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Predictive ANN models of ground heat exchanger for the control of hybrid ground source heat pump systems Wenjie Gang, Jinbo Wang ⇑ School of Environmental Science and Engineering, Huazhong University of Science and Technology, Wuhan, PR China

h i g h l i g h t s " A new control method is proposed for the hybrid ground source heat pump systems. " A new modeling method for the ground heat exchanger is developed without knowing its thermal properties. " It is the ﬁrst time in this ﬁeld to use artiﬁcial neural networks to model the ground heat exchanger instead of the ground source heat pump systems. " Various cases are tested. The optimal model is obtained which has a very high accuracy.

a r t i c l e

i n f o

Article history: Received 24 September 2012 Received in revised form 6 December 2012 Accepted 10 December 2012 Available online xxxx Keywords: Hybrid ground source heat pump system Artiﬁcial neural network Ground heat exchanger Predictive model

a b s t r a c t Hybrid ground source heat pump (HGSHP) system coupled with supplemental heat rejection equipment in parallel conﬁguration is suitable for buildings where the cooling load is much higher than the heating load. Appropriate control is expected to improve its energy efﬁciency. A control strategy is proposed for cooling season as to compare the temperatures of the water exiting the ground heat exchanger (GHE) and the cooling tower (CT) directly. The logic is to choose the GHE or the CT to reject the condensing heat whenever the corresponding exit cooling water temperature is lower. During operation such a HGSHP system requires the knowledge of both the exit temperatures to take the shift control action. In many situations, however, only one of the two exit temperatures is measurable because only one is working at one moment. This paper develops artiﬁcial neural network (ANN) models for predicting the temperature of the water exiting the GHE. A numerical simulation package of a HGSHP system is adopted for training and testing the model. These models are also optimized regarding inputs, learning algorithms and neurons in the hidden layers. Results show that the ANN model can predict the GHE exit temperature with an absolute error less than 0.2 °C. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Ground source heat pump (GSHP) systems have become increasingly popular due to their year-round high efﬁciency and environmental friendliness [1,2]. In summer, the system extracts heat from the building and rejects it into the ground. In winter the process is reversed. The heat extraction from and rejection into the soil are realized by circulating heat carrier ﬂuid (water or antifreeze liquid) through high-density polyethylene pipes that are buried underground horizontally or vertically. The Hybrid GSHP (HGSHP) system employs a supplemental cooling device, such as cooling tower (CT), in addition to the ground loop heat exchangers for cooling purpose in cooling dominated areas [3]. The reason of adopting HGSHP system is to avoid the soil temperature rise and,

⇑ Corresponding author. E-mail address: [email protected] (J. Wang).

as a consequence, the refrigeration performance deterioration due to the excessive heat rejection into the ground. The ground heat exchanger (GHE) and the CT of a HGSHP system may be conﬁgured as either in series (Fig. 1) or parallel (Fig. 2) [4]. During the cooling season the parallel system rejects the condensing heat to the soil or the air through shifting total or partial condensing water ﬂow to the GHE loop and/or the CT loop. It reduces the heat rejection into the soil by reducing the water ﬂow entering the GHE. The serial system rejects less condensing heat to the soil with lower temperature entering the GHE by rejecting partial heat to the air via CT. CTs in both system conﬁgurations help reduce the amount of the heat rejected into the soil. However, the parallel system allows the GHE to be idle during the cooling period. This enables the soil to recover the temperature condition, which is considered to be beneﬁcial for the HGSHP system. Energy saving potential exists in HGSHP systems when appropriate control strategies are implemented. Literatures show that three strategies are frequently adopted for the serial systems [5–9].

0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.12.031

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Nomenclature cp w 0 ha ha hd afi Afr Lfi mw Qe Me Me0 qe T cl;in T cl;out qc

water speciﬁc heat at constant pressure (J/kg K) enthalpy of saturated air at the local bulk water temperature (J/kg dry air) enthalpy of air (J/kg dry air) mass transfer coefﬁcient (kg/m2 s) surface area per unit volume (m1) ﬁll area of the cooling tower (m2) ﬁll height (m) mass ﬂow rate (kg/s) cooling capacity (kW) the required Merkel number the available Merkel number rate of internal losses at the evaporator side (kW) condenser coolant inlet temperature (K) evaporator coolant outlet temperature (K) rate of internal losses at the condenser side (kW)

(1) Fixed temperature set-point control. A HGSHP system turns on/off the CT loop when the inlet or outlet cooling water temperature of the chiller condenser exceeds a pre-set value. (2) Temperature differential control. This strategy compares the temperature of the cooling water entering or leaving the condenser with the outdoor air wet-bulb or dry-bulb temperature. When the temperature difference exceeds a preset limit the CT loop is turned on or off. (3) Time schedule control. Turning on or off of the CT is determined according to a pre-set time table. Xu [10] studied the application of the strategies to several parallel HGSHP systems at different locations in USA. He concluded that even after optimization the three control strategies produced only marginal difference in the system energy performances and could be regarded as negligible. Accordingly, he proposed and studied the following three strategies to control the operation of the CT: (1) Load based control. The CT is turned on or off according to the temperature difference across the heat pump condenser. When the temperature difference exceeds a pre-set value the CT is turned on; when the difference is lower than another pre-set value the CT is turned off. (2) Energy model based control. At a given instant the power consumption of the HGSHP system with the CT loop on and off is modeled (estimated) and compared. The turning on or off of the CT is determined according to preference of the less power consumption condition.

Fig. 1. Schematic diagram of HGSHP system in parallel.

fHX T out T in t pre;m t cal;m n1 n2

factor related to the unit water temperature at the outlet of GHE water temperature at the inlet of GHE predicted value from ANN models calculated value from the numerical model the number of inputs of ANN models the neuron number in the hidden layer of ANN models

T in=outþp=bf =gþnum in at the inlet side of the GHE out at the outlet side of the GHE p the outside wall of the buried pipe bf the outside wall of the backﬁlling material num the distance from the location of the monitored point to the center of the borehole

(3) Adaptive temperature set-point control. The CT’s turning on or off is still controlled based on the comparison of the condenser water temperature with a pre-determined setpoint, but the setpoint is variable. The setpoint is determined according to the soil temperature and the loop average temperature. It should be noted that in almost all the studies, the GHE is assumed to be continuously running during the cooling time. However, it is anticipated that intermittently running of the GHE may result in better system performance because this kind of operation may allow the soil to take a period to recover its temperature from being over-heated [11]. In such a parallel HGSHP system, the CT and GHE will be controlled to run alternatively or simultaneously, depending on the speciﬁc system design, cooling load, air temperature condition and application of control strategy. For a parallel HGSHP system with the CT and GHE being controlled to run intermittently and alternatively, the cooling water temperature entering the condenser is of great interest. The lower the temperature is, the better the performance of the chiller is. Therefore, when decision is to make regarding the turning on or off of the CT loop and/or the GHE loop, it is most convenient to compare directly, if available, the outlet temperatures from the CT and GHE. Based on the comparison of the temperatures a simple control strategy may be established. If the temperature exiting the CT is lower than that of the GHE, the CT runs, otherwise, the GHE runs. A problem arises now, i.e., only one of the two temperatures can be measured at real time. The temperature from the GHE cannot be measured when the CT is on while the GHE is off. Similarly

Fig. 2. Schematic diagram of HGSHP system in series.

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the temperature at outlet of the CT cannot be measured when the GHE is on while the CT is off. A possible solution is to use suitable models to predict the temperatures instantly as if the cooling tower or the GHE is just turned on from idle state. Methods to predict the temperature of the water leaving a CT is already realized [12,13]. The problem is the prediction of the GHE loop because its outlet temperature depends on the history of the soil temperature, past heat injection and so on. An accurate analytical GHE model is extremely difﬁcult if not impossible because of the dimensionality and complexity of the heat exchange process underground. A two dimensional inﬁnite line-source model was used by Michopoulos and Kyriakis [14] to predict water temperature exiting the GHE. The model bias was found to be 2 °C on average and 6 °C at the maximum. Such an accuracy level is far from being enough for the control. Artiﬁcial neural network (ANN) modeling may be a good candidate. It has been widely used in prediction, classiﬁcation, pattern recognition and function approximations. For the prediction of the performance of GSHP systems, Esen [15–21] has used several methods such as adaptive neuro-fuzzy inference system, support vector machine and ANN. Results showed that ANN model was of high accuracy when predicting system coefﬁcient of performance (COP). Temperature prediction of the circulating water was not included in their papers. This study develops ANN models of the GHE for the purpose of the control of HGSHP systems which requires the knowledge of the water temperature exiting the GHE in advance. In Section 2 a HGSHP system is introduced. In Section 3 the dynamic numerical model of the HGSHP system is described brieﬂy, which is used to generate the training and testing samples for ANN models. In Section 4 several ANN models are developed in order to test ANN’s feasibility and accuracy. The study results and discussions are covered by Section 5. 2. System description 2.1. Heating and cooling loads of the building The simulated building is an ofﬁce building located in Wuhan, a typical Cold Winter & Hot Summer city in China. The annual hourly load (Fig. 3) is calculated with DeST [22], a software to calculate the heating and cooling loads of buildings in various climate regions of China. The peak cooling and heating load is 1302 kW and 883 kW, respectively. The total annual cooling demand is 1381963.53 kW h and the total annul heating demand is 628398.94 kW h. Both the peak cooling load and annual accumulative demand of cooling are much higher than that of heating. HGSHP system with CT in parallel is adopted to avoid heat buildup underground. 2.2. The HGSHP system Two identical heat pump units with a nominal cooling capacity of 770 kW and heating capacity of 830 kW are selected. The GHE is

Building Loads [kW]

1500 1000 500 0 -500 heating load

-1000 -1500

0

2000

4000

6000

Time [hrs] Fig. 3. Annual hourly heating and cooling loads.

8000

3

Fig. 4. Schematic diagram of the GHE.

designed to satisfy the heating load. 281 boreholes with a depth of 60 m are designed. The vertical buried U-pipe has an external diameter of 32 mm and an internal diameter of 26 mm. The diameter of the borehole is 200 mm. The schematic diagram of the GHE is shown in Fig. 4. The borehole is 6 m apart from each other. Two identical CTs are determined by the cooling peak load. 3. Dynamic numerical model of HGSHP system The numerical model is built via the software FLUENT. GAMBIT is used to mesh the GHE model. The meshed model is imported into FLUENT and calculation is carried out after the boundary conditions are set. Models of other main components, i.e., the CT and heat pump, are programmed with C language, which are imported into the FLUENT as user deﬁned functions (UDFs). 3.1. Ground heat exchanger Many numerical models of GHE are studied. Cui et al. [11] predicted the heat transfer behavior of the GHEs in a short time scale successfully via numerical modeling. Fayegh and Rosen [23] studied the interaction of multiple vertical GHEs by numerical models under the FLUENT environment. Partenay et al. [24] quantiﬁed the borehole short-time response impact on the system efﬁciency and system operation. They showed that the numerical model had almost no difference while the duct ground storage model (DST) had a 2 °C difference. Florides et al. [25] built a 3-D numerical model of GHE and validated the model with experimental data. In our model, for the consideration of simplicity, the horizontal and vertical external surfaces of the GHE are set as thermal insulation. The initial temperature is 291.15 K. During simulation the inlet and outlet temperatures (Tin, Tout) of the GHE are monitored every 300 s. Temperatures of several points underground are monitored in the symmetry face at the depth of 5 m, as illustrated in Fig. 5, including the pipe’s external surface temperatures (Tinp, Toutp), backﬁll external surface temperature (Tinbf, Toutbf), soil’s temperatures locating at 0.2 m (Ting0.2, Toutg0.2),0.5 m (Ting0.5, Toutg0.5), 1 m (Ting1, Toutg1), 1.5 m (Ting1.5, Toutg1.5), 2 m (Ting2, Toutg2), 2.5 m (Ting2.5, Toutg2.5), 3 m (Ting3, Toutg3) from the GHE center. These monitored temperatures are to be used as input candidates of the ANN models. The numerical results are validated by comparing with the experimental data from Ref. [26], as shown in Fig. 6.

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4. ANN model of GHE 4.1. Artiﬁcial neural networks

Fig. 5. Distribution of the monitored points.

3.2. Cooling tower Two identical counterﬂow cooling towers are selected. The height of the packing is 3.1 m. At design condition with wet-bulb temperature of 28 °C, the difference between the water temperature exiting the cooling tower and the air wet-bulb temperature is 4 °C. The ratio of air-to-water is 0.61. A concise CT model based on Merkel’s enthalpy theory is used [27]. Eq. (1) is the required Merkel number Me, which is determined by the water and air parameters entering and exiting the CT. Eq. (2) deﬁnes the available Merkel number Me0 , which is determined by the structure and properties of the CT. The equality of the two numbers should be satisﬁed for any speciﬁed condition. In this study, the available Me0 is 1.1.

Me ¼

Z

t win

twout

Me0 ¼

cpw dtw 0 ha ha

ð1Þ

ha afi Afr Lfi mw

ð2Þ

The heat pump model is obtained based on Gordon’s method which is initially developed for the centrifugal chiller [28]. The chiller performance is a function of condenser inlet coolant temperature and evaporator outlet coolant temperature, as shown in Eq. (3). We use the indicative relationship of the chiller to model the heat pump. With speciﬁc condenser inlet coolant temperature, evaporator outlet coolant temperature and load fraction, the power consumption can be calculated. Remaining coefﬁcients or constants are determined by ﬁtting manufacture’s catalog data. Eq. (4) represents the heat pump model. The evaporator outlet coolant temperature is set at 7 °C for cooling.

Q e þ qe T ch;in qc þ ðfHX 1ÞQ e T ch;out

ð3Þ

Temperature [ºC]

0:667 T cl;in 0:651 Qe 1:001 1 þ W ¼ Qe 1 þ Ld Ld T ch;out

32 30 28 26 24 22 20 18

ð4Þ

Experimental GHE inlet temperature Experimental GHE outlet temperature GHE numerical model outlet temperature

0

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Pn 2 m¼1 ðt pre;m t cal;m Þ RMS ¼ n

ð5Þ

4.2. Modelling of GHE with ANN Two types of predictive ANN models of the similar structures and algorithms are studied. The difference is with the input variables, as described below.

3.3. Heat pump

W¼

Artiﬁcial neural networks (ANNs), developed to mimic basic biological neural systems, are composed of a number of interconnected simple processing elements called neurons. One of the major applications of ANNs is forecasting. Several outstanding features of ANNs make them valuable and attractive for prediction purpose. Firstly, they are data-driven self-adaptive methods. Few priori assumptions are required for the models. Secondly, ANNs can generalize. After learning, ANNs can often correctly infer the unseen relationship even if the sample data contain noisy information. Finally, ANNs are universal functional approximators [29]. There are different types of ANNs. One of the most popular is the back propagation (BP) network. BP neural network is a multilayer network proposed in 1986 [30]. It uses the gradient descent method to change the weight values and yield values as quickly as possible to reduce the error. Typical BP network includes the input layer, the hidden layers and the output layer. This paper tries to predict water temperature exiting the GHE with three-layer BP networks. There are many learning algorithms for the BP networks and it is difﬁcult to conclude which is optimal for a given problem. It is usually chosen by trial and error, which is also adopted in this paper. The root mean squared error (RMS) is used to estimate the performance. The equation for RMS is deﬁned as Eq. (5).

3

6

9

12

15

Time [hrs] Fig. 6. GHE validation results.

18

21

24

4.2.1. Input layer Of the ﬁrst type, inputs are the monitored temperature measurements at current time step. We call it static model. Of the second type, inputs are the temperature measurements at both the current and one past time step. We call it ‘‘dynamic model’’ because the dynamic underground temperature history enters the model for prediction in certain sense. Among all the monitored temperatures, we need to determine the most important ones as the effective inputs for the ANN model. Different methods may be used for this purpose, such as the methods that rely upon a priori knowledge of the system being modeled, methods based on linear cross-correlation, methods that utilize a heuristic approach, methods that extract knowledge contained and methods combining the former four ways [31]. In this study, the method combining prior knowledge and correlation is adopted. The Pearson correlation coefﬁcients of all the candidate inputs with the output are shown in Table 1. It shows Tin, Tinp, Tinbf, Toutp and Toutbf have larger correlation coefﬁcients with the output with values above 0.98. These ﬁve variables are taken as inputs for the ANN static model. The dynamic models have nine inputs by including the temperatures measurements at one former time step, as denoted by Tinp-1, Tinbf-1, Toutp-1, Toutbf-1. 4.2.2. Hidden layer There is still not a reliable way to determine the optimal number of neurons in the hidden layer. One method is trial and error, which is applied in the static model. The trial number ranges from

Please cite this article in press as: Gang W, Wang J. Predictive ANN models of ground heat exchanger for the control of hybrid ground source heat pump systems. Appl Energy (2013), http://dx.doi.org/10.1016/j.apenergy.2012.12.031

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Table 1 Pearson correlation coefﬁcients of Tout with other variables. Variable Result Variable Result Variable Result Variable Result

Tin 0.9683 Ting0.2 0.7544 Ting2.5 0.509 Toutg1.5 0.4864

Tinp 0.9913 Ting0.5 0.4529 Ting3 0.5107 Toutg2 0.5015

Toutp 0.9972 Ting1 0.4629 Toutg0.2 0.7072 Toutg2.5 0.5092

Tinbf 0.9972 Ting1.5 0.4855 Toutg0.5 0.446 Toutg3 0.5109

Toutbf 0.9811 Ting2 0.501 Toutg1 0.4643

3 to 25. For the dynamic model the heuristic method as expressed by Eq. (6) is used

n2 ¼ 2n1 þ 1

ð6Þ

4.2.3. Output layer The predicted temperature of water at the exit of GHE is the output.

Fig. 8. Schematic diagram of the static ANN model.

4.2.4. Learning algorithms Three learning algorithms are used, including Levenberg– Marquardt (LM), Scaled Conjugate Gradient (SCG) and Broyden– Fletcher–Goldfarb–Shanno (BFGS) in order to determine the optimal. They are known as trainlm, trainscg and trainbfg in MATLAB toolbox. 4.2.5. Training and testing samples The monitored data from the HGSHP system operation are used as training and testing samples. Nine weeks of HGSHP system operation in cooling season is simulated with a time step of 300 s. The heat pump works from Monday to Friday and is off on Saturday and Sunday. System keeps running from 7:00 to 20:00 on the working days. In the former four and the ninth weeks the GHE and CT run according to the schedule illustrated in Fig. 7. From the ﬁfth to the eighth week, the working time of the GHE and CT is variable. All the ANN models are performed under MATLAB environment using the neural network toolbox. The structure diagrams of the static and dynamic model are shown in Figs. 8 and 9. Fig. 9. Schematic diagram of the dynamic ANN model.

5. Results and discussion 5.1. The static model For the consideration of conciseness, abbreviations are used to name the different ANN models. For example, LM-9-19-1 is used to denote the model with 9 neurons in the input layer, 19 neurons in the hidden layer, 1 neuron in the output layer, with LM denoting the learning algorithm.

ON/OFF

1

0

-1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Time [hrs] Fig. 7. HGSHP system operation schedule. 1-CT ON, GHE OFF; 1-GHE ON, CT OFF; 0-heat pump OFF

To train and test the static model, data of the simulated system operation in the 4 weeks are used: the former 3 weeks data as the training samples and the fourth week for testing. Results of different static models are shown in Figs. 10–12. All the RMSs of training and testing are small, less than 0.08. Models with BFGS algorithm perform better than SCG with smaller RMSs. LM performs better than BFGS and all the RMSs of LM models are smaller than those in BFGS models. LM could achieve the smallest training and testing RMSs. Results also show that models with SCG and BFGS algorithms do not achieve the performance goal within the maximum echoes. While all the models trained with LM achieve the goal with much less echoes. For the model with the same neuron number in the hidden layer, the more echoes are demanded, the more calculation time is required. LM models consume much less time than the other two. Besides, model of LM-5-11-1, LM-5-22-1 needs fewer echoes compared with other LM models. The more neurons are used in the hidden layer, the more time is consumed per echo. Thus, model LM-5-11-1 is better than LM-5-22-1 with less calculation time. It can be concluded that the ANN model of the GHE has good accuracy and strong generalization ability. LM is the optimal learning algorithm among the three, with highest accuracy and least

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0.09

SCG

0.2

BFGS

0.08

RMS

0.15

Absolute error ºC

LM

0.07 0.06 0.05

0.1 0.05 0 -0.05 -0.1 -0.15

0.04 0.03

-0.2

5

8

11

14

17

20

23

26

300

0

Neurons in the hidden layer

SCG

Absolute error ºC

LM

BFGS

RMS

0.08 0.07 0.06 0.05 0.04 0.03

5

8

11

14

17

20

23

26

Fig. 11. Testing results with different learning algorithms and neurons in the hidden layer.

LM

SCG

BFGS

2000

Echoes

1200

0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2

0

100

200

300

400

Sample numbers Fig. 14. Testing results of model LM5-11-1.

Neurons in the hidden layer

1500 1000 500 0

900

Fig. 13. Training results of model LM5-11-1.

Fig. 10. Training results with different learning algorithms and neurons in the hidden layer.

0.09

600

Sample numbers

5

8

11

14

17

20

23

26

Neurons in the hidden layer Fig. 12. Echoes demanded in models with different learning algorithms and neurons in the hidden layer.

calculation time. Model LM-5-11-1 is optimal because of its smallest RMSs and fewest echoes. The training and testing results of LM-5-11-1 are shown in Figs. 13 and 14. Errors are within the interval of [0.2 °C, 0.2 °C]. Most training and testing errors are close to 0 °C. The result is very encouraging.

5.2. Different operation modes and dynamic models For studying the performance of the static model, structured time spans were scheduled for the HGSHP system to operate with either the ground loop or the CT loop for heat rejection. In practice the operation mode may vary. In order to study the prediction ability of the ANN models, all the data from the 9 weeks operation with variable modes are used for training and testing. In addition,

dynamic ANN models are also investigated with the 9 weeks data. Six cases are designed for static and dynamic ANN models, respectively. Details of the selection of the training and testing samples for the six cases are given in Table 2. The static model structure is LM-5-11-1. The dynamic model structure is LM-9-19-1. The training and testing results of the six cases are shown in Table 3.The results show that all the ANN models can predict the water temperature exiting GHE with good accuracy, with RMSs being less than 0.07. However, system operation modes do affect the performance of the ANN models. When the training and testing samples are both from the structured operation mode, the RMSs are the smallest. When the training samples are from structured mode but the testing samples are from unstructured mode, the testing RMS values are the largest. When the training samples are from unstructured mode and testing samples are from structured mode, the testing RMS is smaller than the training RMS, which is opposite to the other ﬁve cases. These mean that only when an ANN model has learned sufﬁciently the knowledge of the system under different modes high accuracy and good generalization can be achieved. Performances of the static and dynamic ANN models are different to certain degree. From Table 3 it can be seen that the RMSs of the dynamic models are smaller than that of the static models. It may be concluded that the dynamic models bear better accuracy Table 2 ANN models under different cases. Name

Training samples source

Testing samples source

Case Case Case Case Case Case

1st, 2nd, 3th week 2nd, 3th, 4th week 3th, 4th, 5th week 4th, 5th, 6th week 5th, 6th,7th week 6th, 7th, 8th week

4th week 5th week 6th week 7th week 8th week 9th week

1 2 3 4 5 6

Note: The italic mean structured operation mode and the roman mean unstructured operation mode.

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Table 3 Results of static and dynamic models for six cases. Name

Static Training RMS

Testing RMS

Training RMS

Testing RMS

Case Case Case Case Case Case

0.027 0.026 0.028 0.034 0.041 0.047

0.034 0.062 0.056 0.057 0.059 0.039

0.019 0.019 0.02 0.019 0.026 0.032

0.022 0.036 0.037 0.036 0.035 0.021

1 2 3 4 5 6

Dynamic

Absolute error ºC

W. Gang, J. Wang / Applied Energy xxx (2013) xxx–xxx

0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2

0

100

200

300

400

Sample numbers Fig. 16. Testing results of the static model under Case 5.

Time based control

250

Power [kW]

and better generalization ability. Since the difference is relatively small, the static model LM-5-11-1 may be a good choice when less calculation time is emphasized. If the ANN predictive model of GHE is to be applied to engineering practice, the running time of the GHE or the CT will be most likely variable. Case 5 presents such a situation where the ANN model is trained with samples from variable operation mode. The case study result shows that the absolute errors of both the training and testing samples of the dynamic model are small as shown in Figs. 15 and 16. All the absolute errors are within the interval of [0.2 °C, 0.2 °C], and most of the errors are close to 0 °C. The result is very promising.

ANN based control

200 A

150

B

100 50

7

Absolute Error ºC

0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2

0

300

600

900

1200

Sample numbers Fig. 15. Training results of the static model under Case 5.

11

13

15

17

19

Time [h]

5.3. Performance of HGSHP system controlled with ANN models In order to illustrate the performance of the HGSHP system under the proposed control method, 1-day operation of the system is simulated. The predictive model for CT is also built with ANN. The detail information is introduced in Ref. [32]. The implemented control logic is as follows. (1) The GHE is set to run at the ﬁrst half hour in the morning; (2) Water temperatures exiting the GHE and plate heat exchanger, which is connected with the CT, are compared with each other directly. If the water temperature leaving the GHE is higher, start the CT and turn off the GHE. Otherwise let the GHE continue to run. (3) When the CT is on, compare the two temperatures. If the water temperature leaving the plate heat exchanger is higher, turn off the CT and start the GHE. Otherwise the CT continues. The adopted GHE predictive model is the static model with the structure of LM-5-11-1. The power consumptions of the heat pump of the HGSHP system under the ANN predictive control and the time schedule control are presented in Fig. 17. It can be seen that at the beginning period the power consumptions are identical. At point A the system under the time schedule control turns off the GHE and starts the CT, while the system under the ANN model predictive control still runs the GHE. At this moment the heat pump of the system under the predictive control consumes less power. This indicates that the ANN predictive model based control holds the potential to achieve higher energy efﬁciency in certain condition. At point B the system controlled by the time schedule changes to run the GHE and the power consumption is low at the intermediate period.

9

Fig. 17. Power required by the heat pump on the ﬁrst working day under two control methods.

The reason is that the GHE has just undergone temperature recovery during its idle period and, thus, allows a better cooling temperature for the heat pump. In the simulated operation of the whole day the energy consumption by the heat pump chiller is 2003 kW h for the system under the time schedule control and, 1986 kW h for the system under the control with the ANN predictive model. The system controlled by the ANN predictive model is a little more energy efﬁcient. At the same time, it should be noticed that the underground soil may achieve better temperature recovery under the time schedule control. More through study is deﬁnitely necessary in the future. The performance of the whole system in a much longer period, such as the life cycle, needs further investigation. In addition, the model would be improved and the feasibility of ANN modeling the GHE should be tested by considering more complex underground heat transfer conditions, such as water migration. Experimental tests would also be a necessity in the future to justify the proposed ANN model based control method. 6. Conclusions Static and dynamic models of GHE based on ANNs were developed to predict the temperature of the water at the GHE outlet for the purpose of the shift control between the GHE loop and CT. Simulation of a HGSHP system was employed for training and testing the ANN models. Several schemes of the ANN models of GHE were tested, and main conclusions are summarized as follows: (1) ANNs can be used to predict the temperature of the water at the GHE exit with very good accuracy. It offers an effective approach to model the GHE without the requirement of the relevant ground and U-tube thermal physical properties for the prediction purpose. (2) LM is the best among the three learning algorithms. It achieves the performance goal with least calculation time and highest precision. The best LM model predicts the water temperature with absolute errors less than 0.2 °C.

Please cite this article in press as: Gang W, Wang J. Predictive ANN models of ground heat exchanger for the control of hybrid ground source heat pump systems. Appl Energy (2013), http://dx.doi.org/10.1016/j.apenergy.2012.12.031

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Please cite this article in press as: Gang W, Wang J. Predictive ANN models of ground heat exchanger for the control of hybrid ground source heat pump systems. Appl Energy (2013), http://dx.doi.org/10.1016/j.apenergy.2012.12.031

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