Photovoltaic module model parameter identification method

Abstract

Disclosed in the present invention is a photovoltaic module model parameter identification method, comprising the following steps: 1) measuring and recording an I-V curve of a photovoltaic module in a standard test environment; 2) deriving an explicit expression of voltage and current on the basis of an equivalent circuit of a single-diode model; 3) converting a parameter identification problem into an optimization problem, determining a parameter search space of a target function in the optimization problem, solving the optimization problem and obtaining five parameter values of the model by means of parameter conversion; and 4) using the explicit expression in step 2) to simulate the I-V curve, and calculating a simulation error. The present invention improves a parameter identification method for a single-diode model, which requires only one calculation, thereby reducing the calculation amount and improving the accuracy and stability of identification.

Description

A photovoltaic module model parameter identification method TECHNICAL FIELD

[0001] The present application relates to the technical field of photovoltaic module identification, and particularly refers to a photovoltaic module model parameter identification method. BACKGROUND

[0002] There are various types of cell structures for photovoltaic modules, such as PERC, TOPCon, HJT, perovskite, etc. In the future, in order to pursue higher photoelectric conversion efficiency and adapt to different application scenarios, it is also necessary to have multiple cell structures, but the cell structure types and market share will change, and the existence of multiple cells poses new requirements for modeling.

[0003] The photovoltaic cell model includes a single diode model, a double diode model, a power law model, etc. Among these models, the single diode model is applied to modeling of different cells due to its balanced performance and strong applicability. The single diode model is generally associated with an I-V curve, and the process of obtaining the I-V curve from the model is the process of applying the model, while the process of obtaining the model parameters from the I-V curve is called parameter identification. Parameter identification is the basis for model application, and the usual method starts from the solving algorithm, although certain achievements have been made, but there are still problems of large amount of calculation and unstable calculation.

[0004] SUMMARY

[0005] The purpose of the present application is to provide a photovoltaic module model parameter identification method, which is accurate and stable.

[0006] The above-mentioned purpose of the present application is realized by the following technical scheme: a photovoltaic module model parameter identification method, characterized in that the method comprises the following steps:

[0007] Step 1: obtaining an I-V curve under standard test conditions (STC) of the module;

[0008] Step 2: obtaining an explicit expression of voltage and current from the single diode model equivalent circuit;

[0009] Step 3: constructing and solving an optimization problem to obtain three parameter values, and converting the three parameter values to obtain five parameters of the model.

[0010] Optionally, the I-V curve under the STC environment of the module is measured according to the requirements in the standard IEC 61215-2:2021 Terrestrial photovoltaic (PV) modules-Design qualification and type approval-Part 2: Test procedures.

[0011] In the present application, the step 2 specifically comprises:

[0012] Step 2.1: obtaining an implicit expression of voltage and current according to a single diode model and Kirchhoff's law:

[0013] Wherein, R s is a series resistance, R sh is a parallel resistance, I is a port current, I ph is a battery photoelectric current, I o is a reverse saturation current of a diode, exp is an exponential power of natural constant e, V is a port voltage, q is an electron charge (1.6×10 -19 C), n is an equivalent diode factor of a component, k B is a Boltzmann constant (1.38×10 -23 J / K), and T is an absolute temperature of the component.

[0014] Step 2.2: converting the implicit expression into an explicit expression by introducing a Lambert W function:

[0015] In the formula, f(V) represents a function relationship about voltage V, is a temperature potential, and W is a Lambert W function.

[0016] In the present application, the step 3 specifically comprises:

[0017] Step 3.1: obtaining a continuous target function g(x, DIV, V, I) by introducing a derivative of an I-V curve and characteristic information of a short-circuit point: g(x, DIV, V, I) = K(DIV·x1+1)(x2-V+KI)+(K·DIV-1)x3 (3)

[0018] Wherein, g(x, DIV, V, I) represents a continuous target function, represents a first-order derivative of current to voltage, V represents a port voltage, I represents a port current, is characteristic information of a short-circuit point, and x = [x1, x2, x3] represents a target function parameter.

[0019] Step 3.2: discretizing the continuous target function g(x, DIV, V, I) to obtain:

[0020] Wherein, g(x, div, v, i) represents a discrete target function, · represents a dot product, represents a Hadamard product, 1 represents a vector full of 1s, div represents a first-order difference quotient of a sampling point, v represents a voltage of a sampling point, i represents a current of a sampling point, and k is a resistance value:

[0021] where I sc is the short-circuit current, v0and i0are the voltage and current at the first sampling point, v1and i1are the voltage and current at the second sampling point, j is the index of the I-V curve data point, j ∈ [1, N-1], v j-1 and i j-1 are the voltage and current at the jth sampling point, v j and i j are the voltage and current at the (j+1)th sampling point, and v j-1 satisfies:

[0022] where |·| denotes the absolute value, v m-1 is the voltage at the mth sampling point, N is the number of I-V curve data points, is an arbitrary symbol, & denotes and, denotes the integer field.

[0023] Step 3.3: Determine the value range of each parameter in the discrete objective function of step 3.2;

[0024] Step 3.4: Construct the optimization problem:

[0025] where min denotes the minimum value of the function, denotes the square of the 2-norm of the vector, x m and x M denote the minimum and maximum values of the objective function parameter x, respectively.

[0026] Step 3.5: Solve the optimization problem to obtain the objective function parameter x = [x1, x2, x3];

[0027] Step 3.6: Convert the objective function parameter to the photovoltaic module model parameter, with the conversion method being: R s = x1 (8) R sh = -k - R s (9)

[0028] where v N-1 and i N-1 are the voltage and current at the Nth sampling point. When the open-circuit voltage V oc is given, equation (12) simplifies to:

[0029] The application can be improved as follows: the method further comprises step 4: calculating the simulation current corresponding to each sampling point voltage in the I-V curve by using the explicit expression obtained in step 2.2 and the photovoltaic module model parameters obtained in step 3.6, and calculating the normalized root mean square error of the simulation current, and finally verifying the accuracy and stability of the application by judging whether the simulation error of the algorithm is within the set threshold.

[0030] Compared with the prior art, the application has the following beneficial effects:

[0031] First, the information of the I-V curve is fully utilized, a continuous objective function is constructed by introducing the derivative of the I-V curve and the feature information of the key points, and the continuous objective function is further discretized, thereby reducing the parameter amount of the objective function.

[0032] Second, the value range of the parameters is determined based on the objective function, thereby reducing the search space.

[0033] Third, the parameter identification problem is converted into an optimization problem to obtain a more accurate parameter identification result, thereby reducing the model calculation error.

[0034] Fourth, the explicit expression of the SDM is used to calculate the performance indicators of the component, thereby reducing the calculation amount.

[0035] Fifth, the parameter identification method provided by the application is less affected by the solving algorithm, and the calculation is accurate and stable, thereby having wide application value. BRIEF DESCRIPTION OF DRAWINGS

[0036] The application will be further described in detail below in combination with the drawings and specific embodiments.

[0037] Fig. 1 is a schematic diagram of a single-diode equivalent circuit provided in an embodiment of the application;

[0038] Fig. 2 is a schematic diagram of a photovoltaic module model parameter identification method in an embodiment of the application;

[0039] Fig. 3 is a comparison of algorithms provided in an embodiment of the application, wherein the (a)(b)(c)(d) subgraphs are the simulation results of different algorithms for actual sampling points, specifically: Fig. (a) contains the simulation curve of the genetic algorithm (GA), Fig. (b) contains the simulation curve of the particle swarm algorithm (PSO), Fig. (c) contains the simulation curve of the interior point method (IPM), and Fig. (d) contains the simulation curve of the active set method (ASM). DETAILED DESCRIPTION

[0040] As shown in Fig. 2, an accurate and stable photovoltaic module single-diode model parameter calculation method comprises the following steps:

[0041] Step 1: Obtain the I-V curve of the component under standard test conditions (STC);

[0042] Step 2: Obtain the explicit expression of voltage and current according to the single diode model equivalent circuit;

[0043] Step 3: Convert the parameter identification problem into an optimization problem, solve the optimization problem to obtain the three parameter values, and convert the three parameter values to obtain the five parameters of the model;

[0044] Step 4: Obtain the simulated I-V curve by applying the single diode model, and compare the simulated curve with the real curve to obtain the model calculation error.

[0045] The specific process of each step is as follows:

[0046] In step 1, the I-V curve under the STC environment of the component is measured according to the requirements in the standard “IEC 61215-2:2021 Terrestrial photovoltaic (PV) modules-Design qualification and type approval-Part 2:Test procedures”, and the voltage and current values of each sampling point of the I-V curve are retained.

[0047] In step 2, the steps to obtain the explicit expression of the single diode model include:

[0048] The single diode model (SDM) of the photovoltaic component is improved from the theoretical physical model, which takes into account the voltage drop of the p-n junction and the heat generated during operation. The equivalent circuit of SDM is shown in Figure 1. According to Kirchhoff's law, the function relationship of the port current and voltage of Figure 1 is:

[0049] where R s is the series resistance, R sh is the parallel resistance, I is the port current, I ph is the light-generated current of the battery, I o is the reverse saturation current of diode D, exp is the exponential power of natural constant e, V is the port voltage, q is the electron charge (1.6×10 -19 C), n is the equivalent diode ideality factor of the component, k B is the Boltzmann constant (1.38×10 -23 J / K), and T is the absolute temperature of the component. In practice, the component temperature is measured in Celsius t, and the conversion relationship between T and t is: T=t+273.15

[0050] Equation (1) can be simplified as:

[0051] where, temperature potential.

[0052] Equation (2) is an implicit expression, and the voltage and current are interrelated, which is not convenient for solving performance indicators. By introducing the Lambert W function, the implicit expression is changed to an explicit expression:

[0053] In the formula, f(V) represents the function relationship about voltage V, W is the Lambert W function, and the expression is W(x)exp(W(x)) = x (4)

[0054] Where x is used to refer to the variable.

[0055] In step 3, the steps of SDM parameter identification include:

[0056] Step 3-1, construct the objective function.

[0057] Directly taking the expression f(V)-I as the objective function expression is still complex, and the number of to-be-solved parameters is also large. On the basis of the explicit expression of the photovoltaic cell circuit, the derivative information of the I-V curve and the key features of the short-circuit point are added to simplify the objective function. The initial objective function obtained is: g(x, DIV, V, I) = K(DIV-x1+1)(x2-V+KI)+(K-DIV-1)x3 (5)

[0058] Where g(x, DIV, V, I) represents a continuous objective function, represents the first-order derivative of the current with respect to the voltage, V represents the port voltage, and I represents the port current, is the feature information of the short-circuit point, x = [x1, x2, x3] represents the parameters of the objective function, and the function relationship between these parameters and the SDM parameters is x1 = R s (6) x2 = R sh (I ph +I o ) (7) x3 = -nV t K (8)

[0059] The existing objective function is a continuous function, in order to apply the function, the variables in it are discretized to obtain a discrete objective function. Assuming that the I-V curve has N data points, the coordinates of the j+1th data point are (v j ,i j ). Equation (5) can be discretized as:

[0060] where g(x, div, v, i) is the discrete objective function, · denotes the dot product, denotes the Hadamard product, 1 denotes a vector of all ones, v = [v1,..., v j ,...v N-1 ] denotes the partial sampled point voltage, j is the index of the I-V curve partial data point, j ∈ [1, N-1], i = [i1,..., i j ,...i N-1 ] denotes the partial sampled point current, div = [div1,..., div j ,...div N-1 ] denotes the partial sampled point first-order difference quotient, k denotes the resistance value. div j is expressed as:

[0061] where div j denotes the first-order difference quotient of the j+1th data point.

[0062] k is expressed as:

[0063] where I sc is the short-circuit current, v0and i0are the voltage and current of the first sampling point, respectively, v1and i1are the voltage and current of the second sampling point, respectively, v j-1 and i j-1 are the voltage and current of the jth sampling point, respectively, v j and i j are the voltage and current of the j+1th sampling point, respectively, v j-1 satisfies:

[0064] where |·| denotes the absolute value, v m-1 is the voltage of the mth sampling point, is an arbitrary symbol.

[0065] Step 3-2, determine the definition domain of the objective function parameters.

[0066] The objective function of formula (9) contains three parameters, and their definition domains are respectively: x1∈[0, R sM ] (13) x2∈[-(k+R sM )I sc ,-kI sc ] (14) x3∈[-V t N s k,-2V t N s k] (15)

[0067] where R sM represents the series resistance R s , and k is the maximum value that can be achieved. N s represents the number of series-connected cells, and I sc represents the short-circuit current of the module, which can be obtained from the short-circuit point on the I-V curve or by consulting the product manual.

[0068] Step 3-3, constructing and solving the optimization problem.

[0069] The optimization problem can be constructed in combination with the objective function and the parameter domain of the objective function:

[0070] where min represents the minimum value of the function, represents the square of the 2-norm of the vector, x = [x1, x2, x3] represents the parameters of the objective function, and x m and x M are the minimum and maximum values of x, respectively, determined in step 3-2.

[0071] The solution of the optimization requires specifying an initial value x0 to start the iteration process, and let x0 = [x 10 , x 20 , x 30 ], their values are respectively:

[0072] Preferably, the solution of equation (16) is not unique, which can be divided into meta-heuristic algorithms and iterative algorithms, and the meta-heuristic algorithms further include genetic algorithms, particle swarm optimization algorithms, etc., and the iterative algorithms include interior point methods, active set methods, etc.

[0073] Step 3-4, restoring the SDM parameters from the objective function parameters.

[0074] The objective function of the optimization problem only contains three parameters, while the SDM model contains five parameters, so after solving the optimization problem, the objective function parameters need to be restored to the SDM parameters. The corresponding expression for the restoration process is: R s = x1 (20) R sh = -k - R s (21)

[0075] where V N-1 and I N-1 are the voltage and current of the Nth sampling point, respectively. When the open-circuit voltage V oc is given, equation (24) is simplified as:

[0076] In step 4, the steps of simulating the I-V curve are as follows:

[0077] For N sampling points of the I-V curve, the voltage and current values corresponding to the j+1th data point are (V j ,I j ), and the simulated current corresponding to each sampling point voltage is calculated using the formula in step 2, and the simulation curve is drawn. The normalized root mean square error (NRMSE) corresponding to the simulated current is defined as:

[0078] wherein, represents the simulated current corresponding to the voltage V j of the j+1th data point.

[0079] In this embodiment, the I-V curve of the module under the STC environment is measured according to the requirements in the standard “IEC 61215-2:2021 Terrestrial photovoltaic (PV) modules-Design qualification and type approval-Part 2:Test procedures”, and the specific data and calculation results obtained by parameter identification through the formula based on the related data of voltage and current of each sampling point of the obtained I-V curve are as follows:

[0080] S1, measure the I-V curve of the photovoltaic module under the STC environment, and the information of the curve sampling points is shown in Table 1:

[0081] Table 1: Information of I-V curve sampling points

[0082] wherein, the resolution of voltage is 1 mV, and the resolution of current is 0.1 mA.

[0083] S2, let R sM = 1 Ω, N s = 72, I sc = 5.5238 A, V t = 0.0257 V, Thus, the optimization problem can be constructed as: s.t.0≤x1≤1,1251.1≤x2≤1256.7,421.0≤x3≤841.9

[0084] wherein, v = [v1, v2, …, v 47 ] = [1.001, 2.005, …, 46.601], i = [i1, i2, …, i 47] = [5.5194, 5.5150,..., 0.004], div = [div1, div2,..., div 47 ] = [-0.0044, -0.0044,..., -1.0414], x = [xl, x2, x3].

[0085] The initial value of iteration x0 = [0.5, 1253.9, 631.45] is used to solve the above optimization problem by using genetic algorithm (GA), particle swarm algorithm (PSO), interior point method (IPM) and active set method (ASM), and the solving parameters are converted into model parameters. The parameter identification results obtained by different algorithms are shown in Table 2.

[0086] Table 2: Parameter identification results of four typical algorithms

[0087] S3, according to the formula (3), (4) of step 2, the simulation current corresponding to the voltage of each sampling point is obtained, and the true value and the simulation value are shown in Fig. 3. The simulation curves of (a), (b), (c), (d) four algorithms in the figure are close, which shows that the parameter identification method is less affected by the solving algorithm, and the algorithm is stable; the simulation error of four algorithms is calculated according to formula (26) and shown in Table 3.

[0088] Table 3: Simulation error of four algorithms

[0089] As shown in Table 3, the errors of various algorithms in the table are all within the range of (0, 0.1), and accurate fitting results are obtained.

Claims

1. A method for photovoltaic module model parameter identification, characterized in that, The method comprises the following steps: Step 1: obtaining the I-V curve of the component standard test condition; Step 2: obtaining the explicit expression of voltage and current according to the single diode model equivalent circuit; Step 3: constructing and solving the optimization problem to obtain the three parameter values, and converting the three parameter values to obtain the five parameters of the model.

2. The photovoltaic module model parameter identification method according to claim 1, wherein The step 2 specifically comprises: Step 2.1: Implicit expressions for voltage and current are obtained from the single-diode model and Kirchhoff's law: where R s is the series resistance, R sh is the parallel resistance, I is the port current, I ph is the battery photocurrent, I o is the reverse saturation current of the diode, exp is the exponential power of the natural constant e, V is the port voltage, q is the electron charge (1.6 x 10 -19 C), n is the equivalent diode ideality factor of the component, k B is the Boltzmann constant (1.38 x 10 -23 J / K), and T is the absolute temperature of the component. Step 2.2: Convert the implicit expression to an explicit expression by introducing the Lambert W function: In the formula, f(V) represents a functional relationship with respect to the voltage V, For temperature potential, W is the Lambert W function.

3. The photovoltaic module model parameter identification method of claim 2, wherein, The step 3 specifically comprises: Step 3.1: obtaining the continuous objective function by introducing the derivative of the I-V curve and the characteristic information of the short-circuit point: g(x, DIV, V, I) = K(DIV*x1+1)(x2-V+KI)+(K*DIV-1)x3 (3) where g(x, DIV, V, I) represents a continuous objective function, denotes the first derivative of the current with respect to the voltage, V denotes the port voltage, I denotes the port current, The characteristic information of the short-circuit point is x = [x1, x2, x3] represents the objective function parameters; Step 3.2: The continuous objective function g(x, DVI, V, I) is discretized to: where g(x, div, v, i) represents a discrete objective function, and • represents a dot product, denotes the Hadamard product, 1 denotes a vector of all ones, div denotes the first difference quotient of the sampling points, v denotes the voltage of the sampling points, i denotes the current of the sampling points, k is the resistance value: where I sc is the short-circuit current, v0and i0are the voltage and current at the first sampling point, v1and i1are the voltage and current at the second sampling point, j is the index of the I-V curve partial data point, j ∈ [1, N-1], v j-1 and i j-1 are the voltage and current at the jth sampling point, v j and i j are the voltage and current at the j+1th sampling point, v j-1 satisfies: where |·| denotes the absolute value, v m-1 Vm is the voltage of the mth sampling point, and N is the number of I-V curve data points, For any symbol, & denotes a logical AND, Indicates an integer domain; Step 3.3: determining the value range of each parameter in the discrete objective function of step 3.2; Step 3.4: Formulate the optimization problem: where min denotes the minimum value of the function, denotes the square of the vector 2-norm, x m and x M denotes the minimum and maximum value of the objective function parameter x, respectively; Step 3.5: solving the optimization problem to obtain the objective function parameters x = [x1, x2, x3]; Step 3.6: converting the objective function parameters into photovoltaic component model parameters, and the conversion mode is: R s = x1 (8) R sh = -k - R s (9) where v N-1 and i N-1 are the voltage and current at the Nth sample point, respectively; when the open circuit voltage V oc is given, equation (12) simplifies to:

4. The photovoltaic module model parameter identification method of claim 3, wherein, The method further comprises step 4: calculating the simulation current corresponding to each sampling point voltage in the I-V curve by using the explicit expression obtained in step 2.2 and the photovoltaic component model parameters obtained in step 3.6, and calculating the normalized root mean square error of the simulation current, and finally verifying the accuracy and stability of the method by judging whether the simulation error is within the set threshold.

Images