Performance evaluation of building integrated photovoltaic system arrays (SP, TT, QT, and TCT) to improve maximum power with low mismatch loss under partial shading

Abstract

Global electricity demand is increasing with the rising population and rapid urbanization. Building Integrated photovoltaic (BIPV) system is a new method of renewable energy generation where solar photovoltaic (PV) modules are integrated into the building surfaces such as façade, shades, windows, roofs, and tiles. BIPV systems reduce the urban energy demand. Utilization of vertical surfaces makes the BIPV system a preferable choice where land scarcity affects the implementation of large PV systems. The economic viability depends on the maximum power generated by the BIPV array. In urban environments, the BIPV arrays experience severe partial shading conditions (PSCs). The PSCs cause mismatch losses, reducing the global maximum power of the BIPV array and efficiency. Fixed array configurations such as series-parallel (SP), total-cross-tied (TCT), triple-tied (TT), and quarter-tied (QT) are designed to solve this issue. The cross ties across the rows of the BIPV array improve the performance at the expense of more wiring. Researchers proposed various optimal array configurations with different shading patterns. This research attempts to generalize the design of the BIPV array configurations by considering the trade-off between wiring requirements and shading losses. The performance of SP, TT, QT, and TCT configurations under four different shading conditions is simulated with the proposed BIPV array design algorithm. A 9 × 8 BIPV array of 3.6 kW is considered. QT configuration reduces the wiring requirement by 10.45% compared to TCT and improves up to 8.43% maximum power than SP. The fill factor is improved to 48.49%, and the mismatch loss is limited to 34.10%. Therefore, QT and TCT are considered favorable configurations for BIPV array design.

Introduction

Buildings and construction activities contribute to 36% of global energy consumption (41388.9 TWh) and 37% of greenhouse gas emissions (11.7 Gton equivalent CO₂). The operational energy demand of buildings for heating, cooling, lighting, water pumping, and cooking has reached 135 Exajoule. As world economic activities have rebounded since the COVID-19 pandemic, the residential sector witnessed a 4% increase in energy consumption (United Nations Environment Programme 2022). Due to rapid urbanization between 2010 and 2020, the floor area has increased from 199.5 billion m² to 244.1 billion m². In spite of advanced construction strategies and efficient electrical appliances, the average energy consumption per unit of floor space has declined by only 25% since 2010 (IEA 2021). Climate change and extreme weather events have increased the requirement for heating, ventilation, and air-conditioning, further intensifying the electricity demand from the residential and commercial sectors. Researchers are exploring distributed renewable energy generation for the urban sector to achieve near-zero emissions over the lifetime of the buildings. Building Integrated photovoltaic (BIPV) system is widely recognized as a method of on-site clean energy generation (Sarkar et al. 2019). In the BIPV system, the photovoltaic modules are integrated into building surfaces such as roofs, walls, façade, windows, and shades, thus eliminating the need for land area for PV installation. The major components of the BIPV system include PV modules, DC converters, and connecting wires, accompanied by a battery energy storage system (BESS) for stand-alone systems or inverters for grid-connected systems. So, the generated energy can be utilized, stored, and fed to the grid.

Singh et al. (2022) identified the combination of rooftop solar and BESS as an ideal candidate among the BIPV systems applicable to India. Dobrzycki et al. (2020) proposed the application of the BIPV system in Poland for the reduction of electricity and fuel consumption due to heating. The proposed BIPV on wall cladding had an economic payback period of 11 years. Ahmadi et al. (2023) modeled the capability of BIPV systems to enhance the passive cooling of air in a building. Liu et al. (2021) presented a study on the feasibility of BIPV systems in different geographical areas with high solar irradiance. The design of BIPV systems like PV module types, module temperature, solar irradiance, orientation and tilt angle of the module, and inverter. Peng et al. (2011) discussed the BIPV system from the structural perspective and proposed a novel architectural design as a roof-mounted and wall-mounted PV system. Bándy and Rencz (2013) developed a semi-transparent BIPV module for façade and windows with an energy conversion efficiency of 6.12%. Do et al. (2017) evaluated the performance of semi-transparent PV modules on windows for residential buildings in hot and humid climate areas. The electricity generated from the BIPV-based windows has the potential to supply 12–21% of the annual electricity demand and 16–24% of the peak energy demand caused by the air-conditioning systems. By 2030, the improvement in the efficiency of BIPV modules and reduced energy consumption due to sustainable urban planning would create possibilities of nearly zero-energy buildings (nZEB). If the BIPV panel efficiency of 25% and BIPV glass efficiency of 13% is achieved, glazing in 30% of the building surface area would be sufficient to achieve energy sufficiency (Gholami et al. 2021). The sizing of the BIPV system has architectural constraints. Kumar et al. (2017) estimated rooftop PV potential considering nine types of roof area ranging from 2 to 100 m². Gopalan and Venkataraman (2015) presented affordable housing with a 500 ft² to 1200 ft² super built-up area for lower-income and middle-class groups in India. Singh and Bannerjee (2015) estimated the ratio of available area for PV generation to building footprint area for Mumbai suburban from 0.3 to 0.7 for various types of buildings.

Moreover, the efficiency of the BIPV system is severely affected by partial shading conditions (PSCs). Yadav and Mukherjee (2021) presented the cause of PSCs as nearby trees, towers, and buildings, as well as the environmental conditions such as clouds, fog, smoke, and soiling. The nonuniform irradiance conditions create an anomaly in power generation from each module, commonly called mismatch losses (Devakirubakaran et al. 2023). Moreover, the Power-Voltage (P–V) and Current-Voltage (I–V) characteristics of the partially shaded PV array have multiple local peaks that complicate the maximum power point tracking (MPPT) systems. Sarkar et al. (2021) presented a comparative study of different MPPT methods in BIPV systems under partial shading. Lyden and Haque (2019) identified the power generation at the global maximum power point (GMPP) and the corresponding voltage at GMPP from the P–V curve for static and transient PSCs, respectively.

Various researchers have proposed different fixed array configurations for mitigating the problems related to PSCs. Series parallel connections modified with crosstie connections improve the performance of maximum power point tracking systems (Narne et al. 2023). Different patterns of non-uniform irradiance conditions, such as row-wise, column-wise, frame, center, and corner PSCs, are considered for evaluating the performance of the PV system (Sarkar et al. 2019). Common performance parameters are GMPP, voltage and currents at GMPP, open circuit voltage, fill factor (FF), short circuit current, mismatch losses, and percentage efficiency. Satpathy et al. (2018) designed and compared Series-Parallel (SP), Bridge-Linked (BL), and Total-Cross-Tied (TCT) PV array configurations. The SP connection has the simplest design due to the absence of cross ties. However, the performance of the SP connection deteriorates with a greater number of shaded modules in a string. The TCT connection, in spite of higher redundancy, performs better in most cases. Bonthagorla et al. (2020) presented a 7 × 7 Triple-Tied (TT) configuration as an optimal choice for both stand-alone and grid-connected PV systems. Sarkar and Sadhu (2022a, b) proposed a 7 × 8 quarter-tied (QT) configuration and a hybrid TT configuration to reduce mismatch losses in partially shaded BIPV systems. Bonthagorla and Mikkili (2020a) reported that TCT topology generates maximum power under most PSCs except in corner and L-shaped shading patterns. Pendem et al. (2021) attribute the better performance of TCT to the highest number of cross-ties that bypass the shaded PV modules in a string. Murugesan et al. (2023) validated the superiority of TCT configuration with batteries for mismatch loss reduction and fault mitigation. However, cross-ties in each row lead to higher redundancy, electrical connections, and wiring losses (Mishra et al. 2023). Khan et al. (2020) proposed a mathematical model to calculate wiring requirements and additional ohmic losses for conventional rooftop PV configurations. Chandra Sekhar and Ramesh (2023) demonstrated a double cross-tied connection that reduces the wiring requirement without compromising the PV generation under non-uniform irradiance conditions. Several configurations are being designed and compared to each other to achieve the best performance with fewer cross-ties.

There is a lack of consensus regarding the best BIPV array configurations in the literature. Although the early research supported the superiority of TCT configuration, the concern regarding the unaccounted wiring losses and higher cable requirements is reflected in the recent works. This resulted in the proposal of numerous configurations that perform well in different shading conditions. The present work aims to develop an iterative and generalized design procedure for shadow-resilient BIPV arrays. Realistic design parameters such as spacings, module dimension, and wire gauge are incorporated to quantify the wiring requirement and system losses. The design process is demonstrated along with performance analysis of four fixed array BIPV configurations, SP, TT, QT, and TCT, regarding their electrical parameters. The salient features of this study are as follows:

1. Design of 3.6 kW_p BIPV array with four different configurations.

2. Simulation of each configuration under four critical shading patterns (Frame, Centre, Left Corner, and Left Side). Each shading pattern has six different irradiance levels.

3. Performance analysis and comparison of the configurations based on GMPP with the corresponding voltage and current, open circuit voltage and short circuit current, fill factor, percentage mismatch losses, efficiency, and wiring requirement.

4. A generalized algorithm for selecting BIPV array configuration with improved performance and reduced wiring length.

5. Analysis of additional wiring loss for currents circulating through the tie connections in partial shading conditions.

6. Building-integrated photovoltaics (BIPV) system.

A building-integrated photovoltaic (BIPV) system is an architectural innovation where PV modules are integrated into building surfaces such as windows, facades, roofs, and sunshades. The electricity generated is supplied to the grid or stored and utilized for the building alone, as shown in Fig. 1.

Fig. 1 [Images not available. See PDF.]

Block diagram of the BIPV system

BIPV enables cost offset of building materials, reduced transmission loss due to on-site electricity generation, and utilization of unused vertical and tilted surfaces. The replacement of conventional building materials with BIPV modules and the incremental cost of PV systems can be avoided (Bándy and Rencz 2013). Such benefits felicitate the growth of near-zero energy buildings and sustainable urban expansion. BIPV is regarded as one of the novel technologies for reducing CO₂ emissions in the building and construction industry, accounting for 37% of GHG emissions worldwide (IEA 2021). Another benefit is the production of electricity during peak load demand of the building. This provides an added economic advantage (Rigone and Giussani 2022). However, the economic and environmental benefits can offset the installation and maintenance cost of the BIPV system only if it operates with the maximum energy conversion efficiency. The efficiency is affected by the choice of PV modules and inverter, operating temperature, and mismatch losses in the PV array. In urban environments, mismatch losses are primarily caused due to partial shading conditions .

Partial shading conditions

Non-uniform irradiance over the BIPV array is prominent in the urban landscape. Nearby buildings, trees, towers, and the complex architecture of the BIPV surface itself lead to partial shading conditions. Soiling, fog, smoke, and clouds can also cause graded irradiance over the BIPV array (Yadav and Mukherjee 2021). The tilt angle of the PV module affects the incident solar irradiation and reduces the efficiency and power output (Mamun et al. 2022). The IEC 63092-1 classification of BIPV systems based on tilt angle and accessibility is presented in Table 1. The vertical walls (75°–90°) receive higher irradiation during sunrise and sunset, while rooftop surfaces (0°–30°) receive the highest insolation during noon (Bonomo et al. 2021).

Table 1. Variation of tilt angle for different BIPV categories

Category	Description	Tilt angle	Accessible from within the building
A	Sloping, Roof integrated	0°–75°		Yes
B	Sloping, Roof integrated	0°–75°		No
C	Non-sloping, Envelop integrated	75°–90°		Yes
D	Non-sloping, Envelop integrated	75°–90°		No
E	Externally integrated, balcony, shutter, shades, awning etc.	0°–90°		No

Environmental condition, wind load, tilt angle influences the nature of soiling on PV modules. Such effects also cause non-uniform irradiance conditions equivalent to partial shading. Geometry, irradiation, and PV array interconnection are three determining factors for optimal power generation (Acosta and Gutiérrez 2022). Researchers have proposed a few shading patterns for modeling the effect of partial shading on PV arrays. Row-wise and column-wise side shading, diagonal, random, center, and frame are common patterns used as test cases (Pendem et al. 2021).

The shaded module behaves as a reverse-biased diode, providing a high resistive path to the photocurrent generated by other unshaded modules in the string, as shown in Fig. 2 (Rodrigues et al. 2022). Therefore, the mismatch loss increases during PSCs, affecting the efficiency and power generation of PV systems (Desai and Mikkili 2022).

Fig. 2 [Images not available. See PDF.]

Shading conditions in PV arrays

Here, the currents through four PV modules are shown. Two modules are connected in series, forming a string. Two such strings are connected in parallel. As the top left PV module is shaded, the current generated by that module ($I_1$) is less than the unshaded module in the same string ($I_2$). Since these two modules are in series, the additional current has to flow through the parallel resistance of the shaded module, causing mismatch losses (Devakirubakaran et al. 2023). Bypass diodes across each module can partially mitigate this problem but cause multiple peaks in the P–V curve (Sarkar et al. 2021).

Another method includes cross-tie wires connected across modules of different strings in a row as shown in Fig. 3. A tie-connection between the middle part of two strings allows a part of $I_2$ to flow through the unshaded module 3. As a result, $I_{\mathit{Out}}$ increases, and the output power improves (Jha 2023).

Fig. 3 [Images not available. See PDF.]

PV array with tie-connections

It is necessary to identify the PV array configurations where cross-ties improve the power output. Moreover, the additional wiring requirements and corresponding ohmic losses should be estimated for maximum benefits. This study focuses on the performance investigation of four BIPV array configurations with cross-tie connections for GMPP enhancement and on reducing wiring requirements.

Research methodology

The performance investigation of fixed BIPV array configuration comprises the design of the PV array, simulation of common shading patterns, comparison of different configurations, and selection of the best array for each shading case. Achievement of the highest GMPP and lowest mismatch loss with reduced wiring requirement is the aim of BIPV array design. An algorithm for BIPV array design is proposed in Sect. 3.1.

BIPV array design algorithm

The proposed algorithm for the selection of the best BIPV array configuration is as follows.

Step 1.

Start.

Step 2.

Receive input regarding the available surface area, common shading patterns, power demand, type of modules, array dimension, and possible array configurations.

Step 3.

Choose the number of PV modules such that sum of module area is within the limit of maximum surface area, Power rating of the PV array should be more than the demand.

Step 4.

Estimate the cross-section of tie wires from the short circuit current of the PV module. Calculate wire lengths and resistances.

Step 5.

Compute additional wiring requirements from Eqs. 19 and Eq. 20.

Step 6.

Simulate different array configurations in MATLAB / Simulink. The operating temperature and irradiance are given as inputs for each module.

Step 7.

Record the power and current by varying operating voltages under different shading conditions.

Step 8.

Identify GMPP, Compute FF, mismatch loss, and efficiency from Eqs. 16–18.

Step 9.

Repeat steps 5, 6, 7, and 8 for different array configurations with the same dimension. Note the configuration with the highest GMPP in each case.

Step 10.

For a shading pattern, if the TCT configuration has the highest GMPP, note the second-highest GMPP configuration and the corresponding number of cross-ties.

Step 11.

If the second highest GMPP configuration has 1% or more improvement in GMPP compared to the lowest GMPP configuration and more than 10% reduction of wiring requirement, it is considered the best performance.

Step 12.

If any other configuration except TCT has the highest GMPP, the configuration is considered best.

Step 13.

Tabulate the best configurations against each shading condition.

Step 14.

End.

The design flow and selection of the BIPV array are described in Fig. 4.

Fig. 4 [Images not available. See PDF.]

Proposed flowchart of BIPV array design

Mathematical modelling

The single diode representation of a PV cell is illustrated in Fig. 5. The current of the PV cell ($I$) is the algebraic sum of the diode current ($I_d$) and photocurrent ($I_{\mathit{PV}}$), as shown in Eq. 1. The value of the diode current ($I_d$) is given by Eq. 2 (Oufettoul et al. 2023).

1

$$I=I_{\mathit{PV}}-I_d-\frac{V+R_{S}I}{R_P},$$

2

$$I_d=I_0\left(e^{\frac{\left(V,+,R_s,I\right)}{a{V}_t}},-,1\right),$$

Fig. 5 [Images not available. See PDF.]

The single diode model of a PV cell

Here $I_{\mathit{PV}}$ is the current generated due to photoelectric effect, $I_d$ is the diode current, $I_0$ is the diode saturation current flowing in the reverse direction due to thermally generated carriers. Here, $a$ is the degree of ideality of the diode, a constant between 1 and 1.5. Here, $V$ is the voltage across the cell, and $V_t$ is the thermal voltage given by Eq. 3.

3

$$V_t=\frac{\mathit{kT}}{q},$$ where $k$ is the Boltzmann constant 1.38 × 10⁻²³ J/K, $q$ is the charge of an electron (1.602 × 10⁻¹⁹ C), and T is the temperature in kelvin. The photovoltaic current as a function of irradiance ($L$) and temperature ($T_c$) is given by Eq. 4. The difference between cell temperature ($T_c$) and reference temperature ($T_{\mathit{ref}}$) is termed as${\Delta }_T$ in Eq. 5

4

$$I_{\mathit{PV}}=(I_{\mathit{PVref}}+K_I{\Delta }_T)\frac{L}{L_{\mathit{ref}}},$$

5

$${\Delta }_T=T_c-T_{\mathit{ref}},$$

Here $I_{\mathit{PVref}}$ is the nominal value of photocurrent at standard temperature condition (STC) and standard irradiation$L_{\mathit{ref}}$. The temperature dependence of diode saturation current ($I_0$) at the cell temperature ($T_c$) is shown in Eq. 6

6

$$I_0\left(T\right)=I_{0_{\mathit{ref}}}{\left(\frac{T_c}{T_{\mathit{ref}}}\right)}^3{e}^{\frac{q{E}_g}{\mathit{ak}}\left(\frac{1}{T_{\mathit{ref}}},-,\frac{1}{T_c}\right)},$$

Here, $a$ is the diode ideality factor. The value is between 1 and 1.5. $E_g$ is the semiconductor band-gap energy in electron-volt (eV).

Fig. 6 [Images not available. See PDF.]

The scaled single diode model of a PV array (Villalva 2009)

A $N_M\times N_S$ BIPV array is modeled as one equivalent light-dependent current source, series-parallel combinations of diodes, and equivalent series and parallel resistances as shown in Fig. 6. The array current ($I_{\mathit{Ar}}$) expressed in terms of terminal voltage of BIPV array ($V_{\mathit{Ar}}$) is given as in the Eq. 7 (Devakirubakaran et al. 2023).

7

$$I_{\mathit{Ar}}=N_S{I}_{\mathit{PV}}-N_S{I}_O\left\{e,x,p,\left(\frac{q\left(V_{\mathit{Ar}},+,{{R_{\mathit{se}}}_{\mathit{Eq}}I}_{\mathit{Ar}}\right)}{{\mathit{akTN}}_M}\right),-,1\right\}-\left(\frac{V_{\mathit{Ar}}+{{R_{\mathit{se}}}_{\mathit{Eq}}I}_{\mathit{Ar}}}{\frac{N_M}{N_S}{R}_P}\right),$$

8

$${R_{\mathit{se}}}_{\mathit{Eq}}=\frac{N_M}{N_S}\times R_{\mathit{se}},$$

9

$${R_P}_{\mathit{Eq}}=\frac{N_M}{N_S}\times R_P,$$

Here $I_{\mathit{PV}}$ is the photocurrent generated due to irradiation on PV cell. The photocurrent increases with higher irradiance and more cell area. The saturation current is denoted by $I_O$. The series resistance ($R_{\mathit{se}}$) and parallel resistances ${(R}_P)$ are introduced for modeling the leakage current and voltage drops across different layers of PN junction and contact materials respectively. Due to series-parallel combinations of BIPV modules in the $N_M\times N_S$ array the equivalent series resistances (${R_{\mathit{se}}}_{\mathit{Eq}}$) and parallel resistances (${R_P}_{\mathit{Eq}}$) are modified as presented in Eqs. 8 and 9.

The effect of temperature and irradiance on the open circuit voltage ($V_{\mathit{OC}}$) and short circuit current ($I_{\mathit{SC}}$) of PV module are expressed by Jha (2023) as shown in Eqs. 10 and  11.

10

$$I_{\mathit{SC}}=\frac{L}{L_{\mathit{STC}}}(I_{{\mathit{SC}}_{\mathit{STC}}}+K_{I_{\mathit{SC}}}^T{\Delta }_T),$$

11

$$V_{\mathit{OC}}=\left(1,+,K_{V_{\mathit{OC}}}^L,\text{log},\left(\frac{L}{L_{\mathit{STC}}}\right)\right)\left(V_{{\mathit{OC}}_{\mathit{STC}}},+,K_{V_{\mathit{OC}}}^T,{\Delta }_T\right),$$

Here, the solar irradiation at standard condition (1000 W/m² and 25${}^{\circ }\text{C}$) is denoted by $L_{\mathit{STC}}.$ The temperature coefficients of short circuit current and open circuit voltage are expressed as $K_{I_{\mathit{SC}}}^T$ and $K_{V_{\mathit{OC}}}^T$. The irradiance coefficient of open circuit voltage is denoted as $K_{V_{\mathit{OC}}}^L$. The open circuit voltage can be approximated in Eq. 12.

12

$$V_{\mathit{OC}}=\frac{\mathit{kT}}{q}ln\left(\frac{I_{\mathit{PV}}}{I_0},+,1\right),$$

The efficiency of the PV module ($\eta$) is expressed in terms of fill factor ($\mathit{FF}$), open circuit voltage ($V_{\mathit{OC}}$), short circuit current ($I_{\mathit{SC}}$) as shown in Eq. 13.

13

$$\eta =\frac{FF{V}_{\mathit{OC}}{I}_{\mathit{SC}}}{\mathit{AL}}$$

From Eqs. 10 and 11, it is observed that the $I_{\mathit{SC}}$ and $V_{\mathit{OC}}$ values reduce when the value of irradiance is lower than the standard test conditions. The relation between irradiance and short circuit current is linear. The open circuit voltage changes logarithmically with irradiance.

The change of efficiency ($\Delta \eta$) with respect to the irradiation factor ($n$) is given by Eq. (14)

14

$$\frac{\Delta \eta }{\eta }=\frac{\mathit{kT}}{q}\frac{\text{ln}\left(n\right)}{V_{\mathit{OC}}},$$

Here, $n$ is radiation intensity factor. The value of $n$ is 1 for standard solar irradiance i.e., one sun condition. When $n$ is 0.5, the irradiance in 50% of the standard condition (Solanki 2015).

Therefore, in a string of PV modules, when some of the modules receive less irradiation than others, the shaded modules produce less current and less voltage. This increases the mismatch losses and reduces the DC power generation. The cumulative effect of reduced DC power generation affects the array efficiency and yield of the PV plant.

The DC power generated by the PV array under uniform irradiance is described as in Eq. (15)

15

$$P_{\mathit{PV}}=N_M{N}_S{\eta }_E{A}_{m}L\{1-{\alpha }_p(T_C-T_{\mathit{ref}}\left)\right\},$$

Here ${\eta }_E$ represents the energy conversion efficiency of the BIPV array. The module area is denoted by $A_m$. $L$ denotes the solar irradiation upon the BIPV module in W/m². The temperature coefficient of power is denoted by ${\alpha }_p$. The module temperature and the reference temperature are represented by $T_C$ and $T_{\mathit{ref}}$, respectively. However, at non-uniform irradiance conditions, the values of $L,$${\eta }_E$ and $T_C$ changes in modules as well as in different strings of the BIPV array. Therefore, simulation is required to investigate the performance of the BIPV array under severe partial shading conditions.

System design

For a typical building with a 1000 ft² footprint area and 50% available area for PV generation, the module area has to be less than 500 ft². This study considers a BIPV system with an area under 500 ft². A 3.6 kW_p system is designed with 72 modules of BIPV052-T86 Sun Energy tiles (Solarhub Catalog 2022). Each 52 W tile occupies an area of 0.53 m². The total module area is 38.16 m² or 410.75 ft². The extra area is used for spacing, cabling, and combiner box and power converters. The specifications of BIPV modules are given in Table 2.

Table 2. Specifications of PV module (Solarhub Catalog 2022)

Module parameters	Value
CSI Model No	BIPV052-T86
Maximum power (W)	51.9435
Cells per module	14
Open circuit voltage $V_{\mathit{OC}}$ (V)	8.7
Voltage at maximum power $V_{\mathit{GMP}}$ (V)	6.7
Short circuit current $I_{\mathit{SC}}$ (A)	8.07 A
Temperature coefficient of $V_{\mathit{OC}}$ (%/°C)	−0.36
Temperature coefficient of $I_{\mathit{SC}}$ (%/°C)	0.06
Photocurrent $I_{\mathit{Photo}}$ (A)	8.1561
Reverse current $I_O$ (A)	2.7581 × 10−10
Diode ideality factor $a$	1.0037 S
Shunt resistance $R_P$ (Ω)	98.9408
Series resistance $R_{\mathit{se}}$ (Ω)	0.11486
Module area $A_m$ (m2)	0.53

In this study, 72 PV modules are arranged as; 9 modules in series, and 8 strings in parallel. The common practice of choosing the wire-gauge for DC wiring of PV module, is to take 156% of the rated short circuit current ($I_{\mathit{SC}}$) of PV modules (Khan et al. 2020). The requirement of current capacity of wires is of 12.6 A for a module with rated $I_{\mathit{SC}}$ of 8.07 A. The current density of copper wires is 3 A/mm². Therefore, connecting wires with 4.2 mm² cross-section area, i.e. AWG 11 wires are chosen. This wire has a resistance of 4.12 × 10⁻³ Ω/m. Considering the PV module width of 70 cm and a spacing of 30 cm between PV modules, each tie-connections have a resistance of 0.00412 Ω.

Partial shading patterns

Four severe partial shading conditions are considered in this study. Six different irradiance conditions ranging from 155 W/m² to 1000 W/m² are considered. This graded irradiance is required to simulate the variation in soiling, complex geometry of BIPV surface, spatial distribution of cloud, fog and smoke. The Center type shading condition presented in Fig. 7 has 5 × 4 modules with varying degrees of irradiance. Frame type shading presented in Fig. 8 considers all the modules except the central ones as shaded. In corner shading presented in Fig. 9, the 5 × 4 modules in top left corner are shaded. In the side shading presented in Fig. 10 9 × 5 modules in the left side are shaded.

Fig. 7 [Images not available. See PDF.]

Center shading pattern

Fig. 8 [Images not available. See PDF.]

Frame shading pattern

Fig. 9 [Images not available. See PDF.]

Left corner shading pattern

Fig. 10 [Images not available. See PDF.]

Left side shading pattern

Fixed array configurations

Four fixed BIPV array configurations are selected for this comparative study. Figure 11 represents Series Parallel (SP) configuration. The strings are tied at two ends only. In spite of the simplest design and minimal wiring requirement the SP configuration performs poorly under row wise shading conditions. To overcome this limitation, crossties are provided as in each row of Total Cross Tied (TCT) configuration as shown in Fig. 12.

Fig. 11 [Images not available. See PDF.]

Series parallel (SP) configuration

Fig. 12 [Images not available. See PDF.]

Total cross tied (TCT) configuration

The cross-ties provide bypass path for the photocurrent generated by the unshaded modules in a string. However, more wiring requirement in large BIPV systems make the TCT configuration cost prohibitive. To optimize the wiring requirement as well as to maintain a satisfactory maximum power output, Triple Tied (TT) and Quarter Tied (QT) configurations are designed as shown in Figs. 13 and 14.

Fig. 13 [Images not available. See PDF.]

Triple tied (TT) configuration

Fig. 14 [Images not available. See PDF.]

Quarter tied (QT) configuration

Parameters of performance evaluation

The parameters used for performance analysis of BIPV array configurations are as follows.

• Global Maximum Power Point ($\mathit{GMPP}$)

The maxima of the P ~ V curve is called global maximum power point ($\mathit{GMPP}$). The $\mathit{GMPP}$ and corresponding voltage (V_GMP) and current (I_GMP) are important parameters that convey information regarding variation of maximum power, current and voltage across the PV array at different irradiance condition and temperature.

• Percentage Mismatch loss ($\mathit{ML}$)

The mismatch loss is the difference between GMPP at uniform irradiance (${\mathit{GMPP}}_U$) and the GMPP at PSCs (${\mathit{GMPP}}_{\mathit{PSC}}$). The difference in generated power in the modules under partial shading conditions cause mismatch loss in BIPV array. The percentage mismatch loss ($ML)$ is defined as in the Eq. 16.

16

$$ML\left(\%\right)=\frac{{\mathit{GMPP}}_U-{\mathit{GMPP}}_{\mathit{PSC}}}{{\mathit{GMPP}}_U}\times 100,$$

• Percentage Fill Factor ($\mathit{FF}$)

The percentage Fill Factor is calculated as shown in Eq. 17.

17

$$FF\left(\%\right)=\frac{\mathit{GMPP}}{I_{\mathit{SC}}\times V_{\mathit{OC}}}\times 100,$$

Here $I_{\mathit{SC}}$ is the short circuit current and $V_{\mathit{OC}}$ is the open circuit voltage. The fill factor gives an idea of the energy conversion efficiency and the shape of the I ~ V characteristics of the entire BIPV array.

• Percentage efficiency ${(\eta }_E$)

Energy conversion efficiency of BIPV array${(\eta }_E)$ is defined in Eq. 18 as the ratio of maximum power produced under certain irradiance and temperature condition to total irradiation incident on the total module surface area. Under severe non-uniform irradiance conditions, the efficiency of BIPV array decreases due to increase in mismatch losses.

18

$${\eta }_E\left(\%\right)=\frac{\mathit{GMPP}}{{{\sum }_{i=1}^{i=n}{J}_{{\mathit{IR}}_i}\times A_m}_i}\times 100,$$

Here $J_{{\mathit{IR}}_i}$is the solar irradiation in W/m² on the ith module and ${A_m}_i$ denotes the ith module area in m² and $n$ is the number of modules.

• Wiring Requirement ($N_W$)

The wiring requirement ($N_W$) is estimated in terms of the number of wires with same length as of cross ties. For BIPV configurations, the length of wire between two consecutive modules is considered to be same as the length of cross tie. Total wiring requirement for a $N_M\times N_S$ BIPV array ($N_W$) is computed as in Eq. 19

19

$$N_W=N_S\left(N_M,-,1\right)+2\left(N_S,-,1\right)+N_{{\mathit{CT}}_A},$$

Here $N_S$ denotes the number of strings, $N_M$ denotes the number of modules in a string. The first two terms in Eq. 19 are fixed with the dimension of PV array. $\left(N_M,-,1\right)$ is the number of wires in one string. The wiring requirement for each of the positive bus and negative bus is given as$\left(N_S,-,1\right)$. The third term $N_{{\mathit{CT}}_A}$ denotes the additional wiring requirement for cross-ties in each of the BIPV configurations.

• Reduction in wiring requirement ($R_{\mathit{NW}}$)

The percentage reduction in wiring requirement ($R_{\mathit{NW}}$) for Step 11 in BIPV array design algorithm is calculated as in Eq. 20.

20

$$R_{\mathit{NW}}\left(\%\right)=\frac{N_{W_{\mathit{TCT}}}-N_W}{N_{W_{\mathit{TCT}}}}\times 100,$$

Here $N_{W_{\mathit{TCT}}}$ is the wiring requirement for TCT configuration.

• Improvement in global maximum power ($N_{\mathit{GMP}}$)

The percentage improvement in global maximum power with respect to the lowest $\mathit{GMPP}$ configuration ($N_{\mathit{GMP}}$) for Step 11 in BIPV array design algorithm is calculated as in Eq. 21

21

$$N_{\mathit{GMP}}\left(\%\right)=\frac{GMPP{-GMPP}_L}{{\mathit{GMPP}}_L}\times 100,$$

Here ${\mathit{GMPP}}_L$ is the lowest $\mathit{GMPP}$ among four configurations under a particular shading pattern.

Simulation and calculation

MATLAB/Simulink environment is used to simulate the shading patterns and their impact on the BIPV array configurations. The BIPV configurations are manually created with Simulink blocks as shown in Fig. 15.

Fig. 15 [Images not available. See PDF.]

Simulink model for BIPV array

The parameters are saved in output files and necessary calculations are done using simple MATLAB programming as shown in the Fig. 16. Wiring resistance, short circuit current, maximum power, efficiency, fill factor, additional loss due to wiring is calculated and tabulated in the results section.

Fig. 16 [Images not available. See PDF.]

Program for calculation of design and performance parameters

Results and discussions

Simulation is conducted for four different configurations under four severe partial shading conditions presented in literature. The variation of current with the operating voltage is recorded. Comparison of mismatch loss for each configuration under four shading conditions is illustrated in Fig. 17. The trade-off for higher wiring requirement and better efficiency is shown in Fig. 18 Under the Center shading, the TCT configuration gives the highest $\mathit{GMPP}$ of 2484.28 W at the array voltage of 68 V. The second-best performance is QT configuration as shown in Table 3. Under the Frame shading, the QT configuration gives the highest $P_{\mathit{GMP}}$ of 2008.358 W closely followed by TCT configuration as presented in Table 4. Under left corner shading, the performance of TCT configuration is best with the $\mathit{GMPP}$ of 2484.281 W followed by SP configuration with the $\mathit{GMPP}$ of 2450.051 W as shown in Table 5. The performance of four configurations under left side shading is presented in Table 6. Here TCT configuration has the $\mathit{GMPP}$ of 1983.150 W, followed by QT, TT and SP respectively. A minimal change in open circuit voltage and short circuit current has been observed in each simulation.

Table 3. Performance evaluation under Center shading

Array Config.	SP	TT	QT	TCT
GMPP (W)	2450.05	2429.65	2454.19	2484.28
VGMP (V)	54.00	66.00	66.00	68.00
IGMP (A)	45.37	36.81	37.18	36.53
$V_{\mathit{OC}}$ (V)	77.57	77.63	77.65	77.66
$I_{\mathit{SC}}$ (A)	65.20	65.19	65.18	65.18
$\mathit{FF}$(%)	48.44	48.01	48.49	49.08
$\mathit{ML}$ (%)	34.20	34.75	34.10	33.28
${\eta }_E$ (%)	7.52	7.45	7.53	7.62

Table 4. Performance evaluation under Frame shading

Array Config.	SP	TT	QT	TCT
GMPP (W)	1731.28	1925.99	2008.36	2008.33
VGMP (V)	50.00	50.00	48.00	48.00
IGMP (A)	34.63	37.10	41.84	41.84
$V_{\mathit{OC}}$ (V)	76.25	76.29	76.45	77.66
$I_{\mathit{SC}}$ (A)	60.38	65.19	55.74	55.74
$\mathit{FF}$(%)	37.60	43.76	47.27	43.76
$\mathit{ML}$ (%)	53.50	50.18	46.06	46.06
${\eta }_E$ (%)	7.35	7.87	8.52	8.52

Table 5. Performance evaluation under Left Corner shading

Array Config.	SP	TT	QT	TCT
GMPP (W)	2350.05	2379.32	2395.01	2484.28
VGMP (V)	54.00	62.00	66.00	68.00
IGMP (A)	43.51	38.38	36.29	36.53
$V_{\mathit{OC}}$ (V)	77.57	77.58	77.62	77.62
$I_{\mathit{SC}}$ (A)	65.20	65.19	65.18	65.18
$\mathit{FF}$(%)	46.46	47.05	47.33	49.10
$\mathit{ML}$ (%)	52.20	50.18	46.06	46.06
${\eta }_E$ (%)	7.22	7.30	7.45	7.62

Table 6. Performance evaluation under Left Side shading

Array Config.	SP	TT	QT	TCT
GMPP (W)	1786.86	1925.99	1935.92	1983.15
VGMP (V)	62.00	64.00	64.00	66.00
IGMP (A)	28.82	30.09	30.25	30.05
$V_{\mathit{OC}}$ (V)	76.57	76.59	76.60	76.64
$I_{\mathit{SC}}$ (A)	59.19	59.08	59.14	59.11
$\mathit{FF}$(%)	39.43	42.56	42.73	43.78
$\mathit{ML}$ (%)	52.01	48.27	48.01	46.74
${\eta }_E$ (%)	7.25	7.82	7.86	8.05

Table 7. Selection of best array configuration considering fewer wiring requirement and higher GMPP

Shading Patterns	Highest GMPP	Second highest GMPP	$N_{\mathit{GMP}}$ (%)	$R_{\mathit{NW}}$ (%)
Center	TCT	QT	1.01	10.45
Frame	QT, TCT	TT	7.15	13.43
Left Corner	TCT	QT	1.91	10.45
Left Side	TCT	QT	8.34	10.45

Fig. 17 [Images not available. See PDF.]

Percentage mismatch loss under different shading patterns

Fig. 18 [Images not available. See PDF.]

Comparison of efficiency and wiring requirement

The summarized result from BIPV array design algorithm is shown in.

Table 7. For Center and left side shading the highest $\mathit{GMPP}$ is reported for TCT configuration. However, QT configuration provide 1.01–8.34% more power than SP with a reduction in wiring requirement of 10.45% compared to TCT. Also, performance of QT configuration is same as the TCT for frame shading condition. In frame shading condition TT configuration provides 7.15% more power than SP with a 13.43% less wiring requirement compared to TCT. Therefore, QT configuration is considered an optimal choice except for corner shading. In the corner shading, SP has the second highest GMPP with a 14 V shift in operating voltage (V_GMP). Under frame shading SP configuration provides 2.97% more GMPP than TT with a 41.79% reduction in wiring requirement compared to TCT. But SP configuration performs poorly in left side, center and frame shading.

Fig. 19 [Images not available. See PDF.]

Maximum current through tie-connections at different operating voltages

The scatter plot of maximum current through tie-connections at different operating voltages is presented in Fig. 19. There are 38, 42 and 56 tie-connections in TT, QT and TCT configurations respectively. The maximum tie currents and the corresponding operating voltages are recorded. Near the short circuit conditions, the tie-currents are limited to 4.8 A. The maximum current values increase near the array voltage at maximum power. The maximum value of tie current is recorded to be 6.73 A at the operating voltage of 64 V. This current can be handled by AWG 11 wires chosen previously for the design. The additional wiring losses caused by the PV system is illustrated in Fig. 20. With higher number of AWG wires, the wiring loss will increase linearly with the resistance. The maximum additional wiring loss is found to be 2.49 W for TCT configuration during corner shading and minimum is 0 W for SP configurations.

Fig. 20 [Images not available. See PDF.]

Additional wiring loss due to tie connections

Conclusion

This study investigates the performance of four BIPV array configurations; SP, TT, QT and TCT under four severe partial shading conditions. A 9 × 8 BIPV array of 3.6 kW_p rating occupying an area under 500 ft²is designed. For four different shading conditions i.e. center, frame, left corner and left side, the parameters such as global maximum power ($\mathit{GMPP}$), corresponding voltage and current ($V_{\mathit{GMP}},I_{\mathit{GMP}}$), open circuit voltage ($V_{\mathit{OC}}$) and short circuit current ($I_{\mathit{SC}}$), fill factor ($\mathit{FF}$), efficiency (${\eta }_E$), mismatch losses ($\mathit{ML}$) and wiring requirement are calculated. In all the shading conditions TCT gives highest $\mathit{GMPP}$but it has the maximum wiring requirement. The wiring requirement is significant for large BIPV arrays as it indicates more resistive loss and wiring cost. The proposed BIPV array design algorithm considers 1% or more improvement in $\mathit{GMPP}$ compared to the lowest $\mathit{GMPP}$ configuration and more than 10% reduction in wiring requirement ($R_{\mathit{NW}}$) than TCT configuration as the best configuration. The wiring additional wiring losses due to tie-connection are typically less than 1% of the output. In comparison to TCT configuration, the QT configuration requires 10.45% less wiring. It increases $\mathit{GMPP}$ by up to 8.43% compared to SP. The mismatch loss is limited at 34.10% while the fill factor is increased to 48.49%. Therefore, QT and TCT are recommended as a favourable configuration for the design of a BIPV array. This study might be helpful to the researchers and engineers for implementing BIPV systems in urban conditions where partial shading conditions are more prevalent.

In the upcoming works, the proposed methodology shall be extended to more realistic shading conditions and complex geometry of the buildings. The simulation process can be further automated. The future works shall address the long-term effect of these shading conditions on the techno-economic parameters. Life-cycle analysis, annual electricity generation, and payback time will be estimated and compared between different configurations under various shading conditions. Moreover, emerging topics, such as reconfigurable PV arrays optimization of circuit components, can also be explored.

Funding

The authors acknowledge the help of Department of Electrical Engineering, IIT (ISM) Dhanbad for offering the necessary facilities to perform the research.

Declarations

Conflict of interest

SB declares that he has no conflict of interest. PKS declares that he has no conflict of interest. DS declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent is not applicable since human participants were not involved in the study.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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