CN108306617B - Method for solving maximum power point parameter of ideal solar cell - Google Patents
Method for solving maximum power point parameter of ideal solar cell Download PDFInfo
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- CN108306617B CN108306617B CN201810064916.1A CN201810064916A CN108306617B CN 108306617 B CN108306617 B CN 108306617B CN 201810064916 A CN201810064916 A CN 201810064916A CN 108306617 B CN108306617 B CN 108306617B
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- 238000013499 data model Methods 0.000 abstract 1
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- 238000010248 power generation Methods 0.000 description 4
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- 239000002210 silicon-based material Substances 0.000 description 2
- JBRZTFJDHDCESZ-UHFFFAOYSA-N AsGa Chemical compound [As]#[Ga] JBRZTFJDHDCESZ-UHFFFAOYSA-N 0.000 description 1
- 229910017214 AsGa Inorganic materials 0.000 description 1
- 229910004613 CdTe Inorganic materials 0.000 description 1
- 229910021417 amorphous silicon Inorganic materials 0.000 description 1
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02S—GENERATION OF ELECTRIC POWER BY CONVERSION OF INFRARED RADIATION, VISIBLE LIGHT OR ULTRAVIOLET LIGHT, e.g. USING PHOTOVOLTAIC [PV] MODULES
- H02S50/00—Monitoring or testing of PV systems, e.g. load balancing or fault identification
- H02S50/10—Testing of PV devices, e.g. of PV modules or single PV cells
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/50—Photovoltaic [PV] energy
Abstract
The invention discloses a method for solving a maximum power point parameter of an ideal solar cell, which comprises the following steps: establishing a mathematical model of an ideal solar cell and solving an output characteristic expression according to a data model; deducing an initial expression of the maximum power point according to the maximum power theory and the output characteristic expression; and correcting the initial expression of the maximum power point of the solar cell by adopting the temperature and the daily intensity of the cell to obtain a solving formula of the maximum power point of the solar cell. The invention has the advantages that: (1) the analytical solving method is established on the basis of strict theoretical derivation, avoids a loop iteration algorithm, has clear variable relation and convenient solution, and overcomes the defects of a common numerical solving method. (2) The analytical solving method can visually reflect the influence of factors such as the temperature and the sunlight intensity of the solar cell on the parameter of the maximum power point, the practical engineering application is more convenient, and the parameter solving precision is higher than that of the general analytical solving method.
Description
Technical Field
The invention relates to the technical field of solar photovoltaic power generation, in particular to an ideal solar cell power prediction and parameter analysis solving method.
Background
The solar cell has the advantages of direct photoelectric conversion, cleanness, no pollution, high power density and the like, so that the proportion of solar power generation to the total power generation in China shows a trend of exponential increase year by year. However, the solar cell needs to obtain the corresponding maximum power point parameter in the process of maximum power point tracking. In addition, the efficiency of the solar cell is gradually reduced when the solar cell is exposed to sunlight and severe weather for a long time, and meanwhile, a certain proportion of faults occur in the solar cell panel, so that the solar power generation system needs to be periodically maintained and replaced. And the judgment of the faults of the solar cell module and the replacement of the equipment also need to be carried out according to the maximum power point parameter.
However, the mathematical expression of the output characteristic of the solar cell is a transcendental equation containing an index, and the values of a plurality of variables in the expression are related to the sunlight intensity and the cell temperature, so that the calculation process of the electrical parameters of the solar cell is complex and the solution is difficult. The common numerical solving method based on the algorithms such as the Lambert W function, the mode search, the artificial bee colony and the like has large calculated amount, difficult convergence and larger influence of the calculated result on the initial value. While other analytic solving formulas derived by the median theorem and the linear least square method have the defect of large parameter calculation error.
Therefore, the existing technologies have yet to be improved and developed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for solving the maximum power point parameter of an ideal solar cell.
In order to achieve the purpose, the invention adopts the technical scheme that: a method for solving the maximum power point parameter of an ideal solar cell comprises the following steps:
establishing a mathematical model of an ideal solar cell and solving an output characteristic expression according to the mathematical model;
deducing an initial expression of the maximum power point according to the maximum power theory and the output characteristic expression;
and correcting the initial expression of the maximum power point of the solar cell by adopting the temperature and the sunshine intensity of the cell to obtain a solving formula of the maximum power point of the solar cell.
The ideal solar cell model is a current source and a diode connected in parallel.
The expression of the output characteristic found from the mathematical model of an ideal solar cell is:
wherein I, V is the output current and output voltage, I, respectively, of an ideal solar cellphIs a photo-generated current representing a current source, IoIs the reverse saturation current of the diode, q is the charge of an electron, k is the boltzmann constant, NsIs the number of cells connected in series, T is the temperature of the solar cell, and n is the desired factor for the solar cell.
Photo-generated current I of solar cellphThe calculation formula of (2) is as follows:
wherein S is the intensity of sunlight, SrIs reference to the intensity of sunlight, TrIs the reference temperature of the solar cell, Iph_rIs the short-circuit current mu of the solar cell under the standard test condition provided by the solar cell manufacturerIIs the short circuit current temperature coefficient provided by solar cell manufacturers.
Short-circuit current temperature coefficient mu provided by solar cell manufacturersIAnd open circuit voltage temperature coefficient muVThe calculation formula for obtaining the corrected reverse saturation current is as follows:
wherein, Voc_rIs the open circuit voltage, mu, of the solar cell under the standard test condition provided by the solar cell manufacturerVThe open-circuit voltage temperature coefficient is provided by solar cell manufacturers, and the value of the ideal factor n of the solar cell is determined by the materials used by the solar cell.
The maximum power point initial expression obtaining method comprises the following steps:
when the ideal solar cell is at the maximum power point (V)mp,Imp) And then, according to the maximum power theory, the following steps are obtained:
calculating a derivative of an ideal solar cell output voltage V on an output characteristic expression and combining a maximum power theory to obtain:
maximum power point voltage:
maximum power point current:
considering the influence of the battery temperature and the solar intensity on the maximum power point, introducing a linear relation among the battery temperature, the solar intensity and the maximum power point to simplify an initial expression of the maximum power point, wherein the linear relation among the battery temperature, the solar intensity and the maximum power point voltage is as follows:
Vmp_ris the maximum power point voltage under the standard test conditions provided by the solar cell manufacturers; substituting the linear relation into the initial expression of the maximum power point to obtain solving expressions of the maximum power point voltage, the maximum power point current and the maximum power of the solar cell, wherein the solving expressions are respectively as follows:
Pmp＝Vmp·Imp。
the invention has the advantages that:
(1) the analytical solving method is established on the basis of strict theoretical derivation, avoids a loop iteration algorithm, has clear variable relation and convenient solution, and overcomes the defects of a common numerical solving method.
(2) The analytical solving method can visually reflect the influence of factors such as the temperature and the sunlight intensity of the solar cell on the parameter of the maximum power point, the practical engineering application is more convenient, and the parameter solving precision is higher than that of the general analytical solving method.
Drawings
The contents of the expressions in the various figures of the present specification and the labels in the figures are briefly described as follows:
FIG. 1 is a flow chart of the solution of the maximum power point parameter of an ideal solar cell according to the present invention;
fig. 2 is an equivalent circuit model of an ideal solar cell of the present invention.
Detailed Description
The following description of preferred embodiments of the invention will be made in further detail with reference to the accompanying drawings.
Fig. 1 shows a preferred embodiment of the present invention, which includes the following implementation steps:
and step S1, establishing a mathematical model and an output characteristic expression of the ideal solar cell.
The internal structure of a solar cell is a PN junction made of semiconductor material that converts solar energy directly into direct current, much like a diode. Therefore, if the factors such as the resistance characteristic and the loss of the cell material are neglected, the solar cell can be equivalent to a parallel connection of a current source and a diode, i.e. an ideal solar cell, as shown in fig. 2.
In addition, the voltage of a single solar cell is only about 0.5V, the power generally does not exceed 2W, and manufacturers generally adopt NsThe individual cells are connected in series to obtain sufficient voltage and power. Therefore, from the mathematical model of fig. 2, it can be derived that the output characteristic expression of an ideal solar cell is:
wherein I, V is the output current and output voltage, I, respectively, of an ideal solar cellphIs a photo-generated current representing a current source, IoIs the reverse saturation current of the diode, q is the charge amount of one electron (1.6 × 10)-19C) K is Boltzmann constant (1.38X 10)-23J/K), T is the temperature of the solar cell, and n is the desired factor for the solar cell.
Step S2, solving the photo-generated current I of the ideal solar cellphReverse saturation current IoAnd an ideality factor n.
When the solar cell is open-circuited (I ═ 0) and short-circuited (V ═ 0), the solar cell short-circuit current I can be obtained by the formula (1) respectivelyscAnd an open circuit voltage VocExpression (2)
Isc＝IphFormula (2)
The magnitude of the photo-generated current of the solar cell depends on the sunlight intensity and the working temperature of the cell, and the calculation formula is generally as follows:
wherein S is the intensity of sunlight, SrIs the reference solar intensity (1000W/m)2)，TrIs the reference temperature (25 ℃) of the solar cell Iph_rIs a standard test condition provided by solar cell manufacturers (the sunlight intensity is 1000W/m)2Short circuit current, mu, at a temperature of 25 ℃ C.)IIs the short circuit current temperature coefficient provided by solar cell manufacturers.
When the solar cell is open-circuited, the reference temperature T can be obtained by the formula (1)rLower, reverse saturation current Io_rThe expression of (a) is:
wherein, Voc_rIs the open circuit voltage of the solar cell under the standard test conditions provided by the solar cell manufacturer.
While a reverse saturation current IoThe solar cell is determined by the structure and material properties of the PN junction of the solar cell, is greatly influenced by the temperature of the solar cell and has no relation with the solar intensity S basically. Therefore, under the common temperature, the temperature coefficient mu of the short-circuit current provided by a solar cell manufacturer is introducedIAnd open circuit voltage temperature coefficient muVThe short circuit current and the open circuit voltage are expressed as a linear function of the battery temperature T. Thus reverse saturation current IoThe calculation formula for the battery temperature T is:
in addition, the value of the ideal factor n of the solar cell is determined by the materials used by the solar cell, and in the solving method, the value of n is taken according to the materials used by the cell: the monocrystalline silicon material n is 1.2, the polycrystalline silicon and AsGa material n is 1.3, the CdTe and CIS material n is 1.5, and the amorphous silicon material n is 1.8.
Step S3, solving the maximum power point current I of the ideal solar cellmpMaximum power point voltage VmpAnd maximum power Pmp。
When the ideal solar cell is at the maximum power point (V)mp,Imp) Then, equation (7) holds according to the maximum power theory:
the derivative with respect to the ideal solar cell output voltage V is taken for equation (1), then equation (7) holds true for equation (8):
by combining the formulas (1) and (8), the maximum power point voltage V can be deducedmpAnd maximum power point current ImpExpression (c):
as can be seen from equation (9), it belongs to the transcendental equation, and there is no way to do with VmpDirect solution, in turn, leads to ImpAnd PmpThere is no way to solve directly. At present VmpThe more general analytical solution formula is to the right of equation (9)
By open circuit voltage VocInstead of, Isc+IoBy short-circuit current IscInstead, then VmpBecomes equation (11):
as can be seen from equation (11), this is VmpAnd V derived by median theoremmpAre completely consistent and are adopted as V by many documentsmpThe calculation formula of (2). Although the solution of equation (11) is more convenient than equation (9), the open-circuit voltage V is usedocInstead of the former
And with IscIn place of Isc+IoAfter that, make VmpThe parameter error of (2) becomes significantly larger, so that the formula (11) cannot be applied to the occasion with higher requirement on parameter solving precision.
Another treatment for formula (9) is to introduce ε (0)<ε<1) Factor, using epsilon factor to characterize open circuit voltage VocAnd maximum power point voltage VmpBetweenSo that V ismpBecomes high in solution accuracy, corresponding to VmpThe calculation formula becomes:
but the maximum power point voltage V of the actual solar cellmpThe numerical value is ε V on the right side of the formula (12) in relation to the battery temperature and the solar radiation intensityocThis cannot be reflected, and therefore, equation (12) also has a large parameter error.
On the other hand, the maximum power point voltage VmpAnd the relationship between the battery temperature and the solar radiation intensity can be expressed by an approximate linear estimation formula of equation (13):
wherein, Vmp_rIs the maximum power point voltage under the standard test conditions provided by solar cell manufacturers.
The formula (13) can accurately reflect the maximum power point voltage VmpAs a function of the battery temperature T and the solar radiation intensity S. Therefore, in the present invention, V on the right side of the formula (9)mpThe linear estimation formula of the formula (13) is used for replacing, so that accurate analytic solving formulas of the maximum power point voltage, the maximum power point current and the maximum power of the ideal solar cell can be obtained, and the formulas are respectively shown as the formulas (14), (15) and (16):
Pmp＝Vmp·Impformula (16)
The equations (14), (15) and (16) are analytical solving equations of the parameters of the maximum power point of the ideal solar cell, and it can be seen that the variable relationship is direct, the solution does not need an iterative algorithm, and higher parameter solving accuracy can be obtained. Equations (14), (15) and (16) do not have transcendental equations compared with equations (9) and (10), calculation is more convenient, equations (14), (15) and (16) are obtained by transforming equations (9) and (10) by adopting an approximate linear estimation equation of equation (13), although partial errors of the approximate estimation equation (13) are introduced, the equations are close to accurately calculating equations (9) and (10) through engineering actual calculation, the actual errors are smaller than the errors directly adopting equation (13), the errors are within an allowable range of the engineering calculation, the purpose of fast calculation can be achieved, the actual engineering application is also more convenient, and the parameter solution accuracy is higher than that of equations (11) and (12) of a general analytic solution method.
It is clear that the specific implementation of the invention is not restricted to the above-described embodiments, but that various insubstantial modifications of the inventive process concept and technical solutions are within the scope of protection of the invention.
Claims (4)
1. A method for solving the maximum power point parameter of an ideal solar cell is characterized by comprising the following steps: comprises that
Establishing a mathematical model of an ideal solar cell and solving an output characteristic expression according to the mathematical model;
deducing an initial expression of the maximum power point according to the maximum power theory and the output characteristic expression;
correcting an initial expression of the maximum power point of the solar cell by adopting the temperature and the sunshine intensity of the cell to obtain a solving formula of the maximum power point of the ideal solar cell;
the expression of the output characteristic found from the mathematical model of an ideal solar cell is:
the maximum power point initial expression obtaining method comprises the following steps:
when the ideal solar cell is at the maximum power point (V)mp,Imp) And then, according to the maximum power theory, the following steps are obtained:
calculating a derivative of an ideal solar cell output voltage V on an output characteristic expression and combining a maximum power theory to obtain:
will express the formula
The initial expression of the maximum power point obtained by combining the output characteristic expression is as follows:
maximum power point voltage:
maximum power point current:
considering the influence of the battery temperature and the solar intensity on the maximum power point, introducing a linear relation among the battery temperature, the solar intensity and the maximum power point to simplify an initial expression of the maximum power point, wherein the linear relation among the battery temperature, the solar intensity and the maximum power point voltage is as follows:
Vmp_ris the maximum power point voltage under the standard test conditions provided by the solar cell manufacturers; substituting the linear relation into the initial expression of the maximum power point to obtain solving expressions of the maximum power point voltage, the maximum power point current and the maximum power of the solar cell, wherein the solving expressions are respectively as follows:
Pmp＝Vmp·Imp；
wherein I, V is the output current and output voltage, I, respectively, of an ideal solar cellphIs the photo-generated current of a current source, IoIs the reverse saturation current of the diode, q is the charge of an electron, k is the boltzmann constant, NsIs the number of cells connected in series, T is the temperature of the solar cell, n is the ideal factor of the solar cell, S is the solar intensityrIs reference to the intensity of sunlight, TrIs the solar cell reference temperature, μVIs an open-circuit voltage temperature coefficient, I, provided by solar cell manufacturersscShort-circuit current for the solar cell.
2. The method of claim 1, wherein the method comprises the following steps: the ideal solar cell model is a current source and a diode connected in parallel.
3. The method of claim 1, wherein the method comprises the following steps: photo-generated current I of solar cellphThe calculation formula of (2) is as follows:
wherein S is the intensity of sunlight, SrIs reference to the intensity of sunlight, TrIs the reference temperature of the solar cell, Iph_rIs the short-circuit current mu of the solar cell under the standard test condition provided by the solar cell manufacturerIIs the short circuit current temperature coefficient provided by solar cell manufacturers.
4. The method of claim 1, wherein the method comprises the following steps: short-circuit current temperature coefficient mu provided by solar cell manufacturersIAnd open circuit voltage temperature coefficient muVThe calculation formula for obtaining the corrected reverse saturation current is as follows:
wherein, Voc_rIs the open circuit voltage, mu, of the solar cell under the standard test condition provided by the solar cell manufacturerVThe open-circuit voltage temperature coefficient is provided by solar cell manufacturers, and the value of the ideal factor n of the solar cell is determined by the materials used by the solar cell.
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