simultaneous selection of the type (gas engine, diesel, gas turbine) and .... Applying genetic algorithm (GA) optimization of a CCHP plant for estimating the ...
Heat Transfer—Asian Research, 45 (6), 2016
Soft Computing based Optimization of Cogeneration Plant with Different Load Demands Hassan Hajabdollahi,1 Zahra Hajabdollahi,2 and Farzaneh Hajabdollahi3 of Mechanical Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran 2 Department of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China 3 Department of Mechanical Engineering, University of Colorado, Denver, USA 1 Department
Thermal modeling and optimal design of a combined cooling, heating, and power (CCHP) generation system are presented in this paper. A new procedure for simultaneous selection of the type (gas engine, diesel, gas turbine) and number of available prime movers (PMs) in a market, selecting PMs partial load, selecting the heating capacity of backup boiler as well as selecting the cooling capacity of electrical and absorption chillers available in the market are presented. A genetic algorithm (GA) with discrete and continuous decision variables is applied to select the equipment for the CCHP system by maximizing the actual annual benefit (AAB) as the objective function. The optimization problem is carried out for 1000 alternative states for electricity, cooling, and heating (E-Q-H) loads in the range of 500 kW to 5000 kW to investigate the effect of E-Q-H loads. Moreover, the optimization is performed at two SELL and NO-SELL modes. In the former case is the sale of the excess electricity to the network is allowed and in the latter one, it was not allowed to sell the excess electricity to the grid. A correlation in terms of E-Q-H loads is obtained to specify the effect of E-Q-H loads on optimum AAB values in SELL and NO-SELL modes. Using these correlations, designers can predict the maximum accessible AAB for any electricity, cooling, and heating loads in the above specified range. C⃝ 2015 Wiley Periodicals, Inc. Heat Trans Asian Res, 45(6): 556–577, 2016; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21176 Key words: combined cooling heating, and power, actual annual benefit, genetic algorithm, triple loads 1. Introduction The combined production of a cooling, heating, and power (CCHP) system may be defined as a system which generates electricity, cooling, and heating simultaneously. CCHP systems play a significant role in efficient usage of energy in industrial and domestic applications. Furthermore, these systems have less harmful effects on the environment and reduce the energy consumption, in comparison with independent generation of heat and power, due to the utilizing the heat recovery system [1–4]. There are many research activities regarding selection procedures for prime mover (PM) number and nominal power (capacity) as well as for capacity selection of equipment in a C⃝
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2015 Wiley Periodicals, Inc.
CCHP plant from both technical and economic aspects [5–7]. Kong and colleagues minimized the energy purchase in both forms of electricity and fuel by adjusting the fuel and hot water flow rate in a CCHP system as operational/design parameters [8]. They selected gas engines as PMs and minimized the energy purchase using a nonlinear programming method in specific load demands. Jiang and colleagues obtained the PM capacity as a design parameter of a CCHP system by maximizing the benefits achieved by this system in comparison to the traditional separated production systems from the energy (fuel reduction), economic (total annual cost), and environmental (CO2 emission) analyses in three different climate zones in China. They also considered two operational modes, that is, thermal demand management (TDM) mode in which thermal load was followed and electrical demand management (EDM) mode in which electrical load was followed [9]. Mago and colleagues minimized the primary energy consumption, operational costs, and carbon dioxide emissions by a CCHP system driven by a gas turbine under different operational strategies including, following electrical load (FEL), following thermal load (FTL), and following seasonal demand [10]. In the latter case, the CCHP system operated in either modes of FEL or FTL strategies depending on monthly electric-to-thermal load ratio which was the target of that research. Liu and colleagues presented a new operational strategy based on variable electric cooling to the total cooling load ratio during a year to minimize the total cost of a CCHP system [11]. In this method, the electric cooling to total cooling load ratio varied based on different electrical and thermal loads during the year. The capacity of PM in the CCHP system was also considered as a design parameter. Wang and colleagues studied a CCHP system with energy, environmental, and cost analysis in different climate zones in China [12]. The implementation of a CCHP plant highly depends on input parameters especially the triple loads including electrical cooling and heating load demands. Thus, for some combinations of triple load demands, applying a CCHP system is more costly in comparison with that of a traditional system. Given the above mentioned points and due to the large numbers of parameters encountering in a CCHP optimization problem, it was impossible to present a closed form relation for making decisions regarding issues such as whether being a CCHP system was profitable in comparison with the traditional system. Therefore, the main goal of this study is modeling and optimizing a CCHP plant for different load demands. As a summary, the followings are the contribution of this paper on the subject: ●
Thermal modeling of CCHP system by considering three types of PMs including gas turbine, gas engine, and diesel engine as well as boilers and chillers.
●
Applying genetic algorithm (GA) optimization of a CCHP plant for estimating the optimum values of design parameters with AAB as the objective function.
●
Selecting eight design parameters (decision variables) including the type of PMs, their number and nominal powers (as well as their partial load), the backup boiler, the type and cooling load of electrical and absorption chillers as well as the electrical cooling ratio.
●
The nominal capacity of the CCHP equipments are selected from market available equipment.
●
Performing the optimization for 1000 different E-Q-H (electricity, cooling, and heating) loads in the range of 500 kW to 5000 kW and extracting a correlation between the optimum value of objective function and E-Q-H loads.
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In this paper, after introducing the thermal modeling, objective function and optimization algorithm, the system are optimized for two cases including Sell and NO Sell modes. Each case was optimized for different 1000 electricity, cooling and heating loads and then a closed form equations were derived for objective function versus triple loads using soft computing method. Nomenclature a: AC: Cin : COP: E: H: ir: k: LHV: mf: N: PL: RAB: Sep: t: Tstack : TAC: TES: Q:
annualized factor (–) annual cost ($/year) investment cost ($) chiller coefficient of performance (–) electrical power (kW) heat rate (kW) interest rate (–) equipment life cycle (year) fuel lower heating value (kJ/kg) mass flow rate (kg/s) number of month in a year (–) partial load (%) relative annual benefit ($/year) separate production time step (month) stack temperature (K) total annual cost ($/year) thermal energy storage cooling rate (kW) Greek abbreviation
𝜓em : 𝜙: 𝜙e,b : 𝜑: 𝛼: 𝜏: 𝜂:
pollutant emission factor ($∕kgCO2 ) price factor ($/kW h) price of buying electricity ($/kWh) maintenance factor (–) electric cooling ratio (–) hours of a month (hr) efficiency (–) Subscript
ab: b: cool: ch: dmn: el:
absorption chiller electricity bought from the grid or boiler cooling chiller demand load electrical chiller
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ele: ex: f: heat: nom: stor: t: th:
electricity exhaust heat fuel heating nominal stored heat total thermal 2. Energy Analysis
Generally, the operation of a CCHP system is based on a two-way grid connection. However, by changing the input parameters, it is possible just to buy electricity from the network without selling the excess electricity generated. A CCHP system with interconnection to the grid is shown in Fig. 1. Engine (PM) characteristics such as thermal efficiency or heat rate, exhaust mass flow rate and the exhaust temperature at the part and nominal loads at various ambient conditions are important data required for analysis of CCHP systems. Usually vendors of PMs provide the engine specifications, however, the numerical values obtained from the following appropriate relations which are derived from graphical or mathematical information provided in Refs. [ 13–20] may be used instead as approximate values. In the following suggested relations a function (equipment efficiency and fuel mass flow rate in partial load) is expressed in terms of a variable PL (which is the running partial load as a percentage of nominal load). These relations apply for reciprocating engines with nominal power in the range of 50 kW to 6000 kW, gas turbines with nominal power in the range of 500 kW to 6000 kW and boiler capacity in the range of 10 kW to 10000 kW. The maximum 10% difference is observed between the numerical values obtained from the mentioned references and the proposed relations.
Fig. 1. Schematic of a combine cooling, heating, and power generation system. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]
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Fig. 2. Power and heat produced by gas engine versus partial load (points indicate the actual data and lines indicate the curve fitting) [13]. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.] 2.1. Thermal efficiency of PMs and COP of chillers at partial load The thermal efficiency of PMs and boilers as well as the COP of electrical and absorption chillers at partial load in a CCHP system were assumed to be a function of the partial load (PL) as follow: Gas engine (Fig. 2): 𝜂th,𝑃 𝐿
= −0.0001591(𝑃 𝐿)2 + 0.024(𝑃 𝐿) + 0.1904.
(1)
= 1.07 exp(−0.0005736(𝑃 𝐿)) − 1.259 exp(−0.05367(𝑃 𝐿)).
(2)
𝜂th,𝑛𝑜𝑚 Diesel engine (Fig. 3): 𝜂th,P L 𝜂th,𝑛𝑜𝑚 Gas turbine: 𝜂th,𝑃 𝐿 𝜂th,𝑛𝑜𝑚
=
−0.002551(𝑃 𝐿)2 + 1.135(𝑃 𝐿) + 11.71 . 100
(3)
Boiler: 𝜂th,𝑃 𝐿 𝜂th,𝑛𝑜𝑚
= 0.0951 + 1.525(𝑃 𝐿) − 0.6249(𝑃 𝐿)2 .
560
(4)
Fig. 3. Power and heat produced by diesel engine versus partial load (points indicate the actual data and lines indicate the curve fitting) [13]. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.] Absorption chiller: 𝐶𝑂𝑃 𝑃 𝐿,ab 𝐶𝑂𝑃 nom,ab
=
𝑃𝐿 . 0.75(𝑃 𝐿) + 0.0195(𝑃 𝐿) + 0.213 2
(5)
Electrical chiller: 𝐶𝑂𝑃 𝑃 𝐿,el 𝐶𝑂𝑃 nom,el
= 1.819(𝑃 𝐿) − 0.819(P L)2 .
(6)
2.2. Fuel mass flow rate of PMs at partial load The fuel mass flow rate of PMs is also assumed to be a function of their fuel mass flow rate at nominal load: Gas engine: m f ,P L m f ,nom
= 0.2408 exp(0.01403(P L)) + 0.03553 exp(−0.02494(P L)).
(7)
= −0.02836 exp(0.03254(P L)) + 0.2556 exp(0.01912(P L)).
(8)
Diesel engine: m f ,P L m f ,nom
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Gas turbine: m f ,P L m f ,nom
= 0.4772 exp(0.007565(P L)) − 0.21236 exp(−0.02677(P L)).
(9)
2.3. Energy recovered from the water jacket at the partial load The energy recovered from the water jacket of reciprocating engines is a function of partial load as follows (Fig. 2): Gas engine: Energy recovered f rom water jacket = 5.1396 exp(−0.02619(P L)) + 11.346 exp(0.001194(P L)). m f ,P L .L H V f (10) Diesel engine (Fig. 3): Energy recovered f rom water jacket = 24.01 exp(−0.0248(P L)) + 15.35 exp(0.002822(P L)). m f ,P L .L H V f (11) 2.4. Exhaust gas enthalpy of PMs at partial load The exhaust gas enthalpy of PMs at partial load is a function of partial load as follows: Gas engine (Fig. 2): Hex,P L m f ,P L .L H V f
= 3.4264 exp(−0.02619(P L)) + 7.564 exp(0.001194(P L)).
(12)
Diesel engine (Fig. 3): Hex,P L m f ,P L .L H V f
= 0.001016(P L)2 − 0.1423(P L) + 31.72.
(13)
Gas turbine: Hex,P L m f ,P L .L H V f
= 0.0061(P L) + 0.3868.
(14)
The following relations are used to explain the condition of buying electricity from or selling electricity to the grid as well as total heating demand. Es = 0 and
when E 𝐶𝐶𝐻𝑃 ≤ E dmn,t
(15)
E b = 0 when E 𝐶𝐶𝐻𝑃 > E dmn,t ,
(16)
E b = E dmn,t − E 𝐶𝐶𝐻𝑃
Es = E 𝐶𝐶𝐻𝑃 − E dmn,t
and
562
where E dmn,t is the total electricity demand (for both building and electrical chiller electricity loads): E dmn,t = E dmn + 𝛼 Q dmn ∕𝐶𝑂𝑃 el,ch ,
(17)
where E dmn and Q dmn are the building electricity and cooling demands, respectively. Here 𝛼(electric cooling ratio) is defined as the ratio of cooling load provided by electrical chillers to the total cooling load demand as follows: Q ch,el
𝛼=
Q dmn
,
(18)
where 𝛼 is defined to estimate the absorption chiller cooling load (Q ch,ab = (1 − 𝛼)Q dmn ) [7]. The total heating demand for both building heat load (Hdmn )and heat demand for generator of absorption chiller is obtained as follows [7]: Hdmn,t = Hdmn + (1 − 𝛼)Q dmn ∕𝐶𝑂𝑃 ab,ch .
(19)
3. Optimization 3.1. Objective function and constraints The actual annual benefit (AAB) is considered as the objective function in this study. In fact, AAB is defined as the difference between the total annual cost for separate systems and that for a CCHP plant to provide the electricity, heating, and cooling demand loads. The AAB which should be maximized is defined as follow: A AB($∕year ) = T AC Sep − T AC𝐶𝐶𝐻𝑃 ,
(20)
where T AC Sep and T AC𝐶𝐶𝐻𝑃 are the annual cost of providing the electrical, heating, and cooling loads in separate system and CCHP system, respectively. The annual cost of the separate system, in which electricity cooling and heating loads are provided by the grid, boilers and chillers, respectively, is estimated in the following form: T AC Sep ($∕year ) = AC Sep,ele + AC Sep,heat + AC Sep,cool ,
(21)
where AC Sep,ele , AC Sep,heat , and AC Sep,cool are the total annual cost of separate system to provide the electricity, heating, and cooling load demands, respectively. The electricity in the separate system is provided by the grid and the annual cost of electricity in the separate system is the sum of multiplying the electrical load demand (E dmn,i ) and electricity unit price (𝜙e,b,i ) and is estimated as follow:
AC Sep,ele ($∕year ) =
N ∑ ( i=1
563
) E dmn,i × 𝜙e,b,i 𝜏i ,
(22)
where N = 12 is the number of months and 𝜏i is operating hours in a month. The heating load demand during a year in the separate system is provided by a boiler. As a result, the annual cost of heating demand during a year in the separate system included the sum of investment, operational, environmental and maintenance cost estimated as:
AC Sep,heat ($∕year ) = a𝜑Cin,b +
N ∑
(
Hdmn,i × 𝜙 f ,i 𝜂b
i=1
) + 3600 × m 𝐶𝑂2 ,i × 𝜓em
𝜏i ,
(23)
where 𝜑, 𝜙 f,i , and 𝜂b are maintenance factor, price coefficients of fuel for boiler (natural gas) and boiler efficiency, respectively. In addition Cin,b is the investment cost of boiler and a is the annual cost coefficient defined as: a=
ir , 1 − (1 + ir )−k
(24)
where ir and k are interest rate and life time, respectively. Moreover, the cooling load demand in the separate system is provided by an electrical or absorption chiller, where the annual cost of them are estimated, respectively as follows:
AC Sep,cool,el ($∕year ) = a𝜑Cin,ch,el +
N ∑
(
Q dmn,i × 𝜙e,b,i
i=1
AC Sep,cool,ab ($∕year ) = a𝜑Cin,ch,ab +
N ∑
(
Q dmn,i × 𝜙 f ,i 𝐶𝑂𝑃 ab
i=1
𝐶𝑂𝑃 el
) 𝜏i
(25) )
+ 3600 × m 𝐶𝑂2 ,i × 𝜓em
𝜏i . (26)
It is worth mentioning that, the minimum value of annual cost for an electrical or absorption chiller is selected for providing cooling in the separate system. Furthermore, the total annual cost of CCHP plant is estimated as: 5 N [ ∑ ∑ E b,i × 𝜙e,b,i + m f ,i × L H V f × 𝜙 f ,i (a𝜑Cin ) j + T AC𝐶𝐶𝐻𝑃 ($∕year ) = j=1
i=1
] + 3600 × m 𝐶𝑂2 ,i × 𝜓em × 𝜏i ,
(27)
where j represents the j-th equipment in the CCHP system (including gas engine, boiler, absorption chiller, electrical chiller, and storage tank). The unit prices of buying electricity (𝜙e,b ), natural gas (𝜙 f ), and pollutant emission cost (𝜓em ) should be given in each case study. With the addition of the last term in the bracket the environmental effects are considered in the bracket the environmental effects were considered in the analysis for optimum selecting of the CCHP system equipment. The following constraint was introduced for the optimization procedure: TStack − 148.8 > 0.
564
(28)
This constraint was applied for keeping the stack temperature above the dew point temperature and avoiding formation of sulfuric acid and stack corrosion. The entire CCHP component should operate at the partial load between 0% and 100%. Moreover, the amount of excess electricity in the NO-SELL mode should not be positive.
3.2. Genetic algorithm In recent years, optimization algorithms have received increasing attention by the research community as well as industry. In the area of evolutionary computation (EC), such optimization algorithms simulate an evolutionary process where the goal is to evolve solutions by means of crossover, mutation, and selection based on their quality (fitness) with respect to the optimization problem. Evolutionary algorithms (EAs) are highly relevant for industrial applications, because they are capable of handling problems with nonlinear constraints, multiple objectives, and dynamic components properties that frequently appear in real problems [22]. Uniform crossover and random uniform mutation are employed to obtain the offspring population. The integer-based uniform crossover operator takes two distinct parent individuals and interchanges each corresponding binary bits with a probability, 0 < pc ≤ 1. Following crossover, the mutation operator changes each of the binary bits with a mutation probability, 0 < pm < 0.1. GAs are an optimization technique based on natural genetics. The GAs were developed by Holland in an attempt to simulate growth and decay of living organisms in a natural environment [23]. Even though originally designed as simulators, GAs proved to be a robust optimization technique. The term robust denotes the ability of the GAs in finding the global optimum, or a near-optimal point, for any optimization problem.
4. Case Study The CCHP optimization procedure was performed for various values of electricity, cooling, and heating loads each one in the range of 500 kW to 5000 kW (10 case studies for each load with a 500 kW step size which included 10 × 10 × 10 = 1000 total case studies). It was assumed that the electricity, cooling and heating loads were constant during a year to simplify optimization computations. However there are some discussions in Section 6.4 regarding the validity of this assumption where E-Q-H loads vary during a year. The excess electric power requirement was provided by the grid. The investment cost and efficiency (or performance) of some market available CCHP equipments are listed in Tables 1 to 3 [17]. The cost of fuels (natural gas with LHV about 49,191 kJ/kg and diesel fuel with LHV about 47,828 kJ/kg) and electricity which depended on the amount of consumption during a month, heating and cooling cost as well as the penalty cost for emission of pollutants are listed in Table 4 and Fig. 4 [21, 24, 25]. The cost of selling electricity was assumed to be zero in the NO-SELL mode. The values of equipment lifetime (k) and interest rate (i) were considered to be 15 years and 12%, respectively and maintenance factor considered to be 1.06. It was also assumed that all PMs at partial load under 20% (under 50% for gas turbine) were off and just the boiler provided the heating load demand while the electricity load demand was provided by the grid in this situation.
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Table 1. The Specifications of Market Available Prime Movers [17] Name1
Nominal power (kW)
Electrical efficiency (%)
Investment cost ($/kW)
Gas engine A
100
25.56
2873
B
300
31.14
2522
C
800
31.50
2132
D
3000
32.40
1469
E
5000
35.10
1469
A
150
27.90
2405
B
350
33.12
2093
C
800
33.66
1838
D
2500
36.90
1625
E
5500
38.70
1287
A
1150
19.14
4321
B
5457
24.94
1708
C
10,239
25.59
1687
D
25,000
30.87
1426
E
40,000
33.30
1263
Diesel engine
Gas turbine
1
Equivalent (virtual) name for commercial brands in the market.
5. Discussion and Results 5.1. Model verification To validate the modeling and optimization results, the PM specifications at nominal power such as thermal efficiency/COP, fuel consumption as well as capital cost was extracted from the equipment catalogues. In addition the operational specifications of running equipment at partial load were collected from graphical or mathematical relations derived and presented in Sections 2.1 to 2.4. The maximum 10% difference was observed between the numerical values obtained from the mentioned references and the proposed relations in this paper. 5.2. NO-SELL mode In this paper, two NO-SELL and SELL modes of operation were investigated. The selling electricity to the grid was not allowed in NO-SELL mode while it was allowed in the SELL mode. In the presented work, several selected PMs of one type could have nonsimilar capacities (nominal powers) and operational strategies (similar partial load variation during a year). This case is named
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Table 2. The Specifications of Market Available Boilers [21] Name1
Nominal power (kW)
Thermal efficiency (%)
Investment cost ($/kW)
A
450
84
15.07
B
700
84
14.26
C
1300
85
13.36
D
1630
86
12.59
E
1950
86
11.56
F
2600
87
11.82
G
3250
87
12.59
H
3900
90
11.05
I
4560
90
11.27
J
5200
90
11.05
1
Equivalent (virtual) name for commercial brands in the market.
NCNO. To maximize the AAB value, eight design parameters including the type (gas engine, diesel engine, gas turbine) and number of PMs with nominal powers mentioned are in Table 1, their required partial load, as well as the heating capacity of backup boiler is mentioned in Table 2, the cooling capacity of electrical/absorption chillers is mentioned in Table 3 and finally electric cooling ratio(𝛼) was selected. The price list for economic parameters in AAB is shown in Table 4 and the design parameters (decision variables) and the range of their variations are listed in Table 5. The value of zero in this table means there was not need to select that specific equipment in the studied CCHP system. All design variables were in discrete form. The GA Optimization was performed 1000 times for various values of E-Q-H loads for 300 generations, using a search population size of M = 100 individuals, crossover probability of pc = 0.9, gene mutation probability of pm = 0.035. The normalized optimum value of AAB versus H/Q and E/Q are shown in Figs. 5 and 6, respectively for NO-SELL and SELL modes. The AAB was normalized by its maximum value which are 2.5379 × 106 $∕year and 3.6060 × 106 $∕year for NO-SELL and SELL modes, respectively. These figure are separated by 10 surfaces each one related to a specific cooling load and AAB increased by increase of cooling load.
5.2.1 Estimation of AAB versus triple loads (E-Q-H) This section presents two approaches for estimation of optimum values of AAB in various E-Q-H loads. The estimations were based on results obtained for 1000 optimized cases mentioned in Section 4. For this purpose, both AAB and triple loads were normalized with their maximum values in 1000 cases (2.5379 × 106 $∕year and 5000 kW), respectively.
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Table 3. The Specifications of Market Available Electrical and Absorption Chillers [21] Name1
Nominal capacity (kW)
COP
Investment cost ($/kW)
A
474.16
2.75
152.43
B
526.84
2.90
151.56
C
632.21
3.10
135.51
D
790.26
3.10
133.18
E
1053.7
3.10
124.19
F
1580.5
3.20
116.07
G
1685.9
3.20
127.01
H
2107.4
3.20
126.04
I
4214.7
3.30
116.59
J
5268.4
3.30
118.48
A
421.47
0.72
262.32
B
632.21
0.75
241.79
C
702.45
0.77
228.02
D
1229.3
0.79
191.74
E
1404.9
0.81
198.23
F
1580.5
0.85
202.95
G
1826.4
0.85
194.46
H
2107.4
0.92
192.17
I
4214.7
0.94
182.57
J
5268.4
0.95
176.80
Electrical chiller
Absorption chiller
1
Equivalent (virtual) name for commercial brands in the market.
Table 4. The Price List [23, 24] Items
Price
Selling electricity (𝜙e,s ) ($/kWh)
0.093
Natural gas fuel (𝜙 f ,ng ) ($/kWh)
Fig. 4
Buying electricity (𝜙e,b ) ($/kWh)
Fig. 4
CO2 emission factor (𝜓em ) ($∕kgCO2 )
0.02086
Diesel fuel (𝜙 f ,d f ) ($/kWh)
0.0226
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Fig. 4. The cost of buying electricity and buying natural gas as a function of electricity and gas consumption. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.] In the first approach any possible simple combination (first order) of loads such as E+H+Q, E+H-Q, E+(H×Q), E+(H/Q), E-H+Q, E-H-Q, E-(H×Q), E-(H/Q), E×H+Q, (E×H)-Q, E×H×Q, (E×H)/Q, (E/H)+Q, (E/H)-Q, (E/H)×Q, (E/H)/Q, E+H, H+Q, E×H, H×Q, H/Q, E/H, were considered and named 𝜆. The normalized values of AAB were drawn versus 𝜆 and a curve fit to their variations provided a polynomial curve or 𝜆 = f (A AB). The variations of optimum values of AAB with 𝜆 were obtained for all first order combinations of E, Q and H (all possible form of 𝜆) and the minimum values of errors defined as: √ √1000 √∑ e1 = √ (𝜆 − f (A AB))i2
(29)
i=1
Table 5. The Design Parameters, Their Range of Variation and Their Step Change Variables
From
To
Step change
Type of prime mover
1
3
1
Number of prime movers (–)
0
3
1
Prime movers (Table 1)
1
5
1
Partial load (%)
0
100
10
Boiler (Table 2)
0
10
1
Electrical chiller (Table 3)
0
10
1
Absorption chiller (Table 3)
0
10
1
Electric cooling ratio (–)
0
1
569
0.001
Fig. 5. The normalized optimum value of AAB versus E/Q and H/Q for 1000 states of E-C-H loads (NO-SELL mode). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]
Fig. 6. The normalized optimum value of AAB for 1000 states of E-C-H loads (SELL mode). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.] was obtained for 𝜆 = E × Q × H combination. The normalized optimum values of AAB versus normalized values of E×H×Q for 1000 cases of E-Q-H loads are shown in Fig. 7. This figure shows that by increasing each cooling, heating or electricity load (or E × H × Q), the normalized optimum values of AAB increase. In the second approach, a more complicated (and more accurate) form for combination of E, Q and H loads was obtained as: R1 =
c1 (E@1 H )c2 @2 c3 (E@3 Q)c4 , c5 (H @4 Q)c6 @5 c7 (E@6 Q)c8
570
(30)
Fig. 7. Normalized optimum values of AAB versus normalized values of E×H×Q for 1000 cases of E-Q-H loads (NO-SELL mode). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.] where the coefficients ci , i = 1, 8 are constant and @ are mathematical signs including (+, −, ∕, ×). To obtain the above coefficients, a cubic relation between normalized optimum values of AAB and R1 was considered as: A AB = f (R1 ) = a × R1 3 + b × R1 2 + d × R1 + e.
(31)
Then the coefficients (c1 − c8 and a, b, d, e) as well as basic mathematical signs(+, −, ∕, ×) were obtained to reach the lowest possible of errors defined as: √ √1000 √∑ ( )2 f (R1 ) − A AB i . e2 = √
(32)
i=1
To obtain the optimum values of constants and signs for minimizing the value of e2 , the GA Optimization was performed for 2000 generations, using a search population size of M = 400 individuals, crossover probability of pc = 0.8, gene mutation probability of pm = 0.05. All constants (decision variables) were selected to be in the range of –5 to +5 amount of error. Finally the following equation with the maximum ±13% deviation in AAB was derived in terms of the normalized E-Q-H loads (which actually combines the effect of E-Q-H load variation into one single parameter R1 ). R1 =
−0.59(E × H )0.85 − 0.54(E × Q)0.75 −1.16(H ∕Q)0.012 + 0.13(E∕Q)−0.75
.
(33)
Variation of R1 with the normalized optimum values of AAB can be fitted into one single curve as shown in Fig. 8. Results show that by increasing R1 , the normalized optimum values of AAB increased. In addition, for R1 values in the range of 0.17 < R1 < 0.22, the normalized optimum values of AAB is zero which means that the CCHP system is not profitable in this range. For example,
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Fig. 8. Normalized optimum values of AAB versus R1 (NO-SELL mode). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]
when electricity, cooling and heating loads are 2000 kW, using Eq. (30), theR1 value obtained was 0.2533. The corresponding value of optimum normalized AAB for R1 = 0.2533 is 0.1355 is shown in Fig. 8 or was 0.6428 $∕year when it is denormalized. Correspondingly another example shows 0.4149 and 1.0636 $∕year for R1 and an optimum value of AAB when electricity load doubled. Using Fig. 8 and correlation 33 enable designers to find the maximum values of AAB and whether the selected CCHP plant for each chosen E, Q, and H loads in the range of 500 kW to 5000 kW is profitable or not. 5.3. SELL mode Selling electricity to the grid is allowed in the SELL mode. The price of selling electricity was 0.093 $/kWh (Table 4). Optimization tune up parameters were adjusted as those for the electricity tacking mode. Moreover both AAB and triple loads were normalized based on their maximum permitted values which is 3.6060 × 106 $∕year and 5000 kW, respectively. 5.3.1 Estimation of AAB versus triple loads (E-Q-H) The same two approaches described in the previous section were followed in SELL mode to obtain a relationship between optimum values of AAB and normalized combinations of E-Q-H loads. In the first approach any possible simple combination (first order) of the loads such as (E+H+Q, E+H-Q, E+(H×Q), E+(H/Q), E-H+Q, E-H-Q, E-(H×Q), E-(H/Q), E×H+Q, (E×H)-Q, E×H×Q, (E×H)/Q, (E/H)+Q, (E/H)-Q, (E/H)×Q, (E/H)/Q, E+H, H+Q, E×H, H×Q, H/Q, E/H) were considered and named 𝜆. The normalized values of AAB were drawn versus 𝜆 and a curve fit to their variations provided a polynomial curve or 𝜆 = f (A AB).
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Fig. 9. The normalized optimum values of AAB versus normalized values of H×Q for 1000 states of E-Q-H loads (SELL mode). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.] The variations of optimum values of AAB with 𝜆 were obtained for all simple combinations of E, Q, and H (all possible form of 𝜆) and the minimum values of errors defined as: √ √1000 √∑ e1 = √ (𝜆 − f (A AB))i2
(34)
i=1
was obtained for 𝜆 = Q × H combination. The results of optimum values of normalized AAB versus normalized values of Q × H for 1000 cases of E-Q-H loads are shown in Fig. 9. In the second approach, a more complicated (and more accurate) form for combination of E-Q-H loads was obtained as:
R2 =
−1.73(E × H )0.34 − 2(E × Q)0.33 −3.06(E∕H )0.26 − 0.81(E∕Q)0.58
.
(35)
The maximum deviation of ±11% was obtained for optimum values of AAB and R2 . Therefore by using R2 , the optimum values of AAB were presented in the form of one single curve as shown in Fig. 10. Results show that by increasing R2 , the normalized value of AAB increased. For example, when electricity, cooling and heating loads are 2000 kW, the corresponding value of R2 obtained was 0.5220 using Eq. (35). The corresponding value of optimum normalized AAB for R1 = 0.2533 is obtained 0.4795 using Fig. 8 or 1.7291 × 106 $∕year when it is denormalized. The corresponding value of R2 and optimum AAB obtained were 0.5226 and 1.7411 × 106 $∕year when electricity load is doubled. It is observed that the optimum value of AAB is just improved about 0.7% when the electricity load demand doubled.
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Fig. 10. Normalized optimum values of AAB versus R2 (SELL mode). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]
Fig. 11. Electrical, heating, and cooling load demands for hot and cold climates. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]
5.4. The effect of variable load demands during a year In this paper, cooling, heating, and electricity loads were considered to be constant during a year. This assumption was made to perform the optimization computations easier for a specific group of loads. However, to check the validity of the results for variable load change during a year, typical variable E, Q, and H loads shown in Fig. 11 were selected for hot and cold climates applications, respectively. Then AAB was maximized for these case studies. The optimum value of AAB in the hot climate was 0.916 × 106 $∕year and 1.51 × 106 $∕year for NO-SELL and SELL modes, respectively. These results had a 6.29% difference with constant load demand (average values of E, Q, and H during a year). In addition the optimum value of AAB in the cold climate was were 0.58 × 106 $∕year
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Fig. 12. The values of RSD for 1000 various states in NO-SELL and SELL modes. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.] and 1.27 × 106 $∕year for NO-SELL and SELL modes, respectively. These results showed a 7.41% difference with constant load demand (average values of E, Q, and H during a year). 5.5. Verification of GA optimization results To verify the optimum results of the GA and to ensure reaching the global optimum in each optimization run, the optimization problem was performed 10 times for the same input values for both NO-SELL and SELL mode and the values of relative standard deviation (RSD) were computed, which is defined as follows: √ 𝑅𝑆𝐷 (%) =
N ∑
i=1
1 ( A ABi N −1
− A ABave
A ABave
)2 × 100,
(36)
where N and A ABave are the number of runs (10 runs) and the average value of AAB (in 10 runs), respectively. The corresponding values of RSD for both NO-SELL and SELL modes for 1000 cases are shown in Fig. 12. The value of RSD is in the range of 0.5% to 2% which is acceptable in engineering problems. 6. Conclusions A combined cooling, heating, and power generation (CCHP) system was optimally designed using a GA optimization technique. The design parameters (decision variables) were type of PMs, their number as well as their partial load, backup boiler heating capacity, type and cooling loads of electrical and absorption chillers as well as the electric cooling ratio. In the presented optimization problem, the AAB was considered as the objective function. Two operational modes SELL and
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NO-SELL were studied. The GA was performed for 1000 different cases of various electrical, cooling and heating loads in the range of 500 kW to 5000 kW. The results of optimization for our case study showed that the diesel engine was the selected PM in both NO-SELL and SELL modes. In addition it was found that the optimum AAB value had a meaningful relation with multiplying of three loads (E×Q×H) in NO-SELL mode and with multiplying of Q×H in SELL mode. Furthermore two more accurate correlations (R1 and R2 ) were introduced to relate the values of three loads (cooling, heating, and electricity) with optimum values of AAB in both NO-SELL and SELL modes. It was observed that application of CCHP system with the value of R1 in the range of 0.17 < R1 < 0.22 was not profitable in the NO-SELL mode. References 1. Fumo N, Mago P, Chamra L. Emission operational strategy for combined cooling, heating, and power systems. Appl Energ. 2009;86:2344–2350. 2. Fu L, Zhao XL, Zhang SG, Jiang Y, Li H, Yang WW. Laboratory research on combined cooling, heating and power (CCHP) systems. Energ Convers Manag. 2009;50:977–982. 3. Arteconi A, Brandoni C, Polonara F. Distributed generation and trigeneration energy saving opportunities in Italian supermarket sector. Appl Therm Eng. 2009;29:1735–1743. 4. Hern´andez-Santoyo J, S´anchez-Cifuentes A. Trigeneration: an alternative for energy savings. Appl Energ. 2003;76:219–227. 5. Kwak HY, Byun GT, Kwon YH, Yang H. Cost structure of CGAM cogeneration system. Int J Energ Res. 2004;28:1145–1158. 6. Balli O, Aras H, Hepbasli A. Exergetic performance evaluation of a combined heat and power (CHP) system in Turkey. Int J Energ Res. 2007;31:849–866. 7. Balli O, Aras H, Hepbasli A. Exergoeconomic analysis of a combined heat and power (CHP) system. Int J Energ Res. 2008;32:273–289. 8. Kong XQ, Wang RZ, Li Y, Huang XH. Optimal operation of a micro-combined cooling, heating and power system driven by a gas engine. Energ Convers Manag 2009;50:530–538. 9. Jiang-Jiang W, Chun-Fa Z, You-Yin J. Multi-criteria analysis of combined cooling, heating and power systems in different climate zones in China. Appl Energ. 2010;87: 1247–1259. 10. Mago PJ, Hueffed AK. Evaluation of a turbine driven CCHP system for large office buildings under different operating strategies. Energ Buildings. 2010;42:1628–1636. 11. Liu M, Shi Y, Fang F. A new operation strategy for CCHP systems with hybrid chiller. Appl Energ. 2012;95:164–173. 12. Wang J, Zhang C, Jing YY. Multi-criteria analysis of combined cooling, heating and power systems in different climate zones in China. Appl Energy. 2010;87:1247–1259. 13. ASHRAE HANDBOOK, 1999, Chapter S7, Cogeneration Systems and Engine and Turbine Drives. 14. Consonni S, Lozza G, Macchi E. Optimization of cogeneration systems operation, Part A: prime movers modelization. ASME CONGEN-TURBO, 1989. 15. Boyce MP. Handbook for cogeneration and combined cycle power plants, ASME Press; 2002. 16. The European educational tool on cogeneration, 2nd ed., www.cogen.org; December 2001. 17. Catalogue of CHP Technologies, US Environmental Protection Agency, February, 2008. 18. Kostyuk A, Frolov V. Steam and gas turbines, Moscow: Mir Publishers; 1988. 19. Kalina J, Skorek J. CHP plants for distributed generation equipment sizing and system performance evaluation, in: Proceeding of the ECOS; 2002, Berlin, Germany.
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