Modeling of a photovoltaic-thermal evaporator of solar assisted heat pumps

using artificial neural networks N. Gunasekara, M. Mohanrajb,*, V. Velmuruganc

a Department of Mechanical Engineering, Sri Krishna College of Technology, Coimbatore- 641042. India

b Department of Mechanical Engineering, Hindusthan College of Engineering and Technology, Coimbatore-641032, India cDepartment of Mechanical Engineering, Sri Sakthi Engineering College, Coimbatore 641104. India

Abstract

Artificial neural networks (ANN) modeling of a photovoltaic-thermal evaporator (PV-TE) used in solar

photovoltaic-thermal heat pumps (SPV-THP) was investigated in this work. The experiments were carried

out under the meteorological conditions of Coimbatore city (latitude of 10.98oN and longitude of 76.96oE)

in India. The performance parameters of a PV-TE such as evaporator heat gain (QPV-TE), solar energy input

ratio (SEIR), photovoltaic efficiency (ηpv) and photovoltaic panel temperature (Tpv) were observed with

reference to solar intensity, ambient temperature, ambient wind velocity and ambient relative humidity.

The experimentally observed results were used as training data for the network. The back propagation

learning algorithm with Lavenberg-Marguardt (LM) variant and log-sigmoid transfer function were used.

The network was optimized to 4-11-4 configuration. The network predicts the QPV-TE, SEIR, ηpv and Tpv

with maximum fraction of absolute variance values (R2) of 0.9999, minimum root mean square errors

(RMS) and minimum coefficient of variance (CoV) values. The results confirmed that ANN is quite

suitable for modeling of PV-TEs.

Key words: Photovoltaic-Thermal evaporator, Artificial neural network modeling.

1. Introduction

Photovoltaic energy conversion has been widely used for generating electricity [1]. The photovoltaic cells

have conversion efficiencies around 10-20% due to increase in cell temperature. The remaining 80-90%

of the heat energy is exhausted to the surroundings [2]. The photovoltaic-thermal hybrid technology

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* Corresponding author: Tel.: +91 9486411896

Email: mohanrajrac@yahoo.co.in

improves the photovoltaic conversion efficiency by absorbing the heat from photovoltaic cells [3]. Many

researchers proposed air and water as the working fluids to extract the heat from photovoltaic cells and

utilized for drying, space heating and domestic water heating [4]. The photovoltaic-thermal hybrid

technology can be used in heat pumps for performance enhancement [5-7]. The SPV-THP directly

incorporates the PV-TE, where the refrigerant is directly expanded and undergoes phase change from

liquid to vapour by absorbing the solar and ambient energy sources from the surroundings [8]. The PV-

TE performs dual functions such as electricity and heat energy generation [9]. A fraction of solar

illumination falls on the PV-TE is converted into electricity by the photovoltaic cells and the remaining

portion of thermal energy was absorbed by the refrigerant [10]. The PV-TE hybrid collector controls the

cell temperature and improves the photovoltaic efficiency [11]. The thermal performance of a PV-TE can

be improved by using refrigerant as working fluid [12-14].

Many investigators developed different configurations of PV-TE for SPV-THP and evaluated its

performance by both theoretically and experimentally. Xu et al. [15] theoretically simulated the

performance of a SPV-THP using modified aluminum extruded evaporator for the meterological

conditions of China. In another work, Xu et al. [16] experimentally investigated the performance of a

SPV-THP using concentrator integrated PV-TE. In another work, Zhang et al. [17] developed and

experimentally investigated the performance of a heat pipe assisted PV-TE used in SPV-THP for water

heating applications and for power generation. Chen et al. [18] experimentally investigated the

performance of a SPV-THP using vacuum tube PV-TE. Pei et al. [19] theoretically improved the energy

performance of a SPV-THP using PV-TE covered with glass sheet. The performance simulation of a PV-

TE at different ambient conditions is essential for sizing and standardization. In previous investigations,

the performance of a PV-TE evaporator was simulated theoretically and experimentally [15-20]. The

theoretical method of performance simulation involves more assumptions and complicated equations,

whereas the experimental methods are more expensive due to its initial investment in developing an

experimental setup. ANN modeling of heat exchangers overcomes the limitations of theoretical and

experimental approaches [21-25]. Similarly, ANN modeling was successfully used for modeling of

refrigeration, air conditioning and heat pump systems with acceptable accuracy [26-28].

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The cited literatures confirmed that there is no specific work reported on ANN modeling of PV-TE.

Hence, the main objective of this work is to investigate the suitability of ANN for modeling of a PV-TE

with reference to four ambient parameters such as solar intensity, ambient temperature, wind velocity and

relative humidity.

2. Experiments with solar photovoltaic-thermal heat pump

The experimental observations were made under the meteorological conditions of Coimbatore city in

India during January 2014-March 2014.

2.1 Experimental setup

The line diagram of a SPV-THP and cross sectional view of PV-TE is depicted in Fig. 1. The

photographic view of PV-TE evaporator is illustrated in Fig. 2. The SPV-THP consists of basic

components such as R134a sealed type constant frequency reciprocating compressor, forced convection

air cooled condenser, capillary tube expansion device and photovoltaic-thermal hybrid heat exchanger of

face area 1.92m2 (1.96m × 0.98m), which acts as an evaporator. The accessories such as liquid receiver,

sealed type refrigerant drier and sight glass were also included in the heat pump circuit. The PV-TE was

designed to take a maximum heat load of 2.9 kW from solar and ambient sources by maintaining the

evaporator plate temperature around 25±2oC. The heat load acting on evaporator collector varies with

respect to ambient conditions and heat pump operating temperatures. The PV-TE has 1.2 mm thick

copper plate attached with 9.52 mm circular tube and 10 mm equilateral triangular tubes as shown in Fig.

2. In this work, circular tube was used in experimentation. The top surface of the evaporator-collector

absorber plate was covered with photovoltaic panels. Bottom side of the PV-TE was covered with 10 mm

thick poly-euro-ethylene foam to reduce the cooling loss from the bottom side. The heat loss due to

conduction, convection and radiation in the collector are within 5% of evaporator load. Hence, the heat

leakage in solar collector was not considered in the present work. The PV-TE is tilted to an angle of about

20o with respect to horizontal and oriented towards south to maximize the solar radiation incident on the

collector [28].

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2.2 Instrumentation

The refrigerant temperatures at typical locations in a SPV-THP circuit (compressor suction, compressor

discharge, condenser outlet and expansion valve outlet) were measured by four calibrated PT-100

temperature sensors. Air temperatures at inlet and exit of an air cooled condenser were measured by two

temperature sensors with same specifications and accuracy. Temperature of photovoltaic panels at three

locations shown in Fig. 2 was measured with the help of same specification temperature sensors. All the

temperature sensors are connected to the digital temperature indicator with 0.1oC resolution. Four

bourdon tube pressure gauges with ± 2% accuracy were used to measure the pressure at typical locations

in a heat pump loop. Instantaneous compressor power consumption was measured with the help of a

digital Wattmeter having ± 1W accuracy. The ambient temperature was measured with the help of

thermometer of ± 0.3oC accuracy. The ambient relative humidity was measured with a help of sling

psychrometer (two thermometers with ± 0.3oC accuracy - one covered with wet wick and other with bare

bulb). From the measured wet bulb and dry bulb temperatures, relative humidity was calculated by using

standard psychrometric chart. The photovoltaic output was measured by using multimeter. A pyranometer

with an accuracy ± 10W/m2 was placed near the PV-TE to measure the instantaneous solar intensity.

Ambient wind velocity was measured with the help of cup type anemometer with ± 0.2 m/s. The air flow

rate through the condenser was measured with the help of orifice meter and manometer setup. The

specifications and accuracy of the measuring instruments used in the experiments are shown in Table 2.

2.3 Experimental procedure

The moisture and foreign materials present inside the system was flushed and leak tested with nitrogen

gas. Then the system was charged with 750g of R134a. The experiments were conducted during potential

sunshine hours (more than 200W/m2). The PV-TE was warmed up one hour before experimental

observations to avoid initial transients. During experimentation, temperature and pressure of refrigerant at

entry and exit of PV-TE, average temperature of photovoltaic panel at three different locations over the

panel surface and photovoltaic output were recorded every 30 minutes. Similarly, solar intensity, ambient

temperature, ambient relative humidity and ambient wind velocity were measured at same time interval.

Experimental observations were made during sixty days duration were used for experimental calculation.

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More frequent experimental data observations are more useful to study the nature of variations to avoid

erroneous data.

2.4 Data analysis

The observations made in series of experiments were used for evaluating the performance of PV-TE.

2.4.1 Photovoltaic-thermal evaporator heat gain

The capacity of a PV-TE is given by following equation.

(2)

Here, is the mass flow rate of air (kg/s), cp is the specific heat of air at constant pressure (in J/kgK), T5

and T6 are the temperature of air at entry and exit of the air cooled condenser in ( oC), P is the compressor

power consumption in terms of (W).

2.4.2 Solar energy input ratio

The solar energy input ratio (SEIR) is the ratio between the amount of solar energy absorbed to the total

amount of energy absorbed by the refrigerant from the ambient conditions (ambient source and solar

source) [Ref.]. SEIR is given by following relation.

(3)

Here, A is the panel area exposed to solar radiation (in m2), I is the solar intensity (W/m2).

2.4.3 Photovoltaic panel efficiency

The ηpv of a PV-TE is the ratio between photovoltaic power output to the total amount of energy incident

on the photovoltaic panel surface. The ηpv is given by following relation

(4)

2.5 Uncertainty analysis

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Uncertainties of the measured and calculated parameters are estimated according to Holman [30]. In this

work, refrigerant pressures, refrigerant and air temperatures, solar radiation, photovoltaic output were

measured with instruments as mentioned in the previous section. The uncertainties in measured and

calculated parameters are given by Eq. (3).

(5)

Here R is a given function, wr is the total uncertainty, x1 x2…..xn is the independent variables, w1, w2…wn is

the uncertainty in the independent variables. The uncertainties for , SEIR, and panel surface

temperature are ________________and ___%, respectively.

3. ANN modeling of photovoltaic-thermal evaporator

ANN modeling of PV-TE involves the experimental data for training the network. The performance of a

photovoltaic panel is influenced by solar intensity, ambient temperature, ambient relative humidity,

ambient wind velocity and dust accumulation over the photovoltaic surface [31]. The accumulation of

dust over the photovoltaic surface has minimum effect. Hence, in the present analysis, the effect of dust

accumulation is ignored. The solar intensity, ambient temperature, ambient wind velocity and ambient

relative humidity were taken as network input parameters, while the performance parameters of a PV-TE

such as QPV-TE, SEIR, ηpv, and Tpv and were taken as output network parameters. The performance

parameters were extracted from series of experiments conducted in a SPV-THP at 60 different ambient

conditions. In order to train and test the ANN model for performance prediction, the data sets obtained

from the experiments are divided as training data sets and testing data sets. Out of 60 data sets, 50 data

sets are used for training the network and remaining 10 data sets were used for testing the performance of

the network, which are not used in the network training.

Multilayer feed forward network (MLFFN) with back propagation learning algorithm is the most widely

used network architecture for modeling of heat exchangers [21-25]. Hence, a MLFFN with four neurons

in input layer and four neurons in output layer was developed. The network parameters such as number of

hidden layers, momentum factors, learning rate needs were optimized by trial and error approach. The

number of neurons in hidden layer was optimized by following Eq. (4) [34].

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(5)

Since the hidden neuron requirement obtained from above equation is in fractional value, it is necessary

to find out the exact number of neurons in hidden layers. After enough trials with different configurations

by changing the number of neurons in hidden layer (10, 11 and 12), changing the transfer function (log-

sigmoid and tangent sigmoid), changing the variant (LM, SCG and CGP), momentum factor and learning

rate, it is decided that the network consists of one hidden layer with 11 neurons and LM variant. Before

training the network, the input-output training and testing data were normalized in the range of 0-1. Log-

sigmoid transfer function was used for hidden and output layers. The structure of MLFFN used for

performance prediction in this work with their names of input and output variables are depicted in Fig. 3.

In this paper, the results obtained in optimized MLFFN architecture are discussed. ANN modeling of a

PV-TE was carried out in MATLAB (version 7.0) by using neural network tool box.

The capability of a MLFFN for modeling of a PV-TE was evaluated by fraction of absolute variance (R2),

root mean square error (RMS) and coefficient of variance (COV) values, which are given by following

Eqs (5-7).

(6)

(7)

(8)

Here, n is the number of data pattern in the independent data set, y pre,m indicates the predicted by ANN,

tmea,m is the measured value of one dated point, tmea,avg is the mean value of all measured data points.

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4. Results and discussion

The results obtained from series of experiments conducted in a SPV-THP under the meteorological

conditions of Coimbatore city in India were used as training data for the network. The ANN predicted

results are compared with experimental results, which are not used in ANN training.

The temperature variations of refrigerant at inlet and outlet of a PV-TE are depicted (in) Fig. 3. From Fig.

3, it is observed that refrigerant temperature variations at inlet and outlet of an evaporator are -------- and

9.3oC-14.7oC, respectively. The compressor discharge temperature is the major influencing parameter that

influences the compressor life. In this work, the maximum compressor discharge temperature was

observed less than 80oC, which ensures better compressor life. The variation in air temperatures at entry

(ambient temperature) and exit of the condenser are plotted in Fig. 4. During the experimentation, the

ambient temperature varied between 27.2 and 35.3oC with an average temperature of 31.5oC. The air

temperature at the condenser exit varied between 32.6 and 44.8oC with an average temperature of 38.6oC.

As expected, all the temperatures measured at typical locations in refrigerant flow path and air flow path

gets increased with increased with increase in solar intensity.

The comparison between experimentally observed and ANN predicted QPV-TE, ηpv, Tpv and SEIPR are

compared in Figs. 5-8. The ambient conditions of ten test data sets for comparison are listed in Table 3.

The solar intensity, ambient temperature and ambient wind velocity are the three major influencing

parameters affecting PV-TE heat gain. The PV-TE capacity varies between 1470 and 2830 W with an

average value of 2190 W. In this work, constant frequency refrigerant compressor was used. Hence, the

refrigerant flow rate through the evaporator was maintained at constant. The evaporator heat gain

increases with increase in solar intensity due to absorption of more heat. The experimentally observed and

ANN predicted PV-TE capacity of a SPV-THP are compared in Fig. 5. The ANN predicted PV-TE

capacity yields maximum R2 value of 0.9999 with minimum RMS and CoV values of 2.036 W and

0.09316, respectively with the experimental results.

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Similarly, SEIR is another performance parameter considered for rating the performance of a PV-TE,

which depends on solar intensity, ambient temperature and ambient wind velocity. Ambient relative

humidity has less influence on SEIR. Figure 6 depicts the comparison between experimentally measured

and ANN predicted SEIR of a PV-TE. The SEIR varies from 0.3 to 0.67 with an average value of 0.56.

The average SEIR is calculated as 0.56. The ANN predicted SEIR yields maximum R2value of 0.9999

with experimental data. Similarly, the ANN predicted SEIR yields minimum RMS value of 0.4743 and

minimum CoV value of 0.0477 with experimentally measured instantaneous compressor power

consumption.

The performance of photovoltaic cells depends on four major ambient parameters such as solar intensity,

ambient temperature, ambient wind velocity and ambient relative humidity. Dust accumulations and

photovoltaic panel area are also affecting the photovoltaic output. However, dust accumulation over the

photovoltaic panel was ignored in this work. The area of photovoltaic panel was fixed. The difference

between experimentally measured and ANN predicted ηpv, of a PV-TE are illustrated in Fig. 8. The ηpv,

values vary between about 9% and 15% with an average value of 11.5%. ANN predicted ηpv yields

maximum R2value of 0.9999, minimum RMS value of 0.0139 and minimum CoV value of 0.1228 with

experimentally calculated values.

The photovoltaic cells become heated during energy conversion and also due to the effect of incident

solar radiation and ambient temperature, which affects the system performance. Thus, it is essential to

maintain the temperature of photovoltaic cells to attain the maximum power output. The photovoltaic

panel temperature depends on solar intensity, ambient temperature and ambient wind velocity [Ref.]. In

Fig. 8, experimentally observed photovoltaic panel temperature is compared with ANN predicted

photovoltaic panel temperature. The photovoltaic panel temperature varies from 20oC to 29oC with an

average temperature of 25oC. ANN predicted photovoltaic output yields maximum R2 values of 0.9999,

minimum RMS value of 0.01391 and minimum CoV value of 0.0545oC with experimentally measured

values. The energy performance of a PV-TE will be enhanced by modifying the evaporator tube

configurations. Such research investigations are making progress in author’s laboratory.

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The ANN predicted performances are closer to experimental values with R2, minimum RMS and CoV

values. The results obtained in this work are similar to the earlier studies reported by Mohanraj et al. [35,

36] for energy and exergy analysis of DXSAHP, Esen et al. [25, 26] for ground coupled heat pumps,

Arcakiloglu et al. [37] for heat pumps using refrigerant mixtures. According to the above mentioned

studies, MLFFN with back propagation learning algorithm, one hidden layer, LM variant, log-sigmoid

transfer function were identified as the good network parameters for performance prediction and

modeling of heat pumps. In the present work, MLFFN with back propagation learning algorithm, LM

variant, one hidden layer containing eleven neurons and log-sigmoid transfer function were identified as

suitable network parameters for modeling of a SPV-THP. The prediction capability of a MLFFN can be

enhanced by optimizing the network parameters by using genetic algorithm, particle swam optimization,

simulated annealing, ANT colony optimization and its hybrid approach.

5. Conclusion

Multilayer feed forward network approach was successfully used for modeling of a PV-TE at different

climatic conditions. The trained MLFFN model is capable of predicting the PV-TE energy performance

with reference to solar intensity, ambient wind velocity, ambient temperature, and ambient relative

humidity. The ANN predicted results are closer to the experimentally predicted values with maximum

R2values, minimum RMS errors and minimum CoV values. The MLFFN was optimized to 4-11-4

configuration for modeling the PV-TE. This new approach helps the researchers to optimize the size of

PV-TE, and to control the operation of a PV-TE at different climatic conditions by using available

experimental data.

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