CN107862125A - A kind of computational methods of polysilicon photovoltaic module carrier wave frequency range AC impedance parameter - Google Patents
A kind of computational methods of polysilicon photovoltaic module carrier wave frequency range AC impedance parameter Download PDFInfo
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Abstract
The invention discloses a kind of computational methods of polysilicon photovoltaic module carrier wave frequency range AC impedance parameter, it is characterised in that comprises the following steps：With Nonlinear Least-Square Algorithm, the real and imaginary parts curve for the impedance frequency characteristic for measuring obtained polysilicon photovoltaic module is fitted to a certain elliptic equation respectively；It is that three parameters are simplified equivalent-circuit model by four parameter predigestings in photovoltaic module AC impedance equivalent-circuit model；The elliptic equation and simple equivalent circuit obtained according to fitting, determines four parameters in photovoltaic module AC impedance equivalent-circuit model.The present invention derives four equivalent circuit parameters that photovoltaic module is calculated by curve matching and simple equivalent circuit, and can characterization parameter with the changing rule of frequency, calculating process is simple, result of calculation is more accurate.
Description
Technical Field
The invention relates to the field of solar photovoltaic power generation, in particular to a method for calculating alternating current impedance parameters of a carrier frequency band of a polycrystalline silicon photovoltaic module.
Background
In recent years, due to increasingly serious energy crisis and environmental pollution, photovoltaic power generation is more and more emphasized by various countries. The photovoltaic module is an important component in a photovoltaic power generation system, and has important significance for the research on the parameters of the alternating current impedance equivalent circuit of the photovoltaic module.
The most common existing photovoltaic cell direct current equivalent circuit model is a single-diode or double-diode circuit model, five parameters of a photovoltaic cell are solved, and inductance and capacitance parameters of the photovoltaic cell or a photovoltaic module are generally ignored. However, when the mutual influence between the photovoltaic modules in the photovoltaic power station and other devices is studied and carrier communication is performed between the photovoltaic modules, the alternating current impedance characteristics of the photovoltaic modules need to be studied.
The existing methods of adopting a time domain, a frequency domain and an alternating current impedance spectrum are used for researching the capacitance in a photovoltaic cell dynamic equivalent circuit model, but the methods are only applied to the photovoltaic cell model neglecting the series inductance, so that the influence and the specific size of the inductance cannot be reflected. Various calculation methods have been disclosed in the prior art, including: a method for determining the parameters of a dynamic equivalent circuit of a photovoltaic module by adopting a least square regression method is disclosed, but the calculation process of the method is more complex; a calculation method for deducing and calculating equivalent circuit parameters of a photovoltaic cell under no illumination according to a baud graph of the photovoltaic cell is provided, but the method only calculates the parameter value of a certain frequency point and cannot reflect the change rule of each parameter along with the frequency.
In summary, no method exists for calculating the alternating-current impedance parameters (equivalent series resistance, equivalent parallel capacitance, and equivalent series inductance) of the carrier frequency band of the photovoltaic module, which has a simple calculation process and can obtain the rule representing the alternating-current impedance equivalent circuit parameters of the polysilicon photovoltaic module along with the change of frequency.
Disclosure of Invention
Aiming at the defects that the parameter research in the photovoltaic component alternating current impedance equivalent circuit model is incomplete, the obtained parameter result cannot reflect the change rule along with the frequency and the like in the prior art, the invention aims to provide a simpler method for researching the alternating current impedance characteristic of the photovoltaic component carrier frequency band by fitting an impedance frequency characteristic curve by applying a nonlinear least square algorithm on the basis of the alternating current impedance equivalent circuit model of the polycrystalline silicon photovoltaic component and the measured photovoltaic component non-illumination impedance frequency characteristic and combining with a simplified equivalent circuit to deduce and calculate the parameter of the polycrystalline silicon photovoltaic component alternating current impedance equivalent circuit.
A method for calculating alternating current impedance parameters of a carrier frequency band of a polycrystalline silicon photovoltaic module is characterized by comprising the following steps:
step 1: measuring to obtain a real part and an imaginary part of the impedance frequency characteristic of the polycrystalline silicon photovoltaic module;
step 2: respectively fitting the real part and imaginary part curves of the measured impedance frequency characteristic of the polycrystalline silicon photovoltaic module into a certain elliptic equation by using a nonlinear least square algorithm;
and 3, step 3: the four-parameter R in the photovoltaic module alternating current impedance equivalent circuit model s 、R p 、C p 、L s Simplified to three parameters Re (Z) and C pe 、L s Obtaining a simplified equivalent circuit model, wherein R s 、R p 、C p 、L s The equivalent series resistance, the equivalent parallel capacitance and the equivalent series inductance of the photovoltaic module are respectively; re (Z), C pe The equivalent series capacitors are respectively the real part of the photovoltaic module and the simplified equivalent circuit model;
and 4, step 4: and determining four parameters in the alternating current impedance equivalent circuit model of the photovoltaic module according to the fitted elliptic equation and the simplified equivalent circuit model.
The photovoltaic module is a polycrystalline silicon photovoltaic module in a serial connection mode of photovoltaic cells. The equivalent impedance of the photovoltaic module is:
Z＝Re(Z)+jIm(Z) (1)
in the formula, Z represents the equivalent impedance of the photovoltaic module, re (Z), im (Z) represent the real part and imaginary part of the equivalent impedance Z of the photovoltaic module, respectively, wherein:
order:
in the formula, R s 、R p 、C p And L s Respectively representing the equivalent series resistance, the equivalent parallel capacitance and the equivalent series inductance of the photovoltaic module, wherein omega is angular frequency.
The center of the ellipse equation is obtained by equations (5) and (6):
in the above two formulae, (a) 0 ，b 0 )、(a 1 ，b 1 ) Is the center of the ellipse, and a 0 、a 1 、b 0 >0，b 1 <0；m 0 、m 1 And n 0 、n 1 Respectively the major and minor axes of the ellipse.
The equivalent parallel resistance and the equivalent parallel capacitance contribute to the imaginary part of the equivalent impedance of the photovoltaic module equivalently to be equivalent series capacitance C pe The contribution of the equivalent parallel resistance and the equivalent parallel capacitance to the real part of the equivalent impedance of the photovoltaic module and the equivalent series resistance are equivalent to a resistance, namely the real part Re (Z) of the equivalent impedance of the photovoltaic module, and the expression of the simplified equivalent circuit is as follows:
where ω is the angular frequency.
Equivalent series resistance R of photovoltaic module s The change with frequency is small and can be regarded as a constant value, R p 、C p 、L s Is a function of frequency, i.e. R p (f)、C p (f)、L s (f) Then R is s Comprises the following steps:
R s ＝b 0 (8)
due to b 1 &0, the first term of the formula (6) is the inductance L s (f) Perceptual part of the presentation, second item b 1 Is a series equivalent capacitor C pe (f) Capacitive part presented:
the imaginary part of the equivalent impedance of the simplified equivalent circuit of the photovoltaic component is represented by the formula (10):
substituting formula (9) for formula (10) to obtain L s (f) As in formula (11):
obtaining an intermediate variable R by an impedance equation of an alternating-current impedance equivalent circuit of the four-parameter photovoltaic module p (f)C p (f) As shown in formula (12):
substituting the formula (12) into an impedance equation of the alternating-current impedance equivalent circuit of the four-parameter photovoltaic module to obtain R p (f) And C p (f) Is represented by the formula (13) and the formula (14):
the curve may be fitted using an L-M iterative algorithm. The specific iterative process of the L-M algorithm is as follows: let x (i) denote the vector formed by the weight and the threshold of the ith iteration, and x (i + 1) is the vector formed by the new weight and the threshold, as shown in equation (15):
x(i+1)＝x(i)+Δx (15)
let the error evaluation function be:
in the formula, e i (x) Is the error (i =1,2, …, N);
in the formula (I), the compound is shown in the specification,is a gradient;is a jacobian matrix of the form:
Δ x is:
Δx＝-[J T (x)J(x)+μI] -1 J(x)e(x) (19)
in the formula (19), the proportionality coefficient μ >0 is constant, and I is a unit matrix.
Compared with the prior art, the invention has the following beneficial effects:
based on the alternating current impedance equivalent circuit model of the photovoltaic module and the measured impedance frequency characteristic, according to the characteristic that the measured real part and imaginary part curves of the photovoltaic module conform to one part of an elliptic equation, the measured real part and imaginary part are respectively subjected to curve fitting by using a nonlinear least square algorithm, and the parameter values of the alternating current impedance equivalent circuit of the photovoltaic module in a carrier frequency band are deduced and calculated by combining with a simplified equivalent circuit. Compared with the existing method for calculating the equivalent circuit parameters, the method not only can represent the change rule of the equivalent circuit parameters of the photovoltaic module along with the frequency, but also has the advantages of simple calculation process and more accurate calculation result.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings used for the embodiments of the present invention are given below for a brief description. It should be apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained according to the technical solution of the present invention without creative efforts for those skilled in the art.
FIG. 1 is a schematic diagram of an equivalent AC impedance circuit model of a photovoltaic module;
FIG. 2 is a graph of real and imaginary measurements of the impedance frequency characteristics of a non-illuminated photovoltaic module;
FIG. 3 is a flow chart of the L-M algorithm;
FIG. 4 is a simplified equivalent circuit diagram of a photovoltaic module;
FIG. 5 is a diagram of fitting real and imaginary components to an ellipse using a non-linear least squares algorithm;
fig. 6 is a graph of the calculation result of the equivalent parallel resistance, the equivalent parallel capacitance, and the equivalent series inductance of the photovoltaic module.
Detailed Description
The following detailed description of the present invention is provided in connection with the accompanying drawings and examples.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments.
A method for calculating alternating current impedance parameters of a carrier frequency band of a polycrystalline silicon photovoltaic module comprises the following steps:
step 1: and measuring to obtain a real part and an imaginary part of the impedance frequency characteristic of the polycrystalline silicon photovoltaic module.
The photovoltaic module is a polycrystalline silicon photovoltaic module in a series connection mode of photovoltaic cells, an alternating current impedance equivalent circuit of the photovoltaic module is shown in figure 1, and the impedance of the equivalent circuit is shown in a formula (1):
Z＝Re(Z)+jIm(Z) (1)
in the formula, Z represents the equivalent impedance of the photovoltaic module, and Re (Z) and Im (Z) represent the real part and the imaginary part of the impedance Z of the photovoltaic module respectively. Wherein:
order:
in the formula, R s 、R p 、C p And L s Respectively representing the equivalent series resistance, the equivalent parallel capacitance and the equivalent series inductance of the photovoltaic module, wherein omega is angular frequency.
Step 2: and respectively fitting the real part curve and the imaginary part curve (100 kHz-500 kHz) of the measured impedance frequency characteristic of the polycrystalline silicon photovoltaic module into a certain elliptic equation by using a nonlinear least square algorithm.
Impedance frequency characteristic measurement is carried out on the polycrystalline silicon photovoltaic module with the model number DM310-P156-72 (formed by connecting 72 cells 156 x 156mm in series) and the model number YL235P-29b (formed by connecting 60 cells 156 x 156mm in series) by using an impedance analyzer, and the change rule of the real part and the imaginary part along with the frequency in the frequency range of 100kHz-500kHz basically conforms to one part of an elliptic equation. The real and imaginary curves measured for the former are shown in fig. 2.
The method adopts the L-M iterative algorithm in the nonlinear least square algorithm to fit the curve, and the L-M algorithm is improved by dozens of times or even hundreds of times compared with the gradient descent method, and has the advantage of high convergence speed. The specific iterative process of the L-M algorithm is as follows: let x (i) denote the vector formed by the weight and the threshold of the ith iteration, and x (i + 1) is the vector formed by the new weight and the threshold, as shown in equation (5):
x(i+1)＝x(i)+Δx (5)
let the error evaluation function be:
in the formula, e i (x) Is the error (i =1,2, …, N).
In the formula (I), the compound is shown in the specification,is a gradient;is a jacobian matrix of the form:
Δ x is:
Δx＝-[J T (x)J(x)+μI] -1 J(x)e(x) (9)
in the formula (9), the proportionality coefficient μ >0 is constant, and I is a unit matrix. A flow chart of the L-M iterative process is shown in fig. 3. Fitting the real part curve and the imaginary part curve of the photovoltaic module 100kHz-500kHz obtained through measurement into a certain elliptic equation by using the algorithm, wherein the equation is shown as the following formula (10) and formula (11):
in the above two formulae, (a) 0 ，b 0 )、(a 1 ，b 1 ) Is the center of the ellipse, and a 0 、a 1 、b 0 >0，b 1 <0；m 0 、m 1 And n 0 、n 1 Respectively the major and minor axes of the ellipse.
And step 3: the method comprises the following steps of enabling four parameters R in an alternating current impedance equivalent circuit model of a photovoltaic module s 、R p 、C p 、L s Simplified to three parameters Re (Z) and C pe 、L s And obtaining a simplified equivalent circuit model. Wherein R is s 、R p 、C p 、L s The equivalent series resistance, the equivalent parallel capacitance and the equivalent series inductance of the photovoltaic module are respectively; re (Z), C pe The real part of the photovoltaic module and the equivalent series capacitance of the simplified equivalent circuit model are respectively.
In general, the series resistance R of a photovoltaic module s The variation with frequency is small and can be regarded as constant, and R p 、C p 、L s Should be a function of frequency, then R is obtained s As shown in formula (12):
R s ＝b 0 (12)
due to b 1 &0, the first term of the formula (11) can be regarded as the inductance L s (f) Perceptual part of the presentation, second item b 1 Can be regarded as a series equivalent capacitor C pe (f) The capacitive part presented, β in formula (4):
and 4, step 4: and determining four parameters in the AC impedance equivalent circuit model of the photovoltaic module according to the fitted elliptic equation and the simplified equivalent circuit.
The contribution of the equivalent parallel resistance and the equivalent parallel capacitance to the imaginary part of the component is equivalent to an equivalent series capacitance C pe If the contribution of the equivalent parallel resistance and the equivalent parallel capacitance to the real part of the component is equivalent to a resistance, i.e., the real part Re of the component, together with the equivalent series resistance, then fig. 1 can be simplified as shown in fig. 4, and the imaginary part can be written as equation (14):
the expression of the simplified equivalent circuit is as follows:
where ω is the angular frequency.
Substituting (13) into formula (14) to obtain L s (f) As in formula (15):
intermediate variable R is obtained from formula (2) and formula (3) p (f)C p (f) As shown in formula (16):
substituting formula (16) into formula (2) and formula (3) to obtain R p (f) And C p (f) Is represented by formula (17) and formula (18):
therefore, the real part Re (Z) and the imaginary part Im (Z) of the impedance of the photovoltaic module are obtained through measurement, and R is obtained through curve fitting s And L s (f) Then R can be calculated p (f) And C p (f) And therefore all parameters in the photovoltaic module alternating current impedance equivalent circuit model are obtained.
One specific embodiment of the invention is: measuring impedance frequency characteristics of a photovoltaic module with the model DM310-P156-72 (formed by connecting 72 pieces of 156mm multiplied by 156mm batteries in series) by using an Agilent 4294A impedance analyzer; the measurement environment is indoor, no illumination, the surface temperature of the component is 25 ℃, the measurement result of the photovoltaic component in the frequency range of 100kHz-500kHz applicable to carrier transmission is shown in figure 2, and the measurement data of partial frequency points are shown in table 1.
TABLE 1 measurement data of partial frequency points
According to the measurement result, performing ellipse fitting on the real part curve and the imaginary part curve without the illumination test in fig. 2 by using an L-M algorithm of a nonlinear least square algorithm, and obtaining fitting expressions of Re (Z), im (Z) and frequency f respectively as follows:
the correlation coefficients of the fitting of the real part and the fitting of the imaginary part ARE 0.94433 and 0.99982 respectively, the measured curve and the fitting curve ARE shown in fig. 5, the relative error of 100kHz-500kHz is shown in tables 2 and 3, and the fitting accuracy of the Absolute Relative Error (ARE) fitting curve to the measured curve is adopted in the error contrast analysis, and the formula is as follows:
TABLE 2 fitting and actual measurement error of 100kHz-500kHz real part
TABLE 3 100kHz-500kHz imaginary part fitting and actual measurement error
From the error analysis in tables 2 and 3, it can be seen that the real part and imaginary part fitting curves have errors ARE respectively less than 7% and 3.5% for the measured curve, which indicates that the fit degree between the ellipse equation obtained by fitting and the measured curve is better.
R of the photovoltaic module is obtained from the formula (19) s =0.61458 Ω; from formula (20) to b 1 = -16.03768, substituting formula (15) into L s (f) Substituting into formula (13) to obtain C pe (f) In that respect Measured values Re (Z) and Im (Z) and the calculated R s And L s (f) Substituting the formulae (17) and (18) to obtain R p (f) And C p (f)，R p (f)、L s (f)、C p (f) And C pe (f) The calculation results of (2) are shown in fig. 6, and the calculation results of partial frequency points are shown in table 4.
Table 4 partial frequency point parameter calculation results
Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (8)
1. A method for calculating alternating current impedance parameters of a carrier frequency band of a polycrystalline silicon photovoltaic module is characterized by comprising the following steps:
step 1: measuring to obtain a real part and an imaginary part of the impedance frequency characteristic of the polycrystalline silicon photovoltaic module;
step 2: respectively fitting the real part and imaginary part curves of the measured impedance frequency characteristic of the polycrystalline silicon photovoltaic module into a certain elliptic equation by using a nonlinear least square algorithm;
and step 3: the method comprises the following steps of enabling four parameters R in an alternating current impedance equivalent circuit model of a photovoltaic module s 、R p 、C p 、L s Simplified to three parameters Re (Z) and C pe 、L s Obtaining a simplified equivalent circuit model, wherein R s 、R p 、C p 、L s The equivalent series resistance, the equivalent parallel capacitance and the equivalent series inductance of the photovoltaic module are respectively; re (Z), C pe The real part of the photovoltaic module and the equivalent series capacitance of the simplified equivalent circuit model are respectively;
and 4, step 4: and determining four parameters in the alternating current impedance equivalent circuit model of the photovoltaic module according to the fitted elliptic equation and the simplified equivalent circuit model.
2. The method for calculating the carrier frequency band alternating current impedance parameter of the polycrystalline silicon photovoltaic module according to claim 1, wherein the photovoltaic module is a polycrystalline silicon photovoltaic module in a photovoltaic cell series connection mode.
3. The method for calculating the alternating current impedance parameter of the carrier frequency band of the polycrystalline silicon photovoltaic module according to claim 2, wherein the equivalent impedance of the photovoltaic module is as follows:
Z＝Re(Z)+jIm(Z) (1)
wherein Z represents the equivalent impedance of the photovoltaic component, re (Z) and Im (Z) respectively represent the real part and the imaginary part of the equivalent impedance Z of the photovoltaic component,
wherein:
order:
in the formula, R s 、R p 、C p And L s Respectively representing the equivalent series resistance, the equivalent parallel capacitance and the equivalent series inductance of the photovoltaic module, wherein omega is angular frequency.
4. The method for calculating the alternating current impedance parameter of the carrier frequency band of the polycrystalline silicon photovoltaic module according to claim 3, wherein the center of the ellipse equation is obtained by the following formulas (5) and (6):
in the above two formulae, (a) 0 ，b 0 )、(a 1 ，b 1 ) Is the center of the ellipse, and a 0 、a 1 、b 0 >0，b 1 <0；m 0 、m 1 And n 0 、n 1 Respectively the major and minor axes of the ellipse.
5. The method as claimed in claim 4, wherein in step 3, the equivalent parallel resistance and the equivalent parallel capacitance are equivalent to an equivalent series capacitance C pe The contribution of the equivalent parallel resistance and the equivalent parallel capacitance to the real part of the equivalent impedance of the photovoltaic module and the equivalent series resistance are equivalent to a resistance, namely the real part Re (Z) of the equivalent impedance of the photovoltaic module, and the expression of the simplified equivalent circuit is as follows:
where ω is the angular frequency.
6. The method for calculating the carrier frequency band alternating current impedance parameter of the polycrystalline silicon photovoltaic module according to claim 5, wherein the equivalent series resistance R of the photovoltaic module s The change with frequency is small and can be regarded as constant, R p 、C p 、L s Is a function of frequency, i.e. R p (f)、C p (f)、L s (f) Then R is s Comprises the following steps:
R s ＝b 0 (8)
due to b 1 &0, the first term of formula (6) is inductance L s (f) Perceptual part of the presentation, second item b 1 Is a series equivalent capacitor C pe (f) Capacitive part presented:
the imaginary part of the equivalent impedance of the simplified equivalent circuit of the photovoltaic component is represented by the formula (10):
substituting formula (9) for formula (10) to obtain L s (f) As in formula (11):
obtaining an intermediate variable R by an impedance equation of an alternating-current impedance equivalent circuit of the four-parameter photovoltaic module p (f)C p (f) As shown in formula (12):
substituting the formula (12) into an impedance equation of the four-parameter photovoltaic module alternating current impedance equivalent circuit to obtain R p (f) And C p (f) Is represented by the formulae (13) and (14):
7. the method for calculating the alternating current impedance parameter of the carrier frequency band of the polycrystalline silicon photovoltaic module according to claim 1, is characterized in that: and fitting the curve by adopting an L-M iterative algorithm in the step 1.
8. The method for calculating the alternating current impedance parameter of the carrier frequency band of the polycrystalline silicon photovoltaic module according to claim 7, wherein the specific iterative process of the L-M algorithm is as follows: let x (i) denote the vector formed by the weight and the threshold of the ith iteration, and x (i + 1) is the vector formed by the new weight and the threshold, as shown in equation (15):
x(i+1)＝x(i)+Δx (15)
let the error evaluation function be:
in the formula, e i (x) Is the error (i =1,2, …, N);
in the formula (I), the compound is shown in the specification,is a gradient;is a jacobian matrix of the form:
Δ x is:
Δx＝-[J T (x)J(x)+μI] -1 J(x)e(x) (19)
in the formula (19), the proportionality coefficient μ >0 is constant, and I is a unit matrix.
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