CN105938504A - Method for precisely simulating performance of photovoltaic battery piece - Google Patents

Abstract

The method brings forward a method for precisely simulating performance of a photovoltaic battery piece. According to a solar battery duodiode model, the method comprises following steps: listing an equivalent equation of the output feature of the model; utilizing a Taylor's formula to descend power to solve such that relations between working current piece and working voltage of the battery is changed to be a linear function; and drawing an I-V curve corresponding to the battery piece based on the electricity performance parameter of the battery piece under the standard condition set by a manufacturer and obtaining electricity performance conditions under different working conditions by controlling light intensity and temperature of the battery piece. The method for precisely simulating performance of the photovoltaic battery piece has following beneficial effects: compared with a single-diode four-parameter method, the method has greater accuracy and especially has greater accuracy than a single-diode model under the condition of low irradiance; and the greatest working point basically coincides with parameters provided by the manufacturer within the range of degree of deviation of 2%.

Description

A kind of method of accurate simulation photovoltaic electrical performance of cell

Technical field

A kind of method that the present invention relates to accurate simulation photovoltaic electrical performance of cell, belongs to technical field of photovoltaic power generation.

Background technology

The model majority of simulation photovoltaic electrical performance of cell the most used is the most all single diode model, as it is shown in figure 1, application It is four parametric methods more widely, ignores parallel resistance R_shThe impact brought, owing to it has certain accuracy and calculating side Just.Document " complex method of polytype silion cell photovoltaic module performance simulation, Bai Jianbo, Hao Yuzhe, Zhang Zhen etc., the sun Can journal, 2014,35 (9): 1586-1591 " five parameter method that describes single diode extracts, and is allowed to result of calculation more accurate.

Along with photovoltaic plant is changed interesting by electrical property during sound state shadow occlusion at the enlarging in the whole world, photovoltaic module, has A lot of articles and patent are the research about this respect, and document " grind by the solar module output characteristics experiment that local shades blocks Study carefully, Zhang Zhen, Shen Hui, Li Da, solar energy journal, 2012,33 (1): 5-12 " describe the shadow occlusion of different proportion in the case of The power loss of assembly, " under the conditions of local shades, photovoltaic array models and Study on output characteristic document, Zhang Xiang, Wang Shisheng, electricity Source technology, 2015,39 (1): 203-206 " method for establishing model of local shades is described, but single diode analogy method pair There is certain error in the simulation under low irradiation.Document " Modelling and Simulation of photovoltaic module Consideringsingle-diode equivalent circuit model in MATLAB, Dominique.B, Zacharie.K, Donatien.N, Certified Journal, 2008,3 (3): 493-502 " describe double diode model can reduce under low irradiation Simulation error, but the Equivalent circuit equations of double diode model is considerably complicated, is non-linear relation between I-V, and be hidden letter How number, be allowed to become the focus that explicit function is problem.Document " double diode models show based on Taylor expansion is expressed, Yang Guihong, human relations are refined refined, electronic design engineering .2015, and 23 (23): 170-176 " propose to use Taylor's formula extracting parameter method to be allowed to into For dominant function, but computational methods are considerably complicated, and simply on the basis of five parameter list diodes, propose to be similar to seven Parametric method solves transcendental equation, does not have direct derivation to go out dominance relation corresponding to I-V.

Summary of the invention

The technical problem to be solved is the defect overcoming prior art, it is provided that a kind of accurately simulation photovoltaic cell is electrical The method of energy.

For solving above-mentioned technical problem, the technical solution used in the present invention is as follows:

A kind of method of accurate simulation photovoltaic electrical performance of cell, comprises the following steps:

1) equivalent equation of photovoltaic cell electrical property is obtained according to double diode equivalent model circuit diagram as follows:

I=I_ph-I_D1-I_D2-I_sh (1)

Wherein:

$I_{D1}=I_{01}\[\exp \left(\frac{V+{\mathrm{IR}}_s}{A_1{V}_T}\right)-1\]---\left(2\right)$

$I_{D2}=I_{02}\[\exp \left(\frac{V+{\mathrm{IR}}_s}{A_2{V}_T}\right)-1\]---\left(3\right)$

Wherein: I is the operating current of cell piece；I_phPhotogenerated current for cell piece；I_D1Dark current for equivalent diode D1； I_D2Dark current for equivalent diode D2；I_shLeakage current for equivalent parallel resistance；I₀₁For equivalent diode D1 due to electricity The reverse saturation current that son, the diffusion in hole cause；I₀₂For equivalent diode D2 owing to electronics, hole are in space-charge region The compound reverse saturation current caused again；A₁Structure factor for equivalent diode D1；A₂Structure for equivalent diode D2 The factor；V is the running voltage of cell piece；R_sFor equivalent series resistance；For the thermal voltage of cell piece, k is Bohr The most graceful constant, T is cell piece temperature, and q is charge coefficient；I₀For the reverse saturation current of equivalent diode, for equivalence two Pole pipe D1, I₀It is I₀₁, for equivalent diode D2, I₀It is I₀₂, I_o,refFor at reference temperature 25 DEG C, structure factor For reverse saturation current during A；T_c,refFor cell piece reference temperature；T_cFor the operating temperature that cell piece is present；E_gIt is partly to lead The energy gap of body silicon；

Bring formula (2), (3) into formula (1), and arrangement obtain:

$I=I_{ph}-I_{01}\{\exp \[\frac{(V+{\mathrm{IR}}_s)}{A_1{V}_T}\]-1\}-I_{02}\{\exp \[\frac{(V+{\mathrm{IR}}_s)}{A_2{V}_T}\]-1\}-\frac{V+{\mathrm{IR}}_s}{R_{sh}}---\left(5\right)$

Wherein: R_shEquivalent bypass resistance for cell piece；

2) formula (5) is written as form:

$I=I_{ph}-I_{01}(e^{\frac{V}{A_1{V}_T}}*e^{\frac{{\mathrm{IR}}_s}{A_1{V}_T}}-1)-I_{02}(e^{\frac{V}{A_2{V}_T}}*e^{\frac{{\mathrm{IR}}_s}{A_2{V}_T}}-1)-\frac{V+{\mathrm{IR}}_s}{R_{sh}}---\left(9\right)$

By in formula (9)Xiang HeItem carries out Taylor expansion, and takes linear segment, obtains:

$\begin{array}{c}I=I_{ph}-I_{01}\[e^{\frac{V}{A_1{V}_T}}*(1+\frac{{\mathrm{IR}}_s}{A_1{V}_T})-1\]-I_{02}\[e^{\frac{V}{A_2{V}_T}}*(1+\frac{{\mathrm{IR}}_s}{A_2{V}_T})-1\]-\frac{V+{\mathrm{IR}}_s}{R_{sh}}\\ =I_{ph}-I_{01}*e^{\frac{V}{A_1{V}_T}}*\frac{{\mathrm{IR}}_s}{A_1{V}_T}-I_{02}*e^{\frac{V}{A_2{V}_T}}*\frac{{\mathrm{IR}}_s}{A_2{V}_T}-I_{01}(e^{\frac{V}{A_1{V}_T}}-1)-I_{02}(e^{\frac{V}{A_2{V}_T}}-1)-\frac{V}{R_{sh}}-\frac{{\mathrm{IR}}_s}{R_{sh}}\end{array}---\left(10\right)$

After shifting to arrange:

$I=\frac{I_{ph}-\frac{V}{R_{sh}}-I_{01}(e^{\frac{V}{A_1{V}_T}}-1)-I_{02}(e^{\frac{V}{A_2{V}_T}}-1)}{1+\frac{I_{01}{R}_s}{A_1{V}_T}*e^{\frac{V}{A_1{V}_T}}+\frac{I_{02}{R}_s}{A_2{V}_T}*e^{\frac{V}{A_2{V}_T}}+\frac{R_s}{R_{sh}}}---\left(11\right)$

Wherein: I_ph, R_sh, R_sThered is provided by cell piece producer；I₀₁, I₀₂Directly obtain according to formula (4)；Take A₁=1, A₂=1.2； V_TRelevant with cell piece temperature；In this up-to-date style (11), only running voltage and operating current are unknown quantitys, just draw operating current I and Dominance relation between running voltage V；

3) use Matlab modeling, set running voltage and start until open-circuit voltage V from 0_ocTill, set step-length, just obtain Go out a series of working current value, draw curve, obtain the I-V curve of cell piece.

Aforesaid step 3) step-length be set to 0.001V.

The beneficial effect that the present invention is reached:

(1) the double diode Model Calculating Method of the inventive method is fairly simple, it is to avoid need in conventional simulation to use iterative method Or Lambert W function method, and there is the highest accuracy；

(2) (parallel resistance R is ignored relative to single diode four parametric method_sh) there is higher accuracy, particularly under low irradiation More single diode model is accurate；The parameter that maximum functional point substantially provides with producer overlaps, and the degree of deviation is within 2%；

(3) programming that the inventive method is some simulation softwards provides convenient, directly can be edited into function library by functional relationship, By given voltage step size directly draw cell piece difference irradiation and at a temperature of electrical property change.

Accompanying drawing explanation

Fig. 1 is single diode equivalent model；

Fig. 2 is double diode equivalent model；

The electrical performance of cell parameter of Fig. 3 producer offer and I-V curve；

Fig. 4 is that the cell piece of Fig. 3 uses single diode equivalent model simulation results；

Fig. 5 is that the cell piece of Fig. 3 uses double diode equivalent model analog result；

Fig. 6 is analog result and measured value comparison diagram；

Fig. 7 is analog result and the measured value degree of deviation of the present invention.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings.Following example are only used for clearly illustrating the technology of the present invention Scheme, and can not limit the scope of the invention with this.

The method accurately simulating photovoltaic electrical performance of cell of the present invention, comprises the following steps:

1) equivalent equation of photovoltaic cell electrical property is obtained according to double diode equivalent model circuit diagram as follows:

I=I_ph-I_D1-I_D2-I_sh (1)

Wherein:

$I_{D1}=I_{01}\[\exp \left(\frac{V+{\mathrm{IR}}_s}{A_1{V}_T}\right)-1\]---\left(2\right)$

$I_{D2}=I_{02}\[\exp \left(\frac{V+{\mathrm{IR}}_s}{A_2{V}_T}\right)-1\]---\left(3\right)$

The double diode equivalent model of photovoltaic cell as in figure 2 it is shown,

In formula: I is the operating current of cell piece；I_phPhotogenerated current for cell piece；I_D1Dark current for equivalent diode D1； I_D2Dark current for equivalent diode D2；I_shLeakage current for equivalent parallel resistance；I₀₁For equivalent diode D1 due to electricity The reverse saturation current that son, the diffusion in hole cause, relevant with cell piece temperature；I₀₂For equivalent diode D2 due to electronics, Hole is at the compound again reverse saturation current caused of space-charge region, relevant with cell piece temperature；A₁For equivalent diode D1 Structure factor；A₂Structure factor for equivalent diode D2；V is the running voltage of cell piece；R_sFor equivalent series resistance；For the thermal voltage of cell piece, k is Boltzmann constant, generally 1.38 × 10^-23J/K, T are cell piece temperature, Using kelvin degree, q is charge coefficient, generally 1.6 × 10^-19C；I₀For the reverse saturation current of equivalent diode, For equivalent diode D1, I₀It is I₀₁, for equivalent diode D2, I₀It is I₀₂, I_o,refFor at reference temperature 25 DEG C, Structure factor is reverse saturation current during A；T_c,refFor cell piece reference temperature, take 25 DEG C；T_cFor the work that cell piece is present Make temperature；E_gEnergy gap (typically E at 25 DEG C for semiconductor silicon_g=1.12eV).

Bring formula (2), (3) into formula (1), after arrangement:

$I=I_{ph}-I_{01}\{\exp \[\frac{(V+{\mathrm{IR}}_s)}{A_1{V}_T}\]-1\}-I_{02}\{\exp \[\frac{(V+{\mathrm{IR}}_s)}{A_2{V}_T}\]-1\}-\frac{V+{\mathrm{IR}}_s}{R_{sh}}---\left(5\right)$

Wherein: R_sFor cell piece equivalent series resistance, it is by the sheet resistance in diffusion top district, the bulk resistor of battery and upper and lower electricity Ohmage and the resistance of metallic conductor between pole and solar cell are constituted；R_shFor the equivalent bypass resistance of cell piece, mainly Formed by following two factor: the tracking current along battery edge that battery surface pollutes and produces；Along dislocation and crystal grain The irregular of boundary is spread or after electrode metallization processes, is formed along micro crack, grain boundary and crystal defect etc. Tiny bridge and the leakage current that produces.

2) it is nonlinear equation due to the equivalent equation of formula (5), and the corresponding relation of operating current I and running voltage V is Implicit function, it is impossible to solved by direct method, therefore the present invention propose use Taylor's formula carry out drop power solve, be allowed to become Become dominant function.

Taylor's formula: if function f (x) open interval (a, b) has until the derivative on n+1 rank, then when function is in this interval, At x=x₀The expansion at place is:

$f\left(x\right)=f\left(x_0\right)+f^{\′}\left(x_0\right)(x-x_0)+\frac{f^{\′\′}\left(x_0\right)}{2!}{(x-x_0)}^2+...+\frac{f^{\left(n\right)}\left(x_0\right)}{n!}{(x-x_0)}^n+R_n---\left(6\right)$

So having:

$e^x=1+x+\frac{x^2}{2!}+...+\frac{x^n}{n!}---\left(7\right)$

Take linear segment therein i.e.:

e^x=1+x (8)

Formula (5) can be to be written as form:

$I=I_{ph}-I_{01}(e^{\frac{V}{A_1{V}_T}}*e^{\frac{{\mathrm{IR}}_s}{A_1{V}_T}}-1)-I_{02}(e^{\frac{V}{A_2{V}_T}}*e^{\frac{{\mathrm{IR}}_s}{A_2{V}_T}}-1)-\frac{V+{\mathrm{IR}}_s}{R_{sh}}---\left(9\right)$

By in formula (9)Xiang HeItem carries out Taylor expansion, and takes linear segment, obtains:

$\begin{array}{c}I=I_{ph}-I_{01}\[e^{\frac{V}{A_1{V}_T}}*(1+\frac{{\mathrm{IR}}_s}{A_1{V}_T})-1\]-I_{02}\[e^{\frac{V}{A_2{V}_T}}*(1+\frac{{\mathrm{IR}}_s}{A_2{V}_T})-1\]-\frac{V+{\mathrm{IR}}_s}{R_{sh}}\\ =I_{ph}-I_{01}*e^{\frac{V}{A_1{V}_T}}*\frac{{\mathrm{IR}}_s}{A_1{V}_T}-I_{02}*e^{\frac{V}{A_2{V}_T}}*\frac{{\mathrm{IR}}_s}{A_2{V}_T}-I_{01}(e^{\frac{V}{A_1{V}_T}}-1)-I_{02}(e^{\frac{V}{A_2{V}_T}}-1)-\frac{V}{R_{sh}}-\frac{{\mathrm{IR}}_s}{R_{sh}}\end{array}---\left(10\right)$

After shifting to arrange:

$I=\frac{I_{ph}-\frac{V}{R_{sh}}-I_{01}(e^{\frac{V}{A_1{V}_T}}-1)-I_{02}(e^{\frac{V}{A_2{V}_T}}-1)}{1+\frac{I_{01}{R}_s}{A_1{V}_T}*e^{\frac{V}{A_1{V}_T}}+\frac{I_{02}{R}_s}{A_2{V}_T}*e^{\frac{V}{A_2{V}_T}}+\frac{R_s}{R_{sh}}}---\left(11\right)$

In formula: I_ph, R_sh, R_sAll can be provided by cell piece producer；I₀₁, I₀₂The cell piece temperature coefficient provided with producer has Close, can directly obtain according to formula (4)；According to document " Modelling and Simulation of photovoltaic module Consideringsingle-diode equivalent circuit model in MATLAB, Dominique.B, Zacharie.K, Donatien.N, Certified Journal, 2008,3 (3): 493-502 " take A₁=1, A₂=1.2；V_TRelevant with cell piece temperature； In this up-to-date style (11), only running voltage and operating current are unknown quantitys, just draw showing between operating current I and running voltage V Sexual relationship.

3) use Matlab modeling, according to cell piece producer provide associated technical parameters be set, set running voltage from 0 starts until open-circuit voltage V_ocTill, step-length is set to 0.001V, just draws a series of working current value, draws curve, Obtain the I-V curve of cell piece.And can exist using solar irradiance and cell piece temperature as control variable, simulated battery sheet Arbitrarily irradiance and the electrical property arbitrarily blocked under ratio exports situation.

Embodiment:

The electrical performance of cell parameter that Tu3Shi cell piece producer provides, standard conditions (AM1.5 spectrum, light intensity 1000W/m2, 25 DEG C) under test, use 3A level solar simulator.Fig. 4 is to utilize single diode equivalent model to be simulated, and ignores Parallel resistance R_shImpact because R_shResistance relatively large, ignore R_shOriginal single diode model can be made to become Dominant equation, and the accuracy of simulation can be ensured to a certain extent.Set according to the associated technical parameters that cell piece producer provides Fixed, set operating current and start until short circuit current I from 0_scTill, step-length is set to 0.001A, just draws a series of work Magnitude of voltage, draws curve, obtains the I-V curve of cell piece.Fig. 5 is the double diode modeling using the inventive method I-V curve, rightXiang HeItem carries out Taylor expansion, and takes linear segment, after arranging an accepted way of doing sth (11), according to cell piece The associated technical parameters that producer provides is set, and sets running voltage and starts until open-circuit voltage V from 0_ocTill, step-length sets For 0.001V, just draw a series of working current value, draw curve, obtain the I-V curve of cell piece.Fig. 6 is battery Producer, single diode die fit the cell piece I-V characteristic curve that double diode simulation draws and contrast, and verify double diode mould The correctness of type and accuracy.Fig. 7 is the method simulation of a kind of accurate simulation photovoltaic electrical performance of cell utilizing the present invention to propose Go out cell piece Performance Characteristics of determining under different operating voltage to contrast with measured value, analysis mode and the degree of deviation of experiment.

Conclusion:

(1) rightXiang HeItem carries out Taylor expansion, and takes linear segment, makes double diode model domination, according to electricity The associated technical parameters that Chi Pian producer provides is set, and sets running voltage and starts until open-circuit voltage V from 0_ocTill, step Length is set to 0.001V, just draws a series of working current value, draws curve, obtains the I-V curve of cell piece.Than now The single diode model used is more accurate, feasible.

(2) use double diode dominant models that electrical performance of cell is simulated, at cell piece best operating point, optimal work Making voltage difference and be less than 0.05V, the parameter that maximum functional point substantially provides with producer overlaps, and the degree of deviation is within 2%.

The above is only the preferred embodiment of the present invention, it is noted that for those skilled in the art, On the premise of without departing from the technology of the present invention principle, it is also possible to make some improvement and deformation, these improve and deformation also should be regarded as Protection scope of the present invention.

Claims (2)

1. the method for an accurate simulation photovoltaic electrical performance of cell, it is characterised in that comprise the following steps:

1) equivalent equation of photovoltaic cell electrical property is obtained according to double diode equivalent model circuit diagram as follows:

I=I_ph-I_D1-I_D2-I_sh (1)

Wherein:

$I_{D1}=I_{01}\[\exp \left(\frac{V+{\mathrm{IR}}_s}{A_1{V}_T}\right)-1\]---\left(2\right)$

$I_{D2}=I_{02}\[\exp \left(\frac{V+{\mathrm{IR}}_s}{A_2{V}_T}\right)-1\]---\left(3\right)$

Wherein: I is the operating current of cell piece；I_phPhotogenerated current for cell piece；I_D1Dark current for equivalent diode D1； I_D2Dark current for equivalent diode D2；I_shLeakage current for equivalent parallel resistance；I₀₁For equivalent diode D1 due to electricity The reverse saturation current that son, the diffusion in hole cause；I₀₂For equivalent diode D2 owing to electronics, hole are in space-charge region The compound reverse saturation current caused again；A₁Structure factor for equivalent diode D1；A₂Structure for equivalent diode D2 The factor；V is the running voltage of cell piece；R_sFor equivalent series resistance；For the thermal voltage of cell piece, k is Bohr The most graceful constant, T is cell piece temperature, and q is charge coefficient；I₀For the reverse saturation current of equivalent diode, for equivalence two Pole pipe D1, I₀It is I₀₁, for equivalent diode D2, I₀It is I₀₂, I_o,refFor at reference temperature 25 DEG C, structure factor For reverse saturation current during A；T_c,refFor cell piece reference temperature；T_cFor the operating temperature that cell piece is present；E_gIt is partly to lead The energy gap of body silicon；

Bring formula (2), (3) into formula (1), and arrangement obtain:

$I=I_{ph}-I_{01}\{\exp \[\frac{(V+{\mathrm{IR}}_s)}{A_1{V}_T}\]-1\}-I_{02}\{\exp \[\frac{(V+{\mathrm{IR}}_s)}{A_2{V}_T}\]-1\}-\frac{V+{\mathrm{IR}}_s}{R_{sh}}---\left(5\right)$

Wherein: R_shEquivalent bypass resistance for cell piece；

2) formula (5) is written as form:

$I=I_{ph}-I_{01}(e^{\frac{V}{A_1{V}_T}}*e^{\frac{{\mathrm{IR}}_s}{A_1{V}_T}}-1)-I_{02}(e^{\frac{V}{A_2{V}_T}}*e^{\frac{{\mathrm{IR}}_s}{A_2{V}_T}}-1)-\frac{V+{\mathrm{IR}}_s}{R_{sh}}---\left(9\right)$

By in formula (9)Xiang HeItem carries out Taylor expansion, and takes linear segment, obtains:

$\begin{array}{c}I=I_{ph}-I_{01}\[e^{\frac{V}{A_1{V}_T}}*\left(1+\frac{{\mathrm{IR}}_s}{A_1{V}_T}\right)-1\]-I_{02}\[e^{\frac{V}{A_2{V}_T}}*\left(1+\frac{{\mathrm{IR}}_s}{A_2{V}_T}\right)-1\]-\frac{V+{\mathrm{IR}}_s}{R_{sh}}\\ =I_{ph}-I_{01}*e^{\frac{V}{A_1{V}_T}}*\frac{{\mathrm{IR}}_s}{A_1{V}_T}-I_{02}*e^{\frac{V}{A_2{V}_T}}*\frac{{\mathrm{IR}}_s}{A_2{V}_T}-I_{01}\left(e^{\frac{V}{A_1{V}_T}}-1\right)-I_{02}\left(e^{\frac{V}{A_2{V}_T}}-1\right)-\frac{V}{R_{sh}}-\frac{{\mathrm{IR}}_s}{R_{sh}}\end{array}---\left(10\right)$

After shifting to arrange:

$I=\frac{I_{ph}-\frac{V}{R_{sh}}-I_{01}\left(e^{\frac{V}{A_1{V}_T}}-1\right)-I_{02}(e^{\frac{V}{A_2{V}_T}}-1)}{1+\frac{I_{01}{R}_s}{A_1{V}_T}*e^{\frac{V}{A_1{V}_T}}+\frac{I_{02}{R}_s}{A_2{V}_T}*e^{\frac{V}{A_2{V}_T}}+\frac{R_s}{R_{sh}}}---\left(11\right)$

Wherein: I_ph, R_sh, R_sThered is provided by cell piece producer；I₀₁, I₀₂Directly obtain according to formula (4)；Take A₁=1, A₂=1.2； V_TRelevant with cell piece temperature；In this up-to-date style (11), only running voltage and operating current are unknown quantitys, just draw operating current I and Dominance relation between running voltage V；

3) use Matlab modeling, set running voltage and start until open-circuit voltage V from 0_ocTill, set step-length, just obtain Go out a series of working current value, draw curve, obtain the I-V curve of cell piece.

The method of a kind of accurate simulation photovoltaic electrical performance of cell the most according to claim 1, it is characterised in that described Step 3) step-length be set to 0.001V.