Module-Level Performance Evaluation for a Smart PV System Based on Field Conditions

Abstract

This study presents an approach with a simple structure, low complexity and low costs to evaluate the real-time status and localize the faults of a smart PV system at module level based on field conditions. The performance evaluation approach of a PV system is developed through the defined performance indicators, a complex data matrix to track module locations and a thermal model to determine the module temperature. The generalization potential of the proposed approach has been demonstrated through the successful experiment validation. The results show that the performance indicators are greatly corrected by the estimated module temperature with great linear agreement in R² of 0.922 compared to actual measured temperature under same conditions. Due to the effective performance indicators capturing more performance differences caused by faults of cracks in 0.22 of PV_{_ΔV}, partial shading in 0.47 of PV_{_ΔV}, broken sensors in 0.17 of PI_{_ΔI} and 1 of PV_{_ΔV} separately, the proposed approach is very effective in evaluating the performance of PV modules at module level. Meanwhile, the faulty modules are diagnosed and located through these findings and the data matrix in the smart PV system. Additionally, the sensitivity of the proposed approach to fault in cracks is much higher than that of monitoring only the power.

1. Introduction

As the energy mix continues to change around the world, fossil fuels are being replaced by renewable energy sources. Renewable energy, unlike fossil fuels, never run out and no greenhouse gasses or other pollutants are created during the process of energy generation. With the rapid growth of renewable energy over the last 10 years, solar and wind power are now the cheapest sources of electricity in many parts of the world [1]. In 2021, global electricity power generation capacity from solar sources achieved 849 GW [2]. According to statistics published by Fraunhofer [3], the solar energy of electricity production in Germany reached 9.1% in 2021. Furthermore, Germany is planning to fully implement a 100% renewable energy plan and guarantee photovoltaic growth up to 215 GW until 2030 [4]. Thus, photovoltaic power has a very high potential for future power development.

In recent years, as the installed capacity of photovoltaic (PV) systems continues to increase, their performance and energy yield have received increasing attention from investors and researchers. In addition to the inherent limitations of module materials, there are many important and uncertain factors that have an impact on the power-generation efficiency of PV systems in complex and changeable climate conditions [5] such as:

• Faults of PV modules, e.g., manufacturing defects, cracks of solar cells, potential induced degradation (PID), defective bypass diodes, natural aging, etc.;
• Shadow, soiling, irradiation deviation, snow coverage;
• Efficiency decreasing by temperature rise;
• Series–parallel unbalance and direct current (DC) losses;
• Inverter losses, mismatch to maximum power point (MPP).

If the presence and interaction of these effects are undetected or non-monitored of a prolonged time, these can lead to reversible or irreversible damage that reduces the output power of the PV system and may even cause safety issues [6]. Therefore, performance assessment of PV systems is essential to provide early warning of faults to maintain uptime through proper monitoring.

The most common approach is the framework of International Electrotechnical Commission IEC 61724 standard, which forms the base for evaluation of field performance of PV plants in 1998 [7]. It includes few parameters of the reference yield (Y_r), array yield (Y_a), final yield (Y_f), the performance ratio (PR), system losses (L_S) and array capture losses (L_C). These quantities express the system-level performance in relation to energy generation, solar resources and the overall effect of PV system losses [8,9,10]. Since then, many studies have investigated, evaluated and analyzed PV systems with the standard IEC 61724 in different locations. In France, Mohaned EI Hacen Jed et al. [11] studied the performance of the 4.5 MWp photovoltaic power plant with 7 years operation, which is located in a warm and temperate climate area. The annual performance ratios are between 84.12% and 90.54% (yearly average 87.18%), with higher rates in the spring and lower rates in the summer. In the literature [12], the performance and degradation evaluation of a 1 MWp utility-scale photovoltaic system located in the tropical semiarid climate of India was observed through 4 years of monitored data. The reference yield, final yield, system efficiency, capacity factor, and performance ratio were 6.23 h/day, 4.64 h/day, 11%, 19.33% and 74.73%, respectively. After 50 months of operation, the degradation rates were assessed through the linear least squares regression (LLS), the classical seasonal decomposition (CSD), the Holt–Winters seasonal model (HW), and the seasonal and trend decomposition using loess (STL) to be 0.27%/year, 0.32%/year, 0.50%/year and 0.27%/year respectively. As we know, the weather conditions including irradiance, ambient temperature, humidity, wind speed and direction have great effect on the efficiency of a PV system, which is also affected by other environmental factors, such as dirt and dust. The study [13] investigated the performance analysis of a 954 MWp PV array in Mauritania; the monthly performance ratio varied from 61% in August to 71% in November because of the high temperature difference between different seasons. Furthermore, in Djibouti, the average performance ratio of a 302.4 kWp PV system operating under a dusty desert maritime climate [14] is 84%. For every 1 °C increases in ambient temperature, the performance ratio decreases by 0.7%.

Beyond this, the above-mentioned standard has also stimulated the development of technologies that enable the performance of photovoltaic system to be estimated or monitored. José Miguel Paredes-Parra et al. [15] implemented a wireless Raspberry Pi for a PV module monitoring system based on the IEC 61724 standard. Kun Kunaifi et al. [16] developed the methodology, including performance analyses of few PV systems and the degradation rate studies using NREL/RdTools. Although the standard IEC61724 is widely used in different types of photovoltaic systems, it has proved to be well evaluated. Rather than describing the performance of individual components, it concentrates on assessing the performance of the array as part of the system, and providing a summary of performance suitable for comparing PV installations of various sizes operating in different climatic conditions [17].

Furthermore, some studies in module level monitoring were applied in performance evaluation and fault diagnosis in the PV system. In order to localize the faulty PV module, a wireless sensor network connecting to each module is presented to compare the measured and predicted maximum power of PV string through an innovative maximum power point algorithm [18]. Bruno Andò et al. [19] employed an intelligent multi-sensor architecture to detect the causes of efficiency losses for the monitoring of photovoltaic systems at the panel level, which is equipped with voltage, current, irradiance, temperature and inertial sensors. Although it may be effective to detect which module is underperforming by comparing estimated and measured parameters, these methods have the disadvantages of the inability to detect and locate faults in a timely manner, as unautomated methods for fault diagnosis without human intervention. They also need a large number of sensors which can entail high costs. Yihua Hu et al. [20] presented an online fault diagnosis technique with optimized voltage sensor locations, which used the low voltage and high voltage sections to locate the faulty module position. This method still requires a number of voltage sensors to be installed in the PV strings, which makes it particularly difficult for large-scale PV array.

The new contribution of this study is to propose an approach to automatically evaluate the real-time status of each module and locate the anomalies at module level in a smart PV system. The performance evaluation is based on the performance indicators in current and voltage that are defined and calculated under field conditions. Section 2 briefly introduces the test site including the used commercial PV modules, meteorological sensors, electrical sensors and monitoring system to form an advanced PV system. Section 3 demonstrates the key parts for performance evaluation of the proposed module-level performance evaluation approach, which comprises input data filtering and data matrix, defining performance indicators based on I-V characteristics, a thermal model to evaluate module temperature and the process of performance evaluation. Section 4 provides the outdoor experiments to verify the effectiveness of proposed approach and discussion. Section 5 includes the conclusions and future work.

2. PV System Monitoring

In actual fact, the basic effective monitoring of PV modules requires data on current, voltage, power, temperature and irradiance, etc. It is, however, technically feasible to install sensors for each PV module, but this would inevitably increase the costs of the PV system. Moreso, they are not applicable to large PV systems and raise the question of how to transfer large amounts of data efficiently and quickly to the datalogger. By utilizing fewer sensors or simpler devices to measure a variety of parameters and developing accurate mathematical models to calculate the necessary parameters for performance evaluation, the cost-effectiveness and intelligence of PV system performance monitoring can be improved. For these reasons, this study uses the intelligent commercial polycrystalline PV modules which integrate the digital sensors in the junction boxes in Figure 1 and are made by a manufacturer [21]. The digital sensors delivery string current at MPP, voltage at MPP and temperature in the junction box for each PV module. They have lower costs than the conventional current-voltage sensors, temperature sensors (PT100/PT1000), and are independent of module type and junction box. The sensors can be mounted inside or outside the junction box and are also suitable for other module types and junction boxes.

The specification of the used PV modules (AEG AS-P603) [21] under standard test conditions (STC) is shown in

Table 1. The specification of PV (AEG AS-P603) module under STC.

Parameters	Variable	Values
Maximum Power	Pm,ref	255 W
Voltage at MPP	Vm,ref	30.93 V
Current at MPP	Im,ref	8.24 A
Open Circuit Voltage	Voc,ref	38.16 V
Short Circuit Current	Isc,ref	8.91 A
Temperature Coefficient of Isc,ref	α	0.06%/℃
Temperature Coefficient of Voc,ref	β	−0.33%/℃
Irradiance Correction Coefficient of Voc,ref	a	0.06
Solar Cells	--	60
Bypass Diodes	--	3

. Each module consists of 60 solar cells connected in series with three substrings connecting to three bypass diodes. Then, they are arranged in many rows of PV arrays to be a large PV system which comprises 63 modules variously interconnected to each other based on the series–parallel topology structure. This PV system is mounted on the rooftop of the Bielefeld University of Applied Sciences (Campus Minden) and is made up of three different subsystems, as shown in Figure 2. The installed capacities of the individual PV subsystem ranges from 1 kWp to 5.8 kWp. All subsystems are ground mounted with a fixed tilt of 30° or 10°. The common three phase grid-connected PV inverters (one inverters with 10 kW and one inverter with 15 kW) [22] are used for the three subsystems. Each inverter connected the subsystems has three maximum power trackers. Meanwhile, the RT1 smart rooftop monitoring system [23], including a tilted irradiance sensor (range: 0~2000 W/m²) and a temperature sensor PT100 (range: −20 ℃~100 ℃) connected to the backsheet of PV module, was applied to this system, as shown in Figure 3. Furthermore, a professional wireless weather station was connected to a local WIFI, uploading data to a professional weather database with a resolution of 5 min, which provides constant and reliable measured values for air temperature, horizontal solar radiation, wind speed, wind direction, humidity, rainfall and atmospheric pressure. Thus, a powerful sensors network including the sensors in junction box, meteorological sensors, titled irradiance sensor and backsheet temperature sensor was formed in DC side, as shown in Figure 4. All data from single PV module are collected by the sensors in junction box and transferred via powerline to the string reader and further to the gateway via RS485, which does not require the configuration of more sensor cables. Then, the data continues to be passed over the ethernet network from the Gateway and Raspberry Pi to the local database in a monitoring system. The sampled data with the time interval of 2 min are from 00:00 to 24:00 on each day. All data are saved in a MySQL database. Additionally, the data contains the ID information for system, string, inverter and sensor locations.

Up to this point, a smart PV system including the components mentioned above that can automatically measure individual module current-voltage at MPP, temperature in the junction box, weather data, solar radiation and store the data into the local database is created. Its main purposes are to enable monitoring at module level and undertake the telemetry data collection and transmission, which will further support the science research in following sections. Further, the advantages of this smart PV system are that the real-time status of the whole system at module level can be actively monitored and evaluated, which leads to the appropriate remedial measures being taken before any major disruptions occur and ensure greater reliability throughout the PV system.

3. Methodology

In this section, the following methodology is explained before the evaluation the performance of PV modules in the mentioned smart PV system. It will first discuss the data matrix and input data filtering, defining performance indicators and module temperature evaluation method.

3.1. Data Matrix and Input Data Filtering

The data used in this paper are obtained by the following ways: current and voltage of each PV module, temperature in each junction box from the monitoring system; irradiance and module temperature of the reference module from RT1; and meteorological data from the weather station.

First of all, some related parameters and notations based on data signature are defined as:

ID_system: PV system ID in real plant;

ID_string: PV string ID in PV system;

ID_module: PV Module ID in PV string.

ID_inverter: inverter ID.

t: the local time.

G_h: horizontal irradiance, G_h(i) represents the irradiance of the ith horizontal radiation with time series.

u: wind speed.

T_air: air temperature, T_air(i) represents the temperature of the ith type of environmental configuration.

T_jb: the temperature in junction box, T_jb(i) represents the temperature of the ith type of environmental configuration in junction box.

T_measeured: the measured module temperature, T_measeured(i) represents the module temperature of the ith type of environmental configuration.

T_calculated: the calculated module temperature from temperature model, T_calculated(i) represents the calculated module temperature of the ith type of environmental configuration.

G: irradiance on the surface of module, G(i) represents the irradiance of the ith type of environmental configuration.

I_m: module current at MPP, I_module(k,j) represents the current of the jth module in kth strings.

V_m: module voltage at MPP, V_module(k,j) represents the voltage of the jth module in kth strings.

P_m: module power at MPP, P_module(k,j) represents the power of the jth module in kth strings.

In the following data, the data structure body M in format of MATLAB is further formed from the above parameters, which includes the module location information, weather data and module performance data.

M.Location is used to sign the location of the module: M.Location = [ID_system,ID _inverter,ID_string,ID_module].

M.Time describes the date and time of data: M.Time = [date, time].

M.Weather represents the weather data with time series: M.Weather = [T_jb,T_air,u,G_h, G, T_measured].

M.Module expresses module performance data: M.Module = [I_module, V_module, P_module, T_calculated].

Then, one cell (M) is created as M = {Location, Time, Weather, Module}.

Thus, the data to be evaluated are a complex data matrix consisting of N_s ×N_p cells:

$${\left[\begin{array}{ccccc}{M}_{11}& M_{12}& \cdots & M_{1(Np-1}{}_{)}& M_{1Np}\\ M_{21}& M_{22}& \cdots & M_{2(Np-1)}& M_{2Np}\\ ⋮& ⋮& ⋮& ⋮& ⋮\\ M_{(Ns-1)1}& M_{(Ns-1)2}& \cdots & M_{(Ns-1)(Np-1)}& M_{(Ns-1)Np}\\ M_{Ns1}& M_{Ns2}& \cdots & M_{(Ns-1)(Np-1)}& M_{NsNp}\end{array}\right]}_{N_s\times N_p}$$

where, N_s is module numbers in one substring, N_p is substring numbers in a PV system.

As the data came from three measurement subsystems, it results in inconsistent sampling frequencies. So, all data will be filtered to the same dimensions and data intervals at the same time based on data fusion and data integration in MATLAB. Furthermore, any outliers will be removed during this process.

3.2. Defining Performance Indicators Based on I-V Characteristics

The current–voltage (I-V) output characteristics of photovoltaic modules represent a detailed description of their solar energy conversion capability and efficiency. Understanding the electrical I-V characteristics of PV modules is essential in determining the output performance of PV modules. Furthermore, the open-circuit voltage (V_oc), short-circuit current (I_sc), current (I_m) and voltage (V_m) at MPP on the output characteristic (I-V curves) of the PV module are applied in expressing the performance indicators in current (PI__ΔI) and voltage (PI__ΔV) which is connected to particular irradiance G and module temperature T_module, as following.

$$P{I}_{\_\Delta I}\left(T_{\mathrm{mod}ule},G\right)=\frac{I_{sc}\left(T_{\mathrm{mod}ule},G\right)-I_m\left(T_{\mathrm{mod}ule},G\right)}{I_{sc}\left(T_{\mathrm{mod}ule},G\right)}$$

(1)

$$P{I}_{\_\Delta V}\left(T_{\mathrm{mod}ule},G\right)=\frac{V_{oc}\left(T_{\mathrm{mod}ule},G\right)-V_m\left(T_{\mathrm{mod}ule},G\right)}{V_{oc}\left(T_{\mathrm{mod}ule},G\right)}$$

(2)

I_sc (T_module, G) and V_oc (T_module, G) are calculated from irradiance (G) and module temperature (T_module) using the following equations [24,25]:

$$I_{sc}(T_{\mathrm{mod}ule},G)=I_{sc,ref}\cdot \left\{1+\alpha \cdot \left(T_{\mathrm{mod}ule}-T_{ref}\right)\right\}\cdot \frac{G}{G_{ref}}$$

(3)

$$V_{oc}(T_{\mathrm{mod}ule},G)=V_{oc,ref}\cdot \left\{1+a\cdot \ln \left(\frac{G}{G_{ref}}\right)+\beta \cdot \left(T_{\mathrm{mod}ule}-T_{ref}\right)\right\}$$

(4)

where I_sc (T_module, G) is the short-circuit current for particular irradiance G and module temperature T_module;

V_oc (T_module, G) is the open-circuit voltage for particular irradiance G and module temperature T_module;

I_sc,ref and V_oc,ref are the short-circuit current and open-circuit voltage under STC;

α is the temperature coefficient of I_sc under STC;

β is the temperature coefficient of V_oc under STC;

a is the irradiance correction coefficient of V_oc under STC;

T_ref is the module temperature at 25 °C;

G_ref is the irradiance at 1000 W/m².

The change of I_sc,ref and V_oc,ref over time is very slow in the initial period after the PV module installation in [26]; this paper ignores the natural aging of I_sc,ref and V_oc,ref, the values of both parameters under standard conditions are used in following work.

When the module temperature T_module is replaced directly by the T_jb, the PI__ΔI (T_module, G) and PI__ΔV (T_module, G) turn to PI__ΔI (T_jb, G) and PI__ΔV (T_jb, G) which are expressed as:

$$P{I}_{\_\Delta I}\left(T_{jb},G\right)=\frac{I_{sc}\left(T_{jb},G\right)-I_m\left(T_{jb},G\right)}{I_{sc}\left(T_{jb},G\right)}$$

(5)

$$P{I}_{\_\Delta V}\left(T_{jb},G\right)=\frac{V_{oc}\left(T_{jb},G\right)-V_m\left(T_{jb},G\right)}{V_{oc}\left(T_{jb},G\right)}$$

(6)

where, the I_sc (T_jb,G) and V_oc (T_jb,G) are rewritten as:

$$I_{sc}(T_{jb},G)=I_{sc,ref}\cdot \left\{1+\alpha \cdot \left(T_{jb}-T_{ref}\right)\right\}\cdot \frac{G}{G_{ref}}$$

(7)

$$V_{oc}(T_{jb},G)=V_{oc,ref}\cdot \left\{1+a\cdot \ln \left(\frac{G}{G_{ref}}\right)+\beta \cdot \left(T_{jb}-T_{ref}\right)\right\}$$

(8)

Then, the measured data for irradiance, temperature inside junction box, voltage at MPP, current at MPP on 24 April 2022 are applied in the Equations (5)–(8), which gives the following results in Figure 5. In Figure 5c, the referenced PI_{_ΔI_ref} (0.075) and PI_{_ΔV_ref} (0.189) are calculated from the values on the datasheet under STC. In the period between 10:30 a.m. and 5:00 p.m., the results indicate that PI_{_ΔI} is shifted below the reference value, but PI_{_ΔV} is approximately equal to the reference value. That is because the temperature inside the junction box is higher than the real PV module temperature, which results in a greater degradation on the current and less on the voltage at MPP of PV module. Thus, in order to accurately assess the performance of the used PV modules, the temperature issue needs to be taken seriously.

3.3. Thermal Model to Determine Module Temperature

In fact, it is very difficult to measure the cells temperature directly when a manufactured PV module is in operation under outdoor conditions. Usually, many module-level/string-level studies in a PV field use the module backsheet temperature as the cell temperature. Because the temperature gradient between the module backsheet temperature and the cell temperature is very small when cell temperature is less than 60 °C in [27], the backsheet temperature of the PV module is considered to be the real module/cell temperature in this study.

As described in Section 2, the used PV modules with the intelligent sensors in junction box are used for module-level monitoring in the smart PV system. The measured temperature is the temperature inside the junction box, and this temperature is higher than the real backside temperature of the PV module, as shown by the infrared image (IR) in Figure 6. It leads to the need for further conversion to the true backsheet temperature of the PV module. Therefore, a novel temperature thermal model has been developed to achieve temperature conversion based on the temperature (T_jb) in the junction box and our previous work [28].

According to the law of energy conversion and energy conservation, the junction box-PV module backsheet, junction box-temperature sensor, junction box-air have 3 forms of heat exchange: conductive heat, convective heat and radiative heat, as shown in Figure 7. The thermal model treats the junction box as a steady-state energy balance on the control volume:

$$Q_{cond}-Q_{conv}-Q_{rad}-\rho \cdot v_{jb}\cdot c\frac{d{T}_{jb}}{dt}=0$$

(9)

where Q_cond is the total energy from PV module with heat conduction, Q_conv is the convection energy between the junction box and the flow, Q_rad is the radiation energy from the junction box to the ambient environment, $\rho$ is the density of junction box, v_jb is the volume of junction box, c is the specific heat capacity of junction box.

In the considered thermal model, the following assumptions have been made based on the study [29]:

• One-dimension (1D) thermal model.
• The isothermal surface is approximated as a flow node and therefore edge effects are neglected.
• Negligible thermal capacitances.
• Junction box temperature and backsheet temperature of module are considered uniform.
• Ground temperature is equal to air temperature.
• Convective heat transfer is evaluated using empirical equations and it assumes that the wind flows around the junction box.
• According to the radiative heat transfer, the view factor is assumed to be unity, only the ground is visible on the rear surface of the junction box.
• In fact, the bypass diodes in the junction box have a small forward-bias voltage, even if a current passes through it, it produces only a small amount of heat flow and those heat are neglected.

The original heat of the junction box comes from the conductive heat exchange between the junction box and the PV module backsheet. The heat conduction equation is given by the following equation:

$$Q_{cond}=-\lambda \cdot A_1\cdot \frac{dT\mathrm{mod}ule}{dx}$$

(10)

where λ is the thermal conductivity of the junction box, x is thickness of the contacted surface between the junction box and solar cells in PV module, A₁ is the contacted area between the junction box and back sheet of PV module, T_module is backside temperature of PV module and equal to the following T_calculated. The dT_module/dx is the temperature gradient along the thickness direction of the contacted surface between the junction box and solar cells in PV module.

Further, it considers convection Q_conv and radiation Q_rad exchanges of the back sides of junction box with the surrounding environments. The convection and radiation heat are calculated according to the geometry of junction box and ambient conditions such as wind speed, air temperature and ground temperature.

Convective heat transfer is described as:

$$Q_{conv}=A\cdot \left(T_{jb}-T_{air}\right)\cdot k\cdot \frac{\sqrt[3]{N{u}_{{}_{natural}}^3+N{u}_{{}_{forced}}^3}}{L}$$

(11)

where A is the total surface area of junction box, k is the thermal conductivity of the air, L is characteristic length of junction box, Nu_natural is the Nusselt number with free convection, and Nu_forced is the Nusselt number with forced convection.

In the natural convection, the Churchill–Bernstein equation is valid for a wide range of the Prandtl number and Reynolds number [30]. The Nusselt number with free convection can be written as:

$$N{u}_{natural}=\{\begin{array}{l}0.68+\frac{0.67{\left(G_r\cdot P_r\right)}^{1/4}}{{\left[1+{(\raisebox{1ex}{$0.492$}\!\left/ \!\raisebox{-1ex}{$P_r$}\right.)}^{9/16}\right]}^{4/9}},G_r\cdot P_r<{10}^9\\ {\left(0.825+\frac{0.387{(G_r\cdot P_r)}^{1/6}}{{\left[1+{\left(0.492/P_r\right)}^{9/16}\right]}^{8/27}}\right)}^2,G_r\cdot P_r>{10}^9\end{array},G_r=\frac{g\cdot \cos (\theta )\cdot {\alpha }_v\cdot \left(T_{jb}-T_{air}\right)\cdot L^3}{{\nu }^2}$$

(12)

As described in [31], the transition from laminar to turbulent flow was determined by the critical values. Measurements were taken when the wind speed was not too high, so the Reynolds number was usually less than its critical values. The Nusselt number for the forced convection can be described as [31]:

$$N{u}_{forced}=\{\begin{array}{l}0.664R_e^{1/2}{P}_r^{1/3},R_e=\raisebox{1ex}{$uL$}\!\left/ \!\raisebox{-1ex}{$\nu $}\right.<5\times {10}^5\\ (0.037R_e^{4/5}-871)P_r^{1/3},R_e=\raisebox{1ex}{$uL$}\!\left/ \!\raisebox{-1ex}{$\nu $}\right.>5\times {10}^5\end{array}$$

(13)

where G_r is the Grasshof number, P_r is the Prandtl number, R_e is the Reynolds number, u is wind speed, v is dynamic viscosity, g is gravity acceleration, θ is the angle of PV module and α_v is the swelling coefficient. The G_r, P_r, R_e, v, α_v give the information about the air.

The radiative heat exchange is simplified by considering parallel planar bodies with the same area (A). According to the Stefan–Boltzmann law, the radiation heat equation is rewritten by the air temperature and the horizontal irradiance:

$$Q_{rad}={\epsilon }_1\cdot A\cdot \sigma \cdot \left(2\cdot T_{jb}^4-{\left(0.0552\cdot T_{air}^{2/3}\right)}^4-{\left(T_{air}+0.03\cdot G_h\right)}^4\right)$$

(14)

where ${\epsilon }_1$ is emissivity coefficient of junction box, $\sigma$ is Stefan-Boltzmann number, 5.67 × 10⁻⁸ W·m⁻²·k⁻⁴, G_h is horizontal irradiance.

Finally, the PV module temperature can be estimated using the thermal model based on the steady state approach prediction as:

$$T_{\mathrm{mod}ule}(t)=T_{jb}(t)-\frac{\left(T_{jb}(t+h)-T_{jb}(t)\right)\cdot \rho \cdot V\cdot c+h\cdot (Q_{conv}+Q_{rad})}{h\cdot \lambda \cdot A_1}$$

(15)

where h is the time interval.

Then, the testing outdoor platform is further developed, that includes RT1, and weather station as shown in Figure 8. RT1 measures horizontal irradiance (G_h) and PV module backsheet temperature (T_measured). The weather station obtains the air temperature (T_air) and wind speed (u). Validation experiments show good linearity in R² of 0.922 between the calculated module temperature and the actual measured module backplane temperature in Figure 9. The proposed thermal model is well implemented to convert the temperature in the junction box to the temperature of the PV module backsheet. This will help capture the temperature of each module in PV system and allow for future monitoring at module level. Besides, the calculated temperature will be further input into the data matrix. It was specially noted that the thermal model is independent of module type and junction box. Once the data acquisition module for sensors has been changed, the entire thermal model can still be used by modifying only the other fixed parameter values of the model.

3.4. Process of Performance Evaluation

In this section, the process of performance evaluation for the smart PV system is presented in Figure 10 and it is subdivided into the following four main parts.

In step 1, the measured data for current at MPP, voltage at MPP, temperature in junction box, air temperature, wind speed, horizontal irradiance and module locations are obtained from the local database and further form the data matrix by filtering data to the same time, removing the data outliers, converting the data formation and signing the data locations.

In step 2, temperature in junction box, air temperature, wind speed and horizontal irradiance are extracted from data matrix to estimate the module temperature by thermal model. Then, the estimated temperature is saved into data matrix.

In step 3, the estimated temperature and irradiance are used to simulate the short-circuit current and open-circuit voltage. Next, performance indicators in PI__ΔI and PI__ΔV are finally calculated based on the measured current and voltage at MPP.

In step 4, based on great differences in performance indicators and data signature ID, the anomalies of PV modules in the system are diagnosed and located at module level. Finally, the results are further output and returned.

4. Verification and Testing

In order to validate the proposed performance evaluation approach, the following experiments were conducted which focuses on three topical operation status of PV module, such as faultless, cracks and shadow. The detailed experimental results are described below. Further, all mentioned modules below are connected in series to form PV strings, which have the total power of 5.61 kWp.

4.1. Faultless

When the PV string of the PV system described above is monitored in faultless (no faults) operation, the performance indicators in current and voltage are shown in Figure 11. It is based on data from 10:00 to 16:30 on 19 July 2022 for the following analysis. The calculated temperature (T_calculed) and the actual measured temperature of PV module are used to predict the performance indicators separately. As it can be seen in Figure 11a, PI_{_ΔI} (T_calculated) almost overlaps with PI_{_ΔI} (T_measured). Figure 11b shows that there is a small deviation between PI_{_ΔV} (T_calculated) and PI_{_ΔV} (T_measured), which is caused by accuracy of the temperature from thermal model. In summary, it is clear that no faults emerged in the PV string; the performance evaluation approach has good effectiveness under faultless operation.

4.2. Partial Shading

Firstly, the partial shading conditions are set as shown in Figure 12a, where one part of the PV module is shaded whereas the other part is fully exposed to irradiation. Real-time working environment data for the PV modules with the angle of 30° were collected on a sunny day (on 15 June 2020). The average irradiance is 549 W/m². In the experiment, the freestanding cardboards are used to create shadows of different area on the surface of the PV modules. In condition ①, the same area of cardboards on the surface of modules M1 and M2 are used to shade the assembly from different directions which cover a substring horizontally and three substrings vertically. Due to the large shadow area, the shaded solar cells are bypassed and no longer work. It caused the substring where the shaded solar cells are located to be bypassed by the diode in the junction box. It was specially noted that the sensors in junction box operate on a voltage of 10–45 V. When the operating voltage of the shaded PV module is less than 10 V, the sensor delivers a voltage value of 0 V and a temperature of −273.15 °C. Therefore, the PI_{_ΔV} is 1, whereas the PI_{_ΔI} is higher than normal due to the temperature value of −273.15 °C. In condition ②, when the shading of module M1 was removed and the shading area of module M2 turns to be smaller. PI_{_ΔI} of both modules returns to the normal value. However, PI_{_ΔV} changes from 1 to 0.5 because the substring with the shaded solar cells is bypassed and the voltage of the entire PV module is reduced by one third. In the final condition ③, When M1 is re-shaded by the same shadow area of M2, the results of PI_{_ΔI} and PI_{_ΔV} are obtained to be the same as M2.

4.3. Cracks

The cracks mentioned in this paper are the shattering of solar cells which is caused by mechanical stress. Cracks lead to irregularities in solar cells and serve as sites for carrier recombination, which results in lower electroluminescence (EL) emission and appear as dark in EL image, as shown in Figure 13a. The black part of the EL image from the inactive cell is a special area where the current cannot reach due to the cell cracks.

In actual fact, there are even localized hot spots on the module surface due to cell cracks, and the normal solar cells in a cracked module have a lower temperature than the reference solar cells in a normal PV module in Figure 13b. The impact of cracks on the output performance of PV modules can be expressed by the performance indicators. The PI_{_ΔI} of cracked module is almost the same as the PI_{_ΔI} of the reference module, but the PI_{_ΔV} of the cracked module is higher than the corresponding reference module. Meanwhile, the percentage deviation of PI_{_ΔV} from the reference value is from 0.06% to 13% and its average value is almost 6%, as shown in Figure 13e. With the above results, cracks in PV module can be effectively diagnosed.

4.4. Three Operating States of PV Modules

The cracked module, shaded module and normal module are mounted in the same PV string where the angle of the module is 10°. The experiment is carried out under the same conditions in Figure 14a. Meanwhile, a smaller shaded area is used to ensure that the voltage of the shaded module is higher than 10V. Figure 14b,c show that in the same substring, even the current of each PV module is equal, and the PI_{_ΔV} can be also used to distinguish significantly between cracks, fixed shadow and normal operation. Because PI_{_ΔV} (shadow) is much larger than the other two states, and PI_{_ΔV} (cracks) is also higher than the normal value, it means that the cracks and partial shading can be determined by the PI_{_ΔV} and PI_{_ΔI}.

In addition, the power of the cracked PV module is very close to power under normal conditions in Figure 14b, when the power losses are small, and nothing would be taken seriously as a faulty module. However, the difference between these two states can be obvious through PI_{_ΔV}. It further illustrates that the proposed approach is much more sensitive to faults than monitoring the power only.

4.5. Performance Evaluation for Individual PV Modules in Strings

In this section, three modules in string S6 and twelve modules in string S5 are used in the following experiment. All PV modules have the same mounting angle of 10° in strings S5 and S6. The detail experiment conditions are described as below:

M.Location1 is [PVS1, Inv3, S5, BG032977, BG033404, BG033061].

M.Location2 is [PVS1, Inv2, S6, BG033162, BG033120, BG032981, BG033419, BG033369, BG033415, BG033218, BG033197, BG033968, BG033269, BG032899, BG032290].

M. Time is [29.06.2022, 11:01,11:29,11:45,13:00,15:30,16:00].

Module BG032977 and BG032968 are the reference modules in string S5 and string S6, respectively.

The experiment includes four operating states of PV modules, such as cracks, shadow, broken sensors and normal state. Then, the performance of these modules has been evaluated in two strings, as shown in Figure 15. In the following two heatmaps, the sensor’s problem is more prominent, followed by moving shadow and cracks. When the sensors in the junction boxes are damaged, the collected data will have the voltage of 0V, the current of substring and the temperature of −273.15°C. This will result in the PI_{_ΔV} of 1 and PI_{_ΔI} of 0.17 being slightly higher than the other PV modules in the same substring. If the voltage of the PV module falls below 10V due to other faults, the sensor does not work properly, which leads to the results such as the above. Therefore, in order to use the proposed approach in this paper, the voltage of the PV module needs to be screened firstly.

On the other hand, when the voltage of the PV module caused by small shadows and cracks is higher than 10 V, the PI_{_ΔI} and PI_{_ΔV} values are very effective in distinguishing the shadows and cracks. The negative effects of shading are usually greater, followed by the cracks of solar cells. PI_{_ΔV} for shading is about 0.47 with missing one substring in shaded PV module and the PI_{_ΔV} of cracks is almost 0.22. Furthermore, the cracks evolution of solar cells is a very slow process, and the cracked module has only been installed for 2 years, which is why the evaluation factor is slightly higher than the reference module. However, the difference of PI_{_ΔV} is enough to identify cracks. The PI_{_ΔI} and PI_{_ΔV} of faultless are 0.09 and 0.2, respectively. It can also be seen that the PI_{_ΔI} in string S5 is much higher than the value in string S6 where the cracked module and shaded module locate. PI_{_ΔI} can be used to determine the abnormal strings at string-level. Furthermore, the results of faults detection and the location information of faulty module are shown in

Table 2. Results of faults detection in PV strings.

Faults	Performance Indicators	System ID	String ID	Module ID	Detection
Cracks	PI_ΔV = 0.22	PVS1	S5	BG033404	√
Shadow	PI_ΔV = 0.47	PVS1	S5	BG033061	√
Broken sensors	PI_ΔI = 0.17, PI_ΔV = 1	PVS1	S6	BG033269	√
Faultless	PI_ΔI = 0.09, PI_ΔV = 0.2	PVS1	S5 and S6	Others	--

. The faulty modules locate in strings S5 and S6 of the PVS1 system. The module ID for faulty modules with cracks, shadow and broken sensors are BG033404, BG033061 and BG033268. In summary, the PI_{_ΔI} and PI_{_ΔV} values of PV modules are useful to quickly pinpoint the ID of the module in data matrix and further find the location of the problematic modules.

5. Conclusions

In this work, a novel module-level performance evaluation algorithm of a PV system with the advanced fault detection monitoring is developed under field conditions. The proposed method can distinguish faultless, cracks, static shading and broken sensors under changeable climatic conditions for the individual PV module, which is the most innovative feature of this study. Moreover, the simple structure, low complexity and low costs of the proposed method are key merits to implement performance evaluation for the smart PV system in this study.

Furthermore, the experimental results successfully demonstrate the high feasibility of the proposed method to evaluate performance and locate the anomalies of the smart PV system at the module level based on the data matrix signature. The experimental results also show a good linear agreement between the PV module temperature estimated by the thermal model and the actual measured module temperature with an R² value of 0.922 to prove the validity of thermal model. The similar PI_{_ΔI} and PV_{_ΔV} are calculated through the module temperature from the thermal model and measured module temperature to justify the proposed method being effective in the faultless case. The performance indicators in current and voltage detect and locate the faulty PV modules in the smart PV system because of both PI bringing more differences caused by cracks in 0.22 of PV_{_ΔV}, partial shading in 0.47 of PV_{_ΔV} and broken sensors in 0.17 of PV_{_ΔI} and 1 of PV_{_ΔV} separately. Meanwhile, when the output power of a cracked module is similar to the output power of a normal module, the proposed method is more effective in identifying the cracks than monitoring only the power. Furthermore, it reflects the high validity of the developed performance evaluation methods based on the intelligent PV modules in the smart PV system.

Although the proposed method has successfully achieved the expected performance evaluation and fault location objectives at the module level, an improved fault-location method will still need to be proposed to accurately identify the fault type when the faults cause the voltage of faulty modules to be lower than the critical voltage for sensors during normal operation. At the same time, the proposed method should be further applied to more commercial systems in order to improve the accuracy of the method in the future.