A method of measuring the bandgap of a photovoltaic module

Abstract

This invention discloses a method for measuring the bandgap of photovoltaic modules, belonging to the field of solar cell property analysis technology. The method includes: First, continuously measuring the current-voltage characteristics of the photovoltaic module output in an outdoor environment, recording multiple sets of data and the module temperature during measurement. Second, using the obtained current-voltage data, establishing a three-diode model, where two diodes have fixed ideal factors of 1 and 2, and the ideal factor of the third diode is a variable parameter. Benders parameter decomposition technology and optimization algorithms are used to extract model parameters. Finally, using the relationship between the reverse saturation current with an ideal factor of 1 and temperature, the bandgap of the photovoltaic module is calculated. Compared to existing methods for measuring bandgap, this invention eliminates the need for expensive spectrometers or X-ray photoelectron spectrometers, requires no destructive operations, and is applicable to encapsulated photovoltaic modules of any size with unknown ideal factors. It offers advantages such as low cost and ease of implementation.

Description

Technical Field

[0001] This invention belongs to the field of solar cell property analysis technology, specifically relating to a method for extracting the bandgap width from the outdoor test current-voltage characteristic curve of a photovoltaic module. Background Technology

[0002] The bandgap is one of the important property parameters of solar cells or photovoltaic modules. It refers to the energy difference between the bottom of the conduction band and the top of the valence band in wave vector space. By measuring the bandgap, it is possible to effectively identify the type of solar cell or photovoltaic module, evaluate and improve its manufacturing process, and diagnose and examine its operating status.

[0003] Currently, several methods exist for measuring the bandgap of semiconductor materials. For example, the energy of photons intrinsically absorbed by a semiconductor material is no less than the bandgap value. Therefore, the energy corresponding to the lowest frequency of intrinsically absorbed photons can be equal to the bandgap by measuring the absorption spectrum in the visible light range. Alternatively, X-ray photoelectron spectroscopy can be used to infer the position of the top valence band level, while inverse photoelectron spectroscopy can be used to determine the position of the bottom conduction band level; the difference between the two is the bandgap. However, spectrometers and X-ray photoelectron spectroscopy are expensive, complex to operate, and have certain requirements regarding sample size and surface treatment. For example, for large-sized and encapsulated photovoltaic modules, cumbersome operations such as destructive cutting and removal of encapsulation materials are necessary before measurements can be performed using a spectrometer or photoelectron spectroscopy. Furthermore, for ideal diodes, i.e., when the ideality factor equals 1, the sensitivity and bandgap can be measured by measuring the relationship between their forward voltage and temperature. However, this method is not applicable to photovoltaic modules because the ideality factor of photovoltaic modules is unknown and is typically greater than 1, or even greater than 2. Therefore, how to measure the bandgap of photovoltaic modules in a low-cost, simple, and reasonable manner remains a problem worth tackling in this technical field. Summary of the Invention

[0004] Purpose of the invention: To address the shortcomings of existing technologies, this invention provides a low-cost, simple, and reasonable method for measuring the bandgap of photovoltaic modules, which eliminates the need for destructive operations such as cutting large-size encapsulated photovoltaic modules, and is applicable to photovoltaic modules with unknown ideal factors.

[0005] Technical Solution: To achieve the objective of this invention, the technical solution adopted is: a method for measuring the bandgap width of a photovoltaic module, comprising the following steps:

[0006] Step 1: Under outdoor sunlight, continuously measure the current-voltage (IV) characteristics of the photovoltaic module output using a standard test circuit, recording multiple sets of IV data and the module temperature T during measurement. The standard IV test circuit includes a power supply, an adjustable resistor, and an ammeter connected in series with the photovoltaic module, and a voltmeter connected in parallel across the photovoltaic module.

[0007] Step 2: Using each set of IV data obtained in Step 1, perform a three-diode model fitting to obtain the relevant model parameters. The three-diode IV model is as follows:

[0008]

[0009]

[0010] Where I is current, V is voltage, the function f(I,V) is given by the definition after the symbol “≡”, e is the natural base, and I ph For photocurrent, I s1 The reverse saturation current of a diode with an ideality factor of 1, I s2 The reverse saturation current of a diode with an ideality factor of 2, I s3 R is the reverse saturation current of a diode with an ideality factor of n3. s For series resistance, G sh For parallel conductance, n3 is the ideality factor of the third diode, V T Thermal voltage, defined as V T =N S kT / q, where N S q = 1.602E-19C is the number of series units in the photovoltaic module, k = 1.38E-23J / K is the Boltzmann constant, q = 1.602E-19C is the electron charge, and T is the module temperature recorded in step 1 on the Kelvin scale.

[0011] The above three-diode model has a total of 7 unknown parameters, namely (I ph ,I s1 ,I s2 ,I s3 G sh ,R s In this invention, the Benders parameter decomposition method is used to reduce the number of independent parameters to two, namely n3 and R. s These are two independent parameters. Next, for a specific set of data points (V) i ,I i Given indices i = 1, 2, ..., N, the Nelder-Mead algorithm is used to solve for n³ and R. s Two-parameter optimization problem to extract model parameters:

[0012]

[0013] Among them I cal,i For voltage V i The current value is calculated using the three-diode model. The superscript T indicates transpose, the superscript -1 indicates matrix inversion, M and b are the matrix and vector for performing Benders parameter decomposition, respectively, and they are used to decompose five parameters I according to the three-diode model formula. ph ,I s1 ,I s2 ,I s3 G sh Convert to n3 and R s Regarding the non-independent parameters, the seven model parameters are decomposed into two independent parameters and five non-independent parameters. The specific definitions of M and b are...

[0014]

[0015] All summations include all data points, i.e., sums from i=1 to i=N. Furthermore, D i =-V i -I i R p By solving this optimization problem, the optimal values ​​of all seven model parameters can be obtained. Furthermore, the three-diode model parameters are extracted from the current-voltage data at different temperatures.

[0016] Step 3: Based on the multiple sets of temperatures T recorded in Step 1 and the model parameters I extracted in Step 2... s1 , make ln(I s1 ()–1 / T image. According to semiconductor theory, the current mechanism described by a diode with an ideality factor of 1 is the diffusion-recombination current in the neutral region of the PN junction, and its reverse saturation current has the following relationship with temperature.

[0017]

[0018] Where E g Let k be the bandgap width, and k = 1.38E-23J / K be the Boltzmann constant. Therefore, ln(I s1 The graph of 1 / T is approximately a straight line, and the slope of the line is equal to E. g / k. The slope of this line, denoted as slope, is calculated using the linear least squares method. The final measured bandgap width of the photovoltaic module is then...

[0019]

[0020] Where q = 1.602E-19C is the electron charge, used to convert the bandgap unit to electron volts (eV).

[0021] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0022] Existing spectroscopic methods require measuring the reflectance and transmittance of samples. However, the encapsulation of photovoltaic (PV) modules significantly affects the measurement results of light transmission and reflection. Furthermore, the sample chamber of spectrometers is relatively small and cannot accommodate large PV modules. Similarly, the encapsulation of PV modules also affects X-ray photoelectron spectroscopy (XPS). Therefore, measurements using spectrometers or XPS require cutting the PV module to a suitable size and removing the encapsulation material, which constitutes destructive testing. Additionally, existing methods for measuring the relationship between forward voltage and temperature are only applicable to ideal diodes with an ideality factor of 1, and not to PV modules where the ideality factor is typically greater than 1 and unknown. To address these issues, this invention calculates the bandgap simply by measuring the photocurrent-voltage characteristics at different temperatures. This method eliminates the need for expensive spectrometers or XPS equipment, avoids cumbersome destructive testing of samples, and is applicable to PV modules with an ideality factor greater than 1 and unknown. It offers advantages such as low cost and ease of implementation. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the measurement of the bandgap width of a photovoltaic module according to the present invention;

[0024] Figure 2 The IV test curves of polycrystalline silicon photovoltaic modules at several different temperatures;

[0025] Figure 3 This is a schematic diagram of the three-diode circuit model used in this invention;

[0026] Figure 4 ln(I) for polycrystalline silicon photovoltaic modules s1 )–1 / T diagram;

[0027] Figure 5 ln(I) for copper indium gallium tin photovoltaic modules s1 )–1 / T diagram. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] The method for measuring the bandgap of photovoltaic modules described in this invention has the following overall flowchart: Figure 1 As shown, the specific steps include:

[0030] Step 1: Under outdoor sunlight, measure the current-voltage (IV) characteristics of the photovoltaic module using a standard test circuit and record the IV data. Simultaneously, use an infrared thermometer to record the module temperature T during the measurement. Repeat this operation to obtain multiple sets of IV data at different temperatures.

[0031] The standard IV test circuit includes a power supply, an adjustable resistor and an ammeter connected in series with the photovoltaic module, and a voltmeter connected in parallel across the photovoltaic module. Figure 2 The graph shows the IV (Infrared Illumination) data curves obtained after conducting illumination IV characteristic tests on a standard polycrystalline silicon photovoltaic module at different temperatures. This polycrystalline silicon photovoltaic module consists of 36 cells connected in series. For ease of display, only four sets of data are shown in this graph; in reality, hundreds of sets of data were measured.

[0032] Step 2: Using each set of IV data obtained in Step 1, establish a three-diode model and extract the model parameters. The three-diode model used in this invention is as follows: Figure 3 As shown, the ideality factors of two diodes are fixed at 1 and 2, and the ideality factor of the third diode is an undetermined parameter n3. Other undetermined model parameters include: photocurrent I. ph The reverse saturation current I of the three diodes s1 I s2 I s3 Series resistor R s Parallel conductance G sh The model expression is as follows:

[0033]

[0034] The function f(I,V) is given by the definition after the "≡" sign, where e is the natural base and V is the base of the variable. T Thermal voltage, defined as V T =N S kT / q, where N S =36 is the number of series units in the photovoltaic module, k = 1.38E-23J / K is the Boltzmann constant, q = 1.602E-19C is the electron charge, and T is the module temperature recorded in step 1 on the Kelvin scale. Figure 2 Taking the top curve as an example, the absolute temperature T = 319.65 K (i.e., 46.5 °C), and the thermal voltage V... T =0.9913V.

[0035] The above three-diode model has a total of 7 unknown parameters, namely (I ph ,I s1 ,I s2 ,I s3 G sh ,R sIn this invention, the Benders parameter decomposition method is used to reduce the number of independent parameters to two, namely n3 and R. s These are two independent parameters. Next, for a specific set of data points (V) i ,I i Given indices i = 1, 2, ..., N, the Nelder-Mead algorithm is used to solve for n³ and R. s Two-parameter optimization problem to extract model parameters:

[0036]

[0037] Among them I cal,i For voltage V i The current value is calculated using the three-diode model. The superscript T indicates transpose, the superscript -1 indicates matrix inversion, M and b are the matrix and vector for performing Benders parameter decomposition, respectively, and they are used to decompose five parameters I according to the three-diode model formula. ph ,I s1 ,I s2 ,I s3 G sh Convert to n3 and R s Regarding the non-independent parameters, the seven model parameters are decomposed into two independent parameters and five non-independent parameters. The specific definitions of M and b are...

[0038]

[0039] All summations include all data points, i.e., sums from i=1 to i=N; furthermore, D i =-V i -I i R s .

[0040] Similarly Figure 2 Taking the top curve as an example, with N = 183 data points, the Nelder-Mead algorithm is used to solve the above optimization problem, yielding independent parameters n³ = 6.0, R... s =0.28Ω, therefore, with n3 and R s The relevant matrix M and vector b are

[0041]

[0042]

[0043] Therefore, the other non-independent parameters in the three-diode model are extracted as follows:

[0044]

[0045] Thus, the reverse saturation current I of the diode with an ideality factor of 1 at an absolute temperature T = 319.65 K is obtained. s1 =1.193E-9A. Using the method in step 2 above, the model parameter I at different temperatures can be extracted from each set of current-voltage data. s1 .

[0046] Step 3: Based on the temperature T recorded in Step 1 and the model parameters I extracted in Step 2... s1 , make ln(I s1 ()–1 / T image. According to semiconductor theory, the current mechanism described by a diode with an ideality factor of 1 is the diffusion-recombination current in the neutral region of the PN junction, and its reverse saturation current has the following relationship with temperature.

[0047]

[0048] Where E g Let k be the bandgap width, and k = 1.38E-23J / K be the Boltzmann constant. Therefore, ln(I s1 The graph of 1 / T is approximately a straight line, and the slope of the line is equal to E. g / k. The slope of this line, denoted as slope, is calculated using the linear least squares method. The final measured bandgap width of the photovoltaic module is then...

[0049]

[0050] Where q = 1.602E-19C is the electron charge, used to convert the bandgap unit to electron volts (eV).

[0051] Figure 4 This example demonstrates the temperature T and model parameter I obtained from steps 1 and 2 for the polycrystalline silicon photovoltaic module. s1 The ln(I) made s1 The slope of the straight line obtained by fitting the 1 / T graph using the least squares method is 14147 (absolute value). Therefore, the bandgap E of this polycrystalline silicon photovoltaic module is... g,mSi for

[0052]

[0053] This result is very close to the theoretical bandgap of silicon at absolute zero, which is 1.21 eV, verifying the reliability of this method.

[0054] Figure 5 Further demonstration shows another copper indium gallium tin photovoltaic module produced by steps 1 to 3, using ln(I s1The slope of the straight line obtained by fitting the 1 / T image using the least squares method is 11441 (absolute value). Therefore, the bandgap E of this copper indium gallium tin (CITi) component is... g,CIGS for

[0055]

[0056] In summary, this invention discloses a method for extracting the bandgap width from the outdoor test current-voltage characteristic curve of a photovoltaic module. Compared with existing methods for measuring the bandgap width, this method only requires conventional power supplies, voltmeters, ammeters, and thermometers, without the need for expensive spectrometers or X-ray photoelectron spectrometers. It does not require destructive testing and is applicable to photovoltaic modules with unknown ideality factors. It has the advantages of low cost and ease of implementation.

Claims

1. A method for measuring the bandgap width of a photovoltaic module, characterized in that: Includes the following steps: (1) Under outdoor sunlight, the current-voltage characteristics of the photovoltaic module output are continuously measured, and multiple sets of current-voltage data and module temperature during measurement are recorded; (2) Using the obtained current-voltage data, a three-diode equivalent circuit model was established. The model includes three diodes in parallel, a current source, a parallel resistor, and a series resistor. The ideality factors of two diodes are fixed at 1 and 2, respectively, while the ideality factor of the other diode is a variable parameter. The relevant model parameters were extracted using Benders parameter decomposition technology and optimization algorithm. The three-diode model is as follows: ， in I For current, V For voltage, f ( I , V The function is defined by the symbol The definition is given later. e The base is the natural number. I ph For photocurrent, I s1 The reverse saturation current of a diode with an ideality factor of 1. I s2 The reverse saturation current of a diode with an ideality factor of 2. I s3 The ideal factor is n The reverse saturation current of the diode of type 3. R s For series resistance, G sh For parallel conductance, n 3 is the ideal factor for the third diode. V T Thermal voltage is defined as follows: V T =N S kT / q ,in N S This refers to the number of series-connected units in a photovoltaic module. k =1.38E-23 J / K is Boltzmann's constant. q = 1.602E-19 where C is the electron charge. T The component temperature is measured on the Kelvin scale. The model fitting was performed using the Nelder-Mead algorithm to solve the following optimization problem after Benders parameter decomposition: ， in n 3 and R s For two independent parameters, ( I i , V i () represents the current-voltage data points and subscripts of a certain set of data. i Values ​​range from 1 to N , N The number of data points I cal,i For voltage V i The current value calculated using the three-diode model is superscripted. T This indicates transpose, and the superscript -1 indicates matrix inversion. M and b These are the matrices and vectors for implementing Benders parametric decomposition, respectively, and they will decompose the parameters. Convert to n 3 and R s Relevant non-independent parameters, M and b The specific definition is ， ， All summations include all data points, i.e., from... i =1 accumulated to i=N ,also, , , , By solving the above optimization problem, all seven model parameters are obtained. The optimal value is then obtained, and the three-diode model parameters are extracted from the current-voltage data at different temperatures in each group. (3) The bandgap of the photovoltaic module is calculated by using the relationship between the reverse saturation current of the diode with an ideality factor of 1 and the temperature. Reverse saturation current of a diode with an ideality factor of 1 I s1 logarithm and absolute temperature T There is a linear relationship between the reciprocals of 1 / T As the independent variable, ln( I s1 The data graph of the dependent variable is used to fit the slope of the straight line using the least squares method, denoted as slope, which is the bandgap width of the photovoltaic module. Calculate using the following formula ， in k =1.38E-23 J / K is Boltzmann's constant. q = 1.602E-19 C is the electron charge.

2. The method for measuring the bandgap width of a photovoltaic module according to claim 1, characterized in that: The current-voltage test circuit in step (1) includes a power supply, an adjustable resistor and an ammeter connected in series with the photovoltaic module, and a voltmeter connected in parallel across the photovoltaic module.

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