Multi-objective optimal operation strategy study of micro-CCHP system

Energy 48 (2012) 472e483

Contents lists available at SciVerse ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Multi-objective optimal operation strategy study of micro-CCHP system Jing-yi Wu*, Jia-long Wang, Sheng Li Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 March 2012 Received in revised form 29 August 2012 Accepted 8 October 2012 Available online 3 November 2012

As the practical load conditions vary with time, the performance of micro combined cooling heating and power (micro-CCHP) system depends a lot on the operation strategy. So, it is significant to study the system performance and find the optimal operation strategies for various load conditions. There are many devices can be considered in micro-CCHP system. In this study, a comprehensive micro-CCHP system is built, basing on gas engine and adsorption chiller. Auxiliary devices, such as gas boiler, heat pump and electric chiller, are also considered in the study of operational optimization. In order to find the optimal operation strategies and discuss why they are the optimal ones, a mixed-integer non-linear programming model is developed. Energy saving ratio and cost saving ratio are chosen as the objectives and they are calculated hierarchically. Operation strategies under various load conditions are analyzed in detail and two dimensional distributions of system performance are presented. Results show that, optimal operation strategy changes with load conditions for energy saving optimization while it also changes with energy prices for cost saving optimization. For energy saving optimization, micro-CCHP system is always superior to conventional separated system when the heating load is over 12 kW in CHP (combined heating and power) mode or over 21 kW in CCHP mode. For cost saving optimization, micro-CCHP system can be superior to conventional separated system when the dimensionless energy price ratio is less than 0.45.
2012 Elsevier Ltd. All rights reserved.

Keywords: Combined cooling Heating and power (CCHP) Multi-objective optimization MINLP Operation strategy

1. Introduction In the last few decades, combined cooling heating and power (CCHP) system has become popular all over the world. With the utilization of waste heat (using in cooling, space heating and hot water), CCHP system can be more economical, energy-efficient and environmental friendly than conventional cogeneration plants [1e5]. The CCHP system was firstly applied in large-scale applications such as industry and commercial buildings. In recent years, relatively small-scale CCHP systems have been introduced into relatively small-scale places such as hotels, offices and hospitals, namely micro-CCHP system [6,7]. As the load condition usually fluctuates widely with time, it would be significant to study the optimal operation strategies of CCHP system under various load conditions. In CCHP system modeling, many researchers have developed mixed-integer linear programming (MILP) models to optimize system operation or system design [8e11]. In MILP model, all the devices work in on-off mode and this kind of problem is relatively

* Corresponding author. Tel./fax: þ86 21 34206776. E-mail addresses: [email protected], [email protected] [email protected] (J.-l. Wang), [email protected] (S. Li).

(J.-y.

0360-5442/$ e see front matter
2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.10.013

Wu),

easy to solve. But the solution set is incomplete without considering the part load performance of some main devices. There are also some researchers who developed mixed-integer non-linear programming (MINLP) models [12e15]. Kitagawa S. et al. [14] developed a MINLP model using particle swarm optimization for optimal operational planning of a cogeneration system， but it only focused on the analysis of optimization method. Hongwei Li et al. [15] developed a MINLP model in thermal-economic optimization, its main work is to do system performance evaluation. The objectives of system optimization usually involve cost saving, energy saving and environmental performance. As these objectives often conflict with each other, the main problem of multi-objective optimization is about how to optimize these objectives in a comprehensive way. You-yin Jing et al. [16] developed a multi-objective optimization design method based on life cycle assessment, in which several objectives are combined into a single objective by weighted method. Single-objective function, which is usually a weighted combination of several objectives, may not facilitate the judgment because of the difficulty of combining several objectives in different natures [17e20]. Burer M et al. [21] represented a multi-criteria optimization of a district cogeneration plant by using Pareto-frontier method. The Pareto-frontier is obtained when the global solution makes CO2 emission rates minimal. Gh. Abdollahi et al. [22] developed a multi-

J.-y. Wu et al. / Energy 48 (2012) 472e483

Nomenclature AC CCHP COP COST CSR EC ESR GE GB HW HP SE max P PR PLR Q

h x

adsorption chiller combined cooling, heating and power coefficient of performance operation cost cost saving ratio electric chiller energy saving ratio gas engine gas boiler hot water module electric heat pump module system electric consumption module maximum electric power energy price part load ratio thermal energy efficiency dimensionless energy price ratio

objective approach in thermoenvironomic optimization of a smallscale CCHP system and genetic algorithm was applied to find the set of Pareto optimal solutions. Kavvadias KC et al. [23] developed a multi-objective optimization method based on indicators of economic, energetic and environmental performance. The problem was solved using a multi-objective genetic algorithm and a case was studied to demonstrate the effectiveness of that method. Usually, the genetic algorithm and Pareto-frontier method is used in multi-objective optimization [9,21e25]. There are also works about operation strategies. P. J. Mago et al. [26] studied the system performance under operation strategies of following the thermal and electric loads. Mingxi Liu et al. [27] investigated a new operation strategy based on the variational electric cooling to cool load ratio in CCHP system. This paper presents a MINLP model of micro-CCHP system basing on gas engine, adsorption chiller and some other auxiliary devices. The objective functions include energy saving ratio and cost saving ratio and they are calculated hierarchically. Namely, energy saving ratio is the first one to optimize and the cost saving ratio is the second one to optimize in energy saving optimization. The sequence is reversed in cost saving optimization. This problem is solved by programming in Cþþ language. Detailed operation strategies of devices under various load conditions are analyzed and system performance is evaluated. This paper is organized as follows: Section 2 develops the model of micro-CCHP system and introduces the methodology. Section 3 analyzes system optimal operation strategies and performance when system operates in combined heating and power (CHP) and CCHP modes, respectively. Some conclusions are summarized in the last section. 2. MINLP model and solution method

473

d on-off binary variable a0, a1, a2 quadratic fitting parameters of electric efficiency of GE b0, b1, b2 quadratic fitting parameters of heating efficiency of GE c0, c1, c2 quadratic fitting parameters of COP of AC Subscripts buy electricity buying conv conventional separated system el electricity f fuel heat heating i the index of system type (CCHP or separated system) load energy load opt optimum pump1 hot water pump in AC pump2 cooling water pump in AC pump3 chilled water pump in AC pump4 water pump applied in domestic hot water tank r cooling release heat released to environment

variables. Fig. 1 (a) is the micro-CCHP system, including internal combustion gas engine module (GE), adsorption chiller module (AC), hot water module (HW), gas boiler module (GB), electric chiller module (EC), electric heat pump module (HP), and system electricity consumption module (SE). Fig. 1 (b) is conventional separated system, including GB, EC, and HP. The EC and the HP can be treated as two function modules of one heat pump. In the microCCHP system, public supply network, GB and HP work as auxiliary energy supplies to meet cooling, heating and electric loads varied in any range. The introduction of HP may increase the part load ratio of GE under some load conditions. In Fig. 1 (a), every module is not isolated. Taking SE module as an example, the electricity consumption mainly consists of pump consumption of AC and HW modules, and it is influenced by on-off state of AC module and working condition of HW module. Besides the operational variables shown in Fig. 1, system operation also includes on-off binary variable (d) of some equipment. (d ¼ 1, equipment on; d ¼ 0, equipment off). As shown in Fig. 1 (a), the cooling load can be met by AC and EC; the heating load can be met by HW, GB and HP; the electric load together electricity consumption of EC and HP can be met by either GE electricity output or electricity purchased from public grid. For various load conditions, the micro-CCHP system can work in different operation strategies to meet the energy demands. In particular, if the GE is off, both the AC and HW will stop working, and the micro-CCHP system descends to a separated system shown in Fig. 1 (b). Namely, the micro-CCHP system and separated system are unified in structure and the operation strategies of the microCCHP system are infinite. Once the GE is on, the micro-CCHP system performance should be superior to that of separated system. The optimization mathematical model of micro-CCHP system developed in this paper is mainly based on the following assumptions:

2.1. System construction To carry out this analysis, a conventional separated system is introduced as a reference system. The schematic diagrams of micro-CCHP and separated system are shown in Fig. 1. The systems are divided into different functional modules, which can be regarded as abstract functions mapping input variables to output

1) The micro-CCHP system is connected to public supply network, but not on-grid. Namely, the system can buy electricity from the public supply network when the GE electricity output is not enough, but the system can’t sell electricity to public supply network reversely. It is a common approach of domestic distributed energy system in China.

474

J.-y. Wu et al. / Energy 48 (2012) 472e483

Fig. 1. Schematic diagrams of micro-CCHP and conventional separated system. (a) Micro-CCHP system; (b) Conventional separated system.

2) Electricity efficiency from public supply network, EC coefficient of performance (COP), HP COP and GB efficiency are simplified as fixed values. The impact of external weather condition on device performance is also neglected during the calculation. 2.2. Objective functions Different objectives will lead to different results. People not only care about the energy saving performance but also care about the cost saving performance. So, energy saving ratio (ESR) and cost saving ratio (CSR) are selected as the optimization objectives. Greater ESR means better energy saving performance while greater CSR means better cost saving performance, compared with separated system. The system ESR can be represented as:

ESR ¼

Qf ;conv  Qf ;CCHP Qf ;conv

(1)

where, Qf,CCHP and Qf,conv represent total primary energy consumption of micro-CCHP and separated system, respectively. Similarly, the system CSR is calculated as:

CSR ¼

COSTconv  COSTCCHP COSTconv

(2)

where, COSTCCHP and COSTconv represent operation cost of microCCHP and separated system, respectively. For any load condition, the objective of energy saving optimization is to make ESR maximal, while the objective of cost saving optimization is to make CSR maximal. Energy saving optimization objective function is:

) ( Qf ;conv  Qf ;CCHP Qf ;conv

ESRopt ¼ max

(3)

It reflects the objective of maximizing the energy saving ratio of system under a certain load condition. ESRopt is the optimal energy

J.-y. Wu et al. / Energy 48 (2012) 472e483

saving ratio. The total primary energy consumption can be calculated as:

Qf ;i ¼ Qf ;i þ

Pel;buy;i

hel;buy

(4)

475

are dimensionless coefficients calculated according to results of [28]. AC:

Qr;AC ¼ dAC $Qh;AC $COPAC

(13)

where, subscript i ¼ conv or CCHP and hel,buy is the electricity efficiency of public supply network. Cost saving optimization objective function is:

PLRAC ¼

1

(14)

  COSTconv  COSTCCHP CSRopt ¼ max COSTconv

COPAC ¼ c0 þ c1 PLRAC þ c2 PLR2AC

(15)

(5)

Qr;AC Q r;AC

It shows the objective of maximizing the cost saving ratio of system. CSRopt is the optimal cost saving ratio. COSTCCHP and COSTconv represent the operation cost of CCHP and separated system, respectively. They are calculated as:

where, dAC is on-off binary variable of the AC, dAC ˛f0; 1g; PLRAC is the part load ratio of the AC; Eq. (15) is quadratic fitting formula and c0 w c2 are dimensionless coefficients calculated according to results of [28]. Hot water module:

COSTi ¼ PRf $Qf ;i þ PRel $Pel;buy;i

Qheat;HW ¼ dHW $Qheat;HW $hHW

(6)

where, PRf is the price of gas and PRel is the price of electricity chased from public supply network. According to Eq. (9), Eq. (8) can be calculated as:

CSRopt

where, dHW is on-off binary variable of hot water module, dHW ˛f0; 1g; hHW is the hot water module efficiency which is influenced by heating leak.

  ) (  x$ Qf ;conv  Qf ;CCHP þ Pel;buy;conv  Pel;buy;CCHP ¼ max x$Qf ;conv þ Pel;buy;conv

where, x is a dimensionless energy price ratio expressed as x ¼ PRf/ PRel.

(16)

(7)

System electricity consumption:

Pel;SE ¼ ðdAC þ dHW  dAC dHW Þ$Pel;pump1 þ dGE Pel;pump2 2.3. Constraints

þ dAC $Pel;pump3 þ dHW $Pel;pump4

The constraints include equipment and energy balance constraints. 2.3.1. Equipment constraints Equipment constraints are used to describe the modules in system. They include on-off states of equipment and module performance functions. GE:

Pel;GE ¼ dGE $Qf ;GE $hel;GE

(8)

Qheat;GE ¼ dGE $Qf ;GE $hheat;GE

(9)

PLRGE ¼

Pel;GE P el;GE

1

(10)

hel;GE ¼ a0 þ a1 PLRGE þ a2 PLR2GE

(11)

hheat;GE ¼ b0 þ b1 PLRGE þ b2 PLR2GE

(12)

where, each symbol with overline represents the corresponding parameter under full load condition. dGE is on-off binary variable of GE, dGE ˛f0; 1g; hel,GE and hheat,GE are the electric and thermal efficiency of GE, respectively; PLRGE is the part load ratio of GE; Eqs. (11) and (12) are quadratic fitting formulas and a0 w a2, b0 w b2

(17)

where, Pel,pump1, Pel,pump2, Pel,pump3 and Pel,pump4 are hot water, cooling water and chilled water pump electricity consumptions. Other devices:

Qr;EC ¼ dEC $Pel;EC $COPEC

(18)

Qheat;HP ¼ dHP $Pel;HP $COPHP

(19)

Qheat;GB ¼ dGB $Qf ;GB $hGB

(20)

where, COPEC and hGB represent electric chiller COP and GB efficiency, respectively. 2.3.2. Energy balance constraints Energy balance constraints reflect the energy balance relationships in the micro-CCHP system. Fuel balance:

Qf ¼ Qf ;GE þ Qf ;GB

(21)

Electricity balance:

Pel;buy þ Pel;GE ¼ Pel;EC þ Pel;HP þ Pel;SE þ Pel;load

(22)

476

J.-y. Wu et al. / Energy 48 (2012) 472e483

Heating balance:

2.4. Methodology

Qheat;GE ¼ Qheat;AC þ Qheat;HW

(23)

Qheat;HW þ Qheat;GB þ Qheat;HP ¼ Qheat;load þ Qheat;release

(24)

In particular, Qheat, release is the excess heating discharged to external environment. By introducing the non-negative variable (Qheat, release), the inequality relationship about heating balance in Fig. 1 is converted to equation shown in Eq. (24). Cooling balance:

Qr;EC þ Qr;AC ¼ Qr;load þ Qr;release

(25)

where, Qr, release is the excess cooling discharged to external environment. Besides the equipment constraints and energy balance constraints described from Eq. (8) to Eq. (25), non-negative constraints of the variables should be introduced. That is, all the variables in equations above must be greater than or equal to 0 to ensure physical meanings of all variables.

2.4.1. Multi-objective optimization solution The optimization results of energy saving and cost saving optimization are usually different. Namely, when the system reaches maximal ESR, the CSR is not necessarily the maximum, and vice versa. So, there are two different optimal operation strategies for this micro-CCHP system: energy saving optimization and cost saving optimization. In this paper they are dependent to each other and one is used as the other’s constraint to further limit the solution range of the optimization model, this method is known as the lexicographically stratified method [29]. Fig. 2 shows the solution processes of energy saving and cost saving optimization used in the CCHP system. As shown in Fig. 2 (a), the solution process of energy saving optimization is as follows: Step 1, maximum ESR is calculated under a given cooling, heating, and electric load condition. As the strategy of achieving maximum ESR may be not unique, the solution set may consist of different operation strategies. Step2, to find the maximum CSR from the solution set obtained in step 1. That is the final solution of the optimal model. The cost saving optimization solution process is shown in Fig. 2 (b). By using the same constraints as energy saving

Fig. 2. Multi-objective optimization flowchart of CCHP system to solve energy saving optimization and cost saving optimization. (a). Energy saving optimization; (b). cost saving optimization.

J.-y. Wu et al. / Energy 48 (2012) 472e483

optimization, the final solution can be achieved. The difference is that the optimization model is firstly calculated for maximum CSR, then for maximum ESR. Due to the existence of integer variables (equipment onoff binary variables) and non-linear constraints (equipment constraints), the mathematical optimization model is a typical MINLP model. As shown in Fig. 1 (a), there are seven modules. HP, HW and GB are related by heating load. EC and AC are related by cooling load. AC and HW are related by GE. SE depends on the other six modules. So, there are three degrees of freedom among these modules when the load conditions are given. For example, when the energy output of GE, AC and GB are assumed, the reasonable operation strategy of other devices is only one. So, this problem can be solved by three-dimensional search method. The optimization model is calculated employing programming Cþþ language. The detailed solution flowchart of step 1 in Fig. 2 is shown in Fig. 3. 2.4.2. Parametric values Eqs. (11), (12) and (15) are calculated based on quadratic fitting parameters shown in Table 1. The performance parameters of devices and electricity consumption of pumps are shown in Tables 2 and 3, respectively.

477

Table 1 Quadratic fitting parameters of part load performance [28]. items

i¼0

i¼1

i¼2

ai bi ci

0.32954 0.2816 0.7656

0.5288 0.5068 1.376

0.03125 0.7980 0.2361

Note: For AC studied in this paper, the inlet temperature of chilled water is 15  C and the inlet temperature of cooling water is 30  C.

Table 2 Performance parameters of devices [1,32]. items

Values

Items

Values

P el;GE /(kW) Q r;AC /(kW) COPHP COPEC

16 7 2.8 3.2

hHW hGB hel,buy

0.95 0.9 0.33

In this paper, x ¼ 0.258 corresponds to that natural gas price is 2.1 RMB/m3 (0.213 RMB/kWh) and electricity price is 0.824 RMB/ kWh (electricity price for hotel). x ¼ 0.345 corresponds to that natural gas and electricity price is 2.1 RMB/m3 and 0.617RMB/kWh (electricity price for residence), respectively [30,31]. 3. Numerical results The cooling load of system mainly exists in summer season. When the cooling load is 0 in other seasons, the system works to supply heating and electricity, namely works in a CHP mode. In this part, the CHP mode is firstly analyzed, and then the CCHP mode is analyzed. 3.1. Operational optimization in CHP mode 3.1.1. Energy saving optimization In CHP mode, the system load includes heating load and electric load. The parameters achieving maximal ESR in certain heat and electric load conditions are shown in Figs. 4 and 5, respectively. They are called optimal operation parameters. Fig. 4 shows the variation rules of operational parameters with heating load (Qheat, load) in energy saving optimization under a fixed electric load (Pel, load) of 16 kW. When Qheat, load is less than 10 kW, the GE keeps off, and the system operates as a separated system. As the Qheat, load gradually increases from 0 to 10 kW, both the heating output of HP (Qheat,HP) and the electricity consumption of HP (Pel,HP) increase linearly, making the electricity chased from public supply network (Pel,buy) also increase. When the Qheat, load is greater than 10 kW, the optimal electricity output of GE (Pel, GE) turns to 8.3 kW with a corresponding change of waste heat. It shows that under these load conditions, the running of GE contributes to energy conservation. The reduction of GE electricity output is not happened to reduce waste heat discharged to environment (Qheat, release), because the reduction will sharply decline the electricity generation efficiency of GE. The reason for not increasing Pel, GE to satisfy larger part of the entire electric load is that it will lead to

Table 3 Electricity consumption of pumps.

Fig. 3. Solution flowchart of step 1 in Fig. 2.

Pumps

Electricity consumption(kW)

Pump1 Pump2 Pump3 Pump4

0.25 0.37 0.18 0.18

478

J.-y. Wu et al. / Energy 48 (2012) 472e483

Fig. 4. Variation rules of operational parameters with heating load in energy saving optimization (Pel, load ¼ 16 kW).

much more waste heat (Qheat, release) and cause system performance decreasing. The Pel, GE remains 8.3 kW until the heating load reaches 22 kW. Once the heating load is beyond 22 kW, Pel, GE begins to increase with the heating load and the heating load will be fully satisfied by waste heat of GE (Qheat, GE). When Pel, GE reaches the rated value of 16 kW, Qheat, GE stops increasing. Then, the excess heating load will be met by HP. As the Pel,HP keeps rising, the excess electricity consumption will be met by public supply network. Fig. 5 shows the variation rules of operational parameters with electric load in energy saving optimization under a fixed heating load of 40 kW. When the electric load is 0, the optimal Pel, GE is 7.0 kW. Part of Pel, GE is employed to meet the system electrical consumption, the rest is used to drive HP to generate heat. The waste heat of GE together with heat generated by HP is employed to meet the heating load. In this case, the system is similar to a gas heat pump system. With the increasing of electric load, the optimal Pel, GE increases gradually. The increasing of Pel, GE will lead to the increasing of Qheat, GE, which makes the electricity consumption of HP decrease. After Pel,HP reaches the rated value of 16 kW, it will not be enough to satisfy the need and the system has to chase electricity from the public supply network.

Fig. 5. Variation rules of operational parameters with electric load in energy saving optimization (Qheat, load ¼ 40 kW).

Fig. 6. Variation rules of optimal cost saving operation parameters with Qheat, （Pel, load ¼ 16 kW, x ¼ 0.258）.

laod

As shown in Figs. 4 and 5, the GB is always off. There are mainly two reasons. Firstly, the primary energy efficiency of HP (2.8  0.33 ¼ 0.924) is greater than that of GB. Secondly, part of the electricity consumption of HP can be met by electricity output of GE, which can increase the part load ratio and improve the performance of GE when Pel. laod is low. Therefore, if the system is designed to reach maximal ESR, HP should be used as a supplementary heat generator rather than GB. 3.1.2. Cost saving optimization The system’s optimal cost saving operation strategy is not only affected by load conditions, but also by energy prices condition. The energy prices condition is described by a dimensionless ratio (x). The variation rules of optimal cost saving operation parameters with heating and electric load are given in Fig. 6 and 7, respectively. Comparing Fig. 6 with Fig. 4, it can be found that the optimal operation strategies are quite different from each other even under the same load conditions. For a fixed electric load condition of 16 kW, when the heating load is less than 3 kW the GE is off, namely the system optimal operation strategy is to operate as a separated system. During the engine-off time, the heating load is met by the GB rather than the electric heat pump, which is different from

Fig. 7. Variation rules of optimal cost saving operation parameters with Pel, ¼ 40 kW, x ¼ 0.258）.

load(Qheat, load

J.-y. Wu et al. / Energy 48 (2012) 472e483

energy saving optimization shown in Fig. 4. This is because, the operation cost of GB is less than that of electric heat pump for supplying the same heating. When the heating load is greater than 3 kW, the engine turns on and the optimal Pel, GE is 12.2 kW with corresponding change of waste heat. At this point, heating load is entirely met by Qheat, GE, and some of the electric load is met by purchasing from the public grid. When the heating load is greater than 29 kW, the optimal Pel, GE begins to increase with the heating load, and Qheat, GE starts to fully meet the heating load. When the Pel, GE reaches the rated load of 16 kW, the electricity output and waste heat output of GE can no longer increase, and the lacked heating should be met by the GB. Under all the load conditions, electric heat pump is always off. It can also be found that Qheat, release appeared in Fig. 6 is much greater than that in Fig. 4. If the gas price is 0, the max{CSR}can be got by turning on GE to supply electricity load and releasing all the exhaust heat to environment. Therefore, adding an energy storage device may be significant for a more economical operation [5,33]. Fig. 6 and 7 almost show the same operation strategies when Qheat, load is fixed at a high value of 40 kW. The Pel, load is satisfied by GE and the Qheat, load is mainly satisfied by waste heat of GE and HP. When Pel, load is 0, the GE still keeps on and the Pel, GE is used to meet the requirement of HP and SE. As shown in Fig. 6 and 7, the GB and HP work in some load conditions, and they even should work together under some certain load conditions. As mentioned in Section 3.1.1, the GB is needless in energy saving optimization operation, but it should be considered in cost saving optimization operation. From the comparative analysis above, it is obvious that energy price is an important factor affecting cost saving optimization. Fig. 8 shows the variation rules of optimal Pel, GE with energy prices condition under various load conditions (load conditions 1 to 9 are various types Pel, load/Qheat, load used in Figs. 8 and 9). When the x rises, the Pel, GE shows a downward trend on the whole. That is because the higher gas price decreases the cost saving performance of GE. As for load conditions 1 and 2, due to relatively lower electric and heating load, the GE remains off and the system works as separated system. As shown in load conditions 1 to 9 in Fig. 8, when the Pel, GE drops to 0 from a relatively high value, the corresponding x is called critical price ratio (x*). It is the maximal dimensionless price ratio keeping system working with cost saving performance. If x is lower than x*, the CHP system can have a cost saving performance compared with separated system. If x is greater than x*, the GE should be off and the system will work as separated system. The greater the x* is, the better the system’s cost saving

Fig. 8. Variation rules of optimal Pel,

GE

with x under various load conditions.

479

Fig. 9. Variation rules of optimal operational parameters of GB and HP with x

performance would be. From load conditions 1, 4 and 7, it can be observed that the x*is small when the heating load is low. The system can ensure cost saving only under a low x. It can also be concluded from Fig. 8 that the rising of heating load can obviously make x* increase under the same electric load. When x is greater than 0.45, the GE remains off in any load conditions, and the CHP system would have no cost saving performance compared with separated system. Four load conditions 2, 5, 8 and 9 in Fig. 8 are specially analyzed in Fig. 9, and the variation rules of optimal operation parameters of Qheat,GB and Qheat,HP with x are obtained. As shown that, when x is less than 0.325 the system heating load is met by GB; when x is greater than 0.325, the system heating load is met by HP. This is because that, when x ¼ 0.325, the operation cost of GB equals to that of HP for supplying the same heating. 3.1.3. Distribution of optimal performance coefficient In system analysis, it is usually essential to get the distribution of optimal performance coefficient for various load conditions. It helps to judge whether the CHP system has energy saving or cost saving potential under a certain load condition, and facilitates the determination of system equipment working state. Fig. 10 shows the contour map of optimal ESR with electricity and heating loads in CHP mode. The optimal ESR value is the

Fig. 10. Contour map of optimal ESR with electric and heating loads in CHP mode.

480

J.-y. Wu et al. / Energy 48 (2012) 472e483

maximal ESR that the CHP system can achieve under the corresponding load condition. The shadow region corresponds to optimal ESR of 0, which means that the optimal operation strategy is to work as a separated system with GE off. So, the shadow region is called as engine-off region, while the region outside the shadow region is called as engine-on region. In energy saving optimization, the engine-on region is also known as energy saving adaptive region, where the CHP system can achieve energy saving performance. It can be observed in Fig. 10 that, the optimal ESR is very sensitive to the change of heating load while relatively insensitive to the change of electric load when the electric load is over 3 kW. Meanwhile, when the heating load is less than 12 kW, the energy saving performance of CHP system is always not better than that of separated system; when the heating load is greater than 20 kW, the energy saving performance of CHP system is always better than that of separated system; when the heating load is between 12 kW and 20 kW, the CHP system performance is determined by both heating and electric loads. As shown In Fig. 10, from all the load conditions, the biggest value of optimal ESR can reach 0.23. Fig. 11 and 12 show the contour map of optimal CSR with the electricity and heating loads in CHP mode when x is 0.258 and 0.345, respectively. In Fig. 11, similar to Fig. 10, the shadow region means GE off and the other region means GE on. The engine-on region is also known as cost saving adaptive region, where the CHP system can achieve cost saving performance. The optimal CSR is very sensitive to the heating load change, while it is relatively insensitive to the electric load change when the electric load is over 6 kW. In Fig. 11, the biggest value of CSR is about 0.32. Comparing Fig. 11 with Fig. 10, the difference can be easily observed from the different sizes and shapes of their engine-off regions. When x is 0.258, the engine-off region of CSR is entirely included in the engine-off region of ESR, which indicates that the system cost saving adaptive area is larger than energy saving adaptive area under such prices condition. Comparing Fig. 12 with Fig. 11, it is obvious that as x increases, the system cost saving performance declines and the engine-off region gets larger. It can also be found that the engine-off region of CSR in Fig. 12 is a little larger than that of ESR in Fig. 10. In fact, as x increases further, the engine-off region will continue getting larger while the cost saving adaptive region getting narrower. When x is larger than 0.45 (as concluded in Section 3.1.2), the figure will be full of shadow region, and the system should run as a separated system under any load condition without cost saving performance.

3.2.1. Energy saving optimization Here, the optimal Pel, GE and optimal Qr, AC are chosen as two typical operation parameters. As shown in Fig. 13, the optimal Pel, GE is affected by both Qheat, load and Qr,load. When Qheat, load is less than 10 kW (load conditions 1 and 2), the GE remains off. When Qheat, load increases to 10 kW or more, the GE turns on. For case 3, when Qr,load is greater than 5 kW, the GE turns on, and Pel, GE is 11.8 kW. At this time, part of the GE waste heat is applied to meet the Qheat, load, the rest part is used to drive AC, as shown in Fig. 14. As the Qheat, load increases from case 3 to case 4, the Pel, GE increases to 12.5 kW while the Qr, AC falls to 4.9 kW. It is because that applying waste heat of GE to supply heating load is more energy efficient than applying it to drive AC. Therefore in energy saving optimization, the waste heat of GE should be used to meet the heating load first. The heating load in case 4 is larger than that in case 3, and the rest waste heat after meeting the heating load in case 4 is smaller than that in case 3,

Fig. 11. Contour map of optimal CSR with electric and heating loads in CHP mode （x ¼ 0.258）.

Fig. 13. Variation rules of Pel, GE with cooling and heating loads in energy saving optimization （Pel, load ¼ 16 kW）.

Fig. 12. Contour map of optimal CSR with electric and heating loads in CHP mode （x ¼ 0.345）.

3.2. Operational optimization in CCHP mode Compared with CHP mode, the CCHP mode is much more complicated both in load conditions and in system operation. Some of the conclusions from CHP mode can be good references to understand the CCHP mode.

J.-y. Wu et al. / Energy 48 (2012) 472e483

481

Fig. 14. Variation rules of Qr, AC with cooling and heating loads in energy saving optimization （Pel, load ¼ 16 kW）.

Fig. 16. Variation rules of Qr, （Pel, load ¼ 16 kW, x ¼ 0.258）.

making the AC cooling output decrease in case 4. As the heating load continues increasing, Pel, GE decreases at first (case 4 to case 5) and then increases (case 5 to case 8). That’s because that when the heating load increases to case 5, all engine exhaust heat would be used to meet the heating load and the AC would turns off, making the total heating consumption decrease. From case 5 to case 8, the cooling load is entirely met by the EC. Note that, cooling generated by EC contributes more than that by AC at these conditions.

in cost saving optimization, the waste heat of GE is also used to meet the heating load first, and then the rest part is used to drive the AC.

3.2.2. Cost saving optimization Fig. 15 and 16 show the optimal cost saving operation strategies when Pel, load is 16 kW and x is 0.25. In cost saving optimization, even in working conditions with small heating load (case 1 and case 2), once the cooling load is greater than a certain value, the GE turns on. It is mainly due to the relatively low gas price. Comparing Fig. 15 with Fig. 13, it can be observed that the optimal Pel, GE in cost saving optimization is generally larger than that in energy saving optimization. It is mainly because that x ¼ 0.258 corresponds to a relatively low gas price, which makes the cost saving performance superior to energy saving performance in CCHP system. Comparing Fig. 16 with Fig. 14, the AC keeps off in case 5 to case 9 in Fig. 14, while in Fig. 16 it is case 7 to case 9. These results show that the AC operation range (load conditions under which the AC keeps on) in cost saving optimization is larger than that in energy saving optimization. From case 1 to 9 in Fig. 16, it is obvious that the cooling output of AC decreases as the heating load increases. That’s because

Fig. 15. Variation rules of Pel, （Pel, load ¼ 16 kW, x ¼ 0.258）.

GE

AC

with Qr,load in cost saving optimization

3.2.3. Distribution of system performance coefficient The optimal performance coefficients (ESR and CSR) in CCHP mode are influenced by cooling, heating and electric load simultaneously. So, the distribution of optimal performance coefficient in CCHP mode is three-dimensional spatial distribution. In order to clearly show the distribution of system performance, herein electric load is assumed as constant value. The following analysis is based on 3 special cases with electric load of 0 kW, 8 kW and 16 kW, respectively. Figs. 17, 19 and 21 show the contour maps of optimal ESR in energy saving optimization under the electric load of 0 kW, 8 kW and 16 kW, respectively. Figs. 18, 20 and 22 show the contour maps of optimal CSR in cost saving optimization under the electric load of 0 kW, 8 kw and 16 kW, respectively. As shown in these figures, there are lots of contour lines, which are nearly perpendicular to the x-axis. Those mean that, in many occasions, the optimal performance coefficients are insensitive to cooling load change. In energy saving optimization, when Qheat, load is less than 10 kW, the energy saving performance of CCHP system is always worse than that of the separated system; when Qheat, load is greater than 21 kW,

with Qr,load in cost saving optimization Fig. 17. Contour map of optimal ESR with heating and cooling loads （Pel,

load

¼ 0）.

482

J.-y. Wu et al. / Energy 48 (2012) 472e483

Fig. 18. Contour map of optimal CSR with heating and cooling loads （Pel, x ¼ 0.258）.

load

¼ 0,

Fig. 19. Contour map of optimal ESR with heating and cooling loads (Pel, load ¼ 8 kW).

Fig. 20. Contour map of optimal CSR with heating and cooling loads (Pel, x ¼ 0.258).

load

¼ 8 kW,

Fig. 21. Contour map of optimal ESR with heating and cooling loads (Pel, load ¼ 16 kW).

the energy saving performance of CCHP system is always better than that of the separated system. The shadow region in each figure is engine-off region, where system runs as a separated system. Comparing Fig. 17 with Fig. 19 and Fig. 18 with Fig. 20, it is observed that when the electric load changes from 0 to 8 kW, the engine-off regions get smaller while the system adaptive regions get larger. The size of engine-off region in cost saving optimization is especially sensitive to this kind of change and it is mainly because that the influence of load conditions on optimal cost saving operation is enlarged by the energy prices. Comparing Fig. 19 with Fig. 21 and Fig. 20 with Fig. 22, it is observed that when the electric load changes from 8 to 16 kW, the engine-off region, the system energy saving adaptive region and cost saving adaptive region almost remain unchanged. This is because that when the electric load is greater than 8 kW, the part load performance of GE changes a little which makes the change of micro-CCHP system performance not obvious. In summary, the increasing of electric load can improve the optimal energy saving and cost saving performance. However, when the electric load reaches a certain value, the improvement of system performance is unobvious. We can also find that, the biggest values of optimal ESR and CSR appear when the electricity output of GE is 8 kW, which reminds us that full load operation of GE not necessarily means best performance [34].

Fig. 22. Contour map of optimal CSR with heating and cooling loads (Pel, load ¼ 16 kW, x ¼ 0.258).

J.-y. Wu et al. / Energy 48 (2012) 472e483

4. Conclusions In this work, a micro-CCHP system based on GE, AC and some auxiliary devices is proposed. In order to find the optimal operation strategies and analyze the corresponding performance in various load conditions, a multi-objective MINLP model is built and calculated. Some conclusions can be summarized as follows. For energy saving optimization, optimal operation strategy changes with load conditions. Micro-CCHP system is always superior to conventional separated system when the heating load is over 12 kW in CHP mode or over 21 kW in CCHP mode. The GB is useless and the HP is the appropriate auxiliary heating device in CHP mode. The waste heat of GE should be used to satisfy the heating load firstly and then to drive the AC in CCHP mode. For cost saving optimization, optimal operation strategy not only changes with load conditions but also changes with energy prices. When the x reaches 0.45, the GE should be off and the system works as separated system in CHP mode. When the x is over 0.325, the HP is more economical than GB in CHP mode. The GB is useful when the GE is off or the heating load is very high. Both in energy saving optimization and cost saving optimization, the increasing of electric load can obviously improve system performance when the part load ratio of GE is relatively low. This study will help to understand the optimal operation strategies under various load conditions and energy price conditions. It also supplies references about system performance. There is still some heat released to the environment. So, energy storage devices can also be considered in future works. The COP of adsorption chiller is relatively low, the absorption chiller can also be considered in micro-CCHP system in the future work. Acknowledgments This research has been supported by the National Natural Science Foundation of China (51076099). References [1] Wu DW, Wang RZ. Combined cooling, heating and power: a review. Progress in Energy and Combustion Science 2006;32:459e95. [2] Mago PJ, Chamra LM, Hueffed A. A review on energy, economical, and environmental benefits of the use of CHP systems for small commercial buildings for the North American climate. International Journal of Energy Research 2009;33:1252e65. [3] Lai SM, Hui CW. Integration of trigeneration system and thermal storage under demand uncertainties. Applied Energy 2010;87:2868e80. [4] Maidment GG, Tozer RM. Combined cooling heat and power in supermarkets. Applied Thermal Engineering 2002;22:653e65. [5] Xu Jianzhong, Sui Jun, Li Bingyu, Yang Minlin. Research, development and the prospect of combined cooling, heating, and power systems. Energy 2010; 35(11):4361e7. [6] Kong XQ, Wang RZ, Li Y, Huang XH. Optimal operation of a micro-combined cooling, heating and power system driven by a gas engine. Energy Conversion and Management 2009;50:530e8. [7] Mago a PJ, Chamra LM, Ramsay J. Micro-combined cooling, heating and power systems hybrid electric-thermal load following operation. Applied Thermal Engineering 2010;30:800e6. [8] Ren HB, Gao WJ. A MILP model for integrated plan and evaluation of distributed energy systems. Applied Energy 2010;87:1001e14.

483

[9] Sakawa M, Kato K, Ushiro S. Operational planning of district heating and cooling plants through genetic algorithms for mixed 0e1 linear programming. European Journal of Operational Research 2002;137:677e87. [10] Oh SD, Lee HJ, Jung JY, Kwak HY. Optimal planning and economic evaluation of cogeneration system. Energy 2007;32:760e71. [11] Arcuri P, Florio G, Fragiacomo P. A mixed integer programming model for optimal design of trigeneration in a hospital complex. Energy 2007;32: 1430e47. [12] Zhang B, Long W. An optimal sizing method for cogeneration plants. Energy and Buildings 2006;38(3):189e95. [13] Li CZ, Shi YM, Huang XH. Sensitivity analysis of energy demands on performance of CCHP system. Energy Conversion and Management 2008;49(12): 3491e7. [14] Kitagawa S, Nakazawa C, Fukuyama Y. Particle swarm optimization for optimal operational planning of a cogeneration system. In: Proceedings of the IASTED international conference on modelling, simulation and optimization; 2004. p. 43e8. [15] Li Hongwei, Nalim Razi, Haldi P-A. Thermal-economic optimization of a distributed multi-generation energy systemda case study of Beijing. Applied Thermal Engineering 2006;26:709e19. [16] Jing You-Yin, Bai He, Wang Jiang-Jiang. Multi-objective optimization design and operation strategy analysis of BCHP system based on life cycle assessment. Energy 2012;37(1):405e16. [17] Mago PJ, Chamra LM. Analysis and optimization of CCHP systems based on energy, economical, and environmental considerations. Energy and Buildings 2009;41:1099e106. [18] Piacentino A, Cardona F. EABOT e energetic analysis as a basis for robust optimization of trigeneration systems by linear programming. Energy Conversion and Management 2008;49:3006e16. [19] Kavvadias KC, Tosios AP, Maroulis ZB. Design of a combined heating, cooling and power system: sizing, operation strategy selection and parametric analysis. Energy Conversion and Management 2010;51(4):833e45. [20] Wang JJ, Jing YY, Zhang CF, Zhao JH. Review on multi-criteria decision analysis aid in sustainable energy decision-making. Renewable and Sustainable Energy Reviews 2009;13:2263e78. [21] Burer M, Tanaka K, Favrat D, Yamada K. Multi-criteria optimization of a district cogeneration plant integrating a solid oxide fuel cell-gas turbine combined cycle, heat pumps and chillers. Energy 2009;28:497e518. [22] Abdollahi Gh, Meratizaman M. Multi-objective approach in thermoenvironomic optimization of a small-scale distributed CCHP system with risk analysis. Energy and Buildings 2011;43:3144e53. [23] Kavvadias KC, Maroulis ZB. Multi-objective optimization of a trigeneration plant. Energy Policy 2010;38:945e54. [24] Weber C, Maréchal F, Favrat D, Kraines S. Optimization of an SOFC-based decentralized polygeneration system for providing energy services in an office-building in Tokyo. Applied Thermal Engineering 2006;26(13):1409e19. [25] Wang Jiang-Jiang, Jing You-Yin, Zhang Chun-Fa. Optimization of capacity and operation for CCHP system by genetic algorithm. Applied Energy 2010;87: 1325e35. [26] Mago PJ, Fumo N, Chamra LM. Performance analysis of CCHP and CHP systems operating following the thermal and electric load. International Journal of Energy Research 2009;33:852e64. [27] Liu Mingxi, Shi Yang, Fang Fang. A new operation strategy for CCHP systems with hybrid chillers. Applied Energy 2012;95:164e73. [28] Li S, Wu JY. Theoretical research of a silica gelewater adsorption chiller in a micro combined cooling, heating and power (CCHP) system. Applied Energy 2009;86:958e67. [29] Cheng Hao-zhong, Gao Ci-wei, Ma Ze-liang, Zhu Zhong-lie, Xu Jin, Wang Xiaohui. The lexicographically stratified method for multi-object optimal electric power network planning. Proceedings of the CSEE 2003;23(10):11e6. [30] Statistical data of natural gas price in China, http://www.21ce.cc/search/ detail_11177_1.aspx; 2008 [only in Chinese]. [31] Electricity price in Shanghai of China, http://95598.sh.sgcc.com.cn/produced_ pages/info/pages/0/2012-07-06/20120706151558712964.html; 2012 [only in Chinese]. [32] Wang RZ. Advances in refrigeration and HVAC. Beijing: Science Press; 2007 [only in Chinese]. [33] Lai Sau Man, Hui Chi Wai. Feasibility and flexibility for a trigeneration system. Energy 2009;34:1693e704. [34] Kong XQ, Wang RZ, Wu JY. Experimental investigation of a micro-combined cooling, heating and power system driven by a gas engine. International Journal of Refrigeration 2005;28:977e87.