A Detailed Analysis of the Modified Economic Method for Assessing the Performance of Photovoltaic Module Enhancing Techniques

Abstract

This paper presents a detailed analysis of the modified economic method (${\mathrm{F}}_{\mathrm{MCE}}$) for evaluating the performance of photovoltaic module (PV)-enhancing techniques, aiming to address existing research gaps. The impact of influential parameters on the ${\mathrm{F}}_{\mathrm{MCE}}$ is examined through illustrative examples. These parameters include the output power of a single solar cell without an enhancer, output power of a PV with an enhancer, manufacturing cost of the PV enhancer, one-watt cost of PV power, and maximum output power of a solar cell with an enhancer equivalent to maximum output power at standard test conditions (STC). The results of this study reveal that the output power of a single solar cell without an enhancer, number of solar cells with an enhancer in the PV, and manufacturing cost of the PV enhancer have a proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}$. As these parameters increase, the ${\mathrm{F}}_{\mathrm{MCE}}$ also increases, which negatively affects the cost-effectiveness of the PV enhancer, leading to lower performance. So, it is advisable to maintain the values of these parameters at lower levels. Conversely, the output power of a PV with an enhancer and the one-watt cost of PV power exhibit an inverse proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}$. As the output power of a PV with an enhancer and the one-watt cost of PV power increase, the ${\mathrm{F}}_{\mathrm{MCE}}$ decreases, which positively affects the cost-effectiveness of the PV enhancer, leading to higher performance. Hence, it is recommended to keep these two parameters high for optimal performance. In conclusion, the ${\mathrm{F}}_{\mathrm{MCE}}$ may have potential for application by designers and manufacturers of PV enhancers.

1. Introduction

The correlation between energy and economic development is evident, as an increase in energy consumption corresponds to an increase in economic progress. Presently, the primary energy sources include fossil fuels, nuclear power, hydroelectricity, and other renewable energies. Fossil fuels dominate global energy consumption, accounting for 84% of the total. However, the detrimental effects of fossil fuel emissions on human health have been extensively recognized by scientists for many years. Recent research indicates a doubled global death toll compared to previous estimations [1]. The study reveals that approximately 8.7 million people worldwide lost their lives in 2018 due to exposure to fine particulate matter resulting from the burning of fossil fuels. This staggering number is equivalent to the population of a major city such as London or New York. Remarkably, fossil fuel pollution not only contributes to climate change but also surpasses tuberculosis, HIV, and malaria combined in terms of annual casualties [2]. Solar energy is a sustainable and clean energy source that emits zero carbon dioxide. Utilizing solar energy has the potential to make a significant impact in addressing environmental issues. While solar energy conversion currently has relatively low efficiency, there are opportunities for advancements in this field. One application of solar energy is the photovoltaic module (PV), that converts sunlight directly into electricity [2]. There are series and parallel combinations of PV cells [3]. An example of a commercial PV is Mitsubishi Diamond Premium [4].

The energy production of PV has been consistently increasing over the years [5]. In 2010, the global energy production was recorded at 32.2 TWh, and by 2021 it had surged to 1002.9 TWh, representing a nearly thirty-fold growth compared to the energy production in 2010. This notable expansion in PV energy generation has prompted researchers to focus on enhancing the efficiency of PV. One approach to achieve this is by implementing enhancers such as coolers and reflectors. The choice of the specific enhancement technique depends on the prevailing weather conditions. For instance, in regions with high solar radiation and ambient temperatures, incorporating a cooler can be advantageous in reducing the PV module’s temperature. This is because the flow of fluid can facilitate enhanced heat transfer on the PV’s surface [6,7,8,9,10,11,12,13,14], ultimately leading to improved PV performance [6]. Various types of coolers are available, including passive, active, natural, or forced cooling methods that utilize liquid, air, or phase-change materials (PCM).

A performance analysis of a water-type photovoltaic thermal collector (PVT) was conducted, utilizing artificial neural networks (ANNs) to enhance the accuracy of the analytical model [15]. Input variables such as solar irradiance, mass flow rate, and inlet temperature were considered, and experimental measurements were performed to validate the analytical results, demonstrating good agreement. The proposed model proved its effectiveness in addressing issues related to cost and time associated with experimental setups. To address the limitation of the low output temperature in PVTs, a novel PVT design was proposed [16]. A two-dimensional steady-state model was developed and experimentally validated, revealing relatively high thermal performance but low electrical efficiency compared to conventional PVTs. Furthermore, an air-type PVT was introduced, resulting in a 5.1% and 2.0% increase in electrical efficiency during summer and winter, respectively [17]. A single-pass channel air-type PVT was also investigated, and energy equations were derived for different system components. Experimental results yielded maximum electrical and thermal efficiencies of 13.75% and 56.19%, respectively, for varying mass flow rates and solar irradiance levels [18]. Another mathematical model was developed for an air-type PVT with a glass cover, channel duct, and axial fan, achieving a thermal efficiency of 18.04% [19]. The electrical and thermal efficiencies of an air-type PVT were further investigated using a simulation program, with analytical results showing good agreement with experimental measurements [20]. Integrating a phase-change material (PCM) tank at the back of a PV module improved the electrical efficiency by controlling the PV temperature during the phase-change process [11]. The effects of nanofluids (NFs) on the electrical and thermal efficiencies of PVT and the fluid outlet temperature were investigated theoretically and experimentally [20]. The results indicated that NF-SiO₂ outperformed water, reducing the PV temperature and increasing the outlet temperature, resulting in an enhancement of 12.70% in electrical efficiency and 5.76% in thermal efficiency at a solar irradiance of 1000 W/m².

Conversely, in regions characterized by low solar radiation and ambient temperatures, the use of a reflector is favored. The concept of employing reflectors to increase the collection area of incident solar radiation was first introduced in 1958, aiming to enhance PV efficiency [21,22,23,24,25,26]. Numerical and experimental investigations were conducted on a PV-integrated V-trough concentrating system operating outdoors, yielding a maximum power improvement of 31.2% [27]. Another experiment examined the impact of reflector parameters on output power, demonstrating that reflectors could increase the output power by up to 60% [23]. Constructing an aluminum-sheet-based PV led to a 15% increase in output power [24]. An outdoor experiment involving a PV with a V-trough concentrating system observed a 48% increase in output power [28]. Further research evaluated the feasibility and performance of a PV with both a cooler and a reflector, revealing an increase in PV efficiency to 10.68% and a payback period of 4.2 years [29]. A numerical study on an aluminum-sheet-based PV explored the influence of tilt angles on PV efficiency, indicating that higher tilt angles can enhance PV performance [30]. A novel PV design incorporating a curve-shaped reflector showed a significant increase in spatial solar power, reaching 61% [31]. Analytical and experimental investigations on a PV equipped with a flat plate reflector and cooler demonstrated a PV efficiency improvement to 36% [32]. Additionally, a three-dimensional model utilizing a stainless steel (SS) structure was proposed to achieve a PV efficiency of 34.16% [33].

Motivation of the Present Study

This research paper provides the following:

• A comprehensive analysis of the ${\mathrm{F}}_{\mathrm{MCE}}$ is used to assess the effectiveness of photovoltaic (PV)-module-enhancing techniques. The study aims to bridge existing gaps in research by investigating the parameters affecting the ${\mathrm{F}}_{\mathrm{MCE}}$ which are the number of solar cells in a PV with an enhancer, the output power of a single solar cell without an enhancer, the output power of a PV with an enhancer, the manufacturing cost of the PV enhancer, the one-watt cost of PV power, and the output power of a solar cell with an enhancer equivalent to the maximum output power under standard test conditions (STC).
• It will be shown that the output power of a PV with an enhancer and the one-watt cost of PV power, that have an inverse proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}$, should be kept high, for better PV enhancer performance. On the other hand, the other parameters, including the number of solar cells in a PV with an enhancer, output power of a single solar cell without an enhancer, the manufacturing cost of the PV enhancer, and the output power of a solar cell with an enhancer equivalent to the maximum output power under standard test conditions (STC), have a proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}$. These parameters should have minimum values to achieve better PV enhancer performance.
• Valuable insights into the factors influencing the cost-effectiveness of PV enhancer techniques can guide decision-making processes during the design stage. In conclusion, the ${\mathrm{F}}_{\mathrm{MCE}}$ holds promise for application by PV enhancer designers and manufacturers.

2. Research Methodology

Figure 1 shows the flowchart of the research methodology conducted. Firstly, a comprehensive research on the existing methods for evaluating the performance of PV enhancers is performed. The research gap is determined and broad knowledge is gained, which leads to the second step of studying the modified economic method (${\mathrm{F}}_{\mathrm{MCE}}$) in more detail for the purpose of discovering the parameters that can improve the PV enhancer performance. Furthermore, in the second step, a study is conducted for the minimum value of the ${\mathrm{F}}_{\mathrm{MCE}},$ that is, ${\mathrm{F}}_{\mathrm{MCE},\min },$ which can be used to determine the optimum performance of a PV enhancer. The third step is to test the applicability of the ${\mathrm{F}}_{\mathrm{MCE}}$ and ${\mathrm{F}}_{\mathrm{MCE},\min }$ on different PV enhancer models which have different output power and manufacturing cost values. The last step is to study the influential parameters on the ${\mathrm{F}}_{\mathrm{MCE}}$. These parameters are the manufacturing cost of a PV enhancer, the one-watt cost of PV power, the output power from a PV with and without an enhancer, the maximum output power from a PV at STC, and the number of solar cells. Concluding remarks on the parameters that can enhance or degrade the performance of the PV enhancer will be stated.

3. The Modified Economical Method for a PV Enhancer

The correlation for the modified PV enhancer cost-effectiveness factor, ${\mathrm{F}}_{\mathrm{MCE}}$, is [34]

$${\mathrm{F}}_{\mathrm{MCE}}=\frac{\mathrm{n}\times {\mathrm{P}}_{\mathrm{cell}}+\frac{\mathrm{Z}}{\mathrm{Y}}}{{\mathrm{P}}_{\mathrm{PVE}}}$$

(1)

In Equation (1), ${\mathrm{P}}_{\mathrm{cell}}$ represents the power output from an individual solar cell without any enhancement. ${\mathrm{P}}_{\mathrm{PVE}}$ corresponds to the power output of a PV with an enhancer. The variable n denotes the number of solar cells present in a PV with an enhancer. Z represents the manufacturing cost of the PV enhancer, while Y signifies the cost of generating one watt of PV power.

3.1. The Modified Minimum Value of PV Enhancer Cost-Effectiveness Factor

Sakhr et al. [34] defined the modified minimum value of PV enhancer cost-effectiveness factor

$${\mathrm{F}}_{\mathrm{MCE},\min }=\frac{{\mathrm{P}}_{\mathrm{cell}}}{{\mathrm{P}}_{\mathrm{cell},\max }}$$

(2)

From Equation (2), it is noted that ${\mathrm{F}}_{\mathrm{MCE},\min }$ depends on the output and the maximum output power from a single solar cell without an enhancer.

3.2. Significance of $F_{MCE}$ Value

Based on Equation (1), there are three classifications as follows:

• ${\mathrm{F}}_{\mathrm{MCE},\min }\le {\mathrm{F}}_{\mathrm{MCE}}<1$, indicating the PV enhancer is cost-effective.
• ${\mathrm{F}}_{\mathrm{MCE}}=1$, indicating the PV enhancer is neutral.
• $1>{\mathrm{F}}_{\mathrm{MCE}}>\infty$, indicating the PV enhancer is not cost-effective.

3.3. The Areas of Cost-Effective or Non-Cost-Effective

The areas of cost-effective or non-cost-effective of the PV enhancer can be classified by the following:

• ${\mathrm{F}}_{\mathrm{MCE}}$ falls in the range of ${\mathrm{F}}_{\mathrm{MCE},\min }\le {\mathrm{F}}_{\mathrm{MCE}}<1$, indicating the PV enhancer is in the cost-effective area.
• ${\mathrm{F}}_{\mathrm{MCE}}$ falls in the range of 1$<{\mathrm{F}}_{\mathrm{MCE}}<\infty$, indicating the PV enhancer is in the non-cost-effective area.

4. Results and Discussions on $F_{MCE}$ and $F_{MCE,min}$

To illustrate the analysis of the ${\mathrm{F}}_{\mathrm{MCE}}$ and ${\mathrm{F}}_{\mathrm{MCE},\min }$, several assumptions are made, as follows. The output power of a single solar cell, denoted as ${\mathrm{P}}_{\mathrm{cell}}$, is 0.9 W. The maximum power of a single solar cell at standard test conditions (STC), referred to as ${\mathrm{P}}_{\mathrm{cell},\max }$, is 1.2 W. The cost of one watt of PV power, denoted as Y, is MYR 3. In this scenario, five different models of PV cooling techniques are considered and compared to the single solar cell without a cooler using the aforementioned assumptions. All PV with cooling techniques use the same type of solar cell, and each PV with a cooling technique consists of 200 solar cells. It is assumed that the PVs with cooling techniques produce different output power values, specifically 172.53 W, 187 W, 208.88 W, 217.24 W, and 237.5 W for model A, model B, model C, model D, and model E, respectively. Additionally, each PV cooler has a different manufacturing cost, which amounts to MYR 19, MYR 21, MYR 24, MYR 27, and MYR 30 for model A, model B, model C, model D, and model E, respectively.

Using Equation (1), the ${\mathrm{F}}_{\mathrm{MCE}}$ values for model A, model B, model C, model D, and model E are determined as 1.08, 1, 0.9, 0.87, and 0.80, respectively. If the manufacturing cost for model A is converted to photovoltaic power and added to $\mathrm{n}\times {\mathrm{P}}_{\mathrm{cell}}$ (the number of solar cells in the PV with a cooler multiplied by the output power from a single solar cell without a cooling technique), the result exceeds that of ${\mathrm{P}}_{\mathrm{PVE}}$. Consequently, it is deemed not cost-effective and falls within the range of non-cost-effectiveness (1$<{\mathrm{F}}_{\mathrm{MCE}}<\infty )$. For model B, it remains neutral or at the threshold value, as the sum of $\mathrm{n}\times {\mathrm{P}}_{\mathrm{cell}}$ and the converted manufacturing cost to photovoltaic power equals ${\mathrm{P}}_{\mathrm{PVE}}$. On the other hand, if the manufacturing costs of model C, model D, and model E are converted to photovoltaic power and added to $\mathrm{n}\times {\mathrm{P}}_{\mathrm{cell}}$, the resulting power is lower compared to the power output from PV modules with model C, model D, or model E. Therefore, they fall within the range of cost-effectiveness (${\mathrm{F}}_{\mathrm{MCE},\min }\le {\mathrm{F}}_{\mathrm{MCE}}<1)$ and are considered cost-effective.

To determine the optimal PV cooler among model C, model D, and model E, it is crucial to calculate the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value. By applying Equation (2), the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value is found to be 0.75. Now, any PV cooling technique with an ${\mathrm{F}}_{\mathrm{MCE}}$ value closer to 0.75 indicates optimal performance. By referring to

Table 1. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ and its minimum value.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	0.90	200.00	172.53	3.00	19.00	1.08	0.75	Not cost-effective
B	1.20	0.90	200.00	187.00	3.00	21.00	1.00	0.75	Neutral
C	1.20	0.90	200.00	208.88	3.00	24.00	0.90	0.75	Cost-effective
D	1.20	0.90	200.00	217.24	3.00	27.00	0.87	0.75	Cost-effective
E	1.20	0.90	200.00	237.50	3.00	30.00	0.80	0.75	Cost-effective

, it can be observed that the ${\mathrm{F}}_{\mathrm{MCE}}$ value for model E is 0.8, which is the closest to ${\mathrm{F}}_{\mathrm{MCE},\min }$. Therefore, model E represents the optimal PV cooler. The results demonstrate that the sorting and decision-making process regarding different types of PV coolers becomes feasible with the support of the ${\mathrm{F}}_{\mathrm{MCE}}$ and ${\mathrm{F}}_{\mathrm{MCE},\min }$ values.

4.1. The Effect of Solar Cell Number on $F_{MCE}$

Let us assume that the number of solar cells in a PV with a cooler for all types listed in Table 1 is reduced from 200 to 190, while keeping the other parameters unchanged, as indicated in

Table 2. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the number of solar cells decreased from 200 to 190.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	0.90	190	172.53	3.00	19.00	1.03	0.75	Not cost-effective
B	1.20	0.90	190	187.00	3.00	21.00	0.95	0.75	Cost-effective
C	1.20	0.90	190	208.88	3.00	24.00	0.86	0.75	Cost-effective
D	1.20	0.90	190	217.24	3.00	27.00	0.83	0.75	Cost-effective
E	1.20	0.90	190	237.50	3.00	30.00	0.76	0.75	Cost-effective

. The effect of this change on the ${\mathrm{F}}_{\mathrm{MCE}}$ value becomes apparent. It is evident that the ${\mathrm{F}}_{\mathrm{MCE}}$ values for all types of PV coolers decrease. Specifically, for model A, model B, model C, model D, and model E, the ${\mathrm{F}}_{\mathrm{MCE}}$ values are now 1.03, 0.95, 0.86, 0.83, and 0.76, respectively. Referring to

Table 3. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the number of solar cells increased from 200 to 210.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	0.90	210	172.53	3.00	19.00	1.13	0.75	Not cost-effective
B	1.20	0.90	210	187.00	3.00	21.00	1.05	0.75	Not cost-effective
C	1.20	0.90	210	208.88	3.00	24.00	0.94	0.75	Cost-effective
D	1.20	0.90	210	217.24	3.00	27.00	0.91	0.75	Cost-effective
E	1.20	0.90	210	237.50	3.00	30.00	0.84	0.75	Cost-effective

, it is apparent that model A remains not cost-effective. Model B, on the other hand, has transitioned to a cost-effective status from its previous neutral status. Furthermore, model C, model D, and model E continue to be cost-effective choices. Model E, with an ${\mathrm{F}}_{\mathrm{MCE}}$ value of 0.76, is the closest to the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value and, therefore, represents the optimal model. These results demonstrate that the number of solar cells is a significant factor that directly impacts the ${\mathrm{F}}_{\mathrm{MCE}}$ value.

Alternatively, if the number of solar cells is increased from 200 to 210 while keeping the other parameters unchanged, as presented in Table 3, the updated ${\mathrm{F}}_{\mathrm{MCE}}$ values become 1.13, 1.05, 0.94, 0.91, and 0.84 for model A, model B, model C, model D, and model E, respectively. This reveals a direct relationship between the number of solar cells and the ${\mathrm{F}}_{\mathrm{MCE}}$ value. As the number of solar cells increases, the ${\mathrm{F}}_{\mathrm{MCE}}$ value also increases. It is important to note that any alteration in the number of solar cells will result in a corresponding change in the ${\mathrm{F}}_{\mathrm{MCE}}$ value.

4.2. The Effect of Solar Cell Output Power on $F_{MCE}$ and $F_{MCE,min}$

Now, if the ${\mathrm{P}}_{\mathrm{cell}}$ value in Table 1 is changed from 0.9 to 1 W (see

Table 4. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the output power of the solar cell changed from 0.9 to 1 W.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	1.00	200.00	172.53	3.00	19.00	1.20	0.83	Not cost-effective
B	1.20	1.00	200.00	187.00	3.00	21.00	1.11	0.83	Not cost-effective
C	1.20	1.00	200.00	208.88	3.00	24.00	1.00	0.83	Neutral
D	1.20	1.00	200.00	217.24	3.00	27.00	0.96	0.83	Cost-effective
E	1.20	1.00	200.00	237.50	3.00	30.00	0.88	0.83	Cost-effective

), while the ${\mathrm{P}}_{\mathrm{cell},\max }$, ${\mathrm{P}}_{\mathrm{PVE}},$ n, Z, and Y are unchanged. Then, based on Equation (1), the ${\mathrm{F}}_{\mathrm{MCE}}$ values for model A, model B, model C, model D, and model E are 1.2, 1.11, 1, 0.96, and 0.88, respectively. From Table 4, model A and model B are now not cost-effective. Model C is neutral. On the other hand, model D and model E are now cost-effective. Based on Equation (2), the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value is 0.83. It is observed that model E is the optimum among all models, because its ${\mathrm{F}}_{\mathrm{MCE}}$ value is 0.88, which is the nearest to the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value. Now, if the output power from a single solar cell is decreased from 0.9 to 0.8 W for all models, as shown in

Table 5. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the output power of the solar cell changed from 0.9 to 0.8 W.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	0.80	200.00	172.53	3.00	19.00	0.96	0.67	Not cost-effective
B	1.20	0.80	200.00	187.00	3.00	21.00	0.89	0.67	Neutral
C	1.20	0.80	200.00	208.88	3.00	24.00	0.80	0.67	Cost-effective
D	1.20	0.80	200.00	217.24	3.00	27.00	0.78	0.67	Cost-effective
E	1.20	0.80	200.00	237.50	3.00	30.00	0.72	0.67	Cost-effective

, the new ${\mathrm{F}}_{\mathrm{MCE}}$ values are 0.96, 0.89, 0.80, 0.78, and 0.72 for model A, model B, model C, model D, and model E, respectively. Now, all PV cooler models are cost-effective. However, model E has the optimum performance. It is seen there is a proportional relationship between ${\mathrm{P}}_{\mathrm{cell}}$ and the ${\mathrm{F}}_{\mathrm{MCE}}$. As ${\mathrm{P}}_{\mathrm{cell}}$ increases, the ${\mathrm{F}}_{\mathrm{MCE}}$ increases. It is noted that the change in ${\mathrm{P}}_{\mathrm{cell}}$ will change the ${\mathrm{F}}_{\mathrm{MCE}}$. It is seen that ${\mathrm{P}}_{\mathrm{cell}}$ is an important factor that has an effect on the ${\mathrm{F}}_{\mathrm{MCE}}$.

4.3. The Effect of the Cost of One Watt of PV Power on $F_{MCE}$

Assuming that the cost of one watt of PV power in Table 1, is changed from MYR 3 to 5 (see

Table 6. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the cost of one watt of PV power increased from MYR 3 to 5.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	0.90	200.00	172.53	5.00	19.00	1.07	0.75	Not cost-effective
B	1.20	0.90	200.00	187.00	5.00	21.00	0.99	0.75	Cost-effective
C	1.20	0.90	200.00	208.88	5.00	24.00	0.88	0.75	Cost-effective
D	1.20	0.90	200.00	217.24	5.00	27.00	0.85	0.75	Cost-effective
E	1.20	0.90	200.00	237.50	5.00	30.00	0.80	0.75	Cost-effective

), the ${\mathrm{P}}_{\mathrm{cell},\max }$, ${\mathrm{P}}_{\mathrm{PVE}},$ the number of solar cells available in the PV that has a cooler, n, the cost of manufacturing of the PV coolers, and ${\mathrm{P}}_{\mathrm{cell}}$ values are unchanged. Based on Equation (1), the ${\mathrm{F}}_{\mathrm{MCE}}$ values for model A, model B, model C, model D, and model E are 1.07, 0.99, 0.88, 0.85, and 0.80, respectively. From Table 6, model A is still not cost-effective. Model B, model C, model D, and model E are cost-effective. It is observed that model E is still the optimum among the other models, because it has an ${\mathrm{F}}_{\mathrm{MCE}}$ value of 0.80 which is the nearest to the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value. Now, if the cost of one watt of PV power is decreased from MYR 3 to 1 for all models, as shown in

Table 7. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the cost of one watt of PV power decreased from MYR 3 to 1.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	0.90	200.00	172.53	1.00	19.00	1.15	0.75	Not cost-effective
B	1.20	0.90	200.00	187.00	1.00	21.00	1.07	0.75	Not cost-effective
C	1.20	0.90	200.00	208.88	1.00	24.00	0.98	0.75	Cost-effective
D	1.20	0.90	200.00	217.24	1.00	27.00	0.95	0.75	Cost-effective
E	1.20	0.90	200.00	237.50	1.00	30.00	0.88	0.75	Cost-effective

, the new ${\mathrm{F}}_{\mathrm{MCE}}$ values are 1.15, 1.07, 0.98, 0.95, and 0.88 for model A, model B, model C, model D, and model E, respectively. Model A and model B are now not cost-effective. Model C, model D, and model E are cost-effective. However, model E has the optimum performance. It is seen there is an inverse proportional relationship between the cost of one watt of PV power and the ${\mathrm{F}}_{\mathrm{MCE}}$ value. As the cost of one watt of PV power increases, the ${\mathrm{F}}_{\mathrm{MCE}}$ value decreases. It is noted that the change in the cost of one watt of PV power will change the ${\mathrm{F}}_{\mathrm{MCE}}$ value.

4.4. The Effect of PV Cooler’s Manufacturing Cost on $F_{MCE}$

To illustrate the effect of the manufacturing cost of the PV cooler on ${\mathrm{F}}_{\mathrm{MCE}}$, let us assume that the PV cooler manufacturing cost in Table 1 is changed for all PV cooler models, as shown in Table 7. The new values are MYR 27, 30, 35, 40, and 50 for model A, model B, model C, model D, and model E, respectively. While the ${\mathrm{P}}_{\mathrm{cell},\max }$, ${\mathrm{P}}_{\mathrm{PVE}},$ the number of solar cells available in the PV that has a cooler, n, the cost of one watt of PV power, and the ${\mathrm{P}}_{\mathrm{cell}}$ values are unchanged. Based on Equation (1), the ${\mathrm{F}}_{\mathrm{MCE}}$ values for model A, model B, model C, model D, and model E are 1.10, 1.02, 0.92, 0.89, and 0.83, respectively. From

Table 8. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the PV cooler’s manufacturing cost increased.

PV Cooler Model	${\mathbf{P}}_{\mathbf{cell},\mathbf{max}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{cell}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{PVE}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{MCE}}$	${\mathbf{F}}_{\mathbf{MCE},\mathbf{min}}$	Remarks
A	1.20	0.90	200.00	172.53	3.00	27.00	1.10	0.75	Not cost-effective
B	1.20	0.90	200.00	187.00	3.00	30.00	1.02	0.75	Not cost-effective
C	1.20	0.90	200.00	208.88	3.00	35.00	0.92	0.75	Cost-effective
D	1.20	0.90	200.00	217.24	3.00	40.00	0.89	0.75	Cost-effective
E	1.20	0.90	200.00	237.50	3.00	50.00	0.83	0.75	Cost-effective

, model A and model B are not cost-effective. Model C, model D, and model E are cost-effective. It is observed that model E is still the optimum among the other models, because it has an ${\mathrm{F}}_{\mathrm{MCE}}$ value of 0.83, which is the nearest to the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value. Now, if the PV cooler’s manufacturing cost is decreased, the new values are MYR 15, MYR 17, MYR 20, MYR 22, and MYR 25 for model A, model B, model C, model D, and model E, respectively, as shown in

Table 9. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when the PV cooler’s manufacturing cost decreased.

PV cooler Model	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l},\mathbf{m}\mathbf{a}\mathbf{x}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{P}\mathbf{V}\mathbf{E}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E}}$	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E},\mathbf{m}\mathbf{i}\mathbf{n}}$	Remarks
A	1.20	0.90	200.00	172.53	3.00	15.00	1.07	0.75	Not cost-effective
B	1.20	0.90	200.00	187.00	3.00	17.00	0.99	0.75	Cost-effective
C	1.20	0.90	200.00	208.88	3.00	20.00	0.89	0.75	Cost-effective
D	1.20	0.90	200.00	217.24	3.00	22.00	0.86	0.75	Cost-effective
E	1.20	0.90	200.00	237.50	3.00	25.00	0.79	0.75	Cost-effective

. The new ${\mathrm{F}}_{\mathrm{MCE}}$ values are 1.07, 0.99, 0.89, 0.86, and 0.79 for model A, model B, model C, model D, and model E, respectively. Model A is still not cost-effective. Model B, model C, model D, and model E are cost-effective. However, model E has the optimum performance. It is seen there is a proportional relationship between the PV cooler manufacturing cost and the ${\mathrm{F}}_{\mathrm{MCE}}$ value. As the PV cooler manufacturing cost increases, the ${\mathrm{F}}_{\mathrm{MCE}}$ value increases. It is noted that the change in the PV cooler’s manufacturing cost will change the ${\mathrm{F}}_{\mathrm{MCE}}$ value.

4.5. The Effect of the Output Power of the PV Cooler on $F_{MCE}$

Assuming that the output power of the PV cooler in Table 1 is changed for all PV cooler models, as shown in

Table 10. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when ${\mathrm{P}}_{\mathrm{PVE}}$ increased.

PV Cooler Model	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l},\mathbf{m}\mathbf{a}\mathbf{x}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{P}\mathbf{V}\mathbf{E}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E}}$	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E},\mathbf{m}\mathbf{i}\mathbf{n}}$	Remarks
A	1.20	0.90	200.00	180.00	3.00	19.00	1.04	0.75	Not cost-effective
B	1.20	0.90	200.00	195.00	3.00	21.00	0.96	0.75	Cost-effective
C	1.20	0.90	200.00	220.00	3.00	24.00	0.85	0.75	Cost-effective
D	1.20	0.90	200.00	230.00	3.00	27.00	0.82	0.75	Cost-effective
E	1.20	0.90	200.00	250.00	3.00	30.00	0.76	0.75	Cost-effective

, the new values are 180, 195, 220, 230, and 250 W for model A, model B, model C, model D, and model E, respectively. While, the ${\mathrm{P}}_{\mathrm{cell},\max }$, the number of solar cells available in the PV that has a cooler, n, the cost of one watt of PV power, the PV cooler manufacturing cost, and ${\mathrm{P}}_{\mathrm{cell}}$ values are unchanged. Based on Equation (1), the ${\mathrm{F}}_{\mathrm{MCE}}$ values for model A, model B, model C, model D, and model E are 1.04, 0.96, 0.85, 0.82, and 0.76, respectively. From Table 10, model A is not cost-effective. Model B, model C, model D, and model E are cost-effective. It is observed that model E is still the optimum among the other models, because it has an ${\mathrm{F}}_{\mathrm{MCE}}$ value of 0.76, which is the nearest to the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value. Now, if the output power of the PV cooler is decreased, the new values are 160, 170, 200, 210, and 230 W for model A, model B, model C, model Dm and model E, respectively, as shown in

Table 11. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE}}$ when ${\mathrm{P}}_{\mathrm{PVE}}$ decreased.

PV Cooler Model	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l},\mathbf{m}\mathbf{a}\mathbf{x}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{P}\mathbf{V}\mathbf{E}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E}}$	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E},\mathbf{m}\mathbf{i}\mathbf{n}}$	Remarks
A	1.20	0.90	200.00	160.00	3.00	19.00	1.16	0.75	Not cost-effective
B	1.20	0.90	200.00	170.00	3.00	21.00	1.10	0.75	Not cost-effective
C	1.20	0.90	200.00	200.00	3.00	24.00	0.94	0.75	Cost-effective
D	1.20	0.90	200.00	210.00	3.00	27.00	0.90	0.75	Cost-effective
E	1.20	0.90	200.00	230.00	3.00	30.00	0.83	0.75	Cost-effective

. The new ${\mathrm{F}}_{\mathrm{MCE}}$ values are 1.16, 1.10, 0.94, 0.90, and 0.83 for model A, model B, model C, model D, and model E, respectively. Model A and model B are not cost-effective. Model C, model D, and model E are cost-effective. However, model E has the optimum performance. It is seen there is an inverse proportional relationship between ${\mathrm{P}}_{\mathrm{PVE}}$ and the ${\mathrm{F}}_{\mathrm{MCE}}$ value. As ${\mathrm{P}}_{\mathrm{PVE}}$ decreases, the ${\mathrm{F}}_{\mathrm{MCE}}$ value increases. It is noted that the change in ${\mathrm{P}}_{\mathrm{PVE}}$ will change the ${\mathrm{F}}_{\mathrm{MCE}}$ value.

4.6. The Effect of $P_{cell,max}$ on $F_{MCE,min}$

Now, if the ${\mathrm{P}}_{\mathrm{cell},\max }$ in Table 1 is changed for all PV cooler models, as shown in

Table 12. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE},\min }$ when ${\mathrm{P}}_{\mathrm{cell},\max }$ increased from 1.2 to 1.3 W.

PV Cooler Model	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l},\mathbf{m}\mathbf{a}\mathbf{x}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{P}\mathbf{V}\mathbf{E}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E}}$	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E},\mathbf{m}\mathbf{i}\mathbf{n}}$	Remarks
A	1.30	0.90	200.00	160.00	3.00	19.00	1.16	0.69	Not cost-effective
B	1.30	0.90	200.00	170.00	3.00	21.00	1.10	0.69	Not cost-effective
C	1.30	0.90	200.00	200.00	3.00	24.00	0.94	0.69	Cost-effective
D	1.30	0.90	200.00	210.00	3.00	27.00	0.90	0.69	Cost-effective
E	1.30	0.90	200.00	230.00	3.00	30.00	0.83	0.69	Cost-effective

, the new value is 1.3 W. While the ${\mathrm{P}}_{\mathrm{PVE}}$, the number of solar cells available in the PV that has a cooler, n, the cost of one watt of PV power, the PV cooler manufacturing cost, and ${\mathrm{P}}_{\mathrm{cell}}$ values are unchanged. Based on Equation (2), the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value is 0.69. Now, if ${\mathrm{P}}_{\mathrm{cell},\max }$ is decreased to 1.15 W, the new ${\mathrm{F}}_{\mathrm{MCE},\min }$ is 0.78, as shown in

Table 13. Examples to compare different PV cooling techniques in terms of ${\mathrm{F}}_{\mathrm{MCE},\min }$ when ${\mathrm{P}}_{\mathrm{cell},\max }$ decreased from 1.2 to 1.15 W.

PV Cooler Model	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l},\mathbf{m}\mathbf{a}\mathbf{x}},\mathbf{W}$	${\mathbf{P}}_{\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l}},\mathbf{W}$	Number of Solar Cells in a PV with a Cooler, n	${\mathbf{P}}_{\mathbf{P}\mathbf{V}\mathbf{E}},\mathbf{W}$	Cost of One Watt of PV Power, MYR	Cost of PV Cooling Technique, MYR	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E}}$	${\mathbf{F}}_{\mathbf{M}\mathbf{C}\mathbf{E},\mathbf{m}\mathbf{i}\mathbf{n}}$	Remarks
A	1.15	0.90	200.00	172.53	3.00	19.00	1.08	0.78	Not cost-effective
B	1.15	0.90	200.00	187.00	3.00	21.00	1.00	0.78	Neutral
C	1.15	0.90	200.00	208.88	3.00	24.00	0.90	0.78	Cost-effective
D	1.15	0.90	200.00	217.24	3.00	27.00	0.87	0.78	Cost-effective
E	1.15	0.90	200.00	237.50	3.00	30.00	0.80	0.78	Cost-effective

. It is seen there is an inverse proportional relationship between the ${\mathrm{P}}_{\mathrm{cell},\max }$ and the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value. As the ${\mathrm{P}}_{\mathrm{cell},\max }$ decreases, the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value increases. It is noted that the ${\mathrm{P}}_{\mathrm{cell},\max }$ will change the ${\mathrm{F}}_{\mathrm{MCE},\min }$ value.

4.7. Comparison between Existing and Current Work

In this section, a comparison between the existing and current work is summarized as shown in

Table 14. Comparison between previous and current studies.

Study	Is There a Detailed Analysis for Equations (1) and (2)?	Is There a Direct Recommendation on the Parameters That Can Improve and Degrade the Performance of PV Cooler?
Ref. [34]	No	No
Current study	Yes	Yes

. It is seen that the existing method does not include a detailed analysis of the parameters affecting the ${\mathrm{F}}_{\mathrm{MCE}}$ and ${\mathrm{F}}_{\mathrm{MCE},\min }$ which need to be considered during the PV enhancer designing stage for the purpose of improving the PV enhancer’s performance. These parameters are ${\mathrm{P}}_{\mathrm{cell}},$ n, Z, Y, ${\mathrm{P}}_{\mathrm{PVE}}$, and ${\mathrm{P}}_{\mathrm{cell},\max }$. It is shown that ${\mathrm{P}}_{\mathrm{PVE}}$ and Y have an inverse proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}$. On the other hand, ${\mathrm{P}}_{\mathrm{cell}}$, n, and Z have a proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}.$ It could be stated that the ${\mathrm{P}}_{\mathrm{PVE}}$ and Z should be kept high for better PV enhancer performance. Conversely, ${\mathrm{P}}_{\mathrm{cell}}$, n, and Z values should be minimized to ensure optimum performance. In addition, the analysis on ${\mathrm{F}}_{\mathrm{MCE},\min }$ is illustrated as well. It is shown that ${\mathrm{P}}_{\mathrm{cell}}$ and ${\mathrm{P}}_{\mathrm{cell},\max }$ have proportional and inverse proportional relationships with ${\mathrm{F}}_{\mathrm{MCE},\min }$, respectively. It is shown that the value of ${\mathrm{F}}_{\mathrm{MCE},\min }$ is the minimum value of the ${\mathrm{F}}_{\mathrm{MCE}}$ that determines the optimum performance of the PV enhancer.

5. Conclusions

In this paper, a detailed analysis on the modified economic method (${\mathrm{F}}_{\mathrm{MCE}}$) for assessing the performance of PV-enhancing techniques is conducted. Examples are given to demonstrate the analysis of the ${\mathrm{F}}_{\mathrm{MCE}}$ and ${\mathrm{F}}_{\mathrm{MCE},\min }.$ It is shown that there are six important parameters that control the value of the ${\mathrm{F}}_{\mathrm{MCE}}$ which are the following: the power output from an individual solar cell without any enhancement $\left({\mathrm{P}}_{\mathrm{cell}}\right),$ the number of solar cells available in the PV that has an enhancer (n), the cost of manufacturing of the PV cooler (Z), the one-watt cost of PV power (Y), the output power and the maximum power from the PV with an enhancer (${\mathrm{P}}_{\mathrm{PVE}}$), and the PV power at standard test conditions (${\mathrm{P}}_{\mathrm{cell},\max })$. It is shown that ${\mathrm{P}}_{\mathrm{cell}}$, n, and Z have a proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}$. As these parameters increase, the ${\mathrm{F}}_{\mathrm{MCE}}$ increases, leading to poor PV cooler performance. On the other hand, ${\mathrm{P}}_{\mathrm{PVE}}$ and Y have an inverse proportional relationship with the ${\mathrm{F}}_{\mathrm{MCE}}$. As ${\mathrm{P}}_{\mathrm{PVE}}$ and Y increase, the ${\mathrm{F}}_{\mathrm{MCE}}$ decreases, leading to better PV cooler performance. It is also noted that ${\mathrm{P}}_{\mathrm{cell},\max }$ has an inverse proportional relationship with the minimum value of ${\mathrm{F}}_{\mathrm{MCE}}$ (${\mathrm{F}}_{\mathrm{MCE},\min })$. As ${\mathrm{P}}_{\mathrm{cell},\max }$ increases, ${\mathrm{F}}_{\mathrm{MCE},\min }$ decreases and vice versa. In conclusion, the economic method shows potential for application by designers and manufacturers of PV enhancers.