CN103633937A - Solar cell parameter extracting method based on Lambert W function and polynomial fitting - Google Patents
Solar cell parameter extracting method based on Lambert W function and polynomial fitting Download PDFInfo
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Abstract
一种基于Lambert W函数和多项式拟合的太阳电池参数提取方法，该方法首先利用Lambert W函数将太阳电池电流输出超越方程显化后积分，得显化积分方程；其次，对太阳电池电流电压输出曲线分三段进行拟合，得分段函数；再次，对分段函数积分，得分段积分方程；最后，选取太阳电池伏安特性曲线上测量值，建立分段积分方程与显化积分方程相等的方程组，从而解析求解出太阳电池光生电流、反向饱和电流、理想因子、并联电阻和串联电阻5个电性参数。本发明的技术效果是：通过光照下太阳电池单条伏安特性曲线，可较简单且较高精度的提取电池光生电流等5个电性参数。
A solar cell parameter extraction method based on Lambert W function and polynomial fitting, the method first uses the Lambert W function to manifest the solar cell current output transcendental equation and then integrates to obtain the manifested integral equation; secondly, the solar cell current voltage output The curve is fitted in three sections to obtain a piecewise function; again, the piecewise function is integrated to obtain a piecewise integral equation; finally, the measured values on the volt-ampere characteristic curve of the solar cell are selected to establish a piecewise integral equation and a manifest integral equation Equivalent equations, thus analytically solving five electrical parameters of the solar cell photogenerated current, reverse saturation current, ideality factor, parallel resistance and series resistance. The technical effect of the invention is: through a single volt-ampere characteristic curve of the solar cell under light, five electrical parameters such as the photogenerated current of the cell can be extracted relatively simply and with high precision.
Description
Technical field
The present invention relates to a kind of solar cell parameter extracting method, be specifically related to a kind of solar cell parameter extracting method based on Lambert W function and fitting of a polynomial.
Background technology
Solar cell parameter comprises photogenerated current, reverse saturation current, and ideal factor, parallel resistance and series resistance, solar cell parameter extraction technology obtains broad research in photovoltaic field, because these parameters are to weigh the important evidence of solar cell quality; But the solar cell electric current output equation that comprises above parameter is a transcendental equation, cannot resolve and obtain each parameter.In order to address this problem, people put forward various solar cell parameter extracting method [(Xiao Wenbo etc., photoelectron # laser, 2012.23 (9): 1681), (L L Peng, et aL, JournaL of Power Sources, 2013,227(1): 131)], the target that all methods are pursued is easy and high-precision extraction solar cell parameter.
At this, we propose a kind of based on Lambert W function and fitting of a polynomial, set up the equation group of Analytical Solution solar cell photogenerated current, reverse saturation current, ideal factor, parallel resistance and 5 electrical parameters of series resistance, extract the new method of battery parameter.
Summary of the invention
The object of this invention is to provide a kind of solar cell parameter extracting method based on Lambert W function and fitting of a polynomial, this sun parameter extracting method only relies on solar cell wall scroll volt-ampere characteristic under illumination, can realize the extraction solar cell parameter of simple and degree of precision.
The present invention is achieved by the following technical solutions, and its characterization method step is:
(1) utilize Lambert W function by solar cell electric current output transcendental equation rear integration clear, obtain integral equation clear;
(2) to solar cell volt-ampere characteristic, divide three sections to carry out matching, obtain piecewise function;
(3) to above-mentioned piecewise function integration, obtain segmentation integral equation;
(4) choose measured value in solar cell volt-ampere characteristic, set up the equation group that subsection integral equation equates with integral equation clear, thus the sunny battery photogenerated current of Analytical Solution, reverse saturation current, ideal factor, parallel resistance and 5 electrical parameters of series resistance;
(5) by above-mentioned 5 electrical parameter substitution solar cell electric currents output transcendental equation, the volt-ampere characteristic under overall matching illumination, obtains root-mean-square error.
In step of the present invention (1), utilize Lambert W function by solar cell electric current output transcendental equation in clear and integral process, be take voltage as integration variable electric current be integrand.
In step step of the present invention (2), to solar cell volt-ampere characteristic, divide three sections to carry out matching, three sections of fitting functions are respectively an order polynomial, quadratic polynomial and quadratic polynomial.
In step of the present invention (4), set up in the equation group process that integral equation clear equates with subsection integral equation, need to choose measured value in volt-ampere characteristic.
In step of the present invention (5), by above-mentioned 5 electrical parameter substitution solar cell electric currents output transcendental equation overall situation matching volt-ampere characteristic, can obtain the root-mean-square error of evaluating extracting parameter effect.
Solar cell electric current output transcendental equation of the present invention is:
Utilize LambertW function solar cell electric current clear output transcendental equation, and to its integration, can obtain integral equation clear and be:
Solar cell volt-ampere characteristic is divided into three sections, carries out respectively an order polynomial, quadratic polynomial and cubic polynomial matching; Wherein first paragraph is a fitting of a polynomial, and matching voltage range is
; Second segment is quadratic polynomial matching, and matching voltage range is
; The 3rd section is quadratic polynomial matching, and matching voltage range is
.
Three sections of fitting functions are respectively:
To three sections of fitting functions respectively from 0 volt to
volt interval integral, can obtain segmentation integral equation and be respectively:
（4）
In above formula (1), (2), (3) and (4)
ifor solar cell output current,
i ph for photogenerated current; ,
i 0 for diode reverse saturation current
, Vfor solar cell output voltage,
r s for equivalent series resistance,
nfor Diode Ideality Factor,
v th thermal voltage constant,
r sh for equivalent parallel resistance,
i sc ,
v oc ,
i m with
v m be respectively electric current and the voltage at solar cell short circuit current, open circuit voltage, maximum power point place,
be respectively volt-ampere characteristic piecewise fitting coefficient,
fto obtain function after integration.
Choose measured value in solar cell volt-ampere characteristic, set up the equation group (being the equation group that formula (2) equates with formula (4)) that integral equation clear equates with subsection integral equation, thus the sunny battery photogenerated current of Analytical Solution, reverse saturation current, ideal factor, parallel resistance and 5 electrical parameters of series resistance; By 5 parameter substitution solar cell electric current output equations of the solar cell extracting, overall matching volt-ampere characteristic, obtains root-mean-square error.
Method of the present invention and traditional solar cell parameter extracting method relatively have following characteristics: 1, utilize Lambert W function solar cell electric current output transcendental equation clear and minute three sections of Function Fitting solar cell volt-ampere characteristic, can resolve the equation group that 5 electrical parameters such as battery photogenerated current are extracted in foundation simultaneously; 2, integration clear and minute three sections of Function Fitting means in the method, can avoid the accidental error of certain measurement data in volt-ampere characteristic to affect extracting parameter precision; 3, the method is simple and have the advantages that precision is higher, for solar cell parameter extraction at present provides an effective approach.
Accompanying drawing explanation
Fig. 1 is that measurement of the present invention and matching single solar cell are measured and matching volt-ampere characteristics of figure.
Fig. 2 is that measurement of the present invention and matching assembly solar cell are measured and matching volt-ampere characteristics of figure.
Embodiment
The present invention is a kind of method that only relies on solar cell wall scroll volt-ampere characteristic extraction battery parameter under illumination.
As an example, we utilize the method to propose 5 electrical parameters such as monomer and assembly solar cell photogenerated current.Test and fitting result are as shown in Figure 1 and Figure 2; Concrete operations are that the method for utilizing common making alive to survey electric current is measured the volt-ampere characteristic of solar cell; Then, sharp contents extraction solar cell parameter of the present invention; Finally, adopt volt-ampere characteristic under solar cell electric current output transcendental equation matching illumination.
From Fig. 1-2, measure and fitting result, can find out and coincide finely, for single solar cell, the photogenerated current extracting is 0.7637 ampere, and reverse saturation current is
ampere, ideal factor is 1.5736, and parallel resistance is 73.3281 ohm, and series resistance is 0.0366 ohm; For assembly solar cell, the photogenerated current extracting is 1.0372 amperes, and reverse saturation current is
ampere, ideal factor is 50.7886, and parallel resistance is 553.0657 ohm, and series resistance is 1.2530 ohm.Root-mean-square error for monomer and assembly solar cell is respectively 0.0046 ampere and 0.0181 ampere; From error, can find out very littlely, 5 parameters precisions that namely extract are higher.
Above example illustrates that the solar cell parameter extracting method that we propose is correct, and the method will obtain certain popularization in the middle of the research of current solar cell parameter extraction technology.
The above; it is only the embodiment in the present invention; but protection scope of the present invention is not limited to this; any people who is familiar with this technology is in the disclosed technical scope of the present invention; the conversion that can expect easily or replacement; all should be encompassed in of the present invention comprise scope within, therefore, protection scope of the present invention should be as the criterion with the protection range of claims.
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Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104237805A (en) * | 2014-10-09 | 2014-12-24 | 南昌航空大学 | Method for extracting solar cell parameters based on analytic equation |
| CN104462715A (en) * | 2014-12-24 | 2015-03-25 | 黑龙江科技大学 | Photovoltaic cell output characteristic modeling method based on Bezier function |
| CN104716903A (en) * | 2015-03-17 | 2015-06-17 | 上海交通大学 | Automatic segmentation polynomial fitting method applicable to photovoltaic array output characteristic curve |
| CN105827200A (en) * | 2016-03-01 | 2016-08-03 | 华为技术有限公司 | Photoelectric system battery pack string fault identification method, device and equipment |
| CN106446480A (en) * | 2016-12-06 | 2017-02-22 | 上海动力储能电池系统工程技术有限公司 | Fitting method of open circuit potential curves of electrode materials for lithium ion batteries |
| CN106527145A (en) * | 2016-12-13 | 2017-03-22 | 浙江工业大学 | Multi-mobile rotor single time-delay controller design method based on Lambert W function |
| CN108170199A (en) * | 2017-09-19 | 2018-06-15 | 河海大学常州校区 | A kind of control method of quick realization MPPT |
| CN108717471A (en) * | 2018-03-22 | 2018-10-30 | 杭州电子科技大学 | A kind of modeling method of voltage domain oscillation quantum device C-V characteristic |
| CN108804774A (en) * | 2018-05-22 | 2018-11-13 | 河海大学常州校区 | A method of based on electrochemical impedance spectroscopy test analysis solar cell ideal factor |
| CN112528211A (en) * | 2020-12-17 | 2021-03-19 | 中电科仪器仪表(安徽)有限公司 | Method for fitting solar cell IV curve |
| CN113346842A (en) * | 2021-08-02 | 2021-09-03 | 国网江西省电力有限公司电力科学研究院 | Online calculation method and device for solar cell series resistor resistance value |
| CN114859228A (en) * | 2022-05-23 | 2022-08-05 | 福建师范大学 | Efficient solar cell real-time diagnosis method based on reliable extraction of equivalent circuit parameters |
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Cited By (19)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN104237805A (en) * | 2014-10-09 | 2014-12-24 | 南昌航空大学 | Method for extracting solar cell parameters based on analytic equation |
| CN104462715A (en) * | 2014-12-24 | 2015-03-25 | 黑龙江科技大学 | Photovoltaic cell output characteristic modeling method based on Bezier function |
| CN104462715B (en) * | 2014-12-24 | 2017-09-15 | 黑龙江科技大学 | A kind of modeling method of the photovoltaic cell output characteristic based on Bezier functions |
| CN104716903A (en) * | 2015-03-17 | 2015-06-17 | 上海交通大学 | Automatic segmentation polynomial fitting method applicable to photovoltaic array output characteristic curve |
| CN105827200A (en) * | 2016-03-01 | 2016-08-03 | 华为技术有限公司 | Photoelectric system battery pack string fault identification method, device and equipment |
| US10985696B2 (en) | 2016-03-01 | 2021-04-20 | Huawei Technologies Co., Ltd. | Method, apparatus, and device for identifying cell string fault in optoelectronic system |
| CN105827200B (en) * | 2016-03-01 | 2019-05-03 | 华为技术有限公司 | Recognition methods, device and the equipment of battery pack string failure in electro-optical system |
| CN106446480A (en) * | 2016-12-06 | 2017-02-22 | 上海动力储能电池系统工程技术有限公司 | Fitting method of open circuit potential curves of electrode materials for lithium ion batteries |
| CN106527145B (en) * | 2016-12-13 | 2019-05-31 | 浙江工业大学 | Single controller for time delay design method of multiple mobile robot based on Lambert W function |
| CN106527145A (en) * | 2016-12-13 | 2017-03-22 | 浙江工业大学 | Multi-mobile rotor single time-delay controller design method based on Lambert W function |
| CN108170199A (en) * | 2017-09-19 | 2018-06-15 | 河海大学常州校区 | A kind of control method of quick realization MPPT |
| CN108717471A (en) * | 2018-03-22 | 2018-10-30 | 杭州电子科技大学 | A kind of modeling method of voltage domain oscillation quantum device C-V characteristic |
| CN108717471B (en) * | 2018-03-22 | 2022-01-04 | 杭州电子科技大学 | Modeling method for volt-ampere characteristic of voltage domain oscillation quantum device |
| CN108804774A (en) * | 2018-05-22 | 2018-11-13 | 河海大学常州校区 | A method of based on electrochemical impedance spectroscopy test analysis solar cell ideal factor |
| CN108804774B (en) * | 2018-05-22 | 2022-02-11 | 河海大学常州校区 | Method for analyzing ideal factor of solar cell based on electrochemical impedance spectrum test |
| CN112528211A (en) * | 2020-12-17 | 2021-03-19 | 中电科仪器仪表(安徽)有限公司 | Method for fitting solar cell IV curve |
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| CN114859228A (en) * | 2022-05-23 | 2022-08-05 | 福建师范大学 | Efficient solar cell real-time diagnosis method based on reliable extraction of equivalent circuit parameters |
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