# Study on Fuzzy Control for Air-To-Water Heat Pumps Connected to a Residential Floor Heating System

Authors: Duhui Jiang; Cui Hongshe
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

Reducing the supplied water temperature of the air-to-water heat pump to meet the building heat demand can greatly improve the efficiency of the heat pump unit and give full play to the advantages of energy saving and comfort of the floor radiant heating system with an air-to-water heat pump. Based on the variation of ambient temperature and ambient temperature, the domain of fuzzy control is optimized by particle swarm optimization (PSO), and the optimal fuzzy control table is established to adjust the supplied water temperature of the air-to-water heat pump. A transient simulation model of floor radiant heating system for a typical 100 m2 building in China cold regions was developed by using TRNSYS software, and this heating system is simulated by the fuzzy control variable supplied water temperature and the conventional 45°C supplied water control in the whole heating season. The simulation results show that the system energy consumption is saved by 15.9% and SCOP increased by 18.9% by using this fuzzy control compared with the conventional 45°C supplied water control in the whole heating season under the premise of ensuring stable room temperature. Comparing conventional 45°C supplied water control, the fuzzy control can reduce CO2 emissions by 4.3 kg/m2, 4.7 kg/m2, 5.6 kg/m2, 5.2 kg/m2, and 4.9 kg/m2 in Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou, respectively.


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## Body

## 1. Introduction

Recently, the radiant heating system has been widely applied in residential buildings. Radiant floor heating systems are installed in 85% of rural houses in northern China and almost all residential buildings in Korea [1, 2]. Floor heating can accept lower temperature hot water. The combination of air-to-water heat pump and floor radiant heating can give full play to the advantages of air-to-water heat pump low temperature and high efficiency and floor radiant heating comfort and energy saving.The supplied water temperature of the air-to-water heat pump has a great influence on the efficiency of the heat pump unit. Under the premise of ensuring the stability of the room temperature, reasonable optimization of the supplied water temperature is the key to the control of the heating system. Leiqh et al. analyze and study the relationship between the supplied water temperature of the floor radiant heating system and the outdoor temperature and conclude that there is a linear relationship between the outdoor temperature and the required supplied water temperature [3]. Olesen et al’s. dynamic simulations show that the water temperature in the pipe (the supplied water temperature or the average temperature of the supplied and return water) is controlled by the outdoor temperature, which has better energy conservation and economy [4]. The latest advances in computing software and communications equipment have enabled us to develop optimized control strategies to address the challenges of intrinsic heating system control strategies [5]. Karlsson et al. optimize the supplied fluid temperature by predicting the room heat demand. The control method is applicable to a single room, the supplied fluid temperature is stable, and the predicted heat demand is good [6]. Liu et al. establish the air-to-water heat pump floor radiant heating system simulation model through EnergyPlus and BCVTB and propose a variable supplied water temperature control for the 100 m2 actual residential area in Shanghai. The heating season is energy-saving under the control by 40% [7].Heating efficiency of the air-to-water heat pump is obviously affected by the outdoor temperature, and the outdoor temperature also has an obvious effect on the building heat load. Therefore, there is a basis for controlling the supplied water temperature according to the outdoor temperature. However, due to the thermal inertia of the building envelope, to maintain the stability of the room temperature, the air-to-water heat pump floor radiant heating system needs to supplement the heat lost by the building in time. A building energy model (BEM) is very important for predicting the energy consumption of the heating system. BEM can be broadly classified into a white box model (EnergyPlus [8], TRNSYS [9], etc.), a black box model (artificial neural network (ANN) [10, 11], support vector machine (SVM) [12], fuzzy logic (FL) [13], etc.), and a gray box model (between white and black boxes [14–16]). They use real data and physical equations to determine behavioral buildings [17]. The BEM in TRNSYS is a good model for predicting the state of the building because they allow the definition of all the elements that affect its energy behavior. The accuracy of the TRNSYS software has been validated [18–20].For multiroom buildings, the paper uses MATLAB software to develop a fuzzy control table, taking the ambient temperature during the heating season, the difference between the current ambient temperature and the ambient temperature at the previous hour as the variables, and formulate the fuzzy control table of the variable-supplied water temperature of the air-to-water heat pump. Under the premise of ensuring the heat demand of the building, the heat pump unit operates at the lowest supplied water temperature, which is the key to energy saving. The existing literature mostly uses energy consumption, cost savings, predicted mean vote (PMV), or predicted percentage dissatisfied (PPD) as the optimization target [21–24]. The objective function considers the energy consumption of the heating system and the room temperature to be stable by using the particle swarm optimization (PSO) algorithm to optimize the fuzzy control table on the GenOpt [25] software. There are many commonly used heuristic algorithms including PSO [26], genetic algorithm (GA) [27, 28], firefly algorithm [29], memetic algorithm [30], evolutionary algorithm (EA) [31], and artificial bee colony (ABC) optimization algorithm [32]. PSO algorithm was first proposed by Professor Kennedy in the United States [33]. Through the cooperation and competition among individuals, the optimal solution search in complex space is realized.The organization of this paper is as follows. Section2 builds the model on TRNSYS and explains the proposed methodology. And then, Section 3 takes the typical buildings in rural areas of Beijing as an example. Section 4 discusses energy-saving effect of variable-supplied water temperature control in Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou. Lastly, Section 5 summarizes the conclusions.


## 2. Models and Methods

This paper builds a model of air-to-water heat pump floor radiant heating system through TRNSYS. The building model and the floor radiant coil model use the type56 module in TRNSYS. Buried pipe model comes from RC-models [34]. The climate database TMY2 (typical weather year) includes 10 years of meteorological data and provides statistical climatic conditions for TRNSYS simulation [35].Verhelst et al. [36] discussed the advantages and disadvantages of different degrees of simplification of the heat pump model and applicable conditions. Based on the TRNSYS air-to-water heat pump model, this paper uses the empirical formula in the literature to defrosting the heat pump unit COP [37]. The performance parameters of the heat pump unit and the unit test data are provided by McQuay.(1)CAPr=−0.0001836×to×to−0.0000686×tg×tg−0.0000815×to×tg+0.0190017×to+0.0021383×tg+0.9515673H1R2=0.9972,COPr=−0.0000456×to×to+0.0001571×tg×tg−0.0003565×to×tg+0.0279493×to−0.0338114×tg+2.1128644H1R2=0.9933,where CAPr is the ratio of the performance curve heating capacity to the nominal operating condition, COPr is the ratio of the performance curve COP to the nominal operating condition COP, to is the outdoor temperature, and tg is the heat pump unit outlet temperature.When the ambient temperature is lower than 7°C and higher than 7°C, the COP attenuation valueCOPdf caused by unit defrosting, as shown in the following equations:(2)COPdf=−0.0027to−7+0.1801exp−to25,(3)COPdf=0.1801exp−to25.The actual power consumption of the air-to-water heat pump is calculated as follows:(4)Pm=CAPc×CAPrCOPc×COPr1−COPdf,Qx=m×Cptg−ti,Plr=QxCAPc×CAPr,Pawhp=Pm×Fflp,where Pm is full load power consumption, Pawhp is air-to-water heat pump actual power consumption, Qx is actual heating capacity, Plr is partial load rate, m is flow, and ti is the heat pump unit inlet temperature.The actual power consumption of the water pump is calculated as follows:(5)Ppump=ρgVH3600000η,η=ηpηm,Ps=Ppumpηm,where Ppump is pump power, H is pump head, V is flow of water flowing through the pump, η is total pump efficiency, ηp is pump motor efficiency, ηm is pump shaft efficiency, and Ps is pump shaft power.The heat dissipation of the pipe is calculated as follows:(6)UA=1Rinside+Rpipe+Rinsul+Routside,Rinside=1hinsideπdpipeLpipe,Rpipe=lndpipe,o/dpipe,i2πkpipeLpipe,Rinsul=lndinside,o/dpipe,o2πkinsulLpipe,Routside=1houtsideπdpipeLpipe,Qenv,j=UAjtj−to,where UA is total heat transfer coefficient of pipeline, Rinside is thermal resistance inside the pipe, Rpipe is thermal resistance of the pipe, Rinsul is thermal resistance of thermal insulation, Routside is thermal resistance outside the pipe, kpipe is thermal conductivity of the pipe, kinsul is thermal conductivity of the insulation, hinside is heat transfer coefficient inside the pipe, houtside is heat transfer coefficient outside the pipe, dpipe is pipe diameter, Lpipe is pipe length, Qenv is heat dissipation of the pipe, and j is the various parts of the pipe fluid.The valve is divided into a diverting valve and a mixing valve, and the energy flow models are, respectively, shown as follows:(7)minCptin−tdiv=mout,1tout,1−tdiv+mout,2tout,2−tdiv+mout,3tout,3−tdiv+mout,4tout,4−tdiv+mout,5tout,5−tdiv,moutCptout−tmix=min,1tin,1−tmix+min,2tin,2−tmix+min,3tin,3−tmix+min,4tin,4−tmix+min,5tin,5−tmix,tin=tdiv,tout=tmix,tin=∑i=15mout,itout,i∑i=15mout,i,tout=∑i=15min,itin,i∑i=15min,i.A two-position controller is used to control the room temperature between 18°C and 19°C. On the premise of ensuring the stability of the room temperature, the heat lost by the building is replenished in time. The temperature of the outdoor environment is detected by the temperature sensor, and the current ambient temperature, the difference between the current ambient temperature, and the ambient temperature of the previous hour are used as variables, and the fuzzy control table is developed by using MATLAB. Output fuzzy control calculation results from MATLAB software to the TRNSYS.The method of fuzzy control defuzzification uses the centroid method, and its expression formula is as shown in equation (8). The membership function in fuzzy control is trapmf type, and its expression formula is as shown in equation (9).(8)xn=∑i=1nxiμxi∑i=1nμxi,(9)Az=0,z<c,z−cd−c,c≤z<d,1,d≤z<e,f−zf−e,e≤z<f,0,f≤z,where xn is the final value of the fuzzy control output; xi is the elements in the domain (i = 1, 2, 3, 4, 5, …, n); μ(xi) is the fuzzy membership function; c, d, e, f, and z are constant values, where c < d < e < f; A(z) is membership function output value.We build five fuzzy subsets as {NB, NS, ZO, PS, PB}. The fuzzy control decision table is shown in Table1.Table 1
Fuzzy control decision table.
t
o(o) − to(o-h)
NB
NS
ZO
PS
PB
t
o(o)
NB
PB
PB
PB
PMB
PM
NS
PM
PMS
PS
ZO
NS
ZO
PS
ZO
NS
NMS
NM
PS
NS
NMS
NM
NMB
NB
PB
NM
NMB
NB
NB
NBThe setting supplied water temperaturetset is between 25°C and 45°C. The fuzzy control output table is shown in Table 2.Table 2
Fuzzy control output table.
t
o(o) − to(o-h)
(−∞, −3b)
(−3b, −b)
(−b, b)
(b, 3b)
(3b, +∞)
t
o(o)
(−∞, −3a)
45
45
45
43
41
(−3a, −a)
41
39
37
35
33
(−a, a)
37
35
33
31
29
(a, 3a)
33
31
29
27
25
(3a, +∞)
29
27
25
25
25In order to improve the control precision, the domain of fuzzy control is optimized, that is,a and b are optimized under the condition that the control rule base is unchanged. The two parameters are coupled to each other. It is difficult to get the optimal value quickly and accurately by the conventional method. Therefore, the particle swarm optimization (PSO) algorithm on GenOpt software is used to optimize the parameters. As shown in Figure1, TRNSYS inputs the current room temperature to(o), the previous hour room temperature to(o-h), and optimization value a and b to MATLAB.Figure 1
Fuzzy optimization calculation process.Figure 2
Architectural plane diagram of the typical rural residential building.Let the particle swarm search in an n-dimensional space. The basic formula of the particle swarm algorithm is as shown in the following equations:(10)Vibk+1=wVibk+c1N1Pibbestk−Yibk+c2N2Pgbbestk−Yibk,(11)Yibk+1=Yibk+Vibk+1,where Yib(k) is the position of the particle i in the bth dimension in the kth iteration; Vib(k) is the velocity of the particle i in the bth dimension in the kth iteration; Pibbest(k) is the particle i individual optimal position; Pgbbest(k) is the global optimal position of the whole particle swarm; c1 and c2 are learning factors; w and k are inertia factors and iteration times; and N1 and N2 are random numbers between 0-1.The vonNeumann topology is used, the maximum number of iterations is 500, the cognitive acceleration is 2.8, the social acceleration is 1.3, the max velocity gain continuous is 0.5, the maximum velocity discrete is 4, the initial iteration is 1.2, the final iteration is 0.5, the number of particles is 20, and the number of generations is 5.The objective functionM considers the energy consumption of the heating system and the room temperature to be stable. The stability of room temperature is expressed by unsatisfied time. Unsatisfied time is the time when the room temperature exceeds the setting temperature range of the room. The smaller the unsatisfied time is, the more stable the room temperature is. The objective function is as shown in the following equation:(12)M=∑0HPpump+Pawhp∑0HPpump,45+Pawhp,45+∑0Hhwest+hliv+hbed+hdin∑0Hhwest,25+hliv,25+hbed,25+hdin,25,where H is total hours of heating season, Ppump,45 is pump power under constant supplied water temperature of 45°C, Pawhp,45 is air-to-water heat pump power under constant supplied water temperature of 45°C, hwest,25 is room temperature of west bedroom below 18°C or above 19°C under constant supplied water temperature of 25°C, hliv,25 is room temperature of living room below 18°C or above 19°C under constant supplied water temperature of 25°C, hbed,25 is room temperature of bedroom below 18°C or above 19°C under constant supplied water temperature of 25°C, and hdin,25 is room temperature of dining room below 18°C or above 19°C under constant supplied water temperature of 25°C.


## 3. Engineering Example

The building model uses a type56 module from TRNSYS to simulate a single storey rural house with a building area of 100 m2(see Figure 2) and a height of 3.2 m. The weather file in the model adopts the typical weather year TMY2 data file of Beijing.Figure 3
Floor radiant heating system with air-to-water heat pump.The detailed setting of the building refers to the typical rural residential building in the cold area in reference [38]. The heating season starts on November 15 and lasts for 2,904 hours. The ratio of the south facing window to the wall is 0.1, and the ratio of the north facing window to the wall is 0.05. The number of ventilation is 1/h. The basic information of the building is shown in Table 3.Table 3
Architectural basic information.
Structure
Coefficient of heat transfer (W m−2·K−1)
Exterior wall
0.457
Roof
0.422
Ground
0.039
Exterior window
2.8The floor radiant heating surface is cement, the filling layer is 60 mm concrete, the bottom layer is provided with insulation layer, and the buried pipe adopts PE pipe. The rural residential building radiant coil parameters are shown in Table4.Table 4
Radiant coil parameters.
Unit
Parameter
Pipe spacing
m
0.2
Pipe outer diameter
m
0.02
Pipe wall thickness
m
0.002
Pipe heat transfer coefficient
W m−1 K−1
4.54More information of the radiant coil is given in [39]. The simulation is carried out by considering the McQuay air-to-water heat pump MACO50ER5-AE and the horizontal multistage centrifugal pump. Detail parameters are shown in Table 5.Table 5
Equipment detail parameters.
Quantity
Rated heating capacity (kW)
Rated power (kW)
Air-to-water heat pump
1
14.8
4.4
Pump
1
0.37The air-to-water heat pump floor radiant heating system is built by TRNSYS. The floor radiant heating system with air-to-water heat pump is shown in Figure3.


## 4. Results and Discussion

The optimization result is shown in Table6.Table 6
Optimization value.
Initial value
Range
Step value
Optimization value
a
3
[1, 15]
1
4.8
b
1
[0.1, 6]
0.1
0.5Beijing heating time is 2,904 hours in the whole heating season. Hourly ambient temperature is shown in Figure4, and hourly ambient temperature change is shown in Figure 5.Figure 4
Hourly ambient temperature in the whole heating season.Figure 5
Hourly ambient temperature change in the whole heating season.As shown in Figures4 and 5, the abscissa is the heating season time, and the ordinate in Figure 4 is the hourly ambient temperature. In Figure 5, the ordinate is the hourly ambient temperature change. The dotted lines in Figures 4 and 5 are the domain scopes optimized by PSO. The hourly ambient temperature of the entire heating season is 62.9% at (−a, a). The hourly ambient temperature change of the entire heating season is 36.9% at (−b, b). The temperature change of each room from January 6 to January 12 in the fuzzy control heat pump unit supplied water temperature is shown in Figure 6.Figure 6
Room temperature under varied supplied water temperature fuzzy control.As shown in Figure6, the abscissa is the heating season time, from January 6 to January 12, totaling 168 h. The left ordinate is the room temperature of the west bedroom, living room, bedroom, and dining room and the supplied water temperature setting of the heat pump. The right ordinate is the outdoor ambient temperature. The temperature of each room in the whole heating season can be basically guaranteed at 18-19°C. The room temperature of each room is fluctuated by the change of the outdoor ambient temperature and the supplied water temperature setting of the heat pump unit. The change in trend of the supplied water temperature of the heat pump unit and the outdoor ambient temperature is reversed.As shown in Table7, the SCOP of the whole heating season is 2.43 under constant control. This value is similar to the SCOP of existing air-to-water heat pump heating systems in rural areas of Beijing in the whole heating season [40]. The supplied water temperature under the fuzzy control can be saved energy by 15.9% compared with the constant supplied water temperature of 45°C, and the heating system can increase the SCOP by 18.9%. Comparing with the constant supplied water temperature of 45°C, the room temperature is more stable which the unsatisfied time decrease 3.2% under the fuzzy control supplied water temperature. Under the premise of ensuring the room temperature, the unit supplied heat quantity does not change much, but the heat pump unit supplied water temperature and building load more matching, the average supplied water temperature of the unit is reduced. The efficiency of the heat pump unit is increased, and the power consumption of the heat pump unit is reduced.Table 7
Heating system power consumption in the whole heating season.
Constant 45°C
Fuzzy control
Power consumption (kWh)
5046
4242
Unsatisfied time (h)
3085
2985
SCOP
2.43
2.89Extend the control to other regions without changing the building envelope and air source heat pump heating capacity. Taking the climates of Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou as variables, monthly average ambient temperatures in the heating season are shown in Figure7.Figure 7
Monthly average ambient temperatures in the heating season.Optimization parameters of Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou are shown in Table8.Table 8
Optimization parameters of five cities.
Heating season (h)
a
b
Zhengzhou
2904
13.2
0.4
Qingdao
3384
7.4
0.3
Beijing
2904
4.8
0.5
Taiyuan
3624
4.8
0.2
Zhangjiakou
3624
4.0
0.1As shown in Figure8, room temperatures of Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou are stable under the fuzzy control of varied supplied water temperature. With the decrease of outdoor temperature in the heating season, the supplied water temperature setting of Zhangjiakou is significantly higher than that of Zhengzhou. Compare energy consumption and unsatisfied time of all rooms in each city as shown in Figure 9.Figure 8
Room temperature curve under varied supplied water temperature fuzzy control: (a) Zhengzhou; (b) Qingdao; (c) Beijing; (d) Taiyuan; and (e) Zhangjiakou.
(a)
(b)
(c)
(d)
(e)Figure 9
Energy consumption and unsatisfied time in the heating season.The more the room heat demand matches the heat supply, the less is the unsatisfied time. Comparing constant 45°C supplied water temperature, the unsatisfied time decrease by 0.5%, 0.2%, 3.2%, 2.8%, and 3.8% in Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou under the fuzzy control supplied water temperature. The fuzzy control can not only improve the temperature stability of the room but also save energy. The fuzzy control is 18.0%, 17.2%, 15.9%, 13.2%, and 10.5% compared with constant 45°C in Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou, respectively, of energy conservation. The fuzzy control can reduce CO2 emissions by 4.3 kg/m2, 4.7 kg/m2, 5.6 kg/m2, 5.2 kg/m2, and 4.9 kg/m2 in Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou, respectively.


## 5. Conclusions

In this study, the calculation model of air-to-water heat pump floor radiant heating system with the typical building of 100 m2 in cold regions in the north is built on the TRNSYS software platform. The fuzzy rules are formulated by MATLAB software. The fuzzy control for adjusting the supplied water temperature by the difference between the current ambient temperature and the previous hour’s ambient temperature and the ambient temperature during the heating season. The particle swarm optimization algorithm of GenOpt software platform optimizes the domain in the fuzzy control table to obtain the best fuzzy control table. The study results show that compared with the control of constant supplied water temperature of 45°C, the fuzzy control variable supplied water temperature can save energy 15.9% in the heating season, and improve SCOP 18.9% in the heating season, and room temperature stability has also been improved. The fuzzy control is extended to Zhengzhou, Qingdao, Taiyuan, and Zhangjiakou, which can save 18.0%, 17.2%, 13.2%, and 10.5% energy consumption, respectively. While ensuring the temperature of the room, the fuzzy control can reduce CO2 emissions by 4.3 kg/m2, 4.7 kg/m2, 5.6 kg/m2, 5.2 kg/m2, and 4.9 kg/m2 in Zhengzhou, Qingdao, Beijing, Taiyuan, and Zhangjiakou, respectively.



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