Modeling and Optimization of a Cooling Tower-Assisted Heat Pump System

energies

Article Modeling and Optimization of a Cooling Tower-Assisted Heat Pump System

Xiaoqing Wei, Nianping Li *, Jinqing Peng *, Jianlin Cheng, Jinhua Hu and Meng Wang College of Civil Engineering, Hunan University, Changsha 410082, China; [email protected] (X.W.); [email protected] (J.C.); [email protected] (J.H.); [email protected] (M.W.) * Correspondence: [email protected] (N.L.); [email protected] (J.P.); Tel.: +86-731-8882-2667 (N.L.); +86-731-8484-6217 (J.P.)

Academic Editor: Hongxing Yang Received: 15 April 2017; Accepted: 17 May 2017; Published: 20 May 2017

Abstract: To minimize the total energy consumption of a cooling tower-assisted heat pump (CTAHP) system in cooling mode, a model-based control strategy with hybrid optimization algorithm for the system is presented in this paper. An existing experimental device, which mainly contains a closed wet cooling tower with counter ﬂow construction, a condenser water loop and a water-to-water heat pump unit, is selected as the study object. Theoretical and empirical models of the related components and their interactions are developed. The four variables, viz. desired cooling load, ambient wet-bulb temperature, temperature and ﬂow rate of chilled water at the inlet of evaporator, are set to independent variables. The system power consumption can be minimized by optimizing input powers of cooling tower fan, spray water pump, condenser water pump and compressor. The optimal input power of spray water pump is determined experimentally. Implemented on MATLAB, a hybrid optimization algorithm, which combines the Limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm with the greedy diffusion search (GDS) algorithm, is incorporated to solve the minimization problem of energy consumption and predict the system’s optimal set-points under quasi-steady-state conditions. The integrated simulation tool is validated against experimental data. The results obtained demonstrate the proposed operation strategy is reliable, and can save energy by 20.8% as compared to an uncontrolled system under certain testing conditions.

Keywords: cooling tower-assisted heat pump; theoretical and empirical models; energy saving; hybrid optimization algorithm

1. Introduction With rapid economic development and improvement of living standard, energy demand in buildings has increased in China. Central air conditioning systems have been widely used, and their energy consumptions account for over 40% of the total energy consumption in buildings [1]. In cooling load-dominated areas, the cooling tower-assisted heat pump (CTAHP) system is a suitable alternative as the cold and heat sources for central air conditioning systems with the same advantage as common water-cooling air conditioners and water source heat pumps. Obviously, the efficient operation of CTAHP systems exerts significant implication on the energy-saving of central air conditioning systems. Numerous studies have highlighted the potential impact of optimization on energy consumption of cooling tower-assisted air conditioning systems. The significant energy saving potential of cooling tower-assisted chiller systems can be estimated by using different optimization strategies, such as an energy optimization methodology [2], multi-objective evolutionary algorithms [3], an effective and robust chiller sequence control strategy [4], a multivariable Newton-based extremum-seeking control (ESC) scheme [5], an optimal approach temperature (OAT) control strategy [6], a data-driven approach with a two-level intelligent algorithm [7], etc.

Energies 2017, 10, 733; doi:10.3390/en10050733 www.mdpi.com/journal/energies Energies 2017, 10, 733 2 of 18

Apart from this effort, efficient operation of CTAHP systems can also be effectively achieved by using different optimal operation strategies, such as thermodynamic and thermoeconomic optimization with evolutionary algorithms [8], numerical simulation with TRNSYS [9], a golden section search algorithm [10], etc. In addition, some researchers have focused on the optimal control strategies to reduce the total power consumption of central air conditioning systems. For example, Ma and Wang [11] presented a model-based supervisory and optimal control strategy for a central chiller plant to enhance the system performance and energy efficiency with 0.73–2.25% of daily energy savings via a reference using traditional settings. All these studies above demonstrated the energy-saving potential of air conditioning systems associated with the application of different control techniques. To minimize the total energy consumption of the CTAHP system in cooling mode, a model-based control strategy with hybrid optimization algorithm for the system is presented in this paper. An existing experimental CTAHP system, which has been designed, built and tested in Hunan University, China, is selected as the study object. The system was originally designed to provide hot water. In order to find out the effects of sprayed antifreeze on the system efficiency under frost prevention conditions, Cheng et al. [12] conducted a series of experiments and developed heat and mass transfer models of the cooling tower. They found that when ambient wet-bulb temperature is below 3.6 ◦C, spray antifreeze could improve the system efficiency by 5% to 11%. In this paper, theoretical and empirical formulas are adopted to model the nonlinear relationship among the operating variables of the system. Four variables, viz. the desired cooling load, the ambient wet-bulb temperature, the temperature and flow rate of chilled water at the inlet of the evaporator, are set as independent variables. The system energy consumption can be minimized by optimizing the input powers of the cooling tower fan, the spray water pump, the condenser water pump and compressor. The optimal input power of the spray water pump is determined experimentally. A hybrid algorithm [13] that combines the Limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm [14] with the Greedy Diffusion Search (GDS) algorithm, is used to search for the optimal set points of the other three independent variables. The models, experimental data and the hybrid optimization algorithm are coded and implemented in the Matlab environment. The results demonstrate the proposed control strategy is reliable, and can offer a remarkable energy saving under certain testing conditions.

2. System Description Figure1 illustrates the schematic diagram of the CTAHP system in cooling mode. The system comprises a closed wet cooling tower (CWCT) with counter flow construction, a water source heat pump (WSHP) unit, a condenser water pump, a spray water pump, valves and connection tubes. The counter-flow CWCT is an important component of the CTAHP system. In the CWCT unit, there are three fluids, viz. spray water, condenser water and air. The air enters into the tower and goes through the finned heat-exchanger coil from bottom to top, while the condenser water and spray water flow through the coil from top to bottom, and the heat and mass transfer are completed in the course of flow. Another important part of the system is the WSHP unit which is coupled into the CWCT as a cooling source. The cooling water is fed by the circulating pump to the condenser of the WSHP unit, and then returns to the tower after being heated by the refrigerant of R22. Meanwhile, the chilled water is cooled by the refrigerant in the evaporator. In Figure1, M, T and P indicate the mass flow rate, temperature and input power measurements, respectively. Energies 2017, 10, 733 3 of 18 Energies 2017, 10, 733 3 of 17

Figure 1. SchematicSchematic diagram of the CTAHP system under cooling conditions. M, T and P indicateindicate the mass flow ﬂow rate, temperature and input power measurements, respectively.

3. Formulation of t thehe Optimization Problem

3.1. Mathematical Modeling Nonlinearity and complexity exist exist inherently in the dynamic process of the whole integrated CTAHP system, which makes it different to represent accurately using using only only theoretical theoretical approaches. approaches. Approaches combining combining theoretical theoretical and and empirical empirical methods methods are adopted are adopted herein to allow herein for to performance allow for performanceprediction over prediction a very wideover rangea very of wide operating range of conditions. operating Modelingconditions. approaches Modeling forappro mostaches of thefor mostsystem of components,the system components, including the including heat pump, the heat cooling pump, tower, cooling fan andtower, pumps, fan and as shownpumps, in as Figure shown1, inare Figure described 1, are as described follows. as follows.

3.1.1. Heat Pump Model The cooling load is expressed as follows:

=( − ) QQchwchw c w m chwT Tchw chw,,,i i TT chwchw, oo (1(1))

During the cooling process, the heat pump is is typically a a vapor vapor-compression-compression refrigerant refrigerant device. device. The power power consumption consumption of of the the water water-to-water-to-water scroll scroll heat heat pump pump is a is function a function of the of thecooling cooling load, load, the chilledthe chilled water water temperature temperature at the at inlet the inlet of the of theevaporate evaporate and andthe thecondenser condenser water water temperature temperature at the at inletthe inlet of the of thetower tower [15,16 [15].,16 A]. regression A regression function function is isused used to to describe describe the the relationship relationship of of the the power consumption and these variables, which is expressed as follows [[17].17].

2 P aaT  T  aT  T2  aQ  aQ2 2  aQT  T Pcomp comp= a0 +01,,2,,3a1(Tcw ,i cw− iTchw chw,i) i+ a2(Tcw cw,i − iTchw chw,i i) + a3Q chw+ a 44Q chwchw + 5a5 chwQchw cw(T ,, icw,i − chwT ichw ,i) (2(2))

As the the heat heat pump pump unit unit is treated is treated as a singleas a single unit for unit modeling, for modeling, the energy the balance energy of balance the subsystem of the subsystemcan be expressed can be asexpressed follows [as18 ]:follows [18]: Q = Q + P × η (3) cw chw comp  QQPcw chw comp (3) 3.1.2. Cooling Tower Model 3.1.2.A Cooling counter-flow Tower heatModel exchanger with fins is used in the CWCT. The air inside the tower is sucked into the heat exchanger by means of an axial fan on the tower. The condenser water passing through A counter-flow heat exchanger with fins is used in the CWCT. The air inside the tower is sucked the heat exchange coil heats the air outside the tubes. The heat transfer rate in the heat exchanger can into the heat exchanger by means of an axial fan on the tower. The condenser water passing through be determined by the following relation: the heat exchange coil heats the air outside the tubes. The heat transfer rate in the heat exchanger can be determined by the following relation: Qcw = cwmcw(Tcw,i − Tcw,o) (4)  Qcw c w m cw T cw,, i T cw o  (4) The cooling tower model follows our recent work [19], which is a modification of the work conductedThe cooling by Pascal tower Stabat model and Dominiquefollows our Marchio recent work [20]. The [19], cooling which capacity is a modification of a closed of wet the cooling work conductedtower under by the Pascal counter-flow Stabat and condition Dominique is simply Marchio given [20]. by The [19 cooling]: capacity of a closed wet cooling tower under the counter-flow condition is simply given by [19]:

Energies 2017, 10, 733 4 of 18

Tcw,i − Twb,i Qcw = 0.5 (5) 1 µcw 1 1 0.8 + 0.8 + + βextcpsatma βintmcw 2cpsatma 2cwmcw with µ = 0 µcw 2 (6) 1 + 0.0337Tcw,i + 0.000221Tcw,i

3.1.3. Fan and Pump Models The speeds of pumps and fan can be controlled to improve the whole system’s performance. The power consumptions of the condenser water pump and fan are inﬂuenced by the mass ﬂow rates of the condenser water and air, which are given, respectively, by [18,21]:

2 3 Pf = b0 + b1 × ma + b2 × ma + b3 × ma (7)

2 3 Pcw = c0 + c1 × mcw + c2 × mcw + c3 × mcw (8)

3.1.4. Uncertainty Analysis In Equations (1)–(8), there are seven input variables, viz. ambient wet-bulb temperature, inlet temperature and flow rate of the chilled water, and the power consumptions of the compressor, condenser water pump, spray water pump and cooling tower fan. The eight output variables include water temperatures at the inlet and outlet of the condenser, flow rates of condenser water and air, the cooling capacity of the heat pump unit and the heat rejection rate of the cooling tower unit, the dynamic viscosity coefficient of condenser water, and outlet chilled water temperature. The outcomes can be calculated by solving Equations (1)–(8) simultaneously. In the present study, the coefficient of performance (COP) of the heat pump unit and the CTAHP system were chosen as performance indices, which were introduced as follows:

cwmchw(Tchw,i − Tchw,o) COPhp = (9) Pcomp

cwmchw(Tchw,i − Tchw,o) cwmchw(Tchw,i − Tchw,o) COPsys = = (10) Psys Pf + Psw + Pcw + Pcomp Uncertainty analyses for the experiment results could be calculated by the following equation [22]:

2 2 2 1/2 ∂y 2 ∂y 2 ∂y 2 ∆y = [( ) (∆x1) + ( ) (∆x2) + ... + ( ) (∆xn) ] (11) ∂x1 ∂x2 ∂xn

In order to compare the predicted performance indices and their deviation from the measured data, the mean squared error (MSE) is selected as the performance metric. The values of MSE average errors close to zero means a more useful prediction. Compared to mean bias error and mean absolute error, MSE is analytically tractable and measures the precision (variance) and accuracy (bias) [23], which is deﬁned as follows: (y*: predicted value, y: measured value).

1 n MSE = (y∗ − y )2 (12) n ∑i=1 i i Energies 2017, 10, 733 5 of 18

3.2. Objective Function and Inequality Constraints In the CTAHP system, three types of devices, viz. compressor, fan and pumps, consume electric energy. The objective function, which is to minimize the systemic energy consumption when the required cooling load is satisﬁed, is expressed as follows: minPsys = min Pcomp + Pcw + Psw + Pf (13)

The optimization problem is formulated through the determination of the controlled variables to achieve a minimum of an objective function subject to constraints. The objective is the power consumption of the CTAHP system. The decision variables are the power consumptions of cooling tower fan, condenser water pump, spray water pump and compressor. The uncontrollable variables include ambient wet-bulb temperature, inlet temperature and flow rate of the chilled water. Other dependent variables are the heat rejection rate of the cooling tower, the cooling capacity of the heat pump unit, the dynamic viscosity coefficient of water at the temperatures Tcw,i, the flow rate of air and condenser water. The mathematical formulations of the equality constraints are described as shown in Section 3.1, and the physical explanations of the inequality constraints are given below. The input powers of the compressor, fan, condenser water pump and spray water pump are restricted by boundaries that are often provided by the manufacturers for the safe operation of the CTAHP system, which are expressed as follows:

Pcomp,min ≤ Pcomp ≤ Pcomp,max (14)

Pf ,min ≤ Pf ≤ Pf ,max (15)

Pcw,min ≤ Pcw ≤ Pcw,max (16)

Psw,min ≤ Psw ≤ Psw,max (17) Here, the data for a water-loop heat pump under cooling conditions are speciﬁed in one of China's national industry standards [24], as follows:

◦ ◦ 20 C ≤ Tcw,i ≤ 40 C. (18)

◦ ◦ 5 C ≤ Tchw,i ≤ 15 C. (19) In the cooling tower, the ideal minimum temperature of the condenser water is the ambient wet bulb temperature, while the actual value is larger than the ideal value, which is expressed as:

Twb,i ≤ Tcw,o. (20)

The temperature difference between the inlet and outlet condenser water of tower is usually not greater than 5 ◦C, which can be expressed as [19]:

◦ Tcw,i − Tcw,o ≤ 5 C (21)

3.3. An Appropriate Optimization Algorithm and its Settings for the Problem at Hand In order to better carry out the following analysis, fifteen operating variables of the CTAHP system are reclassified as follows. The four known variables include the ambient wet-bulb temperature, the desired cooling load, the flow rate and temperature of the chilled water at the inlet of the evaporator. The optimal input power of the spray water pump is determined experimentally. The other ten variables are listed in Table1, and their symbols are unified for notational simplicity. Energies 2017, 10, 733 6 of 18

Table 1. Ten unknown variables and their uniform symbols.

Variables Uniform Symbols Variables Uniform Symbols

Pf, kW x(1) µ, kg/(m·s) x(6) Pcw, kW x(2) Qcw, kW x(7) ◦ Pcomp, kW x(3) Tcw,i, C x(8) ◦ ma, kg/s x(4) Tcw,o, C x(9) ◦ mcw, kg/s x(5) Tw,o, C x(10)

The constrained global optimization problem in Section 3.2, which is referred to as Problem (P), can be rewritten as follows:

minPsys = minPsys(x) = minPsys(x(1), x(2), ..., x(10)) = min(x(1) + x(2) + x(3) + Psw)

s.t. hi(x) = 0, i = 1, ..., 8. (22) gj(x) ≤ 0, j = 16, 17. x ∈ X = x ∈ R10 : L ≤ x ≤ U .

Using the exact penalty function approach for nonlinear constrained optimization problems, the constraint functions can be augmented to the objective function, which is proposed in Reference [25]. The constraint violation function on X can be deﬁned as follows:

8 17 2 2 G(x) = ∑ [hi(x)] + ∑ [max{gi(x), 0}] (23) i=1 j=16

For a given e > 0, the following penalty function on X × [0, e] can be deﬁned as follows:  f (x), if e = 0, G(x) = 0;  −α β Fσ(x, e) = f (x) + e G(x) + σe , if e ∈ (0, e]; (24)  ∞, if e = 0, G(x) 6= 0;

Instead of solving Problem (P) directly, the following optimization problem should be considered:

min Fσ(x, e). (25) (x,e)∈X×[0,e]

For notational simplicity, z = (x, e) and Ω = X × [0, e]. Then, Problem (P) can be written as:

minFσ(z) (26) z∈Ω

Algorithm limited memory BFGS (L-BFGS) is usually selected for the unconstrained optimization problem, and it has excellent performance for local search [26]. To enable the algorithm L-BFGS to escape from local minima, Liu et al. [13] proposed a hybrid approach which combined L-BFGS with a stochastic search strategy, namely the Greedy Diffusion Search (GDS). The results have shown that this method can achieve higher accuracy with a lower number of function evaluations. More details on the deﬁnition of Algorithm L-BFGS, Algorithm GDS and Algorithm hybridizing L-BFGS with GDS (L-GDS) can be found in Refs. [13,14]. Based on the hybridizing L-BFGS with GDS algorithms, the MATLAB optimization ﬂowchart proposed in this paper, specifying inputs and outputs of the model, is illustrated in Figure2. Energies 2017, 10, 733 7 of 18 Energies 2017, 10, 733 7 of 17

Figure 2. Flowchart of the optimization approach based on hybridizing L-BFGS with GDS algorithms. Figure 2. Flowchart of the optimization approach based on hybridizing L-BFGS with GDS algorithms. 4. Experiments 4. Experiments In this paper, an experimental CTAHP system has been selected for modeling as an example. In this paper, an experimental CTAHP system has been selected for modeling as an example. The system, located on the rooftop of a single-story building at Hunan University of China, was The system, located on the rooftop of a single-story building at Hunan University of China, originally designed as a heating source for hot water supply [12,27]. As shown in Figure 3a, the closed was originally designed as a heating source for hot water supply [12,27]. As shown in Figure3a, wet cooling tower was an induced draft counter-flow type and specially designed, and Figure 3b the closed wet cooling tower was an induced draft counter-flow type and specially designed, showed that the heat pump system was an integrated water-to-water HP unit with a rated power of and Figure3b showed that the heat pump system was an integrated water-to-water HP unit with a 3.1 kW and a total cooling capacity of 15.3 kW. The rated powers of the fan and the condenser water rated power of 3.1 kW and a total cooling capacity of 15.3 kW. The rated powers of the fan and the pump were 0.55 kW and 0.75 kW, respectively. The rated power of the spray water pump was divided condenser water pump were 0.55 kW and 0.75 kW, respectively. The rated power of the spray water into three grades adjustable, viz. 0.200 kW, 0.175 kW and 0.150 kW. More details of the experimental pump was divided into three grades adjustable, viz. 0.200 kW, 0.175 kW and 0.150 kW. More details of set-up could be found in Reference [12]. the experimental set-up could be found in Reference [12]. A well-equipped instrumentation system was deployed to measure various properties of the A well-equipped instrumentation system was deployed to measure various properties of the cooling process, such as flow rate, power consumption and temperature. The water flow rates were cooling process, such as flow rate, power consumption and temperature. The water flow rates were measured by the ultrasonic flowmeters (PFSE) with an accuracy of 1%. In addition, the air flow rate measured by the ultrasonic flowmeters (PFSE) with an accuracy of 1%. In addition, the air flow rate was measured by standard nozzles (GB14294) with an accuracy of 1%. The input powers of the fan, was measured by standard nozzles (GB14294) with an accuracy of 1%. The input powers of the fan, compressor and condenser water pump were controlled by frequency conversion control cabinet, compressor and condenser water pump were controlled by frequency conversion control cabinet, and the input power of the spray water pump could be adjusted manually. The operating loads of and the input power of the spray water pump could be adjusted manually. The operating loads compressor, condenser water pump and fan, all of which were equipped with VSDs, could vary from of compressor, condenser water pump and fan, all of which were equipped with VSDs, could vary 10% to 110% of their rated values. The actual power consumptions of these energy consuming devices from 10% to 110% of their rated values. The actual power consumptions of these energy consuming were measured by digital clamp multimeters (UT202A UNI-T) with an accuracy of 1.5%. For the devices were measured by digital clamp multimeters (UT202A UNI-T) with an accuracy of 1.5%. measurement of ambient wet-bulb temperature and water temperatures at different locations, For the measurement of ambient wet-bulb temperature and water temperatures at different locations, platinum resistance thermometers (PT100) with an accuracy of 0.2 °C were used. In Figure 3, T1, T2, platinum resistance thermometers (PT100) with an accuracy of 0.2 ◦C were used. In Figure3, T1, T2, T3 and T4 indicate the condense water temperatures sensors at the inlet and outlet of cooling tower, T3 and T4 indicate the condense water temperatures sensors at the inlet and outlet of cooling tower, inlet and outlet chilled water temperatures sensors, respectively. The various readings of instruments inlet and outlet chilled water temperatures sensors, respectively. The various readings of instruments were monitored continuously and recorded with color paperless recorders (EN880) every five were monitored continuously and recorded with color paperless recorders (EN880) every five minutes. minutes. When the acquired temperatures from the color paperless recorders fluctuated within ±0.2 °C for longer than 15 min, each set of data was selected for further analyses.

Energies 2017, 10, 733 8 of 18

When the acquired temperatures from the color paperless recorders ﬂuctuated within ±0.2 ◦C for

Energieslonger 2017 than, 10 15, 733 min, each set of data was selected for further analyses. 8 of 17

(a) (b)

FigureFigure 3. 3. PhotographsPhotographs of: of: (a (a) )closed closed wet wet cooling cooling tower; tower; and and (b (b) )water water source source heat heat pump pump unit. unit. T1, T1, T2, T2, T3T3 and and T4 T4 indicate indicate the the condense condense water water temperatures temperatures sensors sensors at at the the inlet inlet and and outlet outlet of of cooling cooling tower, tower, inletinlet and and outlet outlet chilled chilled water water temperatures temperatures sensors, sensors, respectively. respectively.

5. Results and Discussion 5. Results and Discussion

5.1.5.1. Experimental Experimental Data Data and and Model Model Validation Validation AA number number of of tests tests were were performed performed with with the the CTAHP CTAHP system system under under approximately approximately steady steady states. states. TheThe energy energy consumption consumption of of spr sprayay water water pump pump was was investigated investigated experimentally experimentally when when the the other other variablesvariables were were constant. The results showedshowed thatthat the the power power consumption consumption of of spray spray water water pump pump did did not nothave have a considerable a considerable effect effect on on the the cooling cooling capacity capacity of of the the cooling cooling tower tower unit unit when when it it was was adjusted adjusted to to0.150 0.150 kW, kW, 0.175 0.175 kW kW and and 0.200 0.200 kW. kW. The The reason reason was was that that the spraythe spray water water flow flow rate wasrate influenced was influenced by the bypower the consumption power consumption of spray water of spray pump water monotonically. pump monotonically. Spray water pump Spray power water consumption pump power of consumption0.150 kW could of 0.150provide kW a largecould enough provide spray a large water enough flow tospray ensure water the flow external to e surfacesnsure the of external the heat surfacesexchanger of inthe the heat tower exchanger was fully in wettedthe tower by thewas spray fullywater. wetted When by the the spray spray water. water When moistened the spray all the watersurfaces, moistened the effect all of the the surfaces, variation the of sprayeffect waterof the flowvariation rate onof thespray thermal water performance flow rate on ofthe the thermal cooling performancetower unit could of the be cooling neglected tower [19 ,unit28]. Thus,could thebe powerneglected consumption [19,28]. Thus, of the the spray power pump consumption was selected of theas 0.150spraykW pump for was the followingselected as analysis. 0.150 kW As for shown the following in Table2 analysis., 26 sets of As typical shown experiment in Table 2, data26 sets were of typicalselected experiment for determining data were the corresponding selected for determining coefficients the of the corresponding models as well coefficients as validating of the against models the asproposed well as validating models, which against were the described proposed in models, Section which 3.1. were described in Section 3.1.

TableTable 2. 2. TheThe experimental experimental data data of of the the CTAHP CTAHP tests tests.. Input Parameters Output Parameters Test Twb,i Pf PInputcw P Parameterscomp mchw Tchw,i ma mcw OutputTcw,i ParametersTcw,o Tchw,o No. (°C) (kW) (kW) (°C) (kg/s) (°C) (kg/s) (kg/s) (°C) (°C) (°C) Test No. Twb,i Pf Pcw Pcomp mchw Tchw,i ma mcw Tcw,i Tcw,o Tchw,o 1 21.3 ◦ 0.154 0.570 1.957 ◦ 0.35 12.3 ◦ 0.18 0.35 38.6 ◦ 36.1◦ 10.9◦ 2 22.4( C)0.154 (kW) 0.570 (kW) 1.957 ( C)0.35 (kg/s)12.3 ( C)0.18 (kg/s)0.35 (kg/s)38.7 ( C)36.4 ( C)11.1 ( C) 3 123.2 21.30.154 0.154 0.570 0.570 1.957 1.9570.35 0.3512.5 12.30.18 0.180.35 0.3539.0 38.6 36.7 36.1 11.2 10.9 4 224.0 22.40.154 0.154 0.570 0.570 1.957 1.9570.35 0.3512.1 12.30.18 0.180.35 0.3538.7 38.7 36.6 36.4 10.9 11.1 5 325.6 23.20.220 0.154 0.630 0.570 1.957 1.9570.46 0.3511.8 12.50.83 0.180.86 0.3535.6 39.0 33.6 36.7 9.0 11.2 6 426.1 24.00.220 0.154 0.630 0.570 1.957 1.9570.46 0.3513.1 12.10.83 0.180.86 0.3536.6 38.7 34.5 36.6 10.2 10.9 7 521.7 25.60.220 0.220 0.630 0.630 1.957 1.9570.58 0.4612.0 11.80.83 0.830.86 0.8634.4 35.6 31.9 33.6 8.7 9.0 8 625.6 26.10.275 0.220 0.630 0.630 2.400 1.9570.64 0.4613.2 13.11.27 0.830.86 0.8636.7 36.6 33.7 34.5 10.0 10.2 9 726.2 21.70.275 0.220 0.630 0.630 2.528 1.9570.64 0.5814.3 12.01.27 0.830.86 0.8638.0 34.4 34.9 31.9 10.6 8.7 10 821.1 25.60.275 0.275 0.630 0.630 2.528 2.4000.64 0.6414.6 13.21.27 1.270.86 0.8636.1 36.7 32.1 33.7 10.0 10.0 11 922.7 26.20.275 0.275 0.705 0.630 2.528 2.5280.64 0.6413.5 14.31.27 1.271.38 0.8635.8 38.0 33.5 34.9 9.0 10.6 12 24.3 0.341 0.705 2.715 0.70 14.5 1.71 1.38 36.4 33.7 10.1 13 22.0 0.341 0.705 2.715 0.70 12.9 1.71 1.38 34.5 31.8 8.3 14 20.4 0.341 0.705 2.715 0.70 13.7 1.71 1.38 34.1 31.1 8.6 15 23.9 0.418 0.750 2.820 0.70 12.1 2.15 1.67 34.2 32.0 7.3 16 21.6 0.418 0.750 2.820 0.72 12.6 2.15 1.67 33.2 30.7 7.3 17 23.5 0.418 0.625 3.022 0.58 13.2 2.15 0.82 35.9 31.1 7.2 18 22.2 0.435 0.660 3.130 0.58 10.8 2.25 1.08 33.8 30.1 4.9

Energies 2017, 10, 733 9 of 18

Table 2. Cont.

Input Parameters Output Parameters

Test No. Twb,i Pf Pcw Pcomp mchw Tchw,i ma mcw Tcw,i Tcw,o Tchw,o (◦C) (kW) (kW) (◦C) (kg/s) (◦C) (kg/s) (kg/s) (◦C) (◦C) (◦C) 10 21.1 0.275 0.630 2.528 0.64 14.6 1.27 0.86 36.1 32.1 10.0 11 22.7 0.275 0.705 2.528 0.64 13.5 1.27 1.38 35.8 33.5 9.0 12 24.3 0.341 0.705 2.715 0.70 14.5 1.71 1.38 36.4 33.7 10.1 13 22.0 0.341 0.705 2.715 0.70 12.9 1.71 1.38 34.5 31.8 8.3 14 20.4 0.341 0.705 2.715 0.70 13.7 1.71 1.38 34.1 31.1 8.6 15 23.9 0.418 0.750 2.820 0.70 12.1 2.15 1.67 34.2 32.0 7.3 16 21.6 0.418 0.750 2.820 0.72 12.6 2.15 1.67 33.2 30.7 7.3 Energies 201717, 10, 733 23.5 0.418 0.625 3.022 0.58 13.2 2.15 0.82 35.9 31.1 7.2 9 of 17 18 22.2 0.435 0.660 3.130 0.58 10.8 2.25 1.08 33.8 30.1 4.9 19 24.1 0.435 0.660 2.968 0.70 12.5 2.25 1.08 35.2 31.6 7.9 19 24.1 0.435 0.660 2.968 0.70 12.5 2.25 1.08 35.2 31.6 7.9 20 25.6 0.495 0.750 3.240 0.66 13.5 2.59 1.67 36.1 33.5 7.6 20 25.6 0.495 0.750 3.240 0.66 13.5 2.59 1.67 36.1 33.5 7.6 21 21.9 0.515 0.795 2.142 0.72 12.2 2.59 1.98 30.7 28.8 7.6 21 21.9 0.515 0.795 2.142 0.72 12.2 2.59 1.98 30.7 28.8 7.6 22 21.7 0.550 0.630 2.142 0.72 15.1 2.71 0.86 32.7 28.0 10.1 22 21.7 0.550 0.630 2.142 0.72 15.1 2.71 0.86 32.7 28.0 10.1 23 25.0 0.585 0.750 3.100 0.73 12.0 2.94 1.67 34.3 31.8 7.1 23 25.0 0.585 0.750 3.100 0.73 12.0 2.94 1.67 34.3 31.8 7.1 2424 23.2 23.2 0.585 0.585 0.795 0.795 2.169 2.169 0.72 0.7213.7 13.73.19 3.191.98 1.98 31.5 31.5 29.4 29.4 8.7 8.7 2525 25.6 25.6 0.585 0.585 0.795 0.795 2.764 2.764 0.69 0.6913.6 13.63.19 3.191.98 1.98 34.1 34.1 32.0 32.0 8.4 8.4 2626 25.5 25.5 0.526 0.526 0.674 0.674 3.277 3.277 0.75 0.7512.5 12.52.78 2.781.18 1.18 35.8 35.8 32.3 32.3 7.7 7.7

ToTo verifyverify thethe reliabilityreliability ofof thethe experimentexperiment data,data, thethe energyenergy balancebalance ofof thethe heatheat pumppump unitunit waswas adopted.adopted. Based on the data provided by the manufacturer, the efﬁcienciesefficiencies of compressorcompressor and motor werewere bothboth 86%.86%. Therefore,Therefore, ηη inin EquationEquation (5)(5) waswas equalequal toto 0.7396,0.7396, viz.viz. 0.860.86 multipliedmultiplied byby 0.86.0.86. AtAt thethe samesame time,time, ηη == 11 inin Ref.Ref. [[18]18] waswas alsoalso selected selected for for analyzing analyzing the the energy energy balance. balance. As As shown shown in in Figure Figure4, the4, the unbalanced unbalanced ratios ratios of theof the heat heat gained gained by the by condenserthe condenser water water and theand heat the lostheat by lost the by chilled the chilled water andwater heat and generated heat generated by the by compressor the compressor were were within within±15%. ±15%. When Whenη = η 1= and1 andη η= = 0.7396, 0.7396, thethe averageaverage absoluteabsolute unbalancedunbalanced ratiosratios werewere 5.3%5.3% andand 3.2%,3.2%, respectively,respectively, which which meant meant the the data data were were reliable. reliable.

FigureFigure 4.4. Energy balance ofof thethe HPHP unitunit test.test.

Based on well-established experimental data under quasi-steady-state conditions, when the Based on well-established experimental data under quasi-steady-state conditions, when the least-square method and the confidence level of 95% were used, the regression results of the least-squarecoefficients of method Equations and the (2), conﬁdence (5), (7) and level (8) were of 95% obtained, were used, as listed the regression in Table results3. of the coefﬁcients of Equations (2), (5), (7) and (8) were obtained, as listed in Table3. Table 3. Corresponding coefficients of the models and constraint.

Equations Coefficients (2) a0 = −4.6929; a1 = 0.2698; a2 = −0.0011; a3 = 0.1782; a4 = −9.4509 × 10−5; a5 = −1.102 × 10−3 (5) βext = 0.310; βint = 0.574 (7) b0 = 0.2336; b1 = −0.0961; b2 = 0.1262; b3 = −0.0193 (8) c0 = 0.5417; c1 = 0.0673; c2 = 0.0482; c3 = −0.0083

Figure 5 illustrates the predicted COPs, experimental COPs and their uncertainties. Model validation was carried out for predicting the COPhp, and COPsys. When the predicted values were compared with the measurements for the CTAHP system, the MSEs of COPhp, and COPsys were 0.0179 and 0.0081, respectively. Validation results indicated that the predicted COPs of the heat pump unit and the system were in good agreement with the experimental data, which meant the models were accuracy enough for performance prediction and further analysis of the CTAHP system. The uncertainty of COPhp, calculated based on the experimental data, was (8.1 ± 3.7)%. The uncertainty of COPsys was (9.0 ± 3.9)%, of which the uncertainty caused by the temperature difference between inlet and outlet chilled water accounted for (69.2 ± 0.9)% of the total uncertainty; while the uncertainties caused by the power consumptions of the system and the chilled water mass flow rate were (20.7 ± 6.4)% and (13.8 ± 4.5)%, respectively. Therefore, improving the temperature measurement accuracy can effectively improve the test accuracy.

Energies 2017, 10, 733 10 of 18

Table 3. Corresponding coefﬁcients of the models and constraint.

Equations Coefﬁcients −5 −3 (2) a0 = −4.6929; a1 = 0.2698; a2 = −0.0011; a3 = 0.1782; a4 = −9.4509 × 10 ; a5 = −1.102 × 10 (5) βext = 0.310; βint = 0.574 (7) b0 = 0.2336; b1 = −0.0961; b2 = 0.1262; b3 = −0.0193 (8) c0 = 0.5417; c1 = 0.0673; c2 = 0.0482; c3 = −0.0083

Figure5 illustrates the predicted COPs, experimental COPs and their uncertainties. Model validation was carried out for predicting the COPhp, and COPsys. When the predicted values were compared with the measurements for the CTAHP system, the MSEs of COPhp, and COPsys were 0.0179 and 0.0081, respectively. Validation results indicated that the predicted COPs of the heat pump unit and the system were in good agreement with the experimental data, which meant the models were accuracy enough for performance prediction and further analysis of the CTAHP system. The uncertainty of COPhp, calculated based on the experimental data, was (8.1 ± 3.7)%. The uncertainty of COPsys was (9.0 ± 3.9)%, of which the uncertainty caused by the temperature difference between inlet and outlet chilled water accounted for (69.2 ± 0.9)% of the total uncertainty; while the uncertainties caused by the power consumptions of the system and the chilled water mass ﬂow rate were (20.7 ± 6.4)% and (13.8 ± 4.5)%, respectively. Therefore, improving the temperature Energiesmeasurement 2017, 10, 733 accuracy can effectively improve the test accuracy. 10 of 17

(a) (b)

Figure 5. The predicted COPs, experimental COPs and their uncertainties: (a) COPhp, (b) COPsys. Figure 5. The predicted COPs, experimental COPs and their uncertainties: (a) COPhp,(b) COPsys. 5.2. Sensitivity Analysis 5.2. Sensitivity Analysis A sensitivity analysis was conducted to investigate the influences of the variation of six A sensitivity analysis was conducted to investigate the inﬂuences of the variation of six independent variables, viz. ambient wet-bulb temperature, inlet temperature and flow rate of chilled independent variables, viz. ambient wet-bulb temperature, inlet temperature and ﬂow rate of chilled water, the input powers of compressor, fan and condenser water pump, on the COPs of the heat water, the input powers of compressor, fan and condenser water pump, on the COPs of the heat pump unit and the CTAHP system. Normal probability analyses of these independent variables were pump unit and the CTAHP system. Normal probability analyses of these independent variables were conducted with 26 sets of typical experiment data, as shown in Figure 6. conducted with 26 sets of typical experiment data, as shown in Figure6.

(a) (b)

(e) (f)

Figure 6. Normal probability plots of: (a) ambient wet-bulb temperature; (b) chilled water inlet temperature; (c) chilled water flow rate; (d) fan input power; (e) input power of condenser water pump and (f) compressor input power.

Energies 2017, 10, 733 10 of 17

(a) (b)

Figure 5. The predicted COPs, experimental COPs and their uncertainties: (a) COPhp, (b) COPsys.

5.2. Sensitivity Analysis A sensitivity analysis was conducted to investigate the influences of the variation of six independent variables, viz. ambient wet-bulb temperature, inlet temperature and flow rate of chilled water, the input powers of compressor, fan and condenser water pump, on the COPs of the heat Energiespump 2017unit, 10and, 733 the CTAHP system. Normal probability analyses of these independent variables11 were of 18 conducted with 26 sets of typical experiment data, as shown in Figure 6.

(a) (b)

(e) (f)

Figure 6. Normal probability plots of: (a) ambient wet-bulb temperature; (b) chilled water inlet Figure 6. Normal probability plots of: (a) ambient wet-bulb temperature; (b) chilled water inlet temperature; (c) chilled water flow rate; (d) fan input power; (e) input power of condenser water temperature; (c) chilled water ﬂow rate; (d) fan input power; (e) input power of condenser water pump pump and (f) compressor input power. and (f) compressor input power.

As listed in Table4, the linear regression relations between COPs and these independent variables could be determined by curve fitting of experimental data with the least-square method and a confidence level of 95%. The sensitivity analysis was carried out using a sensitivity tool, Oracle’s Crystal Ball, which was the leading spreadsheet-based application for forecasting. The assumption, decision and forecast of the tool for the CTAHP system are given in Table4. Figure7 illustrates the sensitivity analysis results. Chilled water flow rate had a significant positive effect on the values of COPhp and COPsys, followed by fan input power. Compressor input power had a significant negative effect on the COPhp, while it had little effect on the COPsys. The effect of the other three variables on the COPhp is similar to that of the COPsys. Energies 2017, 10, 733 11 of 17

As listed in Table 4, the linear regression relations between COPs and these independent variables could be determined by curve fitting of experimental data with the least-square method and a confidence level of 95%. The sensitivity analysis was carried out using a sensitivity tool, Oracle’s Crystal Ball, which was the leading spreadsheet-based application for forecasting. The assumption, decision and forecast of the tool for the CTAHP system are given in Table 4. Figure 7 illustrates the sensitivity analysis results. Chilled water flow rate had a significant positive effect on the values of COPhp and COPsys, followed by fan input power. Compressor input power had a significantEnergies 2017, negative10, 733 effect on the COPhp, while it had little effect on the COPsys. The effect of the12 other of 18 three variables on the COPhp is similar to that of the COPsys.

Table 4. The assumption, decision and forecast of Crystal Ball. Table 4. The assumption, decision and forecast of Crystal Ball.

Twb,i Twb,i mchwmchw Tchw,iTchw,i PPff (kW) PcwPcw PcompPcomp ParametersParameters ◦ ◦ ( C) (°C) (kg/s)(kg/s) ( C)(°C) (kW) (kW)(kW) (kW)(kW) DistributionDistribution NormalNormal Normal Normal NormalNormal NormalNormal NormalNormal NormalNormal AssumptionAssumption ArithmeticArithmetic mean mean 23.4823.48 0.610.61 12.9512.95 0.360.36 0.670.67 2.522.52 StandardStandard deviation deviation 1.771.77 0.130.13 1.001.00 0.140.14 0.070.07 0.460.46 DecisionDecision Min.: 0;0; Max.:Max.: 88

COPhphp = 0.0595 ++ 5.3095××PPf f+ +1.3963 1.3963××PcwPcw− − 0.79070.7907××PcompPcomp− − 0.1785××TTwb,iwb,i ++ 8.08588.0858××mmchwchw+ + 0.2053××TTchw,ichw,,i, Forecast RR22 == 0.9431 Forecast COP = −0.5018 + 2.2054×P + 0.3148×P − 0.0199×P − 0.1150×T + 5.5347×m + COPsyssys = −0.5018 + 2.2054×Pff + 0.3148×Pcwcw − 0.0199×Pcompcomp − 0.1150×Twb,iwb,i + 5.5347×mchwchw + 0.1373×Tchw,i, 0.1373×Tchw,i, R2 = 0.9339 R2 = 0.9339

(a) (b)

Figure 7. Sensitivity analysis on the values of (a) COPhp and (b) COPsys. Figure 7. Sensitivity analysis on the values of (a) COPhp and (b) COPsys. 5.3. Energy Analysis 5.3. Energy Analysis The mathematical model and experimental data for the system components were implemented The mathematical model and experimental data for the system components were implemented in in MATLAB. The codes were written with double precision arithmetic. For all the optimization MATLAB. The codes were written with double precision arithmetic. For all the optimization problems problems below, the maximum number of iterations K = 5000. The translation parameter t = 1/3, below, the maximum number of iterations K = 5000. The translation parameter t = 1/3, additional additional points q1 = 10, additional points q2 = 5 in Algorithm GDS. The initial symmetric positive points q1 = 10, additional points q2 = 5 in Algorithm GDS. The initial symmetric positive definite matrix definite matrix H0 = I (the identity matrix), scale factor ζ = 0.25, scale factor η0 = 0.75, tolerance− ε61 = ε2 H0 = I (the identity matrix), scale factor ζ = 0.25, scale factor η0 = 0.75, tolerance ε1 = ε2 = ε3 = 10 and = ε3 = 10−6 and the number of correction pairs m = 5 in Algorithm L-BFGS. During the execution of the number of correction pairs m = 5 in Algorithm L-BFGS. During the execution of Algorithm L-BFGS, Algorithm L-BFGS, the numerical gradients were calculated by a two-point computational formula. the numerical gradients were calculated by a two-point computational formula. The optimal set-points, obtained from the proposed algorithm, were aimed at minimizing The optimal set-points, obtained from the proposed algorithm, were aimed at minimizing systemic systemic power consumption while fulfilling the cooling load. The operating loads of the compressor, power consumption while fulfilling the cooling load. The operating loads of the compressor, condenser condenser water pump, and fan, all of which were equipped with VSDs, could vary from 10% to 110% water pump, and fan, all of which were equipped with VSDs, could vary from 10% to 110% of their of their rated values. The specifications of the system and operating conditions for the considered rated values. The specifications of the system and operating conditions for the considered case are case are given in Table 5. given in Table5.

Energies 2017, 10, 733 13 of 18

Table 5. The speciﬁcations of the system and operating conditions for the considered case. Energies 2017, 10, 733 12 of 17

ParametersTable 5. The Ratedspecifications Values of the system Constant and operating Values for conditions the Case for Study the considered Specified case. Range ◦ Twb,i ( C) 25.0Constant Values for 25.0 the Case — Parameters Rated Values Specified Range mchw (kg/s) 0.73Study 0.73 — ◦ Tchw,i ( C)Twb,i (°C) 12.025.0 25.0 12.0— — Psw (kW)mchw (kg/s) 0.150/0.175/0.2000.73 0.73 0.150— — Qchw (kW)Tchw,i (°C) 15.3012.0 12.0 12.24— 1.53–16.83 Pf (kW)Psw (kW) 0.150/0.175/0.2000.550 0.150 0.450— 0.055–0.605 Pcw (kW)Qchw (kW) 0.75015.30 12.24 0.6501.53–16.83 0.075–0.825 Pcomp (kW)Pf (kW) 3.1000.550 0.450 2.0000.055–0.605 0.310–3.410 Pcw (kW) 0.750 0.650 0.075–0.825 Pcomp (kW) 3.100 2.000 0.310–3.410 5.3.1. Effect of the Two Controlled Variables at a Required Cooling Load 5.3.1. Effect of the Two Controlled Variables at a Required Cooling Load As depicted in Figure8a,b, any addition to the compressor power consumption would lead to decreaseAs depicted the in power Figure consumption8a,b, any addition of condenserto the compressor water power pump consumption or fan power would consumption. lead to Furtherdecrease increasing the power the compressor consumption power of condenser consumption water could pump significantly or fan power increase consumption. the system Further power consumption,increasing which the compressor meant the power compressor consumption power could consumption significantly had increase a high theimpact system on the power system consumption, which meant the compressor power consumption had a high impact on the system power consumption. This was because the compressor power consumption directly affected the power consumption. This was because the compressor power consumption directly affected the refrigerantrefrigerant flow rateflow and rate the and temperature the temperature difference difference of the of refrigerant the refrigerant in the condenserin the condenser and evaporator. and The flowevaporator. rate and The temperature flow rate and of temperature the refrigerant of thein refrigerant the evaporator in the evaporator determined determined the ability the ofability the heat pumpof unit the heat to absorb pump heatunit fromto absorb the chilledheat from water, the chilled while water, those while in the those condenser in the condenser affected the affected heat rejectionthe rate ofheat the rejection unit. Figure rate of8c the illustrates unit. Figure that 8c the illustrates trend of that fan the power trend consumption of fan power was consumption opposite was to that of theopposite power consumptionto that of the power of condenser consumption water of condenser pump. This water meant pump. the This condenser meant the watercondenser flow water rate was increasedflow rate with was the increased decrease with of the the air decrease flow rate of whenthe air theflow heat rate rejection when the rate heat of r theejection cooling rate towerof the was constant,cooling which tower was was consistent constant, which with the was results consistent of our with previous the results study of our [18 previous]. In addition, study [18]. the system In addition, the system power consumption was slightly decreased with the decrease of the pump power consumption was slightly decreased with the decrease of the pump power consumption and power consumption and the increase of the fan power consumption, which meant the impact of the the increase of the fan power consumption, which meant the impact of the power consumption of power consumption of condenser water pump on the system power consumption was greater than condenserthat of water cooling pump tower on fan. the system power consumption was greater than that of cooling tower fan.

(a) (b)

(c)

Figure 8. Two optimal controlled variables at a required cooling load of 12.24 kW: (a) compressor Figure 8. Two optimal controlled variables at a required cooling load of 12.24 kW: (a) compressor input input power versus the input power of condenser water pump; (b) compressor input power versus powerfan versus input thepower input; (c) powerfan input of power condenser versus water the input pump; power (b) compressorof condenser inputwater powerpump. versus fan input power; (c) fan input power versus the input power of condenser water pump. Energies 2017, 10, 733 14 of 18

Energies 2017, 10, 733 13 of 17 5.3.2. Effect of Three Controlled Variables at a Desired Cooling Load 5.3.2. Effect of Three Controlled Variables at a Desired Cooling Load As shown in Figure9a, the variations of the power consumptions of the compressor, condenserAs shown water pumpin Figure and 9a, cooling the variations tower fan of werethe power investigated consumptions for the of case the study. compressor, The results condenser showed water pump and cooling tower fan were investigated for the case study. The results showed that the that the compressor power consumption should be lowered in the process of system optimization compressor power consumption should be lowered in the process of system optimization operation. operation. Figure9b,c shows that the system power consumption changed with the controlled variables Figure 9b,c shows that the system power consumption changed with the controlled variables three- three-dimensionally and two-dimensionally, respectively. At this optimal set-point, the fan power dimensionally and two-dimensionally, respectively. At this optimal set-point, the fan power consumption was very close to its maximum, 0.605 kW. The power consumption of the condenser consumption was very close to its maximum, 0.605 kW. The power consumption of the condenser water waterpump pump was wasslightly slightly higher higher than thanits rated its rated value, value, 0.750 0.750kW, and kW, the and compressor the compressor power powerconsumption consumption was wasapproximately approximately two twothirds thirds of its ofrating. its rating. These results These suggest results that suggest for a thatrequired for acooling required load, cooling moderate load, moderateincrease increase in fan energy in fan energyconsumption consumption is conducive is conducive to reducing to reducing system energy system consumption, energy consumption, while whileexcessive excessive compressor compressor energy energy consumption consumption is not conducive is not conducive to system to energy system saving energy. saving.

(a) (b)

(c)

Figure 9. Three optimally controlled variables at a required cooling load of 12.24 kW: (a) compressor Figure 9. Three optimally controlled variables at a required cooling load of 12.24 kW: power consumption versus the power consumptions of fan and condenser water pump; (b) system (a) compressor power consumption versus the power consumptions of fan and condenser water power consumption versus the power consumptions of fan and condenser water pump (Three- pump; (b) system power consumption versus the power consumptions of fan and condenser water dimensional); and (c) system power consumption versus the power consumptions of fan and pump (Three-dimensional); and (c) system power consumption versus the power consumptions of fan condenser water pump (Two-dimensional). and condenser water pump (Two-dimensional). 5.3.3. Effect of the Three Controlled Variables at Different Required Cooling Loads 5.3.3. Effect of the Three Controlled Variables at Different Required Cooling Loads As the ratio of cooling load to rated load increased, the optimal power consumptions of the CTAHPAs the system ratio ofand cooling its components load to rated were loadinvestigated, increased, as theshown optimal in Figure power 10a. consumptions When the ratio of of the CTAHPcooling system load to and rated its loadcomponents was below were 0.4, investigated, the growth of as system shown power in Figure consumption 10a. When was the mainly ratio of coolingcaused load by tothe rated increase load in was fan belowpower 0.4, consumption. the growth And of system the ratio power of cooling consumption load to rated was mainly load varied caused byfrom the increase 0.4 to 1.1, in fan the powerincrease consumption. of the compressor And the pow ratioer consumption of cooling load directly to rated caused load a significant varied from 0.4increase to 1.1, thein the increase system of power the compressor consumption. power Moreover, consumption Figure 10a directly illustrates caused the power a signiﬁcant consumption increase inof the the system condenser power water consumption. pump increased Moreover, gradually Figure with 10 thea illustrates increase of the the power ratio. consumptionFigure 10b shows of the condenserthat the cooling waterpump capacity increased of the cooling gradually tower with increased the increase with the of increase the ratio. in Figurethe ratio 10 ofb showscooling that load the coolingto rated capacity load, and of the the condenser cooling tower water increasedtemperatures with at the inlet increase and outlet in the were ratio lowest of cooling at the loadratio of to 0.4. rated load, and the condenser water temperatures at the inlet and outlet were lowest at the ratio of 0.4.

Energies 2017, 10, 733 14 of 17 EnergiesEnergies 20172017,, 10,, 733 14 of15 17 of 18

(a)( a) (b) (b)

FigureFigure 10. 10. Optimal Optimal variables variables at atdifferent different ratios ratios of coolingof cooling load load to ratedto rated load: load: (a) minimum(a) minimum power power Figure 10. Optimal variables at different ratios of cooling load to rated load: (a) minimum power consumptionsconsumptions of ofthe the CTAHP CTAHP system system and and its itsoptimal optimal controlled controlled variables; variables; (b) cooling(b) cooling capacity capacity and and consumptions of the CTAHP system and its optimal controlled variables; (b) cooling capacity and condensercondenser water water temperatures temperatures at theat the inlet inlet and and outlet outlet of the of thecooling cooling towe tower. r. condenser water temperatures at the inlet and outlet of the cooling tower. 5.4.5.4. Analysis Analysis of ofEnergy Energy Saving Saving Potential Potential under under Test Test Operating Operating Conditions Conditions 5.4. Analysis of Energy Saving Potential under Test Operating Conditions TheThe required required cooling cooling load, load, measured measured uncontrollable uncontrollable variables, variables, and and other other initial initial values values obtained obtained fromfromThe the the proposed required proposed coolingL -LGDS-GDS algorithm load, algorithm measured were were fed uncontrollable fed to MATLABto MATLAB in variables, order in order to andcompute to compute other the initial optimalthe optimal values set- obtainedpoints set-points fromofof the the the controlled controlled proposed variables. L-GDS variables. algorithm These These optimal wereoptimal fed set set- topoints- MATLABpoints were were inaimed order aimed to to minimize to compute minimize the the the systemicoptimal systemic set-points power power ofconsumptionconsumption the controlled while while variables. fulfilling fulfilling These the the desired optimal desired cooling set-points cooling load. load. were As aimed As shown shown to in minimize Figure in Figure 11a the – 11ad, systemic – thed, the power power power consumptionconsumptionsconsumptions whileof of the the system fulfilling system and and the its its desiredcomponents components cooling without without load. opt optimization Asimization shown were in were Figurecompared compared 11a–d, to those to the those with power with consumptionsoptimization.optimization. The ofThe theresults results system showed showed and that its that componentsthe the average average systemic without systemic power optimization power consumption consumption were with compared with optimization optimization to those was with was optimization.nearlynearly 20.8% 20.8% less Theless than resultsthan that that showed without without thatoptimization. optimization. the average Power systemicPower consumption consumption power consumption values values of the of withthecompressor compressor optimization and and wascondensercondenser nearly water 20.8% water pump lesspump than w ithw thatith optimization optimization without optimization. were were generally generally Power less less than consumption than those those without without values optimization ofoptimization the compressor while while andthethe fan condenser fan power power consumption waterconsumption pump was with was higher optimizationhigher than than that that werewithout without generally optimization. optimization. less than The thoseThe energy energy without savings savings optimization potential potential whileforfor the the the compressor compressor fan power and and consumption condenser condenser water was water higherpump pump were than were 34.1% that 34.1% without and and 3.5%, 3.5%, optimization. respectively, respectively, Thewhil whil energye thee coolingthe savings cooling potentialtowertower fan fan for power the power compressor consumption consumption and condenser increased increased bywater by 40.3%. 40.3%.pump The were The reason 34.1% reason was and was that 3.5%, that a respectively, higher a higher fan fanwhile power power the coolingconsumptionconsumption tower caused fancaused power a lowera lower consumption condenser condenser water increased water temperature temperature by 40.3%. and and The required required reason a lower was a lower that refrigerant arefrigerant higher superheat fan superheat power consumptiontemperaturetemperature entering caused entering athe lowerthe condenser. condenser. condenser When When water the the power temperature power consum consum andption requiredption of condenser of condenser a lower water refrigerant water pump pump slightly superheat slightly temperaturedecreaseddecreased as as enteringa resulta result of theof the the condenser. increased increased fan When fan power power the consumption, power consumption, consumption the thecompressor compressor of condenser power power waterconsumption consumption pump slightly also also decreasedreducedreduced because because as a result a lowera lower of the condensing condensing increased pressure fan pressure power was was consumption, required. required. Meanwhile, Meanwhile, the compressor as the as fanthe power powerfan power consumption consumption consumption also reducedincreased,increased, because the the syst syst aem lowerem power power condensing consumption consumption pressure became became was lower. required. lower. Therefore, Therefore, Meanwhile, an appropriatean as appropriate the fan increase power increase consumption in the in fanthe fan power consumption was conducive to significantly reduce the power consumptions of the CTAHP increased,power consumption the system power was conducive consumption to significantly became lower. reduce Therefore, the power an appropriate consumptions increase of the in theCTAHP fan system and compressor. In addition, the results obtained showed a relatively high influence of the powersystem consumption and compressor. was conduciveIn addition, to the significantly results obtained reduce theshowed power a relatively consumptions high ofinfluence the CTAHP of the compressor power consumption on the system power consumption. From this discussion, the proposed systemcompressor and compressor. power consumption In addition, on the the system results power obtained consumption. showed a From relatively this discussion, high influence the proposed of the optimal control strategy could effectively ensure that the CTAHP system was guaranteed to meet the compressoroptimal control power strategy consumption could oneffectively the system ensure power that consumption. the CTAHP Fromsystem this was discussion, guaranteed the to proposed meet the required cooling load while the system was working in good conditions. optimalrequired control cooling strategy load while could the effectively system was ensure working that thein good CTAHP conditions. system was guaranteed to meet the required cooling load while the system was working in good conditions.

(a) (b) (a) (b)

Figure 11. Cont.

EnergiesEnergies2017 2017, 10,, 10 733, 733 1615 of 18of 17

FigureFigure 11. 11.Power Power consumptions consumptions of of the the devices: devices: (a )(a system;) system (b; ()b compressor;) compressor (c; )(c condenser) condenser water water pump; pump; andand (d )(d cooling) cooling tower tower fan. fan.

6. Conclusions 6. Conclusions In order to minimize the power consumption of a cooling tower-assisted heat pump (CTAHP) In order to minimize the power consumption of a cooling tower-assisted heat pump (CTAHP) system under cooling conditions, the modeling and optimization problem of the system has been system under cooling conditions, the modeling and optimization problem of the system has been addressed, and the proposed approach has been verified on an experimental platform. An existing addressed, and the proposed approach has been verified on an experimental platform. An existing CTAHP system has been used for experimentation and data collection. By using the experimental CTAHP system has been used for experimentation and data collection. By using the experimental data, the mathematical models for the systemic components have been developed and implemented data, the mathematical models for the systemic components have been developed and implemented in in MATLAB to predict the system’s performance operating under various conditions. A novel hybrid MATLAB to predict the system’s performance operating under various conditions. A novel hybrid optimization-simulation algorithm has been adopted to find the optimizing set-points of the power optimization-simulation algorithm has been adopted to find the optimizing set-points of the power consumptions of the compressor, condenser water pump and cooling tower fan. The main consumptions of the compressor, condenser water pump and cooling tower fan. The main conclusions conclusions are summarized below: are summarized below: (1) The predicted coefficient of performances (COPs) of the heat pump unit and the system are in (1) Thegood predicted agreement coefficient with the of experimental performances data, (COP whichs) of themeans heat the pump modeling unit and method the system is reliable are inand goodaccurate agreement for performance with the experimental prediction of data, the CTAHP which means system. the modeling method is reliable and (2) accurateSensitivity for performanceanalysis results prediction demonstrate of the that CTAHP chilled system. water flow rate has a significant positive (2) Sensitivityeffect on the analysis values resultsof COP demonstratehp and COPsys, that followed chilled by water fan input flow power. rate has Compressor a significant input positive power effecthas a on significant the values negative of COP hpeffectand onCOP thesys COP, followedhp, while by it fan has input little power. effect on Compressor the COPsys input. power (3) hasThe a significant average systemic negative power effect on consumption the COPhp, while with optimization it has little effect is nearly on the COP 20.8%sys . less than that (3) Thewithout average optimization systemic under power certain consumption testing conditions. with optimization is nearly 20.8% less than that without optimization under certain testing conditions. The proposed operation strategy proposed in this paper is reliable, and it can significantly reduce theThe energy proposed consumption operation of strategythe CTAHP proposed system in in this cooling paper mode, is reliable, especially andit in can part significantly-load conditions. reduce the energy consumption of the CTAHP system in cooling mode, especially in part-load conditions. Acknowledgments: The study has been supported by the China National Key R&D Program “Solutions to Acknowledgments:heating and coolingThe of studybuildings has in been the supportedYangtze River by the region” China (Grant National No. Key2016YFC0700305). R&D Program The “Solutions authors toalso heatingappreciated and cooling the financial of buildings support in from the Yangtze National River Natural region” Science (Grant Foundation No. 2016YFC0700305). of China (No. 51578220). The authors also appreciated the financial support from National Natural Science Foundation of China (No. 51578220). Author Contributions: Jianlin Cheng designed and built the CTAHP system. The measurement data was Authorcollected Contributions: and analyzedJianlin by Xiaoqing Cheng Wei, designed Jianlin and Cheng, built Jinhua the CTAHP Hu, and system. Meng Wang. The measurement Xiaoqing Wei data conducted was collected and analyzed by Xiaoqing Wei, Jianlin Cheng, Jinhua Hu, and Meng Wang. Xiaoqing Wei conducted the simulations, and accomplished the writing of the paper in close and steady cooperation with all authors. the simulations, and accomplished the writing of the paper in close and steady cooperation with all authors. NianpingNianping Li Li and and Jinqing Jinqing Peng Peng guided guided the the whole whole work work and and edited edited language. language. ConflictsConflicts of Interest:of Interest:The The authors authors declare declare no no conflict conflict of interest.of interest.

Nomenclature m mass flow rate, kg/s T temperature, °C cw specific heat of cooling water at constant pressure, 4.1868 kJ/(kg·°C) cpsat the fictitious specific heat of saturated air at constant pressure, kJ/(kg·°C) H Hessian matrix

Energies 2017, 10, 733 17 of 18

Nomenclature m mass flow rate, kg/s T temperature, ◦C ◦ cw specific heat of cooling water at constant pressure, 4.1868 kJ/(kg· C) ◦ cpsat the fictitious specific heat of saturated air at constant pressure, kJ/(kg· C) H Hessian matrix P power consumption, kW Q heat rejection rate, kW x x = (x(1), x(2), . . . , x(10))∈R10 hi continuously differentiable functions, Equation (i), i = 1, 2, . . . , 8 gj continuously differentiable functions, Equation (j), j = 16, 17 L = [L1, L2, ... , L10] and U = [U1, U2, ... , U10] are, respectively, the lower and upper bounds L,U of the ten unknown variables. Greek Symbols

µcw dynamic viscosity coefficient of water at the temperatures Tcw,i, kg/(m·s) ◦ −3 µo dynamic viscosity coefficient of water at 0 C, 1.792 × 10 kg/(m·s) α, β positive constants, 1 ≤ β ≤ α σ penalty parameter, σ > 0 βint a constant which is influenced by the coil’s geometry and constant water-properties βext a constant which depends on the thermal properties of air and on the coil’s geometry η heat generated efficiency by the compressor ζ, ηo scale factor, 0 < ζ < 0.5, ζ < ηo < 1 Subscripts a air f cooling tower fan sw spray water cw condenser water chw chilled water comp compressor i inlet o outlet wb ambient wet-bulb

References

1. American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE). ASHRAE Handbook—2011 HVACApplications; ASHRAE: Atlanta, GA, USA, 2011. 2. Thangavelu, S.R.; Myat, A.; Khambadkone, A. Energy optimization methodology of multi-chiller plant in commercial buildings. Energy 2017, 123, 64–76. [CrossRef] 3. Sayyaadi, H.; Nejatolahi, M. Multi-objective optimization of a cooling tower assisted vapor compression refrigeration system. Int. J. Refrig. 2011, 34, 243–256. [CrossRef] 4. Shan, K.; Wang, S.; Gao, D.C.; Xiao, F. Development and validation of an effective and robust chiller sequence control strategy using data-driven models. Autom. Constr. 2016, 65, 78–85. [CrossRef] 5. Mu, B.; Li, Y.; Seem, J.E.; Hu, B. A multivariable newton-based extremum seeking control for condenser water loop optimization of chilled-water plant. J. Dyn. Syst. 2015, 137, 111011. [CrossRef] 6. Liu, C.W.; Chuah, Y.K. A study on an optimal approach temperature control strategy of condensing water temperature for energy saving. Int. J. Refrig. 2011, 34, 816–823. [CrossRef] 7. Wei, X.; Xu, G.; Kusiak, A. Modeling and optimization of a chiller plant. Energy 2014, 73, 898–907. [CrossRef] 8. Sayyadi, H.; Nejatolahi, M. Thermodynamic and thermoeconomic optimization of a cooling tower-assisted ground source heat pump. Geothermics 2011, 40, 221–232. [CrossRef] 9. Chargui, R.; Sammouda, H.; Farhat, A. Numerical simulation of a cooling tower coupled with heat pump system associated with single house using TRNSYS. Energy Convers. Manag. 2013, 75, 105–117. [CrossRef] Energies 2017, 10, 733 18 of 18

10. Yuan, S.; Grabon, M. Optimizing energy consumption of a water-loop variable-speed heat pump system. Appl. Therm. Eng. 2011, 31, 894–901. [CrossRef] 11. Ma, Z.; Wang, S. Supervisory and optimal control of central chiller plants using simplified adaptive models and genetic algorithm. Appl. Energy 2011, 88, 198–211. [CrossRef] 12. Cheng, J.; Li, N.; Wang, K. Study of heat-source-tower heat pump system efficiency. Procedia Eng. 2015, 121, 915–921. [CrossRef] 13. Liu, J.; Zhang, S.; Wu, C.; Liang, J.; Wang, X.; Teo, K.L. A hybrid approach to constrained global optimization. Appl. Soft Comput. 2016, 47, 281–294. [CrossRef] 14. Liu, D.C.; Nocedal, J. On the limited memory BFGS method for large scale optimization. Math. Program. 1989, 45, 503–528. [CrossRef] 15. Braun, J.E.; Comstock, M.C. Development of Analysis Tools for the Evaluation of Fault Detection and Diagnostics for Chillers; Deliverable for Ashrae Research Project: Atlanta, GA, USA, 1999. 16. Cheung, H.; Braun, J.E. Empirical modeling of the impacts of faults on water-cooled chiller power consumption for use in building simulation programs. Appl. Therm. Eng. 2016, 99, 756–764. [CrossRef] 17. American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE). ASHRAE Handbook—1999 HVAC Applications Handbook; ASHRAE: Atlanta, GA, USA, 1999; Volume 40, pp. 1–36. 18. Lu, L.; Cai, W.; Soh, Y.C.; Xie, L.; Li, S. HVAC system optimization—Condenser water loop. Energy Convers. Manag. 2004, 45, 613–630. [CrossRef] 19. Wei, X.; Li, N.; Peng, J.; Cheng, J.; Hu, J.; Wang, M.; Sciubba, E. Performance analyses of counter-flow closed wet cooling towers based on a simplified calculation method. Energies 2017, 10, 282. [CrossRef] 20. Stabat, P.; Marchio, D. Simplified model for indirect-contact evaporative cooling-tower behaviour. Appl. Energy 2004, 78, 433–451. [CrossRef] 21. Kreider, J.F.; Curtiss, P.; Rabl, A. Heating and Cooling of Buildings: Design for Efficiency, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2010. 22. Kline, S.J.; Mcclintock, F.A. Describing uncertainties in single sample experiments. Mech. Eng. 1953, 78, 3–8. 23. Afram, A.; Janabi-Sharifi, F. Review of modeling methods for HVAC systems. Appl. Therm. Eng. 2014, 67, 507–519. [CrossRef] 24. General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China. GB/T 19409–2013 Water-Source (Ground-Source) Heat Pump; Standards Press of China: Beijing, China, 2013. 25. Lin, Q.; Loxton, R.; Teo, K.L.; Wu, Y.H.; Yu, C. A new exact penalty method for semi-infinite programming problems. J. Comput. Appl. Math. 2014, 261, 271–286. [CrossRef] 26. Xiao, Y.; Wei, Z.; Wang, Z. A limited memory BFGS-type method for large-scale unconstrained optimization. Comput. Math. Appl. 2008, 56, 1001–1009. [CrossRef]

27. Wei, X.; Li, N.; Peng, J.; Cheng, J.; Su, L. Analysis of the effect of the CaCl2 mass fraction on the efﬁciency of a heat pump integrated heat-source tower using an artiﬁcial neural network model. Sustainability 2016, 8, 410. [CrossRef] 28. Yoo, S.Y.; Kim, J.H.; Han, K.H. Thermal performance analysis of heat exchanger for closed wet cooling tower using heat and mass transfer analogy. J. Mech. Sci. Technol. 2010, 24, 893–898. [CrossRef]

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).