Modified chemical reaction optimization and its application in engineering problems

Shijing Ma; Yunhe Wang; Shouwei Zhang; Shijing Ma; Yunhe Wang; Shouwei Zhang

doi:10.3934/mbe.2021354

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 7143-7160. doi: 10.3934/mbe.2021354

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Research article Special Issues

Modified chemical reaction optimization and its application in engineering problems

1.
School of Physical Education, Northeast Normal University, Changchun 130022, China
2.
School of Artificial Intelligence, Hebei University of Technology, Tianjin 300401, China

Received: 03 June 2021 Accepted: 19 August 2021 Published: 25 August 2021

Chemical Reaction Optimization (CRO) is a simple and efficient evolutionary optimization algorithm by simulating chemical reactions. As far as the current research is concerned, the algorithm has been successfully used for solving a number of real-world optimization tasks. In our paper, a new real encoded chemical reaction optimization algorithm is proposed to boost the efficiency of the optimization operations in standard chemical reactions optimization algorithm. Inspired by the evolutionary operation of the differential evolution algorithm, an improved search operation mechanism is proposed based on the underlying operation. It is modeled to further explore the search space of the algorithm under the best individuals. Afterwards, to control the perturbation frequency of the search strategy, the modification rate is increased to balance between the exploration ability and mining ability of the algorithm. Meanwhile, we also propose a new population initialization method that incorporates several models to produce high-quality initialized populations. To validate the effectiveness of the algorithm, nine unconstrained optimization algorithms are used as benchmark functions. As observed from the experimental results, it is evident that the proposed algorithm is significantly better than the standard chemical reaction algorithm and other evolutionary optimization algorithms. Then, we also apply the proposed model to address the synthesis problem of two antenna array synthesis. The results also reveal that the proposed algorithm is superior to other approaches from different perspectives.

Keywords:

Citation: Shijing Ma, Yunhe Wang, Shouwei Zhang. Modified chemical reaction optimization and its application in engineering problems[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 7143-7160. doi: 10.3934/mbe.2021354

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Abstract

Nomenclature: A: Area; C_p: Specific heat capacity; D_e: External diameter of tube; E: Electrical energy; fw: Collector efficiency factor; G_r: Grash of number; h: Thermal heat transfer coefficient; hf_i: Convection heat transfer of storage; I: Hourly total radiation; k: Thermal conductivity; K_T: Clearness index; l: Length; m : Mass; $\dot m$ : Mass flow rate of water; n: Number of days in a year; N: Number of tubes; N_u: Nusselt number; ${{\dot Q}_u}$ : Useful Heat; Ra: Rayleigh number; T: Temperature; U_l: Overall loss coefficient; V: Volume; V_wind: Wind Velocity; δ: Declination Angle; φ: Packing factor; $\emptyset$ : Latitude angle of the location; ρ: Density; ρ_g: Ground reflection; β: Inclination angle; 𝟉: Hour angle; δ: Declination Angle; η_f: Fin efficiency; η_r: Reference cell efficiency; ατ: Effective absorptance; σ: Stefan Boltzmann constant; β_r: Temperature coefficient

Subscripts: a : Ambient Temperature; b: Beam; c : Convection, inclined surface collector; d: Diffuse; el, a: Annual Electrical; f: Fluid; g : Glass; hws, a: Annual hot water service; i: Inlet, insulation; o: Outlet, Extraterrestrial radiation; p: Absorber Plate; P_el: Electrical Power; pv-t, a: Annual photovoltaic thermal; r: Radiation, reference; st: Storage; t: Time, thickness; th, a: Annual Thermal; w: Water; wt: Water tube

Abbreviations: DWC: Daily hot water consumption in litre; FF_ii: Daily hot water consumption hourly fraction; pv: Photovoltaic panel; pvt: Photovoltaic Thermal; TRNSYS: Transient systems simulation; PVsyst: Photovoltaic sizing software

1. Introduction

Due to the concern of global warming and emission of pollutants, environmental friendly energy resources such as solar energy are becoming popular. While solar energy can be directly converted into electricity by a PV module ^[1] hot water can be generated by converting solar energy into thermal energy by a solar collector ^[2]. Photovoltaic thermal (PV-T) system is a superimposition of PV panel with glazing on a flat plate solar collector to generate thermal and electrical energy simultaneously ^[3]. PV is considered as one of the best options for rural electrification for off-grid areas of developing countries like Ethiopia. Due to falling module unit price, might be necessary for the application of PV-T system where hot water is required in addition to electricity such as off-grid rural clinics and lodges.

A PV-T system consists of PV-T collector, balance of system (BOS) and hot water storage tank as shown in Figure 1. The PV-T collector has glazing from the top and insulation at the back. In between a superimposition of a PV-module with plate and tube absorber is placed. The PV-module converts part of the incident solar irradiance into electricity and converts most of the remaining energy into heat. Hence, heat is transferred to water in the absorber tubes increasing the water temperature and cooling the PV-module. As the water from the storage continuously circulates through the PV-T collector, the water in the storage will be heated and hot water will be continuously flow from the tank to end users.

Figure 1. Experimental prototype (left) ^[4] and PV-T system schematic diagram (right).

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Several researchers have investigated the performance, optimum design parameters and efficiency of PV-T system ^[3]. The performances of the unglazed, single glazed and double glazed PV-T systems were compared and it was concluded that the unglazed system has highest electrical efficiency and the lowest thermal efficiency ^[5]. Another investigation showed that the double glazed system has lowest electrical efficiency and highest thermal efficiency ^[6]. Hence, the single glazed PV-T can be considered as a cost-effective solution for optimum co-generation efficiency. Glazed and unglazed PV-T collectors were built and tested with water and air as working fluid, and thermal efficiency of about 58% and electrical efficiency approximately equal to 11% were obtained ^[7].

Effect of mass flow rate of water on performance of PV-T system was investigated and 25 kg/h was recommended as optimum value ^[8], while 20 kg/h was stated as optimum mass flow rate in another work ^[9]. These are in agreement with the range of optimum mass flow rates given in (0.001–0.0085 kg/s) ^[10]. The electrical, thermal and PV-T (combined) efficiencies were investigated by a dynamic model under different conditions for limited duration ^[11]. The performance of 1.44 kW unglazed PV-T system was investigated for different locations in Taiwan using TRNSYS software as simulation tool and electrical efficiency of 11.7–12.4% and thermal efficiency of 26.78–28.41% were obtained ^[12].

CFD based dynamic analysis of PV-T collectors was also carried-out by several researchers ^[13,14]. But these analyses were performed for limited durations due to long computational time required by multidimensional dynamic models. However, many researchers used TRNSYS software for predicting long-term performance of PV-T systems ^[12]. TRNSYS uses steady state or quasi-dynamic model to compute the outlet water temperature were the collector loss coefficient is considered constant, it could lead to overestimation of thermal efficiency and under estimation of electrical efficiency.

Dynamic models of PV-T system were also developed based on the solution of the transient differential equation obtained from energy balance using explicit finite difference method for time stepping^[11,14]. However, most of these applications do not consider the effect of end-user hot water consumption pattern and size of the storage on hot water end-use efficiency.

The proper use of hybrid solar technology requires a tactful balance between the low-temperature requirement of the water stream to serve as a coolant, and at the same time, the high-temperature requirement for satisfying the hot water need of the end user ^[15]. Thus, PV-T system should be considered and designed to preheat water for a maximum of 45–50 ℃ ^[11].

Current researches in PV-T technology focused on increasing the overall output energy and development of this technology in terms of novel design and high performance ^[15]. For example, investigation of PV-T system with new configuration in Malaysia gave electrical efficiency of 13% and thermal efficiency 61%. Similarly, investigation on concentrated photovoltaic thermal collector (CPV-T) with concentration ratio of 8.5 has shown 4.7 times electrical energy output to conventional PV-T although the electrical efficiency dropped to 8–9% due to high temperature of the PV-module ^[16,17]. CPV-T collectors provides incomparably greater thermal and electrical outputs compared to stand alone PV or PV-T systems as incoming solar energy is maximized inside the unit via energy-efficient concentrators ^[18].

In this work, the potential of conventional PV-T system shown in Figure 1 to generate electricity and preheat water using dynamic computational model based on non-linear transient differential equations. The integrated PV-T collector, storage tank and end-use system to estimate amount of thermal and electrical energy generated, considering the hourly hot water consumption pattern and storage size for tropical areas in Africa, particularly for Dire Dawa, Ethiopia.

2. Mathematical model of PV-T system

2.1. Estimation of solar irradiance on PV-T surface

The isotropic diffuse model radiation on a tilted surface, which consider three components: beam, isotropic diffuse, and solar irradiance reflected from the ground is derived as follows ^[19].

$I = {I_b}{R_b} + {I_d}\left( {\frac{{1 + \cos \beta }}{2}} \right) + I{\rho _g}\left( {\frac{{1 - \cos \beta }}{2}} \right)$

(1)

To calculate the beam and diffuse component for equation (1), a clearness index ${k_T}$ shall be determined from hourly total radiation and extra-terrestrial radiation on the horizontal surface.

${K_T} = \frac{I}{{{I_0}}}$

(2)

The hourly extra-terrestrial radiation on a horizontal surface for a given hour angle $\varpi$ is given as follows.

${I_0} = {I_{sc}}\left( {1 + 0.033\cos \frac{{360n}}{{365}}} \right)x\left( {\cos \phi \cos \delta \sin \omega + \sin \phi \sin \delta } \right)$

(3)

where, the declination, $\left(\delta \right)$ is given as

$\delta = 23.45\sin \left( {360\frac{{284 + n}}{{365}}} \right)$

(4)

The diffuse components of solar irradiance on a horizontal surface are determined from the total radiation on the horizontal surface via ${k_T}$ value range with the following correlation ^[19].

$\frac{{{I_d}}}{I} = \sum {\left[ \begin{array}{l} 1 - 0.09{K_T}for{K_T} \leqslant 0.22 \\ 0.9511 - 0.1604{K_T} + 4.338K_T^2 - 16.638K_T^3 + 12.336K_T^4for0.22 \lt {K_T} \leqslant 0.8 \\ 0.165for{K_T} \gt 0.8 \\ \end{array} \right]}$

(5)

2.2. Transient non-linear ordinary differential equations of PV-T system

For the energy balance analysis, some scientifically accepted assumptions were made for flat plate PV-T collectors. The energy analysis should start from top to bottom components, from the glass cover up to the bottom insulation. For all parts, energy balance was made considering the rate of change of energy stored in the component, energy transferred into it and leaving the component.

2.2.1. Glass cover

In analysing the glass cover, the heat transfer by radiation and convection were considered, by neglecting the conduction heat transfer within the glass. In this case, at the top of the glass heat is transferred by convection and radiation to atmospheric. On the other hand, at the bottom convection and radiation heat transfer occurs between the PV module and the glass cover. Thus, the rate of change of energy stored in the glass cover is obtained from the difference between solar irradiance absorbed by the glass plus the heat received from the PV module and the heat leaving the glass to the ambient as follows ^[14,20].

${\left( {{m_c}} \right)_g}\frac{{\partial {T_g}}}{{\partial t}} = {A_{pv}}\left[ {{I_c}{{\left( \alpha \right)}_g} + {U_{pv - g}}\left( {{T_{pv}} - {T_g}} \right) - {U_{g - a}}\left( {{T_g} - {T_a}} \right)} \right]$

(6)

2.2.2. PV module

In the PV module, heat is transferred by conduction to the absorber plate and water tubes in the backside and by natural convection and radiation to glass cover at the front side. The energy equation of the PV module is obtained by equating the variation of the stored thermal and electrical energy. In the PV module equated consider the difference between solar irradiance absorbed by the PV module, and the heat transferred from the PV module to glass and absorber, also electrical energy generated by the PV module ^[21].

${\left( {{m_c}} \right)_{pv}}\frac{{\partial {T_{pv}}}}{{\partial t}} = {A_{pv}}{I_c}{\tau _g}{\alpha _{pv}} - {P_{el}} - {A_{pv}}\frac{{{k_{pv}}}}{{{\delta _{pv}}}}\left( {{T_{pv}} - {\eta _f}{T_p}} \right) - {A_{pv}}{U_{pv - g}}\left( {{T_{pv}} - {T_g}} \right) - {A_{pv}}{U_{pv - a}}x\left( {{T_{pv}} - Ta} \right)$

(7)

The electrical power output of the PV module is given as follows ^[22].

$E = {I_c} \times pf \times {\tau _v}{\eta _0}\left[ {1 - {\varphi _c}\left( {{T_{pv}} - 25} \right)} \right]$

(8)

2.2.3. Absorber plate

The absorber plate, which is in direct contact with the back of PV module at the top and the insulation at the back, has a function of removing heat from PV module to the water in the tubes. The rate of change of energy stored in the absorber is equated from the difference between the heat transferred to and from the absorber to the PV module. The sum of heat transferred from the absorber to the water in the tubes and to the ambient through the back of insulation, where the following transient energy differential equation of the absorber plated is obtained ^[2].

${\left( {{m_c}} \right)_p}{\eta _f}\frac{{\partial {T_p}}}{{\partial t}} = \left( {{A_{pv}}\frac{{{k_{pv}}}}{{{\delta _{pv}}}}\left( {{T_{pv}} - {\eta _f}{T_p}} \right)} \right) - {A_{wt}}{U_{p - w}}\left( {{f_w} \times {T_p} - \frac{{{T_{w, o}} + {T_{w, i}}}}{2}} \right) - {A_{pv}}{U_{i - a}}\left( {{\eta _f}{T_p} - {T_a}} \right)$

(9)

It shall be noted that η_f is fin efficiency of absorber plate to the tube, T_p is the maximum absorber temperature, ηfT_p mean absorber temperature and ${f_w} = \left({2{\eta _f} - 1} \right)$ is a factor that is used to determine water tube temperature from maximum absorber temperature.

2.2.4. Water stream

From energy balance for the water in the tube, the rate of change of energy stored in the water inside the tube is equal to the difference between the heat transferred from the absorber to the water in the tubes and heat transported with water from the tube to storage. As a result, the following transient differential energy equation of the water in tubes is obtained ^[21].

${m_w}{c_w}\frac{{\partial {T_w}}}{{\partial t}} = {A_{wt}}{U_{p - w}}\left( {{f_w} \times {T_p} - \frac{{{T_{w, o}} + Tw, i}}{2}} \right) - {{\dot m}_w}{c_w}\left( {{T_{w, o}} - {T_{w, i}}} \right)$

(10)

2.2.5. Storage tank

In similar to Eq 10, the rate of change of energy stored in hot water in the tank is obtained from the difference between energy transported from the collector to the tank and energy transported with hot water to the end user plus the heat losses through the insulation of the tank as follows.

${m_w}{c_w}\frac{{\partial {T_{st}}}}{{\partial t}} = {{\dot m}_w}n{c_w}\left( {{T_{w, o}} - {T_{w, i}}} \right) - dhwc\frac{{h{f_i}}}{{3600}}{c_w}\left( {{T_{st}} - Tws} \right) - {U_{st - a}}{A_{st}}\left( {{T_{st}} - {T_a}} \right)$

(11)

3. Computational model

The above transient ordinary differential equations are solved by explicit finite difference time stepping scheme. The temperature of glass, temperature of PV module, and temperature of absorber as well water outlet temperature and water storage temperature are obtained by updating the values of the current time step from the previous time step by approximating time derivatives of temperature by forwarding finite difference technique.

3.1. Glass cover

Expressing the overall heat transfer coefficient in terms of convective and irradiative components, the glass temperature at the current time step is solved as follows.

${T_{g, i + 1}} = {T_{g, i}} + \frac{{\Delta t}}{{m \times {c_p}}}{A_c}\left( {{I_c}{\alpha _g} - \left( {{h_{c, g - a}} + {h_{r, g - a}}} \right) \times \left( {{T_{g, i}} - {T_{a, i}}} \right) + \left( {{h_{c, pv - g}} + {h_{r, pv - g}}} \right) \times \left( {{T_{pv, i}} - {T_{g, i}}} \right)} \right)$

(12)

The radiation and convection heat transfer coefficients at the top and bottom part of the glass are given as follows ^[23].

${h_{r, g - a}} = \sigma {\varepsilon _g}\left( {T_g^2 + T_a^2} \right)\left( {{T_g} + {T_a}} \right), {h_{c, g - a}} = 2.8 + 3{V_{wind}}and, {h_{r, pv - g}} = \frac{{\sigma \left( {T_g^2 + T_{pv}^2} \right)\left( {{T_g} + {T_{pv}}} \right)}}{{{1 \mathord{\left/ {\vphantom {1 {{\varepsilon _{pv}} + {1 \mathord{\left/ {\vphantom {1 {{\varepsilon _g}}}} \right. } {{\varepsilon _g}}}}}} \right. } {{\varepsilon _{pv}} + {1 \mathord{\left/ {\vphantom {1 {{\varepsilon _g}}}} \right. } {{\varepsilon _g}}}}} - 1}}$

(13)

The convection heat transfer coefficient Eq 13 depends on wind velocity ^[24].

For the convective heat transfer between the PV module and the glass cover, the correlation of Nusselt number with Rayleigh number suggested by ^[14] is used.

${N_u} = 1 + 1.44\left[ {1 - \frac{{1708\sin {{(1.8\beta )}^{1.6}}}}{{{R_a} \times \cos \beta }}} \right]{\left[ {1 - \frac{{1708}}{{{R_a} \times \cos \beta }}} \right]^ + } + {\left[ {{{\left[ {\frac{{{R_a} \times \cos \beta }}{{5830}}} \right]}^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.} \!\lower0.7ex\hbox{$3$}}}} - 1} \right]^ + }$

(14)

3.2. PV module

The recursive formula for updating the PV module average temperature at the new time step is obtained as follows.

${T_{pv, i + 1}} = {T_{pv, i}} + \frac{{\Delta t}}{{{{\left( {{m_c}} \right)}_{pv}}}}{A_c}\left[ {I - {P_{el, i}} - \frac{{{k_{pv}}}}{{{t_{pv}}}} \times {A_{pv - p}}\left( {{T_{pv, i}} - {\eta _f}{T_{p, i}}} \right)\left( {{h_{c, pv - g}} + {h_{r, pv - g}}} \right) \times \left( {{T_{pv, i}} - {T_{g, i}}} \right)} \right]$

(15)

3.3. Absorber plate

The maximum temperature of the new time step of the absorber plate is expressed by the following recursive formula.

${T_{p, i + 1}} = {T_{p, i}} + \frac{{\Delta t}}{{{\eta _f}{{\left( {{m_c}} \right)}_p}}}\left( {\frac{{{k_{pv}}}}{{{t_{pv}}}}{A_{pv}}\left( {{T_{pv, i}} - {\eta _f}{T_{p, i}}} \right)} \right) - \frac{{\Delta t}}{{{\eta _f}{{\left( {{m_c}} \right)}_p}}}\left( {{A_{wt}}{U_{p - w}}\left( \begin{gathered} {F_w}\left( {2{\eta _f} - 1} \right){T_{p, i}} \\ - \frac{{{T_{wo.i}} + Twi, i}}{2} \\ \end{gathered} \right) - {U_{p - i}}{A_{pv}}\left( {{\eta _f}{T_{p, i}} - {T_{a, i}}} \right)} \right)$

(16)

3.4. Water outlet

The outlet temperature of the water from the collector for the new time step is given as follows.

${T_{wo, i + 1}} = {T_{wo, i}} + \frac{{\Delta t}}{{{{\left( {{m_c}} \right)}_w}}}\left[ {{A_{wt}}{U_{p - w}}\left( {\left( {2{\eta _f} - 1} \right){T_p} - \frac{{{T_{wo, i}} + Twi, i}}{2}} \right) - {{\mathop m\limits^. }_w}{c_w}\left( {{T_{wo, i}} - {T_{wi, i}}} \right)} \right]$

(17)

The useful heat is evaluated as follows as per Duffie and Beckman ^[19].

$\mathop {{Q_u} = \mathop {{m_w}}\limits^. {c_w}\left( {{T_{wo}} - {T_{wi}}} \right)}\limits^.$

(18)

3.5. Storage

The water temperature in the storage is updated at every time step as follows.

${T_{stw, i + 1}} = {T_{stw, i}} + \frac{{\Delta t}}{{{c_w}{\rho _w}{V_{st}}}}\left[ {{{\mathop m\limits^. }_w}n{c_w}\left( {{T_{wi, i}} - {T_{wo, i}}} \right) - {U_{st, l}}{A_{st}}\left( {{T_{stw, i}} - {T_{a, i}}} \right) + {\rho _w}{V_{st}}DWC \times F{F_{ii}}\left( {{T_{stw, i}} - Tws} \right)} \right]$

(19)

3.6. Program flowchart

The developed dynamic computational model of PV-T integrated with storage was programmed in MATLAB environment. The main input to the program are the beam, diffuse irradiance and ambient temperature for the 8760 hours of the year as well as PV-T collector design parameters, location data, hot water storage and consumption pattern data are input. The incident irradiance on the PV surface is computed and determined at every hour and the useful thermal energy, glass temperature, PV temperature and absorber temperature collector outlet temperature and, hot water temperature in the storage tank and energy of hot water supplied to the end user are determined for every time step.

Figure 2. PV-T dynamic simulation program flowcharts.

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4. Verification with the experimental result

The verification of results of the dynamic computational model of this work was done by comparison with the experimental work of similar PV-T system ^[4]. The input parameter of the experimental work are given in Table 1 Using the weather data of the experimental site and PV-T parameters, simulation was conducted by the MATLAB program of dynamic computational model of PV-T system and the simulation results were compared with the experimental result for validation.

Table 1. Experimental Validation Input parameter.

Parameter	Value
Collector area	0.3
Collector fin efficiency factor	0.55
Fluid thermal capacity	4.174 kJ/kg.k
Collector Plat Absorbance	0.9
Collector loss coefficient	17 W/m².k
Cover Transmittance	0.95
Temperature coefficient for solar cell	0.0045
Reference Temperature for cell	25 ℃
Packing factor	1
Cell Efficiency	14%
Mass flow rate	30 kg/h

| Show Table

DownLoad: CSV

Figure 3 compares the experimental and simulation results for electrical energy generation, water outlet temperature, and PV-T surface temperature. In all cases, simulation and experimental results are in good agreement with an average error of 1.77%, 2.3% and 3% for of electrical energy, water outlet, and PV-T surface temperature, respectively. The computational model has low accuracy compared to experimental investigation due to simplifications in model formation, discretization error in numerical approximation and round off error during computing. Hence, the errors are in acceptable range.

Figure 3. Comparison of the PV-T experimental and the simulation results.

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Comparison was also done with other experimental results ^[16,17] doing simulation using with similar solar irradiance on the collector surface and ambient temperature, and mass flow rate of water. The result shows electrical power out-put and the PV panel temperature have similar trend with slight variation.

5. Results and discussion

Using the PV-T system simulation program, co-generation of hot water with 1 kW of electricity was investigated for an off-grid rural clinic near Dire Dawa, Ethiopia. Hourly ambient temperature and total radiation on the horizontal surface were averaged for 5 years as input to the simulation. The initial size or area of PV-T system was predicted using PVsyst, which is PV design software. As per the result of PVsyst 12 PV-T panels with each module area of 1.64 m² and capacity of 250 Wp are sufficient to yield an average of 1 kW during the working hours. Hence 12 PV-T collectors with a total area of 20 m² are interconnected for cogeneration of electric power and hot water.

5.1. Hourly Solar Irradiance incident on the collector surface

The hourly solar irradiance incident on the inclined PV-T collector was determined using Eq 1 after the clearness index was evaluated from total radiation obtained from meteorology and extra-terrestrial radiation on a horizontal surface by Eq 2 ^[19]. Figure 4 shows the hourly solar irradiance on the PV-T cover during the day for different months considering the geometrical orientation of the collector and location data of Dire Dawa.

Figure 4. Solar irradiances on the collector surface for each month in W/m².

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As shown in Figure 4, the solar irradiance reached a maximum of 780 w/m² on an average day of November and a minimum solar irradiance in August.

5.2. Glass temperature

Figure 5 shows the average hourly temperatures of the glass cover for the representative days of the months. The maximum temperature of the glass cover reached 37 ℃ in June and the minimum temperature in February and January.

Figure 5. Glass temperatures on the representative day of the month.

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5.3. Photovoltaic thermal module temperature

The PV module generates electrical energy and transfers heat to the absorber and subsequently to the water in the tubes. Figure 6 shows the maximum temperature of the PV-module, which reached 57 ℃ in November and the minimum temperature in August. The PV-module temperature is highly dependent on solar irradiance, the mass flow rate of water and many other parameters. It is possible to decrease or increase the temperature of PV by varying these parameters. As the mass flow rate of water increases, the PV module temperature decreases. Hence optimum mass flow rate is required to keep the PV module temperature under a given value and generate hot water at the required temperature.

Figure 6. Photovoltaic module temperatures on representative days of the month.

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5.4. Electrical output

The results of annual performance simulation indicated that PV-T System simulation can generate 3720 kWh electrical energy per year, which is 10.2 kWh per day on average. This result is above the prediction of PV design software (9.22 kWh per day) for the cooling of the PV module resulted in higher PV efficiency.

5.5. Absorber temperature

Figure 7 shows the maximum temperature of the absorber plate (at the middle between tubes). The maximum hourly temperature of the absorber reached 53 ℃ in June.

Figure 7. Maximum absorber temperature on representative days of the monthly.

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5.6. The hot water outlet temperature of PV-T collector

The hot water outlet temperature from the PV-T panel depends on several parameters among which the end user hot water consumption pattern, storage tank size, and cold water supply temperature are the most important ones. Figure 8 shows the outlet temperature of PV-T collector for constant hot water consumption pattern during the working hours of a rural clinic with total daily water consumption of 0.48 m³ per day and storage capacity of 0.48 m³.

Figure 8. PV-T water outlet temperature on representative days of the month at Vs = 0.48 m³.

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The outlet temperature showed a slight increment when the storage volume is decreased. The hot water outlet temperature is highly dependent on the mass flow rate with the other parameters kept constant. Comparing circulation mass flow rate of 0.00138 kg/s per PV-T panel with 0.00164 kg/s, the PV-T water outlet temperature decreased. Table 2 shows that useful heat obtained from the collector increases slightly as the mass flow rate increases.

Table 2. Mass flow rate comparison (energy is given in kWh).

Item for comparisons	${{\dot m}_w}$ = 0.00138kg/s	${{\dot m}_w}$ = 0.00164kg/s ^[11]	Result Difference
Annual elect. energy	3684	3694	+10
Annual useful heat	10094	10621	+527
Annual sol. energy	13464	13464	0
Elec efficiency	15.4%	15.4%	0
Thermal efficiency	50.4%	50.89%	+0.49%
Hot water efficacy	37.99	37.72%	-0.27%

| Show Table

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5.7. Hot water temperature in the storage tank

The computer program requires an input of daily hot water consumption, storage tank size, insulation thickness and an hourly fraction of daily hot water consumption, which affect the hot water temperature in the tank, is affected by besides the climate data and PV-T collector parameters. Figure 9 shows the hot water temperature in the storage tank for the case of 0.48 m³ size tank, 0.48 m³ daily, hot water consumption with constant hot water consumption during the working hour for a rural clinic. Sensitivity analysis of the system for different tank sizes of 0.48 m³, 0.6 m³ and 0.72 m³ resulted in storage tank temperature of 43.45 ℃, 43.19 ℃, and 42.93 ℃, respectively.

Figure 9. Water temperature in the storage tank on the representative days of the month at Vs = 0.48 m³.

DownLoad: Full-Size Img PowerPoint

5.8. PV-T system efficiencies

PV-T generates concurrently hot water and electrical energy within one component, so it has electrical, thermal and cogeneration efficiencies. As shown in cogeneration efficiency (thermal plus electrical) of the system illustrated for each month of the year. The cogeneration efficiency ( ${\eta _0} = {\eta _{th}} + {\eta _{ele}}$ ) evaluates the combined output by taking the yearly total output of the system ^[25].

Figure 10. Cogeneration efficiency of the PVT system.

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a) Electrical efficiency

${\eta _{elc}} = \frac{{{E_{el, a}}}}{{{G_{pv - t, a}}}} = 15.4\%$

(20)

b) Thermal efficiency

${\eta _{th}} = \frac{{{Q_{th, a}}}}{{{G_{pv - t, a}}}} = \frac{{1.012 \times {{10}^3}}}{{2.007 \times {{10}^3}}} \times 100 = 50.4\%$

(21)

c) Hot water end use overall efficiency

${\eta _{th, end}} = \frac{{{Q_{hws, a}}}}{{{Q_{pv - t, a}}}} = 37.9\%$

(22)

d) Cogeneration efficiency

${\eta _o} = \frac{{{E_{el, a}} + {Q_{th, a}}}}{{{G_{pv - t, a}}}} = 65.8\%$

(23)

5.9. Comparison with selected researches of PV-T system

Table 3 shows the comparison of the other four previous works with the results of this study. While paper 1 and paper 2 gives higher thermal efficiency and slightly higher maximum water temperature, the results of these investigations are based only on one sunny day investigation moreover the hot water use pattern is neglected. Definitely, the channel type of absorber can have higher thermal efficiency compared to the tube and plate absorber considered in this study, the average thermal efficiency of paper 4 and maximum water outlet temperature is also less that of this work.

Table 3. Comparison of different papers.

Comparison criteria	1^st paper ^[26] Published 2014	2^nd paper ^[27] Published 2015	3^rd paper ^[28] Published 2015	4^th paper ^[29] Published 2012	5^th Current research paper
Location and types of collector	Malaysia 4.2° N, 101.9° E Glazed PV-T	Algeria 32.4° N, 3.6° E Glazed PV-T	Sydney 33.8° S, 151.2° E Both glazed and unglazed PV-T	Lyon 45.7° N, 4.8° E Both glazed and Unglazed	Dire Dawa 9.6° N, 41.8° E Glazed PV-T
Types of analyses	Numerical Analysis only sunny and cloudy days	Numerical and Experimental	Simulation and Validation with experimental	Simulations using TRNSYS	MATLAB Simulation with validation
Outlet water temperature of PV-T	Sunny 54 ℃ and cloudy 41 ℃ days	Not given	Max of 38 ℃ Tested for 3 days	Max 45 ℃ with axillary heater	Max 50 ℃
Efficiencies	$\begin{array}{l}{\eta_{e l}=12.9 \%} \\ {\eta_{t h}=61.3 \%}\end{array}$ at sunny days	$\begin{array}{l}{\eta_{e l}=11.1 \%} \\ {\eta_{t h}=54.5 \%}\end{array}$ Sunny day in September	Not given	$\begin{array}{l}{\eta_{e l}=11 \%} \\ {\eta_{t h}=72 \%}\end{array}$ at zero reduced temperature	$\begin{array}{l}{\eta_{e l}=15.4 \%} \\ {\eta_{t h}=50.4 \%}\end{array}$ Annual efficiency
Daily hot water Consumption Pattern	Not considered	Not considered	Not considered	Not considered as variable	Considered
Mass flow rate	No specified	No specified	0.217 kg/s m²	0.0125 kg/s m²	0.0013 kg/s
Hot water Storage	Heat up in one day	No description	Yes Temperature of storage is set equal to that of main water every morning	Yes	Yes Storage temp. at every morning is obtained from previous day
Note: The reduced temperature corresponds to the difference between the fluid mean temperature and the ambient temperature, divided by the solar radiation ^[29].

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Hence, it can be concluded most of the studies conducted so far are based on the results of short term duration without considering the actual hot water storage and use pattern. Even there are few long term performance simulation results, dose not considered the effect of daily hot water use pattern by the end-user.

6. Conclusions

A dynamic computational model of a PV-T system integrated with storage tank and hot water end use was developed and the accuracy of the computer program was checked by comparing the model with experimental results. Simulation result of cogeneration of electricity and hot water for rural clinic around Dire Dawa was investigated. The results indicated that a PV-T system can supply hot water up to a maximum of 45 ℃, attaining the following achievements PV efficiency of 15.4%, thermal efficiency of 50.4%, hot water end uses overall efficiency of 37.9% and cogeneration efficiency of 65.8%. The fraction of PV-T system in meeting the hot water energy demand was 44.5% when the hot water supply temperature is 60 ℃. There is about more than 10% difference between the thermal efficiency and overall end-use efficiency of hot water generation due to the time shift between generation and consumption of hot water.

The research indicated that PV-T system has good PV and cogeneration efficiencies. The effect of considering daily hot water demand fraction variability and storage size effect resulted in hot water end use overall efficiency close to the reality and a maximum hot water supply temperature becomes below 45 ℃. Hence, a PV-T system can be used only as a preheater for hot water generation systems even in tropical African areas meeting at maximum up to 50% of the energy demand. Moreover, the time shift between hot water generation and consumption as well as dilution of hot water by cold make-up water causes degradation of thermal energy and lower end-use efficiency and hot water temperature.

Conflict of interest

The authors declare no conflict of interest.

References

[1]	H. Zhu, Y. Wang, Z. Ma, X. Li, A comparative study of swarm intelligence algorithms for ucav path-planning problems, Mathematics, 9 (2021), 171. doi: 10.3390/math9020171
[2]	Y. Wang, Z. Ma, K. Wong, X. Li, Nature-inspired multiobjective patient stratification from cancer gene expression data, Inf. Sci., 526 (2020), 245-262. doi: 10.1016/j.ins.2020.03.095
[3]	S. Lalwani, H. Sharma, S. C. Satapathy, K. Deep, J. C. Bansal, A survey on parallel particle swarm optimization algorithms, Arab. J. Sci. Eng., 44 (2019), 2899-2923. doi: 10.1007/s13369-018-03713-6
[4]	Y. Wang, X. Li, K.-C. Wong, Y. Chang, S. Yang, Evolutionary multiobjective clustering algorithms with ensemble for patient stratification, IEEE Trans. Cybern., 2021.
[5]	X. Li, J. Wang, J. Zhou, M. Yin, A perturb biogeography based optimization with mutation for global numerical optimization, Appl. Math. Comput., 218 (2011), 598-609.
[6]	X. Li, M. Yin, Multiobjective binary biogeography based optimization for feature selection using gene expression data, IEEE Trans. NanoBiosci., 12 (2013), 343-353. doi: 10.1109/TNB.2013.2294716
[7]	B. Liu, M. Tian, C. Zhang, X. Li, Discrete biogeography based optimization for feature selection in molecular signatures, Mol. Inform., 34 (2015), 197-215. doi: 10.1002/minf.201400065
[8]	X. Li, M. Yin, Hybrid differential evolution with biogeography-based optimization for design of a reconfigurable antenna array with discrete phase shifters, Int. J. Antenn. Propag., 2011 (2011).
[9]	X. Li, J. Zhang, M. Yin, Animal migration optimization: an optimization algorithm inspired by animal migration behavior, Neural. Comput. Appl., 24 (2014), 1867-1877. doi: 10.1007/s00521-013-1433-8
[10]	Y. Cao, X. Li, J. Wang, Opposition-based animal migration optimization, Math. Probl. Eng., 2013 (2013).
[11]	X. Li, J. Wang, M. Yin, Enhancing the performance of cuckoo search algorithm using orthogonal learning method, Neural. Comput. Appl., 24 (2014), 1233-1247. doi: 10.1007/s00521-013-1354-6
[12]	X. Li, M. Yin, Modified cuckoo search algorithm with self adaptive parameter method, Inf. Sci., 298 (2015), 80-97. doi: 10.1016/j.ins.2014.11.042
[13]	X. Li, M. Yin, A particle swarm inspired cuckoo search algorithm for real parameter optimization, Soft Comput., 20 (2016), 1389-1413. doi: 10.1007/s00500-015-1594-8
[14]	X. Li, S. Ma, Multiobjective discrete artificial bee colony algorithm for multiobjective permutation flow shop scheduling problem with sequence dependent setup times, IEEE Trans. Eng. Manag., 64 (2017), 149-165. doi: 10.1109/TEM.2016.2645790
[15]	A. Lam, V. Li, Chemical-reaction-inspired metaheuristic for optimization, IEEE Trans. Evol. Comput., 14 (2010), 381-399. doi: 10.1109/TEVC.2009.2033580
[16]	A. Lam, V. Li, J. Yu, Real-coded chemical reaction optimization, IEEE Trans. Evol. Comput., 16 (2012), 339-353. doi: 10.1109/TEVC.2011.2161091
[17]	Y. Xu, K. Li, L. He, T. K. Truong, A dag scheduling scheme on heterogeneous computing systems using double molecular structure-based chemical reaction optimization, J. Parallel Distrib. Comput., 73 (2013), 1306-1322. doi: 10.1016/j.jpdc.2013.05.005
[18]	Y. Xu, K. Li, L. He, L. Zhang, K. Li, A hybrid chemical reaction optimization scheme for task scheduling on heterogeneous computing systems, IEEE T. Parall. Distr., 26 (2014), 3208-3222.
[19]	T.-L. Dam, K. Li, P. Fournier-Viger, Chemical reaction optimization with unified tabu search for the vehicle routing problem, Soft Comput., 21 (2017), 6421-6433. doi: 10.1007/s00500-016-2200-4
[20]	A. Lam, J. Xu, V. Li, Chemical reaction optimization for population transition in peer-to-peer live streaming, In IEEE Congress Evol. Comput., 2010.
[21]	J. Xu, A. Lam, V. Li, Chemical reaction optimization for the grid scheduling problem, IEEE Int. Conf. Commun., 2010, 1-5.
[22]	T. K. Truong, K. Li, Y. Xu, Chemical reaction optimization with greedy strategy for the 0-1 knapsack problem, Appl. Soft Comput., 13 (2013), 1774-1780. doi: 10.1016/j.asoc.2012.11.048
[23]	K. Güney, A. Akdagh, Null steering of linear antenna arrays using a modified tabu search algorithm—abstract, J. Electromagn. Waves Appl., 15 (2001), 915-916. doi: 10.1163/156939301X00878
[24]	H. R. Tizhoosh, Opposition-based reinforcement learning, J. Adv. Comput. Intell. Intell. Inform., 10 (2006), 578-585. doi: 10.20965/jaciii.2006.p0578
[25]	W. Hui, A. Zw, C. Sr, L. D. Yong, E. Mv, Enhancing particle swarm optimization using generalized opposition-based learning, Inf. Sci., 181 (2011), 4699-4714. doi: 10.1016/j.ins.2011.03.016
[26]	R. Storn, K. Price, Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces, J. Glob. Optim., 11 (1997), 341-359. doi: 10.1023/A:1008202821328
[27]	J. Brest, S. Greiner, B. Boskovic, M. Mernik, V. Zumer, Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems, IEEE Trans. Evol. Comput., 10 (2006), 646-657. doi: 10.1109/TEVC.2006.872133
[28]	X. Li, X. Zhao, J. N. Wang, M. Yin, Improved artificial bee colony for design of a reconfigurable antenna array with discrete phase shifters, Prog. Electromagn. Res., 25 (2012), 193-208. doi: 10.2528/PIERC11100803
[29]	S. Baskar, A. Alphones, P. N. Suganthan, Genetic algorithm based design of a reconfigurable antenna array with discrete phase shifter, Microw. Opt. Technol. Lett., 45 (2005), 461-465. doi: 10.1002/mop.20853
[30]	J. A. Rodriguez, F. Ares, E. Moreno, Linear array pattern synthesis optimizing array element excitations using the simulated annealing technique, Microw. Opt. Technol. Lett., 23 (1999), 224-226. doi: 10.1002/(SICI)1098-2760(19991120)23:4<224::AID-MOP10>3.0.CO;2-M
[31]	R. C. Hansen, Phased array antennas, volume 213. John Wiley & Sons, 2009.
[32]	X. Li, M. Yin, Optimal synthesis of linear antenna array with composite differential evolution algorithm - sciencedirect, Sci. Iran., 19 (2012), 1780-1787. doi: 10.1016/j.scient.2012.03.010

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