The Construction of a Mock-Up Test Building and a Statistical Analysis of the Data Acquired to Evaluate the Power Generation Performance of Photovoltaic Modules ^†

Abstract

Traditionally, studies on the power generation performance analysis of the photovoltaic (PV) modules used in building-integrated PV (BIPV) systems have been based on computer simulations and actual experiments with constraints, resulting in the results being inaccurate and limited. This paper proposes a two-step analysis method that results in a more versatile and reliable means of analysis. The steps are: (1) construction of a mock-up test building in the form of BIPV systems and the collection of a massive amount of operational data for one year; and (2) a statistical analysis of the acquired data using Minitab software (Version: 17, Manufacturer: Minitab Inc., State College, PA, USA) to examine the power generation performance. The constructed BIPV mock-up applies design elements such as material types (c-Si and a-Si) and various directions and angles for different module installations. Prior to the analysis, the reliability of the large database (DB) constructed from the acquired data is statistically validated. Then, from the statistical correlation analysis of the DB, several plots that visualize the performance characteristics governed by design elements, including contour plots that show the region of higher performance, are generated. Further, a regression model equation for power generation performance is derived and verified. The results of this study will be useful in determining whether a BIPV system should be adopted in a building’s architectural design and, subsequently, selecting design element values for an actual BIPV system.

1. Introduction

Renewable energy is the world’s fastest-growing source of energy, with an average increase of 2.6% per year [1]. Photovoltaic (PV) technology is an elegant technology that is available for the efficient use of solar power [2]. In particular, building-integrated photovoltaic (BIPV) systems are integrated into building systems to satisfy building functions and solar power functions [3]. According to the International Energy Agency (IEA), the total installed capacity for PV crossed the 500 GW mark in 2018 [4] and the energy consumption of buildings is approximately 45% higher now than it was in 1990. The energy consumption of the building sector has decreased by 1.3% per year since 2010, but electricity consumption has increased by 2.5% per year [5]. A BIPV system must simultaneously satisfy the requirements of building functions and photovoltaic power generation functions [6,7]. These requirements must be applied during the design stage of the BIPV system, where design factors such as the external environment, the aesthetic design, building performance, photovoltaic power generation performance, and economic efficiency are considered [8]. The basic performance of the power generation of a PV system depends on the irradiance, solar spectrum, module temperature and electrical performance of the PV cell [9]. A past study reviewed the proposed methods for reducing the prediction error of the single diode method, which is mainly used in the performance prediction of PV systems [10]. Photovoltaic power performance, in particular, has the most significant effect on the improvement of economic efficiency and is the most crucial factor in determining the direction of architectural design [11,12].

Currently, BIPV system design utilizes the results of analyses of photovoltaic power generation performance and economic efficiency through simple simulations [10,11,12,13,14] and actual experiments [15,16,17] only for a limited number of installation directions and angles. However, an accurate data analysis of PV power generation, building performance, and the substitution effect of existing building materials (replacement cost) at the place where the actual BIPV system is installed has not been carried out, and the results are not reflected in the design stage [18]. Contractors and designers have not been able to make rational decisions about whether to apply a BIPV system. Even when such a decision is made, the selection of installation types and economic evaluations have to be carried out at the design stage.

To rectify this problem, in this paper, we propose a means of designing and constructing a mock-up test building to simulate an actual BIPV site where the power generation performance is affected by a set of design elements such as material type, installation direction, and angle. These design elements significantly affect the photovoltaic power generation performance of BIPV systems. In this study, the effects were researched based on a statistical analysis of the data acquired while the mock-up was in operation [19]. Specifically, the design elements adopted in the mock-up design were as follows: material types, crystalline silicon (c-Si), and amorphous silicon (a-Si) of a thin-film type; installation directions of west, southwest, south, southeast, and east; and installation angle values of 90°, 75°, 30°, 15°, and 3°. To analyze the effects of the selected design elements on power generation performance, we collected operational data for one year. The reliability of the collected data was then analyzed statistically to validate the subsequent analysis of power generation performance. Further, the data were applied to statistically analyze the effects of design elements on power generation performance. These design elements were revealed to affect the power generation performance independent of each other. In addition, the analysis results identified the region of the highest power generation performance of BIPV systems to be centered around (south, ±30°) in both c-Si and a-Si. The results of this study will be useful in determining whether a BIPV system should be adopted in a building’s architectural design and how design element values should be selected for an actual BIPV design. An earlier version of this study was presented at a conference. This paper is based on the improved results obtained from a significant expansion of that study [20].

This paper is organized as follows: Section 1 describes the necessity and research trends in the analysis of power generation performance. Section 2 discusses the problems, research goals, and research methods through an analysis of previous research on BIPV systems. Section 3 presents the design, construction, and test methods for the BIPV mock-up test building. Section 4 outlines the analysis conducted of the solar power generation performance using the data acquired from the mock-up. Conclusions are given in Section 5.

2. Related Work

2.1. Characterization of the Design Elements Used in BIPV Design and Power Generation Performance Analysis

Through an analysis of requirements in the design phase of the BIPV system, the BIPV design process and tasks were defined. A set of design elements was identified in the design phase of the BIPV system, and appropriate values are presented in [11,12]. In other works, the solar power generation performance and economic efficiency of the BIPV system were investigated via simulation. Specifically, the effects of BIPV design elements, such as the solar radiation amount, PV module type, installation angle, and installation direction, were investigated through simulation. In order to maximize the performance of the power generation of the BIPV systems installed in buildings, we performed an optimal design, sizing, and operational performance analysis of PV systems [21]. In addition, an experimental demonstration under limited conditions was performed for the same purpose, and an analysis of the difference between the performance simulation and experimental demonstration was conducted [22]. However, the reliability of the data used in these studies was not adequately examined, and the verification range of the design elements was limited. Consequently, the results of the power generation performance analysis for various types of BIPV systems were found to be erroneous [18].

2.2. Reliability Validation of the Data Used for the Power Generation Performance Analysis

In the design of a BIPV system, sunlight radiation data have a significant impact on power generation performance, and, thus, a validity analysis of the data is crucial. Paul et al. [23] adopted a statistical method to ensure the data validity of the received solar radiation and identified several principal design elements from the designers’ point of view. Validation of the solar insolation data at the BIPV system’s prospective installation site was achieved using the descriptive statistical analysis function of Minitab, which is a statistical analysis software tool [24]. The validity analysis was limited to the solar insolation data, without considering design elements such as the actual PV module types, installation directions, and installation angles. Also, validation of the power generation performance for the design elements was not performed.

For BIPV, the main design elements are influenced by architectural design (such as direction and location) in contrast to conventional solar systems because PVs are integrated into the building [25,26]. Therefore, the installation has various associated directions and angles, and thus, the characteristics of solar irradiance and photovoltaic power generation performance vary depending on the installation direction and angle. To date, however, only simulation analysis results through computer simulation for various types of installation have been used as the basis for judgment, and no empirical data analysis has been conducted. For a reasonable judgment to be made at the BIPV design and decision stage, the power generation performance needs to be analyzed for each design element.

2.3. Problem Definition

In the design phase of a BIPV system, solar power performance is a significant factor in economic analysis and has a significant influence on the decisions made by decision-makers and clients [27,28]. However, to date, analyses of the solar power generation performance of the BIPV system and its reflection at the design stage have not considered the following points:

(1)

Problems exist such as the inaccuracy of power generation performance analysis and insufficient analysis of the interaction between different design elements. Moreover, the simulation and experimental demonstration adopted for the analysis are performed in a limited range of the design element values. As such, they do not provide an accurate basis for decision-making about the applicability and associated design of BIPV systems at the decision-making stage.

(2)

The validity of the data acquired from experiments and used for the analysis of power generation performance has not been examined.

(3)

An impact analysis of the design elements (module type, installation direction, and installation angle) that affect the power generation performance of the BIPV system has not been performed quantitatively; consequently, BIPV systems are not designed to maximize solar power performance.

Considering the above points, we conducted this study to develop a more versatile and reliable method for the analysis of the power generation performance of BIPV systems. To this end, a two-step approach was formulated: (1) A mock-up test building was constructed to collect sufficient data to ensure better reliability of data, and (2) the data acquired from the mock-up were analyzed statistically for a power generation performance analysis. To achieve more realistic and diverse experiments, we designed and constructed a mock-up test building that extensively incorporates various design element values. Throughout the operation of the mock-up over a year, a large amount of reliable data became available. The acquired data were first statistically analyzed to ascertain their validity. Then, photovoltaic power generation performance was examined by statistically analyzing the data in terms of solar radiation and power generation for different values of the design elements.

3. The Design and Construction of a Mock-Up Test Building for BIPV Systems

3.1. The Preliminary Performance Test of PV Modules in the Laboratory

Prior to the design of a mock-up, a preliminary laboratory test of the PV modules to be used was conducted. These results provided reference data for comparing the array configuration and power generation performance at the design stage of the mock-up test building. The PV modules were of two material types, viz., c-Si and a-Si of a thin-film type. The characteristics of the PV modules are summarized in

Table 1. Characteristics of the photovoltaic (PV) modules used.

Classification	c-Si Module	a-Si Module
Type	Glass to Glass	Glass to Glass
Size	1100 × 1300 mm	1100 × 1300 mm
Transmittance	10%	10%
Power	161 W	82 W
Cell Block Diagram

.

The power generation performance of the PV modules using simulated light sources was measured under the international standard for solar energy IEC 61215 (c-Si solar cell) and IEC 61646 (thin-film-type a-Si solar cell) using a maximum power measurement device configured as in Figure 1 [29,30]. The measurement procedures followed Section 10.2 of IEC 61215 and Section 10.2 of IEC 61646 for c-Si and a-Si modules, respectively. The power generation performance of the PV modules is presented in

Table 2. Characteristics of the electric power output of the PV modules (Test conditions: cell temperature, 25 °C; wind speed, below 1 m/s; irradiation, class AAA condition).

(a) c-Si.
Insolation [W/m2]	Pm [W]	Isc [A]	Voc [V]	Vpm [V]	Imp [A]	FF
200	30.95	1.62	24.02	20.37	1.52	0.80
400	64.11	3.23	25.07	20.89	3.07	0.79
600	96.89	4.84	25.59	20.97	4.62	0.78
800	128.97	6.45	25.95	20.94	6.16	0.77
1000	160.21	8.05	26.21	20.83	7.69	0.76
(b) a-Si.
Insolation [W/m2]	Pm [W]	Isc [A]	Voc [V]	Vpm [V]	Imp [A]	FF
200	10.71	0.28	94.36	58.02	0.18	0.41
400	28.13	0.55	112.43	74.96	0.38	0.46
600	45.87	0.80	119.02	80.30	0.57	0.48
800	63.84	1.06	123.40	83.10	0.77	0.49
1000	81.61	1.31	126.48	84.32	0.97	0.49

. At the reference photometric value of 1000 W/m², the c-Si modules generated a voltage (Voc) of 26.21 V, a current (Isc) of 8.05 A, and a maximum power (Pm) of 160.21 W, whereas the a-Si modules exhibited a voltage of 126.48 V, a current of 1.31 A, and a maximum power of 81.61 W. Therefore, the measured power values for the PV modules were reduced by only 0.1% over the maximum rated power of 161 W and 82 W for c-Si and thin-film a-Si modules, respectively. Consequently, the power generation performance of the PV modules to be used in the construction of the mock-up test building can be considered acceptable according to the results of the international standard IEC-based tests.

3.2. Design and Construction of a Mock-Up Test Building

In this study, power generation performance was evaluated using the operational data collected from the mock-up. To achieve this, we incorporated various design element values in the mock-up design. Even if the PV modules are installed in the same floor area, there is a difference in power generation performance depending on the installation direction and installation angle. Therefore, the mock-up test building for the BIPV system required a design that would allow PV modules to have different directions and angles, considering the applicability of various installation types. Further, the mock-up was designed to build a database (DB) quickly by capturing the data representing both power generation performance and external environmental conditions, including radiation, temperature, and humidity.

One of the principal design elements reflected in the mock-up building was the installation direction of the PV modules. We selected five installation direction: west, south, southeast, southwest, and east; the northward direction was not selected because the solar irradiance significantly decreased there. Thus, the direction of south was the axis of symmetry. On the other hand, typical architectural forms were considered for the selection of the installation angles. To reflect a curtain wall, three angles, 90°, 75°, and 30°, were chosen, while two angles, 15° and 3°, were chosen for the roof type. The inside of the mock-up building was designed to maintain 25 degrees Celsius continuously and not affect the PV performance results. One hundred and twenty PV modules were installed in the mock-up test building. Sixty crystal silicon (c-Si) modules and 60 thin-film silicon (a-Si) modules were installed in the same installation direction and angle so that the power generation performance of the two PV module types could be compared. By reflecting on the discussion of the design requirements of BIPV mock-up, we determined the design specifications. The results are summarized in

Table 3. The design specifications for a building-integrated PV (BIPV) mock-up test building.

Design Factors		Values
Construction Size		Floor area 238 m2
Architectural	Integration	Curtain wall type
	Directions	West, southwest, south, southeast, east
	Angles	90°, 75°, 30°, 15°, 3°
Electrical		Power generation, power consumption, etc.
Environmental		Solar radiation, temperature, etc.
Monitoring Method		Maximum power point tracking (MPPT) method using an electronic load

.

Based on the developed design specifications, we constructed a mock-up building at the outdoor test center of the Korea Conformity Laboratories (KCL), which is located in Seosan City (latitude 36.4°, longitude 126.3°), Chungcheongnam-do, Republic of Korea.

Figure 2 shows the model view and the aerial photo of the constructed mock-up test building. Figure 2a depicts the installation directions and angles listed in Table 3, and south direction therein is the opposite of the magnetic north. The analysis period extended for a total of 365 days from 1 January 2017 to 31 December 2017, and, in order to reduce the efficiency loss of the PV modules, a trial run was carried out for 3 months.

3.3. Measurement System Setup for Power Generation Data and Environmental Conditions Acquisition

The monitoring and measurement methods for obtaining the data are depicted in Figure 3. The setup was configured to increase accuracy by adopting the maximum power point tracking (MPPT) method using an electronic load. It is also possible to switch the unit on for 15 min and save data on the power generation performance (maximum power generation, module temperature, current-voltage curve, etc.) and external environment (solar radiation amount, air temperature, wind speed, etc.). Individual inverters are connected in each direction, as shown in Figure 3, and at each angle by a row string.

The PV modules are designed to be connected in series, so while one module is being testing, the other modules are not affected by performance (increased temperature) because individual MPPT function works by each direction and angle.

This series connection of many PV panels that were exposed to different solar irradiance levels may cause, in some of the panels, to have higher module temperatures that can lead to some errors in the measured temperature and PV power values. However, since the data were collected separately for each individual PV panel, the errors were largely reduced. In addition, small module temperature increases do not cause large decreases in measured power generation levels.

In Figure 3, the solid line connected to #N represents the configuration in which data are obtained through a measurement, and the solid line connected to the remaining modules is connected to the inverter to produce power. The dotted line shows that the inverter is not connected to the main equipment (inverter, switching controller, electrical load) while it is being switched. The measurement results of each group can be stored in a server and integrated later with weather data, thereby creating an integrated DB. On the other hand, to measure the influence of external and internal environmental factors that may affect power generation performance, a series of sensors was installed for each type of PV module, installation direction, and angle, as shown in Figure 4.

The sensors and equipment used for the measurement are shown in

Table 4. Sensor and equipment specifications used to measure irradiance and PV temperature.

Measurement Item	Equipment (Manufacturer)	Specifications
Irradiance	SMP11 (Kipp and Zonen)	Classification to ISO 9060: Secondary standard Spectral range: from 285 nm to 3000 nm Output range: from −200 to 2000 W/m2 Temperature dependence of sensitivity: <1%
Temperature	T-type thermocouple	Temperature range: from −270 °C to 370 °C Accuracy: ±1.0 °C
Data logger	GL840 (Graphtec)	Input voltage range: from 20 mV to 100 V Accuracy: ±1.0% voltage, ±1.55 °C temperature

. Pyranometers were installed in the same location as the PV modules, and the leading wires of the temperature sensor were shielded from solar radiation.

4. Statistical Analysis of the Operational Data Acquired from the BIPV Mock-Up

The operation of the mock-up test building began following its construction after a trial run for 3 months. From that point onwards, data were collected from the power generation and environment measurement setup sensors for one year, as described in Section 3. Statistical analysis of the measured data over a total of 312 days was performed; data with measurement errors due to power failure and system malfunction during the period were excluded. Accordingly, a large DB was generated. To verify the validity of the data acquired in large quantities, we performed a data analysis of the external and internal environmental factors using the analysis of variance (ANOVA) method, which can be performed using a function provided by Minitab, a typical data analysis program [31]. Meanwhile, a statistical correlation analysis and significant difference analysis of ANOVA were performed to analyze the data validity and the interrelationship of the design elements that affect power generation performance. For the correlation analysis, a strong correlation was confirmed when the Pearson correlation coefficient, usually denoted R², was 0.9 or more [32]. In the significant difference analysis using ANOVA, the mean value of each group was tested by analyzing the significance p-value based on a 95% confidence level [33].

4.1. Validation of Acquired Data Via Statistical Methods

A large amount of data was collected during the operation of the mock-up test building. During data acquisition, there can be numerous errors due to the failure or malfunctioning of measurement sensors and equipment. Consequently, it is necessary to first examine the data’s validity before engaging in a further extensive analysis of power generation performance. For this purpose, we used the Minitab tool in the subsequent statistical analysis.

We first analyzed insolation data via a statistical analysis using Minitab. For the cases of horizontal irradiation (3°) and oblique irradiation (15°, 30°, 75°, and 90°), the data were analyzed to validate the independence, uniform distribution, and regularity (normality) of the data values using the variance analysis method of ANOVA from Minitab. Figure 5 is the result of Minitab’s normality test to verify the regularity of the insolation data for different installation angles. Normality analysis is a statistical analysis method where, if data are collected randomly in a natural state, a normal distribution is followed if there are no problems in the experimental environment. The data values collected over a year for the various installation angles (3°, 15°, 30°, 75°, and 90°) were determined to have normality because their p-values were higher than 0.05 within a confidence interval of 95%.

For the same data used in Figure 5, a Minitab ANOVA analysis was performed to examine the independence and uniform distribution of the solar insolation data. The result of comparing the dispersion of the insolation data values for different installation angles during the monitoring period (January 2017 to December 2017) is shown in Figure 6, where the significance p-value is less than 0.05 within a confidence interval of 95% (not significant), and R-sq denotes the Pearson correlation coefficient R².

On the other hand, the even distribution and independence can be checked by evaluating the pattern of the distribution of the data (Fits, Order) in the residual plot. Based on an evaluation of the distribution of data (Fits), the plot has equal distribution and independence because it does not show a continuous pattern on the x-axis. From the results of the evaluation of the distribution of the residual image (Fits), it was found that the image has equal distribution and independence because it does not show a continuous pattern on the x-axis.

We then analyzed power generation data via a statistical analysis using Minitab. For the cases of PV module types c-Si and a-Si; the installation directions east, south, south, southwest, and west; and the installation angles 3°, 15°, 30°, 75°, and 90°, the validity of the data normality, independence, and even distribution was examined using Minitab. Figure 7 shows the result of Minitab’s normality test to verify the regularity of the power generation data for different module types, installation directions, and angles. The data values were collected again for one year and found to have normality because the significance of the p-value was greater than 0.05 within a confidence interval of 95%.

Figure 8 shows the result of Minitab’s ANOVA to verify the independence and uniform distribution of power generation data values. Based on a comparison of the variance of power generation data values during the monitoring period (from January to December 2017), the significance of the p-value was found to be less than 0.05 within a confidence interval of 95% (i.e., not significant). In the meantime, by evaluating the pattern of data distribution (Fits, Order) in the residual plot, it is possible to verify the even distribution and independence. From the evaluation of the distribution of the residual image (Fits), the residual image was found to have equal distribution and independence because it does not show a continuous pattern on the x-axis.

In summary, the results of the statistical analysis of the photovoltaic power generation data and solar insolation data collected over the study year show that the data are valid and reliable for different module types, installation angles, and installation directions. The validated data are used for further analyses of photovoltaic power generation in the following subsections.

4.2. Comparison of Two Models for Solar Insolation Effect on PV Power Generation Performance

Solar insolation is known to have the most significant effect on the photovoltaic power generation performance of PV modules. To investigate the effect of solar insolation on the performance of the PV modules for various ranges of solar insolation, we measured the generated power values from the laboratory test and compared them with those of the prediction model by Sandia Lab, which is the preferred model in this domain [34].

Table 4,

Table 5. Comparison of the generated power of the PV modules between the laboratory test (measured) and the Sandia model (predicted).

	c-Si/a-Si Predicted/Measured	c-Si		a-Si
Insolation [W/m2]		Pred.	Meas.	Pred.	Meas.
200		32.65	30.95	15.20	10.71
400		65.14	64.11	30.76	28.13
600		97.26	96.89	47.00	45.87
800		128.95	128.97	63.99	63.84
1000		160.18	160.21	81.79	81.61

and Figure 9 compare the measured and the Sandia model-predicted values of power generation for the insolation range of 200–1000 W/m². From the analysis of the power generation performance in various solar insolation ranges of the c-Si module and a-Si module, it was found that the measured and predicted values tend to vary similarly. In low insolation ranges (200–600 W/m²), a noticeable difference can be seen. However, in those ranges, the power generation performance is less than the drive limit power of the inverter used in the actual BIPV system; consequently, it does not affect the power generation performance of the BIPV system significantly.

4.3. Analysis of the Correlation between the Solar Insolation and Electric Power Generation for Different Design Elements

The most significant factor affecting the power generation performance of the BIPV system is the solar insolation incident on the BIPV module. Solar insolation is also an essential factor in determining building performance (insulation performance, building energy, etc.). Analyzing the relationship between the amount of solar radiation and the amount of power generation for each design element (module type, installation angle, and installation direction) provides reference data for the BIPV building design and simulation program, and thus contributes to improving the accuracy of the design simulation.

The correlation between solar radiation and power generation was analyzed using Minitab. The Pearson correlation coefficient R² (R-sq in the plot) was used as a measure in the correlation analysis. This coefficient ranges from 0.1 to 1.0. A correlation coefficient of 1.0 indicates a perfect linear correlation, 0.7 to 1.0 denotes a high linear correlation, 0.4 to 0.7 represents a moderate linear correlation, and 0.1 to 0.4 denotes a low linear correlation.

Figure 10 is the result of the correlation between the amount of solar radiation and the amount of power generation when the installation angle and direction are 3° and west. In this case, R² has a high value of 0.996, indicating a high linear correlation. To investigate the case for other design element values, we assume the relationship between solar radiation and power generation to be a linear function, as shown in Equation (1):

$$P=aI$$

(1)

where P: Cumulative electric power generation of the BIPV system [W/m²]; I: Daily cumulative solar insolation [W/m²]; a: Influence coefficient (dimensionless).

In Figure 10, The average annual amount of insolation per unit area of Seosan in Korea, where the mock-up test site in this paper is located, is 1654 kWh/m²/year, and 312 days of annual power were generated, with 5.3 kWh/day power generation.

The influence coefficient “a” in the linear model of Equation (1) can vary depending on the different design element values. Using the DB, we estimated the influence coefficient values for various sets of design element values (module type, installation direction, and installation angle). The resulting values for the influence coefficient are summarized in

Table 6. Influence coefficient values for different design elements (BIPV module type, installation direction, and angle).

Module Type	Angle	3°	15°	30°	75°	90°
	Direction
c-Si	West	0.132	0.139	0.134	0.123	0.129
a-Si		0.070	0.081	0.080	0.051	0.050
c-Si	Southwest	0.142	0.145	0.140	0.147	0.147
a-Si		0.076	0.065	0.081	0.075	0.062
c-Si	South	0.128	0.140	0.146	0.144	0.137
a-Si		0.081	0.064	0.085	0.063	0.060
c-Si	Southeast	0.140	0.142	0.145	0.133	0.129
a-Si		0.050	0.069	0.079	0.057	0.061
c-Si	East	0.140	0.144	0.139	0.138	0.138
a-Si		0.089	0.060	0.081	0.058	0.048

.

Other results of the influence coefficient analysis for different design elements (module type, installation angle, and installation direction) of the BIPV system are shown in Figure 11. For different module types (c-Si and a-Si), the analysis of coefficient “a” using the boxplot shows that the value of “a” for the c-Si module is 2.5 times larger than that for the a-Si module in Figure 11. This means that, for the same solar insolation, the c-Si module generates 2.5 times more power than the a-Si module.

4.4. Analysis of the Effect of Design Elements on Power Generation Performance

We also needed to examine how each design element (module type, installation direction, and installation angle) affects the power generation performance of the BIPV system by analyzing the data collected during the one year (January 1 to December 31 of 2017) while the mock-up test building was in operation. We first analyzed how the cumulative solar insolation and cumulative power generation changed monthly in the southern direction, which generally shows excellent power generation performance. The results are shown in Figure 12 and Figure 13. In contrast, the influence of the design elements on the cumulative annual power generation was analyzed through a main effects and interaction analysis using Minitab, with the results shown in Figure 14. Then, a regression analysis was carried out to derive the relational equation that describes how the design elements affect the power generation performance. The results are shown in Figure 15. Conversely, a contour plot analysis was performed to investigate the peculiar region specified by the installation angles and directions with high power generation performance. Figure 15a,b shows the results for the c-Si and a-Si modules, respectively. Table 6,

Table 7. Cumulative annual power generation (kWh /module) for different installation directions and angles.

Module Type	Angle	3°	15°	30°	75°	90°
	Direction
c-Si	West	86.9	85.7	89.3	53.2	49.1
a-Si		44.3	47.3	49.7	38.8	28.8
c-Si	Southwest	92.1	99.5	100.8	77.8	64.8
a-Si		45.9	46.2	50.9	40.8	33.6
c-Si	South	84.6	100.3	103.6	77.1	50.1
a-Si		49.5	51.9	57.1	36.4	32.3
c-Si	Southeast	95.8	100.2	104.2	78.7	64.5
a-Si		38.6	51.5	52.0	31.3	32.6
c-Si	East	89.8	91.5	92.6	60.2	64.8
a-Si		36.1	46.3	46.8	34.2	31.2

shows the variation of the annual cumulative power generation for various design element values.

Hereafter, a more detailed look at the results of the analysis is given. The mock-up test building is located in the City of Seosan, Chungnam Province (in the middle of South Korea). Figure 12 shows how the monthly cumulative solar insolation changes based on the installation direction to the south. Dividing the year into seasons shows the highest amount of solar insolation in spring (March to May), and the order of the rest of the seasons is autumn (September to November), summer (June to August), and winter (December to February).

Figure 13 shows how the monthly cumulative power generation changes for different module types (c-Si, a-Si) and installation angles (3°, 30°, and 90°) based on a south installation direction. Overall, there is a tendency similar to the monthly cumulative insolation. The c-Si module shows higher power generation performance than the a-Si module, and the installation angle shows high power generation performance at an installation angle of 30°.

Figure 14 shows the results of the investigation of the effects of the design elements on the cumulative power generation over the one-year measurement period (January 2017 to December 2017) using Minitab’s main effect analysis. It can be seen from Figure 14 that the BIPV c-Si module showed higher power generation performance than the a-Si module. Moreover, for higher performance, the order of installation angles is 30°, 15°, 3°, 75°, and 90°, and that of the installation directions is south, southwest, and southeast. For east and west, the power generation performance is relatively low.

A different view of the effects of the design elements on the cumulative power generation over the one year is presented in the form of contour plots in Figure 15. Figure 15a,b shows the results of the contour plot analysis of the cumulative power generation for different installation angles and directions with the c-Si and a-Si modules. It can be seen from Figure 15a that the c-Si case has the highest power generation performance around the south in the installation directions and around 30° (between 15° and 45°) in the installation angles. For the installation directions of west and east, the power generation performance sharply decreases as the installation angle increases after 45°. It can also be seen that the lowest power generation performance occurs at installation angles higher than 70° in the west.

Comparing the contour plots in Figure 15a,b shows that the two cases of the c-Si and a-Si modules have similar patterns. Notably, the points of the highest performance are seen around south, 30° in both cases. Nonetheless, these points have distinctions: (1) Overall, the performance of the c-Si case is almost twice that of the a-Si case; (2) for the region of the highest power generation performance, the a-Si case is much narrower than the c-Si case; and (3) the extreme points of the lowest power generation performance are west, 90° and east, 90° for the c-Si and a-Si cases, respectively.

We next discuss the possibility of deriving the regression model for the cumulative power generation over one year. First, we investigated the interactions among the design elements by using an interaction plot analysis of Minitab. According to the analysis results, the design elements of different module types, installation angles, and directions were found to affect the cumulative power generation independently. Then, assuming an equation of a polynomial form for the annual cumulative power generation, we performed a Minitab regression analysis. The result is presented with a set of meaningful terms with a limited order of three in Figure 16, and the regression model is defined in Equation (2) for further discussion.

$$\begin{array}{cc}\hfill P_g\left(P_m,A_i,D_i\right)=& -7849+581.1P_m+394.5D_i+555A_i-2.53{D_i}^2-17.38{A_i}^2\hfill \\ & +0.00311{D_i}^3+0.0831{A_i}^3\hfill \end{array}$$

(2)

where: $P_g$: Output value for the annually generated power; $P_m$: Input value for the power of the installed module; $A_i$: Input value for the installation angle and $D_i$: Input value for the installation direction.

Equation (2) introduces one output variable, $P_g,$and three input variables, $P_m, A_i, \mathrm{and} D_i$, with all four defined as dimensionless here for the sake of numerical calculation. However, the actual output values for $P_g$ have the unit, Wh. The other three input variables are assumed to have no physical meaning and are defined as in

Table 8. Mapping table to select the input values to be used in Equation (2) for different design elements.

BIPV Module Type		Installation Direction		Installation Angle
c-Si or a-Si	Dimensionless Value for Pm	Physical Direction	Dimensionless Value for Di	Physical Angle (°)	Dimensionless Value for Ai
161 W (c-Si)	161	West	0	3°	3
		Southwest	45	15°	15
		South	90	30°	30
82 W (a-Si)	82	Southeast	135	75°	75
		East	180	90°	90

.

To evaluate the regression model of Equation (2), we randomly selected a set of paired values of the installation angle and direction for the c-Si and a-Si modules, as shown in Table 8. For the selected set of the design elements, we estimated the measured values of the annual generated power from the DB. We also calculated the regression equation for the same set of design elements. To quantitatively evaluate the differences between the two values, the errors were computed as error = calculated value − measured value. Then, squared errors and the sum of the squared errors in the underlying group were calculated and normalized by the corresponding measured value and the sum of the squared measured values. The result is presented in

Table 9. Comparison of the annual generated power values for the cases measured from the mock-up and predicted by Equation (2).

BIPV Module Type		Selected Installation Direction		Selected Installation Angle	Annual Generated Power [kWh]		Normalized Error	Normalized Sum of Squared Errors
Pm		Direction	Di	Ai	Measured	Calculated	(%)	(%)	(%)
c-Si	161	West	0	3	86.95	87.22	0.31	0.02	0.04
		South	90	15	106.29	107.68	1.31
		Southwest	45	30	100.82	101.87	1.04
		Southeast	135	75	78.69	79.43	0.94
		East	180	90	64.77	62.64	−3.30
a-Si	82	Southwest	45	3	52.60	54.22	3.09	0.12
		West	0	15	46.08	44.50	−3.44
		South	90	30	58.10	60.33	3.84
		Southeast	135	75	32.57	33.52	2.92
		West	0	90	9.33	9.55	2.39

. The modeling accuracy (Normalized Sum of Squared Errors) was less than 1%, and thus appeared to be acceptable for the data provided.

Thus far, we have statistically analyzed the influence of each design element on the power generation performance and the relationship between the power generation performance and each design element using the data obtained through the mock-up test building that simulates an actual BIPV site in operation. Accordingly, we identified the design elements and the values that need to be addressed in the BIPV system design. This can provide improved reference data for the computer simulation programs used in existing designs. The results of this study can be used effectively in the design stage for determining whether a BIPV system should be applied and the subsequent detailed design.

5. Conclusions

In this study, to improve the existing analyses of the power generation performance of BIPV systems, we designed and constructed a BIPV mock-up test building that can simulate actual BIPV systems. Through this mock-up, a large DB was built by collecting operational data for one year. The constructed DB was then used as the basis for subsequent statistical analyses of the power generation performance of BIPV systems. The main results of this paper are as follows:

(1)

The constructed BIPV mock-up test building can cover a set of design element values, including from different module types (c-Si and a-Si), installation angles (90°, 75°, 30°, 15°, and 3°), and installation directions (west, southwest, south, southeast, and east). The architecture can accommodate future advanced designs for PV modules.

(2)

A large DB was generated by collecting the power generation and solar insolation data together with the associated environmental data for one year through the monitoring system built in the mock-up. The reliability of the acquired data was found to have normality, independence, and even distribution, with a significant p-value higher than 0.05 within a confidence interval of 95% from the analysis using Minitab.

(3)

The influence coefficient that linearly relates the solar insolation to power generation performance was estimated from the data measured by the correlation analysis. The influence coefficient values of the c-Si modules were 2.5 times larger than those of the thin-film a-Si modules.

(4)

The effects of the design elements on the annual cumulative power generation were analyzed. The two-dimensional (2D) contour plots with depths expressing the generated power and the axes defined by the pair of installation directions and angles were obtained. The plots for the cases of the c-Si and a-Si modules have similar patterns and show that the highest performance is concentrated around south, 30° in both cases. However, these plots have a few distinctions: (1) The performance of the c-Si case is almost twice that of the a-Si case; (2) the region of the highest power generation performance for the a-Si case is narrower than that of the c-Si case; and (3) the power generation performance decreases rapidly as the direction and angle approach west, 90° and east, 90° for the c-Si and a-Si cases, respectively.

(5)

After the design elements were found to independently affect the performance using the interaction plot analysis of Minitab, a regression model equation for the performance was derived. The modeling error (normalized sum of squared errors) was less than 1% and thus appeared to be acceptable.

In conclusion, the region of the highest power generation performance of the BIPV systems is centered around south, 30° in both c-Si and s-Si. However, the performance of the BIPV systems for the c-Si case was twice as high, and the region for higher performance was broader than that of the a-Si case. On the other hand, the constructed BIPV mock-up building can be easily modified to accommodate the technological advances in future PV module designs. The results analyzed in this paper can be used as primary data for power generation performance analysis, shading analysis, and economic analysis during the design stage of BIPV systems. Also, they can provide reference data when designers and clients need to make decisions on whether BIPV systems should be applied to new building designs.