Method for calculating parameters of double-diode model of photovoltaic cell

Abstract

The invention provides a method for calculating parameters of a double-diode model of a photovoltaic cell, which comprises the following steps of: obtaining a current characteristic equation of the photovoltaic cell by using a Kirchhoff's current law according to an equivalent circuit diagram of the double-diode model of the photovoltaic cell, establishing a double-diode model of a photovoltaic module by using the current characteristic equation, and calculating the parameters of the double-diode model of the photovoltaic cell. And seven parameters of the photovoltaic module double-diode model are solved by using an analytical method. Finally, the seven parameters obtained through calculation are simulated through Simulink, an I-V curve obtained through simulation is compared with experimental data, and the accuracy of a calculation result is verified. By adopting the method provided by the invention, seven parameters of the photovoltaic cell double-diode model can be accurately obtained, and the problem that some parameters cannot be directly obtained from component nameplate parameters provided by manufacturers is solved.

Description

Technical Field:

[0001] The present invention belongs to the technical field of photovoltaic power generation, and relates to a method for calculating the parameters of a double-diode model of a photovoltaic cell. Background Art:

[0002] In recent years, the domestic interest in the field of photovoltaic power generation has been continuously increasing, attracting a large amount of R & D investment. Since the discovery of the photovoltaic effect, the research on solar photovoltaic power generation technology has continued to make progress and breakthroughs. In China, the research on photovoltaic power generation technology has also become more in-depth and extensive.

[0003] The power generation of photovoltaic modules will be affected by various environmental factors, mainly including light intensity and environmental temperature. When the light intensity weakens or the environmental temperature rises, the electrical energy output of the photovoltaic module will decrease. In addition, due to the differences in production processes inside the photovoltaic module, a series mismatch problem may occur, which will also affect the overall electrical energy output. Since a photovoltaic string is composed of multiple photovoltaic modules connected in series, the mismatch between modules will cause the output power of the entire string to decrease, and in severe cases, it may also cause faults such as hot spots in some modules. To reduce the risk of such faults, when packaging photovoltaic modules, a bypass diode is usually connected in reverse parallel across the series-connected solar cells. The purpose of this is to provide a short-circuit path for the solar cells when the overall output current of the string exceeds the current that the parallel-connected solar cells can withstand. This can prevent the current from flowing back into the solar cells, avoiding problems such as overheating and burning caused by the reverse current, thereby protecting the photovoltaic module and improving the stability and reliability of the system.

[0004] The present invention provides a method for calculating the parameters of a double-diode model of a photovoltaic cell. By using the output characteristic data of the module, the seven parameters of the photovoltaic module (photogenerated current I ph , diode reverse saturation current I o1 , I o2 , diode ideality factors n1, n2, series resistance R s , parallel resistance R sh ) are calculated. The seven parameters of the photovoltaic module comprehensively reflect its operating state and performance. Therefore, when diagnosing the faults of a photovoltaic module, calculating the seven parameters of the module provides an important basis for identifying faults. Summary of the Invention:

[0005] The purpose of the present invention is to provide a method for calculating the parameters of a double-diode model of a photovoltaic cell, and the specific steps are as follows:

[0006] Step 1: According to the physical model of the double-diode of the photovoltaic module, a new analytical formula for the seven parameters of the photovoltaic module is derived.

[0007] Step 2: Connect the PV module to the voltage debugging module to obtain 8 data points required for calculating the seven parameters. Then substitute the obtained data points into the analytical formula in Step 1 to calculate the seven parameters of the module.

[0008] Step 3: Use the Simulink simulation model. Put the seven parameters of the PV module obtained through calculation in Step 2 into the simulation model for simulation, and compare the I-V curve obtained from the simulation with the experimental data to verify the accuracy of the calculation results.

[0009] The derivation of the analytical formula for the seven parameters of the PV module in Step 1 is as follows:

[0010] (1) According to the equivalent circuit diagram of the double-diode model of the PV cell, we can get:

[0011]

[0012] where I ph is the photocurrent, I o1 and I o2 are the reverse saturation currents of the diodes, n1 and n2 are the ideality factors of the diodes, R s is the series resistance, R sh is the shunt resistance, I is the output current of the PV cell, U is the output voltage of the PV cell, q is the electron charge, k is the Boltzmann constant, and T is the temperature of the PV cell. In the following text, kT / q = V th .

[0013] (2) Take the total differential of Equation (1) and find the first derivative to get:

[0014]

[0015] After getting a common denominator and simplifying Equation (2), Equation (2) can be transformed into:

[0016]

[0017] (3) To obtain more parameter information of the solar cell, substitute the short-circuit current point (I = I sc , U = 0) into Equation (1) and Equation (2) to get:

[0018]

[0019] Then substitute the open-circuit voltage point (I = 0, U = U oc ) into Equation (1) to get:

[0020]

[0021] (4) From Equation (4) and Equation (6), we can eliminate I ph to get the following equation:

[0022]

[0023] (V) Simplify Equation (7).

[0024] Simplification principle: R sh ≈R sho >>R s , then 1 + R s / R sh ≈1

[0025] U oc >>I sc R s , then exp(U oc / n i / V th )>>exp(I sc R s / n i / V th )(i = 1, 2)

[0026] It can be obtained that:

[0027]

[0028] (VI) Usually, I o2 is 3 to 4 times of I o1 . The relationship between the two can be approximately expressed as Equation (9). For the convenience of calculation, I o2 in the following text is rewritten as KI o1 .

[0029]

[0030] Combine Equation (8) and Equation (9) to eliminate I o2 , and get:

[0031]

[0032] (VII) It can be known from Equation (3) that the relationship between R s and -dU / dI(R * , I * ) at any point (U so * ), and R sh ≈R sho , it can be obtained that:

[0033]

[0034] (VIII) Take point A(U a , I a ) on the I-V curve and substitute it into Equation (1), and get:

[0035]

[0036] Substitute Equation (12) into Equation (4) and eliminate all terms except I ph , and we get:

[0037]

[0038] Simplify Equation (13). We have R sh ≈R sho >>R s , then 1 + R s / R sh ≈ 1, and we get:

[0039]

[0040] (IX) Substitute Equation (10) into Equation (14) to eliminate I o1 , and we get:

[0041]

[0042] Denote exp((U i +I i R s ) / n j / V th ) as exp(I sc R s / n i / V th ) is denoted as φ i (i = 1, 2), and exp(U oc / n i / V th ) is denoted as γ i (i = 1, 2). Equation (15) can be simplified to:

[0043]

[0044] (X) The value on the right side of Equation (15) is a constant. To solve this problem, we can take a point B(U b , I b ) on the I-V curve, and then according to steps (VIII) and (IX), we get:

[0045]

[0046] From Equation (16) and Equation (17), we can get:

[0047]

[0048] (XI) Eliminate I according to Equation (10) and Equation (11)o1 We can get:

[0049]

[0050] Substituting formula (19) into With φ i (i=1,2), eliminate R s and denoted as θ ij (i=a,b,cj=1,2) and λ i (i=1,2). So far θ ij With λ i It only contains unknown parameters n1 and n2.

[0051] (XII) Substitute equation (19) into equation (18) and eliminate R s , we get an equation containing only the unknowns n1 and n2:

[0052]

[0053] (XIII) To solve for the values ​​of n1 and n2, another equation is needed, so we can take point C (U c ,I c ), according to steps (eight) and (nine), we can get:

[0054]

[0055] Then through steps (10), (11), (12), we can get the second equation:

[0056]

[0057] (XIV) By combining equations (21) and (22), we can solve for the values ​​of n1 and n2.

[0058] (XV) Using equations (9) and (10) to calculate the diode reverse saturation current I o1 ,I o2 :

[0059]

[0060] (XVI) Using formula (11) to calculate the series resistance R s :

[0061]

[0062] (XVII) Use formula (5) to calculate the parallel resistance R sh , and then use formula (4) to calculate the photocurrent I ph .

[0063] The seven parameters calculated are the parameters of m photovoltaic cells in the same state connected in series. The corresponding relationship between the parameters is as follows (the subscripts of the parameters after series connection are all in uppercase):

[0064]

[0065] According to the above seven-parameter analytical formula of photovoltaic modules, the required data points are as follows:

[0066] ①Short-circuit current point (0,I sc );

[0067] ②Short-circuit current point (0,I sc )'s attachment point (δU,I sc +δI), where δU is the minimum step size of the voltage modulation value of the voltage modulation module;

[0068] ③Point A (U a ,I a ), the current at this point I a Close to I sc , actual I a 0.8I is acceptable sc ;

[0069] ④Point B (U b ,I b ), this point should keep a certain distance from point A. b 0.6I is acceptable sc ;

[0070] ⑤C point (U c ,I c ), this point cannot be close to point A and point B, the actual I c 0.4I is acceptable sc ;

[0071] ⑥ Any point (U * ,I * ), which can be close to U oc , actual I * 0.2I is acceptable sc ;

[0072] ⑦ Any point (U * ,I * ) attachment point (δU+U * ,δI+I * ), where δU is the minimum step size of the voltage modulation value of the voltage modulation module;

[0073] ⑧Open circuit voltage point (U oc ,0). Description of the drawings:

[0074] Figure 1Flow chart of the method for calculating the seven parameters of the double diode model described in an exemplary embodiment of this specification;

[0075] Figure 2 Equivalent circuit diagram of the double diode model of the photovoltaic cell described in an exemplary embodiment of this specification;

[0076] Figure 3 Point selection diagram for calculating model parameters using the I-V curve described in an exemplary embodiment of this specification;

[0077] Figure 4 Simulation model diagram for obtaining parameter simulation data described in an exemplary embodiment of this specification;

[0078] Figure 5 Comparison diagram between the simulated I-V curve and experimental data described in an exemplary embodiment of this specification. Detailed implementation method:

[0079] The present invention provides a method for calculating the parameters of the double diode model of a photovoltaic cell. To make the objectives, technical solutions, and effects of the present invention clearer, further explanations are provided. The specific examples described in the present invention are only used to explain the present invention and are not used to limit the present invention.

[0080] The following further illustrates the present invention with reference to the accompanying drawings. The parameter calculation process of the double diode model of the photovoltaic cell is as Figure 1 shown, and specifically includes the following steps:

[0081] Step 1: According to the physical model of the double diode of the photovoltaic module, a new analytical formula for the seven parameters of the photovoltaic module is derived. This analytical formula does not require dU / dI at the maximum power point and the open circuit voltage point, thus reducing the dependence on the complete I-V data of the photovoltaic module.

[0082] The specific derivation process of the formula is as follows:

[0083] (1) According to the equivalent circuit diagram of the double diode model of the photovoltaic cell, the current characteristic equation of the photovoltaic cell is obtained using Kirchhoff's current law. The equivalent circuit of the double diode model of the photovoltaic cell is as Figure 2 shown. The current characteristic equation is as follows:

[0084]

[0085] where I ph is the photocurrent, I D1 is the current passing through the first diode, I D2 is the current passing through the second diode, I R is the current passing through the parallel resistor, I o1 and I o2is the reverse saturation current of the diode, n1 and n2 are the ideality factors of the diode, R s is the series resistance, R sh is the parallel resistance, I is the output current of the photovoltaic cell, U is the output voltage of the photovoltaic cell, q is the electron charge, k is the Boltzmann constant, and T is the temperature of the photovoltaic cell. In the following text, kT / q = V th .

[0086] (2) Taking the total differential of Equation (1) and finding the first derivative, we can obtain:

[0087]

[0088] After getting a common denominator and simplifying Equation (2), Equation (2) can be transformed into:

[0089]

[0090] (3) To obtain more parameter information of the solar cell, substituting the short - circuit current point (I = I sc , U = 0) into Equation (1) and Equation (2), we can obtain:

[0091]

[0092] In Equation (5), R sho is - dU / dI at the short - circuit current point, and the value of R sho can be calculated from Equation (6). During the calculation, points (δU, I sc +δI) need to be sampled near the short - circuit current point.

[0093]

[0094] Then substituting the open - circuit voltage point (I = 0, U = U oc ) into Equation (1), we can obtain:

[0095]

[0096] (4) From Equation (4) and Equation (7), I ph can be eliminated to obtain the following equation:

[0097]

[0098] (5) Simplifying Equation (8)

[0099] Simplification principle: R sh ≈R sho >>R s , then 1 + R s / R sh ≈1

[0100] U oc >>Isc R s , then exp(U oc / n i / V th ) >> exp(I sc R s / n i / V th )(i = 1, 2)

[0101] It can be obtained that:

[0102]

[0103] (6) Usually, I o2 is 3 to 4 times that of I o1 . The relationship between the two can be approximately expressed by Equation (9). For the convenience of calculation, I o2 in the following text is rewritten as KI o1 .

[0104]

[0105] Combining Equation (9) and Equation (10) to eliminate I o2 , we get:

[0106]

[0107] Equation (11) eliminates I ph , R s , R sh , I o2 in the seven parameters, and reflects the relationship between the reverse saturation current I o1 of the diode, the ideality factors n1 and n2 of the diode and the output characteristics, that is, I o1 = f(u, i; n1, n2).

[0108] (7) It can be known from Equation (3) that the relationship between R s and -dU / dI(R * , I * ) at any point (U so * ), and R sh ≈R sho , it can be obtained that:

[0109]

[0110] Equation (12) eliminates I ph , R sh , I o2 in the seven parameters, and reflects the series resistance R s , the reverse saturation current I o1, the relationship between the diode ideality factors n1, n2 and the output characteristics, i.e., R s = g(u, i; n1, n2, I o1 ).

[0111] In Equation (12), the value of R so * can be calculated from Equation (13).

[0112]

[0113] (VIII) Take a point A(U a , I a ) on the I-V curve and substitute it into Equation (1), we get:

[0114]

[0115] Substitute Equation (14) into Equation (4) and eliminate all terms except I ph , we get:

[0116]

[0117] Simplify Equation (15), we have R sh ≈R sho >> R s , then 1 + R s / R sh ≈ 1, we get:

[0118]

[0119] Equation (16) eliminates I ph , R sh , I o2 , and reflects the relationship between the diode reverse saturation current I o1 , the diode ideality factors n1, n2, the series resistance R s and the output characteristics, i.e., I o1 = h(u, i; n1, n2, R s ).

[0120] (IX) Substitute Equation (11) I o1 = f(u, i; n1, n2) into Equation (16) I o1 = h(u, i; n1, n2, R s ) to eliminate I o1 , we get:

[0121]

[0122] Substitute exp((U i + I i R s) / n j / V th ) is denoted as exp(I sc R s / n i / V th ) is denoted as φ i (i = 1, 2), exp(U oc / n i / V th ) is denoted as γ i (i = 1, 2), Equation (17) can be simplified to:

[0123]

[0124] (X) The value on the right side of Equation (17) is a constant. To solve this problem, a point B(U b , I b ) can be taken on the I-V curve, and then according to steps (VIII)(IX), we get:

[0125]

[0126] From Equation (18) and Equation (19), we can obtain:

[0127]

[0128] Equation (20) only contains the seven-parameter n1, n2, R s , which reflects the relationship between the series resistance R s , the diode ideality factors n1, n2 and the output characteristics, that is, x(u, i; n1, n2) = y(u, i; R s ).

[0129] (XI) According to Equation (11) I o1 = f(u, i; n1, n2) and Equation (12) R s = g(u, i; n1, n2, I o1 ), eliminating I o1 we can get:

[0130]

[0131] Equation (21) is the expression of the series resistance R s and the diode ideality factors n1, n2, that is, R s = l(u, i; n1, n2). Substituting R s = l(u, i; n1, n2) into and φ i (i = 1, 2), after eliminating R s they are respectively denoted as θ ij(i=a,b,cj=1,2) and λ i (i=1,2). So far θ ij With λ i It only contains unknown parameters n1 and n2.

[0132] (XII) R s = l(u,i; n1, n2) Substitute into equation (20) and eliminate R s , we get an equation containing only the unknowns n1 and n2:

[0133]

[0134] Let equation (22) be expressed as equation ①.

[0135] (XIII) To solve for the values ​​of n1 and n2, another equation is needed, so we can take point C (U c ,I c ), according to steps (eight) and (nine), we can get:

[0136]

[0137] Then through steps (10), (11), (12), we can get the second equation:

[0138]

[0139] Let equation (24) be expressed as equation ②.

[0140] (XIV) By combining equation ① with equation ②, we can solve for the values ​​of n1 and n2.

[0141] (XV) Using formula (10) and formula (11) o1 =f(u,i;n1,n2) to find the diode reverse saturation current I o1 ,I o2 :

[0142]

[0143] (XVI) Using formula (12) R s =g(u,i;n1,n2,I o1 ) Find the series resistance R s :

[0144]

[0145] (XVII) Using formula (5) R sh =t(u,i;n1,n2,I o1 ,I o2 , R s ) Find the parallel resistance Rsh , and then use Equation (4) I ph = w(u, i; n1, n2, I o1 , I o2 , R s , R sh ) to calculate the photocurrent I ph .

[0146] Step 2: Connect a single photovoltaic module to the voltage debugging module, and combine the analytical formula in Step 1 to sample and calculate the required voltage and current data points. The specific sampling conditions are as Figure 3 shown. The required data points are as follows:

[0147] ① Short-circuit current point (0, I sc );

[0148] ② Attachment point (δU, I sc + δI) of the short-circuit current point (0, I sc ), where δU is the minimum step size of the modulation voltage value of the voltage modulation module;

[0149] ③ Point A (U a , I a ). The current I a at this point can be close to I sc . The actual I a can take 0.8I sc ;

[0150] ④ Point B (U b , I b ). This point should be kept at a certain distance from Point A. The actual I b can take 0.6I sc ;

[0151] ⑤ Point C (U c , I c ). This point cannot be close to Point A and Point B. The actual I c can take 0.4I sc ;

[0152] ⑥ Any point (U * , I * ). This point can be close to U oc . The actual I * can take 0.2I sc ;

[0153] ⑦ Attachment point (δU + U * , δI + I * ) of any point (U * , I * ), where δU is the minimum step size of the modulation voltage value of the voltage modulation module;

[0154] ⑧ Open-circuit voltage point (U oc , 0).

[0155] Combining the obtained 8 data points with the analytical formula can calculate the seven parameters of the photovoltaic module. The calculated seven parameters are the parameters after m photovoltaic cells with the same state are connected in series. The corresponding relationships between the parameters are as follows (the subscripts of each parameter after series connection are represented in capital letters):

[0156]

[0157] Step 3: Put the seven parameters obtained through calculation in Step 2 into the Simulink simulation model. This model is equipped with 72 photovoltaic cells and is simulated under standard test conditions. The structure of the simulation model is as Figure 4 shown. Then, compare the I-V curve obtained from the simulation with the experimental data to verify the accuracy of the calculation results. The comparison between the I-V curve obtained from the simulation and the experimental data is as Figure 5 shown.

[0158] The above gives the specific implementation methods in engineering applications, but the present invention is not limited to the described implementation methods. The basic principle and method of the present invention lie in the above basic solution. Without departing from the principle and spirit of the present invention, changes, modifications, substitutions, and deformations made to the implementation methods still fall within the protection scope of the present invention.

Claims

1. A method for calculating the parameters of a double-diode model of a photovoltaic cell, characterized in that: Obtain the U characteristic curve of the photovoltaic module. By taking partial voltage and current data points of the module, calculate seven parameters (photo-generated current I ph , reverse saturation current of the diode I o1 , I o2 , diode ideality factors n1, n2, series resistance R s , parallel resistance R sh ) that characterize the physical properties of the photovoltaic module. The specific steps are as follows: Step 1: Based on the dual-diode physical model of photovoltaic modules, a new seven-parameter analytical formula for photovoltaic modules is derived. Step 2: Connect the PV panels to the voltage debugging module to obtain the 8 data points required to calculate the seven parameters. Step 3: Substitute the data points into the seven-parameter analytical formula in step 1 to calculate the seven parameters of the component.

2. According to the method of claim 1, the seven-parameter analytical formula in step 1 is derived as follows: (I) According to the double diode model equivalent circuit diagram of photovoltaic cells, we can get: Where I ph is the photocurrent, I o1 and I o2 is the reverse saturation current of the diode, n1 and n2 are the ideality factors of the diode, R s is the series resistance, R sh is the shunt resistance, I is the output current of the photovoltaic cell, U is the output voltage of the photovoltaic cell, q is the electron charge, k is the Boltzmann constant, and T is the temperature of the photovoltaic cell. In the following text, kT / q = V th . (ii) Taking the first-order derivative of the total differential of equation (1), we can obtain: By simplifying formula (2), formula (2) can be transformed into: (3) To obtain more parameter information of the solar cell, substitute the short-circuit current point (I = I sc , U = 0) into equations (1) and (2), and the following can be obtained: Then substitute the open-circuit voltage point (I = 0, U = U oc ) into Equation (1), and we can get: (4) By eliminating I from Equation (4) and Equation (6), ph the following equation is obtained: (V) Simplify formula (7) Simplification principle: R sh ≈R sho >>R s , then 1 + R s / R sh ≈1 U oc >> I sc R s , then exp(U oc / n i / V th ) >> exp(I sc R s / n i / V th )(i = 1, 2) We can get: (6) Usually I o2 is I o1 3 to 4 times that of, and the relationship between the two can be approximately expressed by Equation (9). For the convenience of calculation, I o2 in the following text is rewritten as KI o1 . Combining Equation (8) and Equation (9) to eliminate I o2 , we get: (7) It can be seen from formula (3) that R s is related to -dU / dI(R * , I * ) at any point (U so * ), and since R sh ≈R sho , it can be obtained that: (8) Take point A (U a , I a ) on the I-V curve and substitute it into Equation (1) to obtain: Substitute Equation (12) into Equation (4) and eliminate all terms except I ph , and we get: Simplifying Equation (13), we have R sh ≈R sho >>R s , then 1 + R s / R sh ≈ 1, and we get: (IX) Substitute formula (10) into formula (14) to eliminate I o1 , and we get: Denote exp((U i +I i R s ) / n j / V th ) as Denote exp(I sc R s / n i / V th ) as φ i (i = 1, 2), denote exp(U oc / n i / V th ) as γ i (i = 1, 2), Equation (15) can be simplified to: (10) The value on the right side of Equation (15) is a constant. To solve this problem, a point B(U b , I b ) can be taken on the I-V curve, and then obtained according to steps (8) and (9): From formula (16) and formula (17), we can get: (11) Eliminate I according to Equation (10) and Equation (11) o1 It can be obtained that: Substitute Equation (19) into and φ i (i = 1, 2), eliminate R s and denote them as θ ij (i = a, b, c j = 1, 2) and λ i (i = 1, 2). So far, θ ij and λ i only contain unknown parameters n1 and n2. (12) Substitute Equation (19) into Equation (18) to eliminate R s , obtaining an equation that only contains the unknowns n1 and n2: (13) To solve for the values of n1 and n2, another equation is needed. Therefore, a point C(U c , I c ) can be taken on the I-V curve. According to steps (8) and (9), we can obtain: Then through steps (10), (11), (12), we can get the second equation: (XIV) By combining equations (21) and (22), we can solve for the values ​​of n1 and n2. (15) Use Equation (9) and Equation (10) to find the reverse saturation current I of the diode o1 、I o2 : (16) Calculate the series resistance R using Equation (11). s : (17) Calculate the parallel resistance R using Equation (5) sh , and then calculate the photocurrent I using Equation (4) ph . The seven parameters calculated are the parameters of m photovoltaic cells in the same state connected in series. The corresponding relationship between the parameters is as follows (the subscripts of the parameters after series connection are all in uppercase):

3. According to the seven-parameter analytical formula of the photovoltaic module in claim 2, the required voltage and current data points are: (1) Short-circuit current point (0, I sc ); (2) Short - circuit current point (0, I sc ) attachment point (δU, I sc + δI), where δU is the minimum step of the voltage modulation value modulated by the voltage modulation module; (3)Point A (U a , I a ), the current at this point I a can be close to I sc , the actual I a can take 0.8I sc ; (4) Point B (U b , I b ), this point should be kept at a certain distance from point A, actually I b can take 0.6I sc ; (5) Point C (U c , I c ), this point cannot be close to point A and point B, actually I c can take 0.4I sc ; (6) Any point (U * , I * ), this point can be close to U oc , the actual I * can take 0.2I sc ; (7) Attachment points (δU + U * , I * ) of any point (U * , δI + I * ), where δU is the minimum step of the modulation voltage value of the voltage modulation module; (8) Open circuit voltage point (U oc , 0).

4. In combination with claims 2 and 3, the calculated seven parameters are put into the simulation model for simulation, and the obtained IV curve is compared with the experimental data to verify the accuracy of the calculation results.

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