover size and full load operation time, the pairs (prime mover size and full load operation time) that result in the same PES_min are found and an iso-PES line is drawn. Then in the second step the NPV criterion is applied to the sizes related to the iso-PES line to find the pair that results in the maximum NPV. The pair with the maximum NPV would be the answer. A graphical representation of the high-level MRM is depicted in Figure 6.6.

The advantage of the high-level MRM is that among different options with the same primary energy savings, the one that creates more economic benefit is chosen as the solution.

6.4.1. FTL Sizing

In this method the prime mover size is chosen to provide the maximum thermal demand from the heat recovery of the CCHP system. This means that in case of lack/surplus of electricity it would be purchased/sold from/to the grid respectively. Since the thermal demand changes, the recovered heat from the prime mover may exceed the thermal demand in some conditions. In such conditions the extra heat may be stored in a heat storage system or lost. When working with EMSs, usually FTL is more popular because the extra electricity or lack of electricity can be sold to or bought from the grid and the prime mover also can be programmed to provide the heat demand (no heat lost or storage). In fact in this method the prime mover’s main priority is to produce heat, and electricity is a byproduct of the CCHP system.

EMSs only pay attention to the thermal or electrical loads of the consumer; they pay no attention to other aspects of energy such as the economic and environmental criteria. These criteria may be considered only when comparing different EMS sizing methods to select the best energy management strategy.

A formula for the FLT sizing method is presented here:

$E_{nom}^{FTL}=\left\{E_{nom}\left|(B=0\vee Q_{rec}=AT{D}_{\max })\right.\right\}$

(6-13)

where $E_{nom}^{FTL}$ is the nominal size of the prime mover recommended by the FTL sizing method, and B is the auxiliary boiler size to compensate for the lack of heat for different purposes.

6.4.2. FEL Sizing

In the FEL sizing method the prime mover size is chosen to provide the maximum electrical demand from the prime mover of the CCHP system. This means that when there is a lack of heat it will be compensated for by an auxiliary heating system such as a water boiler. Since in the FEL sizing method the electricity demand is the main priority of the CCHP system in case of surplus recoverable heat, it is recommended to store the heat in a heat storage system for reuse when needed; otherwise it would be wasted.

When the prime mover is programmed to operate in partial load, no surplus electricity is produced, but if it is supposed to operate in full load, since the electricity demand is changeable, the electricity demand may be less than the full load electricity production of the prime mover. In this case the electricity may be sold to the grid, or be consumed by the auxiliary electrical cooling or heating systems integrated into the CCHP system. Electricity storage systems (batteries) can also be used to store the surplus electricity and sell it to the grid during peak hours when electricity is more expensive. In addition by applying some optimization algorithms the prime mover size can be smaller than the maximum electrical demand and instead electricity storage systems can be used to satisfy the peak demand. This helps to reduce fuel consumption and pollution production, but it may cost more.

The prime mover size in FEL sizing ( $E_{nom}^{FEL}$) is calculated as follows:

$E_{nom}^{FEL}=E_{dem,\max }$

(6-14)

6.4.3. FSL Sizing

In this method, the prime mover size is designed to follow thermal and electrical loads depending on the monthly or seasonal electricity to heat demand ratio (LR) of the consumer:

$LR=\frac{Monthly{E}_{dem}}{Monthly{H}_{dem}}$

(6-15)

If LR > 1, the prime mover should be programmed to run in FTL strategy in that month, otherwise it should be programmed to work in FEL strategy. According to this discussion, the prime mover size can be calculated as follows:

$E_{nom}^{FSL}=\max (E_{nom}^{FEL},E_{nom}^{FTL})$

(6-16)

6.7.1. Fitness Function Sizing Method

References [11] and [14] used a fitness function to design CCHP systems. A sample of the ff is presented in Eq. (1-36). By looking at this equation we can see that FESR, annual total cost savings (ATCS), and CO₂ reduction ratio are considered as the nominated criteria of the thermodynamic, economic, and environmental aspects of the energy and CCHP system, respectively. In addition, an equal weight is given to the three criteria. To expand upon this method, we propose considering some criteria that each have several subcriteria. In addition, the weight of every criterion and subcriterion can be calculated using weighting methods such as AHP or the fuzzy method presented in Chapter 4. The fitness function is formulated as follows:

$\begin{array}{l}ff=\sum _{i=1}^n{w}_{i}f{f}_i,\\ \sum _{I=1}^n{w}_i=1\end{array}$

(6-31)

where

$\begin{array}{l}f{f}_i=\sum _{j=1}^{k_i}{\beta }_{ij}{w}_{ij}{C}_{ij}\\ \sum _{i=1}^n\sum _{j=1}^{k_i}{w}_{ij}=1\\ {\beta }_{ij}=\left\{\begin{array}{l}1ifthe{C}_{ij}isconsideredintheanalyses\\ 0ifthe{C}_{ij}isnotconsideredintheanalyses\end{array}\right.\end{array}$

(6-32)

where n is the number of criteria and k_i is the number of subcriteria of the ith criterion. In addition w_i is the weight of ith criterion and w_ij is the weight of the jth subcriterion of the ith criteria. C_ij is the normalization of the jth subcriterion of the ith criteria. According to the normalization method, the optimization may be done by maximizing or minimizing the ff. The C_ij is defined as follows:

$C_{ij}=\frac{c_{ij}^{CCHP}-c_{ij}^{SCHP}}{c_{ij}^{CCHP}},c_{ij}>0$

(6-33)

where c_ij is a profit such as the exergy efficiency where higher the better.

If c_ij is a cost such as the fuel consumption where smaller the better, it would be normalized as follows:

$C_{ij}=\frac{c_{ij}^{SCHP}-c_{ij}^{CCHP}}{c_{ij}^{SCHP}},c_{ij}>0$

(6-34)

Equation (6-31) can be optimized by using different optimization algorithms such as the genetic algorithm. As mentioned previously, the weights of the criteria and subcriteria should be calculated using the weighting methods presented in Chapter 4.

It is important to mention that optimizing the fitness function does not guarantee the optimization of every criteria or subcriteria. In fact the weakness of this method is that the optimum ff may result in some nonoptimum criteria or subcriteria, even those that are most important for the designer. This is because when the ff is being optimized we have no control on the variation of ff_i and C_ij.

Another weakness of this method is that some of the subcriteria may be steadily increasing or decreasing. Such subcriteria may cause the ff to become steadily increasing or decreasing. In such cases, since we optimize all of the subcriteria together, all of the subcriteria should be checked individually and we should find the subcriterion (or criteria) that caused this divergence. The designer may make different decisions about the subcriteria that are to blame; for example their weight can be set to zero, another subcriterion can be used instead, another sizing method can be used, etc.

6.7.2. Multicriteria Sizing Function

The MCSF proposed by [15] optimizes every subcriterion of C_ij individually and finds the optimum CCHP size proposed by the subcriterion. Then after giving weight to every criterion and subcriterion, a linear combination of weights and optimum CCHP sizes proposed by the sub-criteria is calculated, and the prime mover size of the CCHP system is recommended as follows:

$E_{nom}^{MCSF}=\sum _{i=1}^n\sum _{j=1}^{k_i}{\beta }_{ij}{\omega }_i{\omega }_{ij}{E}_{opt}^{ij}$

(6-35)

$E_{opt}^{ij}=\left\{\left.E_{nom}\right|{\left.C_{ij}(E_{nom},Conditions)\right|}_{opt},i=1,\dots ,n\&j=\mathrm{1,2},\dots ,k_i\right\}$

(6-36)

where $E_{opt}^{ij}$ is the optimum CCHP size, or the proposed CCHP size under some conditions and constraints from the jth sub-criterion of the ith criterion, and $E_{nom}^{MCSF}$ is the nominal electrical capacity of the prime mover proposed by the MCSF.

As we discussed previously, in problems such as CCHP sizing where many criteria are encountered, it is basically impossible to find a CCHP size to optimize all of the criteria and subcriteria simultaneously. Therefore we should look for a compromise or quasi-optimum solution. In comparison with the ff method, the MCSF has absolute control over the optimization of every subcriterion. Therefore, $E_{nom}^{MCSF}$ tends to approach the size of $E_{opt}^{ij}$ for which the corresponding criterion and subcriterion is the most important (has the biggest ω_iω_ij) for the designer. In addition, since all of the subcriteria are optimized individually, if there is a subcriterion that is steadily increasing or decreasing, we can use our engineering feelings about the problem and according to the trend of the subcriterion reach an agreement about the recommended engine size from that subcriterion. This means we may use the optimum sizes of some criteria and the agreed sizes proposed by some nonoptimizable subcriteria in the MCSF. In other words, with the MCSF there is always a solution.

6.8.1. Solution Outline

In order to design a CCHP system, first we should decide upon the prime mover type. The prime mover was previously chosen based on the multicriteria decision-making method in Chapter 4 for the five climates. The fuzzy logic and grey incidence approaches recommended using an internal combustion (IC) engine for all five climates. In the second step, the energy demands of the residential building were calculated and presented in Chapter 5. In the third step, the components (apart from the internal combustion engine) that are supposed to be used in the CCHP cycle should be introduced as a basic CCHP system. Since the exhaust gas of an IC engine is about 540 °C, this energy source can be used for cooling production in single-effect absorption chillers. The water is preheated by the lube oil cooler and engine water jacketing before being heated by the exhaust gases. If the water temperature is high enough for the chiller to cover the cooling load (or heating load), the temperature control valve (TCV) bypasses the hot water to the down stream of auxiliary boiler and it enters the chiller (or heating system), otherwise it will be reheated by the auxiliary heater. The CCHP cycle consisting of the IC engine, absorption chiller, auxiliary heater, and heating system are presented in Figure 6.7. Determining the prime mover size dictates the size of the auxiliary boiler. In addition, the chiller size is determined according to the maximum cooling load. Therefore the IC engine should be sized first.

6.8.2. Sizing Using the MRM

The ATD of the building is first determined using the MRM method. The ATD curves of the building for the five climates are depicted in Figure 6.8. Since the load calculation was done based on the TNM, the horizontal axis of ATD curves is presented in percent time of year.

After determining the ATD, the rectangle with maximum area and FLO time should be found for every climate. For our purposes, the area of the rectangle is calculated against the time of year in Figure 6.9. The IC engine size can be found by using the maximum area and its corresponding FLO time in Eq. (6-3). The results of sizing using the MRM are presented in Figure 6.10.

6.8.3. Sizing Using EMS Methods

EMS sizing methods including the FTL, FEL, and FSS can also be used for sizing the IC engine according to Eqs. (6-13), (6-14), and (6-16). In these methods it is enough to determine the peak of ATD and the electrical demand for every climate. In the FTL sizing method the engine size should be chosen to provide as much recoverable heat as ATD_max. Therefore the correlations that were presented for Q_rec and E_nom of the IC engine in the second chapter can be used to calculate the engine size. For example, Eq. (2-10) is used in this example since the electrical demand is below 100 kW. As an example the ATD_max of Ahwaz is 541.40 kW, therefore by using Eq. (2-10) we have 541.40 = 1.368E_nom + 14.57 or E_nom = 385.11 kW. The results of the EMS for the five climates are presented in Figure 6.10 and compared with the MRM results.

As can be seen among the sizing methods, the FTL and FSL approaches recommend the biggest engine size. A bigger engine size means a higher initial investment cost and more heat loss since the recoverable heat high enough to cover the maximum aggregated thermal demand (it means heat is wasted when the ATD decreases). In addition, operation and maintenance of a bigger engine costs more. The positive side of a bigger engine is production of surplus electricity to be sold to the grid and no need for an auxiliary boiler. These can improve the economic benefits of the CCHP system. As can be seen many parameters are interacting with each other and the final decision can only be made when all of the vital criteria and subcriteria are calculated. As opposed to the FTL and FSL, the engine sizes proposed by the FEL are small. A small engine size has its own characteristics as well. For example, smaller initial capital outlay, and lower operation and maintenance costs are the advantages, while the need for an auxiliary boiler and less excess electricity to be sold to the grid can be mentioned as disadvantages. In contrast to the EMS sizing methods, in most cases MRM proposes intermediate engine sizes with respect to those proposed by the FTL, FSL, and FEL sizing methods. The intermediate engine size benefits from the advantages of small and big engine sizes, however again the final decision can only be made when all of the essential criteria are calculated. This means that using the MRM or EMS sizing methods without including thermodynamic, economic, and environmental criteria is risky.

Another weakness of the MRM and EMS sizing methods is that they are completely building-demand oriented and do not consider the impact from the components of the CCHP system. For example if using MRM or EMS as sizing methods there will be no difference between the size of the prime mover of a basic CCHP and a CCHP system that is integrated with solar heating or a thermal storage system.

6.8.4. Sizing Using ff

In order to use ff for sizing the IC engine, the criteria, subcriteria, and their weights should be known.

In this example we consider FESR and EXIR as the thermodynamic subcriteria; NPV, IRR and PB as the economic subcriteria; and the reduction ratio of CO₂, CO, and NO_x as the environmental subcriteria. The AHP weighting method is used and most of the pairwise comparisons presented in Chapter 4 (Tables 4.7A, B, and D) can be used again except for the economic subcriteria (Table 4.7C) due to consideration of different subcriteria. The pairwise comparison of economic subcriteria and weights are presented in Tables 6.1 and 6.2 , respectively.

After calculating the weights, the subcriteria should be calculated according to Eqs. (6-33) and (6-34). Among the subcriteria, FESR, CO2RR, CORR, and NOXRR should be normalized according to Eq. (6-34) and EXIR should be normalized according to Eq. (6-33). The economic subcriteria, however, cannot be normalized using Eqs. (6-33) and (6-34). This is because the net annual cash flow (cf_y) is always negative for the SCHP system, and as a result the NPV, IRR, and PB would become negative (meaningless). This is because we receive no economic benefit from the SCHP system. For this reason NPV, IRR, and PB are normalized as follows:

$C_{31}=\left\{\begin{array}{ll}{c}_{31}^{CCHP}/\left(c_{31}^{CCHP}-c_{31}^{SCHP}\right),\hfill & if{c}_{31}^{CCHP}>0\hfill \\ 0,\hfill & if{c}_{31}^{CCHP}\le 0\hfill \end{array}\right.$

(6-37)

$C_{32}=\left\{\begin{array}{ll}\left(c_{32}^{CCHP}-r\right)/c_{31}^{CCHP},\hfill & if{c}_{32}^{CCHP}>r\hfill \\ 0,\hfill & if{c}_{32}^{CCHP}\le r\hfill \end{array}\right.$

(6-38)

$C_{33}=\left\{\begin{array}{lll}1/c_{33}^{CCHP},\hfill & if\hfill & 0<\overline{cf}<I_{CCHP}\hfill \\ 1,\hfill & if\hfill & I_{CCHP}<\overline{cf}\hfill \\ 0,\hfill & if\hfill & \overline{cf}\le 0\hfill \end{array}\right.$

(6-39)

To calculate the C_ij, we should calculate the c_ij first. For this purpose in the following all of the subcriteria are formulated according to the cycle presented.

The first subcriterion is the fuel consumption of the CCHP and SCHP systems. To present the following equations in a compact form, whenever j is used as a superscript it can take two values of j = 0 or j = 1, in which 0 represents the SCHP system and 1 stands for a CCHP system. In addition an energy vector including four components (E, C, H, and D) is used for the electricity, cooling, heating, and DHW demands. This vector is also used for other subcriteria. Hence

$F^j=(F_E^j,F_C^j,F_H^j,F_D^j),j=0,1$

(6-40)

$c_{11}^j=\sum _{yearly}(F_E^j+F_C^j+F_H^j+F_D^j)$

(6-41)

where the fuel vector components are calculated as follows:

$\begin{array}{ll}{F}_E^0=\frac{E_{dem}}{{\eta }_{pp}{\eta }_g},\hfill & F_E^1=\frac{E_{PM}+Q_{rec}}{{\eta }_{CHP}}+\frac{({E^{\prime }}_{dem})}{{\eta }_{pp}{\eta }_g}\hfill \\ F_C^0=\frac{C_{dem}}{{\eta }_{b}CO{P}_{abc}{\varepsilon }_{FCU}},\hfill & F_C^1=\frac{{C^{\prime }}_{dem}}{{\eta }_{b}CO{P}_{abc}{\varepsilon }_{FCU}}\hfill \\ F_H^0=\frac{H_{dem}}{{\eta }_b{\varepsilon }_{FCU}},\hfill & F_H^1=\frac{{H^{\prime }}_{dem}}{{\eta }_b{\varepsilon }_{FCU}}\hfill \\ F_D^0=\frac{D_{dem}}{{\eta }_{wh}},\hfill & F_D^1=\frac{D_{dem}}{{\eta }_{wh}}\hfill \end{array}$

(6-42)

where

$\begin{array}{l}{E}_{PM}=\left\{\begin{array}{l}{E}_{nom},ifFLO\\ E_{dem},if{E}_{nom}\ge E_{dem}\wedge PLO\\ E_{nom},if{E}_{nom}<E_{dem}\wedge PLO\end{array}\right.\hfill \\ Q_{rec}=\left\{\begin{array}{l}1.368E_{PM}+14.57,30\le E(kW)\le 500\\ 1.854E_{PM},0\le E(kW)<30\end{array}\right.\hfill \\ {E^{\prime }}_{dem}=\left\{\begin{array}{ll}{E}_{dem}-E_{PM},\hfill & if{E}_{dem}>E_{PM}\hfill \\ 0,\hfill & if{E}_{dem}\le E_{PM}\hfill \end{array}\right.\hfill \\ {C^{\prime }}_{dem}=\left\{\begin{array}{ll}{C}_{dem}-CO{P}_{abc}{Q}_{rs},\hfill & if{C}_{dem}>CO{P}_{abc}{Q}_{rs}\hfill \\ 0,\hfill & if{C}_{dem}\le CO{P}_{abc}{Q}_{rs}\hfill \end{array}\right.\hfill \\ {H^{\prime }}_{dem}=\left\{\begin{array}{ll}{H}_{dem}-Q_{rs},\hfill & if{H}_{dem}>Q_{rs}\hfill \\ 0,\hfill & if{H}_{dem}\le Q_{rs}\hfill \end{array}\right.\hfill \\ Q_{rs}=Q_{rec}+Q_{solar}\hfill \end{array}$

(6-43)

Since the DHW energy demand is calculated separately, the CCHP system can be designed with a separate DHW system (sprt-DHW) or be integrated with the heating system and use the recovered heat (intg-DHW). In this example the intg-DHW system is used and the DHW energy demand is combined with the heating energy demand. The prime (′) in the above equations represents the additional energy required (heat from the auxiliary boiler or electricity from the grid) to provide the corresponding energy demand for the building. Q_solar, which is the solar energy collected by a solar water heater, will be calculated in the next chapter.

Since the engine is supposed to operate at full load all time, the recoverable heat may exceed the heat demand at some particular times. The extra heat will be wasted because no heat storage is considered to store the surplus heat. In order to calculate the annual energy loss of the CCHP system the following equation can be used:

$ATD\le Q_{rs}\to H_{loss}^{CCHP}=Q_{rs}-ATD$

(6-44)

Additionally, sometimes the heat demand (for cooling or heating) may exceed the recoverable heat. In this case the lack of heat should be compensated for by burning fuel in the auxiliary boiler and water heater (for the sprt-DHW). The annual lack of heat that should be provided by systems other than the solar and heat recovery systems can be calculated as follows:

$ATD\ge Q_{rs}\to AT{D}^{\prime }={H^{\prime }}_{dem}+{C^{\prime }}_{dem}/CO{P}_{abc}+D_{dem}$

(6-45)

After calculation of fuel consumption for the CCHP and SCHP systems, the FESR can be calculated according to Eq. (6-34).

In the exergy analysis, the supplied exergy to ( ${\dot{\varphi }}_{in}$) and recovered exergy from ( ${\dot{\varphi }}_{out}$) the CCHP and SCHP systems are used to calculate the exergy efficiency (π) as follows:

$\begin{array}{l}{\dot{\varphi }}_{in}^j=({\dot{\varphi }}_{in,E}^j,{\dot{\varphi }}_{in,C}^j,{\dot{\varphi }}_{in,H}^j,{\dot{\varphi }}_{in,D}^j)\hfill \\ {\dot{\varphi }}_{out}^j=({\dot{\varphi }}_{out,E}^j,{\dot{\varphi }}_{out,C}^j,{\dot{\varphi }}_{out,H}^j,{\dot{\varphi }}_{out,D}^j)\hfill \end{array}$

(6-46)

${\pi }^j=\sum _{yearly}({\dot{\varphi }}_{out}^j)/\sum _{yearly}({\dot{\varphi }}_{in}^j)$

(6-47)

The exergy vector components are calculated according to the cycle as follows:

$\begin{array}{l}{\dot{\varphi }}_{in,E}^0=F_E^0\chi (T_{hg})-(F_E^0-E_{dem})\chi (T_{amb})\hfill \\ {\dot{\varphi }}_{in,C}^0={\dot{W}}_{sp}+{\dot{W}}_{rp}+{\dot{W}}_{wp}+F_C^0\chi (T_{hg})-F_C^0(1-{\eta }_b)\chi (T_{amb})\hfill \\ {\dot{\varphi }}_{in,H}^0={\dot{W}}_{wp}+F_H^0\chi (T_{hg})-F_H^0(1-{\eta }_b)\chi (T_{amb})\hfill \\ {\dot{\varphi }}_{in,D}^0=F_D^0\chi (T_{hg})-F_D^0(1-{\eta }_b)\chi (T_{amb})\hfill \end{array}$

(6-48)

$\begin{array}{l}{\dot{\varphi }}_{out,E}^0=E_{dem}\hfill \\ {\dot{\varphi }}_{out,C}^0=C_{dem}\chi (T_{room})\hfill \\ {\dot{\varphi }}_{out,H}^0=H_{dem}\chi (T_{room})\hfill \\ {\dot{\varphi }}_{out,D}^0=D_{dem}\chi (T_{room})\hfill \end{array}$

(6-49)

$\begin{array}{l}{\dot{\varphi }}_{in,E}^1=F_E^1\chi (T_{hg})-(F_E^1-E_{PM}-Q_{rec})\chi (T_{amb})+{E^{\prime }}_{dem}\hfill \\ {\dot{\varphi }}_{in,C}^1={\dot{W}}_{sp}+{\dot{W}}_{rp}+{\dot{W}}_{wp}+F_C^1\chi (T_{hg})-F_C^1(1-{\eta }_b)\chi (T_{amb})\hfill \\ {\dot{\varphi }}_{in,H}^1={\dot{W}}_{wp}+F_H^1\chi (T_{hg})-F_H^1(1-{\eta }_b)\chi (T_{amb})\hfill \\ {\dot{\varphi }}_{in,D}^1=F_D^1\chi (T_{hg})-F_D^1(1-{\eta }_b)\chi (T_{amb})\hfill \end{array}$

(6-50)

$\begin{array}{l}{\dot{\varphi }}_{out,E}^1=E_{PM}+{E^{\prime }}_{dem}+{\dot{\varphi }}_{Q_{rs}}\hfill \\ {\dot{\varphi }}_{out,C^{\prime }}^1={C^{\prime }}_{dem}\chi (T_{room})\hfill \\ {\dot{\varphi }}_{out,H^{\prime }}^1={H^{\prime }}_{dem}\chi (T_{room})\hfill \\ {\dot{\varphi }}_{out,D}^1=D_{dem}\chi (T_{room})\hfill \end{array}$

(6-51)

where ambient temperature is calculated according to the weather information presented in Chapter 5:

$T_{amb}=\left\{\begin{array}{ll}{T}_{db,sum}\hfill & if(H_{dem}=0\wedge C_{dem}\ne 0)\hfill \\ T_{db,win}\hfill & if(C_{dem}=0\wedge H_{dem}\ne 0)\hfill \\ T_{room}\hfill & if{H}_{dem}=C_{dem}=0\hfill \end{array}\right.$

(6-52)

$T_{room}=\left\{\begin{array}{ll}{T}_{room,sum}\hfill & if(C_{dem}=0\wedge H_{dem}\ne 0)\hfill \\ T_{room,win}\hfill & if(H_{dem}=0\wedge C_{dem}\ne 0)\hfill \\ T_{amb}\hfill & if{H}_{dem}=C_{dem}=0\hfill \end{array}\right.$

(6-53)

$\chi (T_x)=1-T_0/T_x$

Since Q_rs comprises the recovered heat from the oil cooler, water jacketing, exhaust, and solar system, its exergy is calculated as follows:

$\begin{array}{l}{Q}_{rs}=Q_{oil}+Q_{jacketing}+Q_{exhaust}+Q_{solar}\to {\dot{\varphi }}_{Q_{rs}}=Q_{oil}\chi (T_{oil})\\ +Q_{jacketing}\chi (T_{jacketing})+Q_{exhaust}\chi (T_{exhaust})+Q_{solar}\chi (T_p)\end{array}$

(6-54)

After calculating the exergy efficiency the EXIR can be calculated according to Eq. (6-33).

In order to investigate the environmental impact of the CCHP with respect to the SCHP system the pollution product by the energy demand components should be evaluated. The pollution vector is defined as follows:

$X^j=(X_E^j,X_C^j,X_H^j,X_D^j)$

(6-55)

where X can be CO, CO₂, or NO_x. The emission production of each pollutant also is determined as follows:

$E{m}_X^j=\sum _{yearly}{(X_E^j+X_C^j+X_H^j+X_D^j)}_t$

(6-56)

The components of the pollution vector are calculated as follows:

$\begin{array}{l}{X}_E^0=E_{PM}\cdot i_{X,\mathrm{\hspace{0.17em} }E}^0,\mathrm{\hspace{0.17em} }{X}_C^0=C_{dem}\cdot i_{X,\mathrm{\hspace{0.17em} }C}^0\hfill \\ X_H^0=H_{dem}\cdot i_{X,\mathrm{\hspace{0.17em} }H}^0,\mathrm{\hspace{0.17em} }{X}_D^0=D_{dem}\cdot i_{X,\mathrm{\hspace{0.17em} }D}^0\hfill \end{array}$

(6-57)

$\begin{array}{l}{X}_E^1=E_{PM}\cdot i_{X,\mathrm{\hspace{0.17em} }E}^1+{E^{\prime }}_{dem}\cdot i_{X,\mathrm{\hspace{0.17em} }E}^0,\mathrm{\hspace{0.17em} }{X}_C^1={C^{\prime }}_{dem}\cdot i_{X,\mathrm{\hspace{0.17em} }C}^1\hfill \\ X_H^1={H^{\prime }}_{dem}\cdot i_{X,\mathrm{\hspace{0.17em} }H}^1,\mathrm{\hspace{0.17em} }{X}_D^1=D_{dem}\cdot i_{X,\mathrm{\hspace{0.17em} }D}^1\hfill \end{array}$

(6-58)

where i is the pollution index based on kg/MWh. After calculation of $E{m}_X^j$ for each pollutant, the emission reduction ratio can be calculated according to Eq. (6-34).

In the economic evaluations, the initial investment cost and net annual cash flow are the key parameters. Initial investment cost is the summation of equipment costs. The capital cost vector and investment cost are presented as follows:

$I^j=(I_E^j,I_C^j,I_H^j,I_D^j)$

(6-59)

$I^j=I_E^j+I_C^j+I_H^j+I_D^j$

(6-60)

The capital vector components are calculated as follows:

$I_E^0=NOU.i_E^0,I_E^1=E_{nom}\cdot i_E^1+I_E^0$

(6-61)

$\begin{array}{l}{I}_C^0=C_{nom}\cdot i_C^0,I_C^1=C_{nom}\cdot i_C^1\hfill \\ C_{nom}=\max (C_{dem})\hfill \end{array}$

(6-62)

$\begin{array}{l}{I}_H^0=B^0\cdot i_H^0,B^0=\max \max (H_{dem},C_{dem}/CO{P}_{abc})\hfill \\ I_H^1=B^1\cdot i_H^1+A_{co}\cdot i_{solar}^1,B^1=\max \max ({H^{\prime }}_{dem},{C^{\prime }}_{dem}/CO{P}_{abc})\hfill \end{array}$

(6-63)

$I_D^0=I_D^1=\left\{\begin{array}{ll}NOU\times i_D\hfill & sprt-DHW\hfill \\ 0\hfill & \mathrm{int}g-DHW\hfill \end{array}\right.$

(6-64)

where i is the price index in currency-unit/kW (for example USD/kW) except for $i_E^0$ which is in currency-unit/NOU. NOU means the number of units in the building (each unit has an electricity counter) to measure the electricity flow from the grid to the building. B, C_nom, and A_co are the nominal capacity of the boiler, chiller, and the solar collector area, respectively.

The net annual cash flow calculation starts with determining the earnings (positive cash flow) and expenses (negative cash flow). The earning (er) and expense (ex) vectors and the net annual cash flow (cf_y) are presented here:

$\begin{array}{l}e{r}^j=(e{r}_E^j,e{r}_C^j,e{r}_H^j,e{r}_D^j),e{x}^j=(e{x}_E^j,e{x}_C^j,e{x}_H^j,e{x}_D^j)\hfill \\ e{r}^j=e{r}_E^j+e{r}_C^j+e{r}_H^j+e{r}_D^j,e{x}^j=e{x}_E^j+e{x}_C^j+e{x}_H^j+e{x}_D^j\hfill \end{array}$

(6-65)

$c{f}_y^j=-I_{OM}^j+{(e{r}^j-e{x}^j)}_y$

(6-66)

where $I_{OM}^j$ is the yearly operation and maintenance costs. The components of the earning and expense vectors are formulated below:

$\begin{array}{c}\hfill e{r}_E^0=0,e{x}_E^0=E_{dem}\cdot t_{be}\hfill \\ \hfill e{r}_C^0=0,e{x}_C^0=F_C^0\cdot t_{gas}\hfill \\ \hfill e{r}_H^0=0,e{x}_H^0=F_H^0\cdot t_{gas}\hfill \\ \hfill e{r}_D^0=0,e{x}_D^0=F_D^0\cdot t_{gas}\hfill \end{array}$

(6-67)

$\begin{array}{l}e{r}_E^1=\left\{\begin{array}{ll}{E}_{dem}\cdot t_{be}+(E_{PM}-E_{dem})\cdot t_{se}\hfill & E_{PM}\ge E_{dem}\hfill \\ E_{PM}\cdot t_{be}\hfill & E_{PM}<E_{dem}\hfill \end{array}\right.\hfill \\ e{x}_E^1=(F_E^1-\frac{({E^{\prime }}_{dem})}{{\eta }_{pp}{\eta }_g})\cdot t_{gas}+{E^{\prime }}_{dem}\times t_{be}\hfill \\ e{r}_C^1=(F_C^0-F_C^1)\cdot t_{gas},e{x}_C^1=F_C^1\cdot t_{gas}\hfill \\ e{r}_H^1=(F_H^0-F_H^1)\cdot t_{gas},e{x}_H^1=F_H^1\cdot t_{gas}\hfill \\ e{r}_D^1=0,e{x}_D^1=F_D^1\cdot t_{gas}\hfill \end{array}$

(6-68)

where t is a tariff and the subscripts of gas, se, and be stand for natural gas, selling electricity, and buying electricity. E_PM is the electrical output of the engine and should not be mistaken with E_nom.

After calculation of I and cf_y the economic criteria of NPV, IRR, and PB can be calculated according to Eqs. (6-26), (6-27), and (6-29), respectively. Also these criteria can be normalized according to Eqs. (6-37) to (6-39), respectively.

Up to now we have formulated all of the subcriteria. By combining these criteria and the corresponding weights in the fitness function (Eq. 6-31) the magnitude of ff can be drawn against the engine nominal size (E_nom) as in Figure 6.11. As can be seen in Figure 6.11 the ff for all five climates has an optimum point and reaches a maximum. The optimum sizes for the five climates are given in Figure 6.10 for comparison with other sizing methods. In addition, the results presented in figure 6.12 shows that every criterion for the climate of Kamyaran has an optimum point. According to the sizes proposed by ff and comparing them with the sizes proposed by the MRM and EMS for the climate of Kamyaran, it can be seen from Figure 6.13 that using MRM and FEL give smaller subcriteria in most cases except for C₂₂ and C₁₁. In addition, in comparison with the ff, using FTL and FSL results in smaller or equal values for all of the subcriteria. It should be noted that using the MRM or EMS sizing methods may result in economically unbeneficial CCHP systems (see the C₃₁, C₃₂ for Kamyaran when using the FEL sizing method). Furthermore, Figure 6.13 reveals that EXIR has no optimum point and is increasing steadily, but fortunately combining it with FESR results in ff₁, which has an optimum point (Figure 6.12).

6.8.5. Sizing Using MCSF

The MCSF and ff methods have many parts in common except in the method they use to calculate the optimum size. The subcriteria calculated in the ff method are used to calculate the optimum or proposed engine size for every subcriterion. An example of the subcriterion is depicted for the climate of Kamyaran in Figure 6.13. As can be seen, except for C₁₂ there are optimum sizes for each subcriterion. Regarding C₁₂, according to the trend of EXIR we have assumed an EXIR of 90% as the design constraint for this subcriterion. After calculating the engine sizes proposed by the subcriteria, they are combined with the weights in Eq. (6-35) to calculate the final size (Figure 6.10). In comparison with the ff, the sizes proposed by the MCSF are smaller in all climates. Smaller engine sizes mean a smaller initial investment. This smaller capital cost does not guarantee the profitability of the CCHP system. This should be checked according to the subcriteria curves that are presented in Figures 6.14 to 6.21 . In addition the profitability of the sizes that were proposed by other sizing methods can be checked with these curves. The chiller size only depends on the maximum cooling load for every climate, but the boiler size depends on the engine size and building demands. The boiler size is plotted against E_nom in Figure 6.22, which can be used for both ff and MCSF. Table 6.3 presents the boiler and chiller sizes when designing with MCSF.