CN104778352A - Seven-parameter photovoltaic cell output characteristic modeling method based on STFT (Short Time Fourier Transform) operator - Google Patents

Abstract

The invention discloses a seven-parameter photovoltaic cell output characteristic modeling method based on an STFT (Short Time Fourier Transform) operator. The method comprises the steps of establishing an equivalent circuit initial model of photovoltaic cell output characteristics; defining the STFT operator to obtain a decoupling explicit equation parameter model of a photovoltaic cell; establishing a nonlinear equation set by using standard working condition basic data provided by a photovoltaic cell manufacturer, and calculating unknown parameters by using a solution algorithm; calculating unknown parameter values of the decoupling explicit equation parameter model under given working conditions; bringing the unknown parameter values under the given working conditions in the decoupling explicit equation parameter model of the photovoltaic cell to obtain a final photovoltaic cell model which comprehensively reflects photovoltaic cell output characteristics under the given working conditions. The method has the beneficial effects that the STFT operator adopted for model decoupling is not limited by a domain of definition, the expected STFT decoupling operator calculation accuracy can be set according to the needs, and the application is more flexible.

Description

Based on seven parameter photovoltaic cell output characteristic modeling methods of STFT operator

Technical field

The invention belongs to technical field of photovoltaic power generation, particularly relate to a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator.

Background technology

Along with socioeconomic development, the situation in short supply of fossil energy and problem of environmental pollution become increasingly conspicuous, people propose more and more higher requirement to the energy, and searching new forms of energy become the urgent problem that current mankind faces, and development and utilization regenerative resource is extremely urgent.Wherein, sun power as a kind ofly cleaning, one of the regenerative resource with large-scale development prospect, be subject to extensive concern and further investigation in fields such as home-use small-sized solar power generation system, the grid-connected power station of large-sized photovoltaic, architecture-integral photovoltaic glass curtain wall, solar street light, wind-photovoltaic complementary power supply systems.

Solar energy power generating utilizes solar cell that solar energy is converted into electric energy.Photovoltaic generating system forms primarily of photovoltaic battery array, energy-storage system of accumulator, controller and inverter, wherein photovoltaic battery array is the key component of photovoltaic generating system, convert solar energy into direct current energy by photovoltaic battery array, by inverter, direct current energy is converted into and the AC energy feed-in electrical network of electrical network with frequency homophase.Because the complexity of photovoltaic cell modeling accuracy and realization degree thereof researches and develops such as maximal power tracing (MPPT) control to rear class system and control strategy, inverter controls etc. have material impact, therefore, significant to the accurate High Efficiency Modeling of photovoltaic cell output characteristic.

The output power of photovoltaic battery array and incident irradiance degree, photovoltaic cell working temperature, incident light inclination angle and loaded impedance etc. are related.Photovoltaic cell manufacturer only provides limited photovoltaic battery panel operational factor usually, as open-circuit voltage V _oc, short-circuit current I _sc, maximum power point electric current I _mpwith voltage V _mp, open-circuit voltage temperature coefficient β _oc, short-circuit current temperature coefficient α _sc, maximum power point temperature coefficient γ _mppand nominal operating temperature NOCT etc.These parameters are (SRC, i.e. irradiance 1000W/m under standard rated condition usually ², panel working temperature 25 DEG C, except NOCT test condition is: irradiance 800W/m ², environment temperature 20 degrees Celsius DEG C) record.Under above-mentioned standard rated condition, the output power of photovoltaic battery panel is maximum, but is difficult to reach in the actual moving process of photovoltaic battery panel.Therefore, though the change of the above-mentioned environmental factor of the output power of photovoltaic cell and self running parameter and changing, its output characteristics is characterized by many groups of non-linear I-V family curves under different operational factor condition.

The output characteristics of photovoltaic cell can be described by the equivalent-circuit model of current widespread use, as shown in Figure 1.This equivalent electrical circuit comprises a photogenerated current source, a backward dioded in parallel with described photogenerated current source, an equivalent parallel resistance in parallel with described backward dioded and series resistance.Above-mentioned equivalent-circuit model comprises 5 unknown parameters, that is, photogenerated current I _ph, diode reverse saturation current I _o, equivalent series impedance R _s, equivalent parallel resistance value R _shand ideal factor a.Because modeling accuracy is high, above-mentioned 5 parameter models are widely used in photovoltaic cell modeling and simulating.But the mathematical form due to above-mentioned equivalent-circuit model has intrinsic transcendental equation characteristic, namely equivalent backward dioded its voltage with there is iteration between electric current and be coupled, thus in system emulation, there will be initial value iteration and unstable phenomenon, particularly in the photovoltaic generating system modeling and simulating of the circuit simulation analysis software based on SPICE.Therefore, how to overcome the transcendental equation characteristic of above-mentioned equivalent-circuit model and effectively utilize producer to provide data to carry out Exact Solution to the unknown parameter in model, becoming the difficult problem that photovoltaic cell output characteristic modeling is urgently to be resolved hurrily.

At present, the decoupling method based on Lambert-W function can be adopted to transcendental equation, but Lambert-W function has strict (-1/e ,+) field of definition restriction, and its computational accuracy and counting yield all have much room for improvement.

And in existing photovoltaic cell equivalent-circuit model unknown parameter method for solving, conventional by fixing ideal factor method and function optimization method.Wherein, fixing ideal factor method supposition, under constant ideal factor condition, utilizes the numerical computation methods such as process of iteration to solve all the other 4 parameters, but secures 1 parameter, accurately can have an impact to the modeling of model entirety.

And for function optimization class methods, mostly usually be at present based on the open-circuit condition of described photovoltaic cell equivalent-circuit model, short circuit condition, maximum power point condition and maximum power point gradient condition the ideal factor a under the standard condition in described 5 parameters, equivalent series resistance R _swith equivalent parallel resistance R _psolve Deng for target variable is optimized, and by optimizing a, R of obtaining _sand R _pthe diode reverse saturation current I under standard condition is solved by open-circuit condition ₀, and the photogenerated current under supposing standard condition is approximately the short-circuit current under standard condition, this have lost the computational accuracy of model to a certain extent.In addition, photovoltaic battery array working point is generally the maximum power point under different operating condition, effectively to utilize the output efficiency of photovoltaic battery array, therefore, constructed photovoltaic cell output characteristic model and Optimal Parameters thereof also expect can there be good model accuracy at maximum power point place, the peak power temperature coefficient parameter that manufacturer provides as mated and the short-circuit current temperature coefficient at maximum power point place and the correction of open-circuit voltage temperature coefficient, and all do not imitate the impact considering above-mentioned factor in current photovoltaic cell output characteristic modeling and parametric solution.

Summary of the invention

Object of the present invention is exactly to solve the problem, propose a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator, the method is while realizing output characteristics unknown-model parameter matching and optimization, realize accurate output characteristics decoupling computation fast, improve the computation efficiency based on the photovoltaic cell capable of generating power system of described photovoltaic cell output characteristic model, the control strategy design for photovoltaic cell capable of generating power system provides accurately model basis efficiently.

To achieve these goals, the present invention adopts following technical scheme:

Based on seven parameter photovoltaic cell output characteristic modeling methods of STFT operator, comprise the following steps:

Step 1: the equivalent electrical circuit initial model setting up photovoltaic cell output characteristic, and the equivalence 5 parameter transcendental equation providing photovoltaic cell output characteristic; Described 5 parameters comprise photogenerated current I _ph, diode reverse saturation current I _o, equivalent series impedance R _s, equivalent parallel resistance value R _shand ideal factor a;

Step 2: definition STFT operator, carries out decoupling zero according to STFT is theoretical to the photovoltaic cell equivalence 5 parameter transcendental equations in step 1, obtains the decoupling zero explicit equation parameter model of photovoltaic cell;

Step 3: utilize the standard condition basic data that photovoltaic cell manufacturer provides, according to the equivalent relation under different operating condition, the equality constraint set of Criterion operating mode decoupling zero explicit equation parameter model unknown parameter, set up Nonlinear System of Equations, ask for described unknown parameter by Solving Nonlinear Systems of Equations algorithm;

Ask in process in parameter, introduce short-circuit current temperature coefficient modifying factor κ _scwith open-circuit voltage temperature coefficient modifying factor κ _oc, the short-circuit current temperature coefficient at Optimized Matching maximum power point place and open-circuit voltage temperature coefficient;

Step 4: try to achieve the unknown parameters ' value of decoupling zero explicit equation parameter model under given operating mode according to the unknown parameters ' value of decoupling zero explicit equation parameter model under the standard condition asked in step 3;

Step 5: brought into by the unknown parameters ' value under described given operating mode in described photovoltaic cell decoupling zero explicit equation parameter model, obtains the photovoltaic cell model of concentrated expression photovoltaic cell output characteristic under final given operating mode.

In described step 1, the equivalence 5 parameter transcendental equation of photovoltaic cell output characteristic is specially:

$I_{\mathrm{PV}}=I_{\mathrm{ph}}-I_0(\exp \left(\frac{V_{\mathrm{PV}}+I_{\mathrm{PV}}{R}_s}{a}\right)-1)-\frac{V_{\mathrm{PV}}+I_{\mathrm{PV}}{R}_s}{R_{\mathrm{sh}}}---\left(1\right);$

Wherein, I _phfor photogenerated current; I ₀for flowing through the reverse saturation current of diode; A=nN _skT/q, n are ideal factor coefficient, characterization model nonlinearity; N _sfor the monocell number that photovoltaic battery panel/array comprises, k is Boltzmann constant: k=1.38 × 10 ²³j/K, T are photovoltaic cell working temperature, and q is the unit quantity of electric charge, q=1.6 × 10 ¹⁹c; R _sand R _shbe respectively equivalent series resistance and equivalent parallel resistance; I _pVand V _pVbe respectively output current and the output voltage of photovoltaic battery panel/array.

In described step 2, the decoupling zero explicit equation parameter model of photovoltaic cell is specially:

$I_{\mathrm{PV}}=\left(\frac{(I_{\mathrm{ph}}+I_0)-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}}}{1+\frac{R_s}{R_{\mathrm{sh}}}}\right)(1-\frac{a(1+\frac{R_s}{R_{\mathrm{sh}}})}{R_s(I_0+I_{\mathrm{ph}}-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}})}{\mathrm{trans}}_{+}\left(D\right))---\left(2\right);$

Wherein, D is STFT operator, $D=\frac{I_0{R}_s\exp \left(\frac{V_{\mathrm{PV}}}{a}\right)\exp \left(\frac{R_s(I_0+I_{\mathrm{ph}}-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}})}{a(1+\frac{R_s}{R_{\mathrm{sh}}})}\right)}{a(1+\frac{R_s}{R_{\mathrm{sh}}})}---\left(3\right);$

Transforming function transformation function trans ₊be defined as,

Wherein, x is accumulative frequency, determines transforming function transformation function trans ₊computational accuracy, m is the cumulative power level of transforming function transformation function.

The standard condition basic data that in described step 3, photovoltaic cell manufacturer provides comprises: open-circuit voltage V under photovoltaic cell standard condition _{oc, ref}, short-circuit current I _{sc, ref}, maximum power point voltage V _{mpp, ref}, maximum power point electric current I _{mpp, ref}, the Series Sheet battery number N that comprises of photovoltaic cell component _ser, short-circuit current temperature coefficient α _scand open-circuit voltage temperature coefficient β _oc;

Decoupling zero explicit equation parameter model unknown parameter under standard condition to be solved comprises: photogenerated current I _{ph, ref}, diode reverse saturation current I _{o, ref}, equivalent series impedance R _{s, ref}, equivalent parallel resistance value R _{sh, ref}and ideal factor a _ref.

The concrete grammar of the equality constraint set of described step 3 Plays operating mode decoupling zero explicit equation parameter model unknown parameter is:

Equality constraint 1: the short circuiting work condition according to photovoltaic cell can obtain:

$I_{\mathrm{sc},\mathrm{ref}}=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(5\right)$

Equality constraint 2: the open-circuit working condition according to photovoltaic cell can obtain:

$0=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{V_{\mathrm{oc},\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{V_{\mathrm{oc},\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(6\right)$

Equality constraint 3: the maximum power point condition of work according to photovoltaic cell can obtain:

$I_{\mathrm{mpp},\mathrm{ref}}=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(7\right)$

Equality constraint 4: can obtain according to the power vs. voltage curve gradient dP/dV=0 of photovoltaic cell at maximum power point place:

${\frac{\mathrm{dP}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}={\frac{\∂\left(\mathrm{VI}\right)}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}={I_{\mathrm{mpp},\mathrm{ref}}-V_{\mathrm{mpp},\mathrm{ref}}\frac{\mathrm{dI}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}---\left(8\right)$

Wherein, ${\frac{\mathrm{dI}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}=\frac{\frac{I_{0,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{1}{R_{\mathrm{sh},\mathrm{ref}}}}{1+\frac{I_{0,\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{R_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}}---\left(9\right)$

Equality constraint 5: in order to the model accuracy at maximum power point place under the different operating mode of Optimized Matching, introduce short-circuit current temperature coefficient modifying factor κ _scwith open-circuit voltage temperature coefficient modifying factor κ _oc, because temperature increment is not remarkable on the impact of photovoltaic cell output characteristic curve shape, get Δ T=5 DEG C, T'=T _ref+ Δ T, considers maximum power point condition, has

$I_{{\mathrm{mpp},T}^{\′}}=I_{{\mathrm{ph},T}^{\′}}-I_{{0,T}^{\′}}(\exp \left(\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}\right)-1)-\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}---\left(10\right)$

Wherein, V _{oc, ref}, I _{sc, ref}, V _{mpp, ref}, I _{mpp, ref}open-circuit voltage, short-circuit current, maximum power point voltage, maximum power point electric current under photovoltaic cell standard condition; I _{ph, ref}, I _{0, ref}, R _{s, ref}, R _{sh, ref}, a _refbe respectively the photogenerated current of the decoupling zero explicit equation parameter model under standard condition, diode reverse saturation current, equivalent series impedance, equivalent parallel resistance value and ideal factor a _ref; I _{mpp, T'}, I _{ph, T'}, V _{mpp, T'}, R _{s, T'}, R _{sh, T'}, I _{0, T'}, a _t'be respectively the maximum power point electric current under delta temperature T', photogenerated current, maximum power point voltage, equivalent series resistance, equivalent parallel resistance, equivalent diode reverse saturation current and ideal factor;

Equality constraint 6: γ _mpp=γ _model(17)

Wherein, γ _mppfor peak power temperature coefficient parameter, γ _modelfor combining the model peak power temperature coefficient parameter that the unknown parameter that solves obtains.

The Nonlinear System of Equations of the standard condition decoupling zero explicit equation parameter model unknown parameter set up in described step 3 is specially:

$F\left(x\right)=\left\{\begin{array}{c}{I}_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}-I_{\mathrm{sc},\mathrm{ref}}\\ I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{V_{\mathrm{oc},\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{V_{\mathrm{oc},\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}\\ I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}-I_{\mathrm{mpp},\mathrm{ref}}\\ I_{\mathrm{mpp},\mathrm{ref}}-V_{\mathrm{mpp},\mathrm{ref}}\·\frac{\frac{I_{0,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{1}{R_{\mathrm{sh},\mathrm{ref}}}}{1+\frac{I_{0,\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{R_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}}\\ I_{{\mathrm{ph},T}^{\′}}-I_{{0,T}^{\′}}(e^{\frac{V_{\mathrm{oc},T^{\′}}}{a_{T^{\′}}}}-1)-\frac{V_{\mathrm{oc},T^{\′}}}{R_{\mathrm{sh},T^{\′}}}\\ {\mathrm{\γ}}_{\mathrm{mpp}}-{\mathrm{\γ}}_{\mathrm{mode}l}\end{array}\right.---\left(23\right)$

The solution procedure of described Nonlinear System of Equations is specially:

Determine that variable vector x to be solved is,

x≌[I _ph,ref,I _0,ref,a _ref,R _s,ref,R _sh,ref,κ _oc,κ _sc] ^T(24)

Non-linear due to equation, and known variables number is no less than nonlinear equation number in system of equations, adopt Iterative search algorithm or non-linear least square optimizing algorithm minimum for objective function with system of equations error of sum square, choose rational initial value and solve overall feasible solution.

The process of choosing of described initial value is:

Wherein, a ₁and a ₂for ideal factor initial estimate coefficient, C _sfor equivalent series resistance initial estimate coefficient, C _shfor equivalent parallel resistance initial estimate coefficient, the int in parameter refers to the initial value of relevant parameter.

The concrete grammar of trying to achieve the unknown parameters ' value of decoupling zero explicit equation parameter model under given operating mode according to the unknown parameters ' value of decoupling zero explicit equation parameter model under the standard condition asked in step 4 is:

Substitute maximum power point condition by open circuit voltage conditions, have

$0=I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(\exp \left(\frac{V_{\mathrm{oc},T^{\′}}}{a_{T^{\′}}}\right)-1)-\frac{V_{\mathrm{oc},T^{\′}}}{R_{\mathrm{sh},T^{\′}}}---\left(11\right)$

Wherein,

$I_{\mathrm{ph},T^{\′}}=\frac{G_{T^{\′}}}{G_{\mathrm{ref}}}\·\frac{{\mathrm{AM}}_{T^{\′}}}{{\mathrm{AM}}_{\mathrm{ref}}}[I_{\mathrm{ph},\mathrm{ref}}+{\mathrm{\α}}_{\mathrm{sc}}(1-{\mathrm{\κ}}_{\mathrm{sc}}/100)\mathrm{\ΔT}]---\left(12\right)$

V _oc,T′≌V _oc,ref+β _oc(1+κ _oc/100)·ΔT (13)

Wherein, G _reffor the irradiance under standard condition; G _t'for the irradiance under delta temperature T'; AM _reffor the optical path factor under standard condition; AM _t'for the optical path factor under delta temperature T'; Δ T=5 DEG C;

The update equation of all the other nonstandard condition conditional parameters is,

$R_{\mathrm{sh},T^{\′}}\≅\frac{G_{\mathrm{ref}}}{G_{T^{\′}}}\·R_{\mathrm{sh},\mathrm{ref}}---\left(14\right)$

$a_{T^{\′}}\≅a_{\mathrm{ref}}\·\frac{T_{\mathrm{cell},T^{\′}}}{T_{\mathrm{cell},\mathrm{ref}}}---\left(15\right)$

$\left\{\begin{array}{c}{I}_{0,T^{\′}}=I_{0,\mathrm{ref}}\·{\left[\frac{T_{\mathrm{cell},T^{\′}}}{T_{\mathrm{cell}-\mathrm{ref}}}\right]}^3\·\exp \left(\frac{1}{k}\left({\frac{E_g}{T}|}_{T_{\mathrm{cell},\mathrm{ref}}}{-\frac{E_g}{T}|}_{T_{\mathrm{cell}},T^{\′}}\right)\right),k=8.617\×{10}^{-5}\mathrm{eV}\·K^{-1}\\ E_g\left(T\right)=E_g\left(0\right)-\frac{a\·T^2}{T+b},E_g\left(0\right)=1.166\mathrm{eV},a=4.73\×{10}^{-4}\mathrm{eV}\·K^{-1},b=636K\end{array}\right.---\left(16\right)$

Ask for γ _modelsubprocess be:

With standard condition work temperature _{cell, ref}=25 DEG C extend, at T for benchmark _cellin ∈ [-10 DEG C, 50 DEG C] scope, with Δ T _cell=3 DEG C is increment, carry out peak power at each temperature extension point T ' to resolve, the Nonlinear System of Equations be made up of at the update equation that temperature extends point formula (7) and formula (8) is solved, namely with nonlinear iteration or Nonlinear least squares optimization scheduling algorithm

$\left\{\begin{array}{c}{I}_{\mathrm{mpp},T^{\′}}=V_{\mathrm{mpp},T^{\′}}\·\frac{\frac{I_{0,T^{\′}}}{a_{T^{\′}}}{e}^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}+\frac{1}{R_{\mathrm{sh},T^{\′}}}}{1+\frac{I_{0,T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}{e}^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}+\frac{R_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}}\\ I_{\mathrm{mpp},T^{\′}}=I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(e^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}-1)-\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}\end{array}\right.---\left(18\right)$

Wherein, I _{0, T '}, a _{t '}and R _{sh, T '}revise by formula (14) ~ (16) respectively, and R _{s, T '}and I _{ph, T '}update equation be,

$\left\{\begin{array}{c}{R}_{s,T^{\′}}=R_{s,\mathrm{ref}}\\ I_{{\mathrm{ph},T}^{\′}}=\frac{G_{T^{\′}}}{G_{\mathrm{ref}}}\·\frac{{\mathrm{AM}}_{T^{\′}}}{{\mathrm{AM}}_{\mathrm{ref}}}(I_{\mathrm{ph},\mathrm{ref}}+{\mathrm{\α}}_{\mathrm{sc}}(1-{\mathrm{\κ}}_{\mathrm{sc}}/100)(T_{\mathrm{cell},T^{\′}}-T_{\mathrm{cell},\mathrm{ref}}))\end{array}\right.---\left(19\right)$

Bring formula (19) into formula (18) to solve and can obtain,

P _mpp,T′＝I _mpp,T′V _mpp,T′(20)

Then asked for the peak power temperature coefficient that peak power obtains can be expressed as by the adjacent temperature point that extends,

${\mathrm{\γ}}_{\mathrm{mpp},T_n^{\′}}\≅\frac{P_{\mathrm{mpp},T_{n-1}^{\′}}-P_{\mathrm{mpp},T_n^{\′}}}{T_{n-1}^{\′}-T_n^{\′}}---\left(21\right)$

Wherein, P _{mpp, T'n-1}and P _{mpp, T'n}be respectively the maximum power point power under the (n-1)th temperature extension point and the n-th temperature extension point; γ _{mpp, T'n}it is the maximum power point gradient under the n-th temperature extension point;

To the peak power temperature coefficient handling averagely that each temperature extension knock type (21) is asked for, as the peak power temperature coefficient γ of photovoltaic cell output characteristic model _model, namely

${\mathrm{\γ}}_{\mathrm{mode}l}\≅\frac{1}{n}\·\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\γ}}_{\mathrm{mpp},T_i^{\′}}\right)---\left(22\right)$

The invention has the beneficial effects as follows:

Compared to prior art, proposed based in seven parameter photovoltaic cell output characteristic modeling methods of STFT operator, the STFT operator that model decoupling adopts there is no the intrinsic (-1/e of Lambert-W function, +) field of definition restriction, and the STFT decoupling zero operator computational accuracy of expectation can be set as required, application is more flexible, and can build SPICE net table easily and effectively be encapsulated by electric for this photovoltaic panel output characteristics model, the circuit-level for photovoltaic cell system emulates.In addition, in photovoltaic cell output characteristic unknown-model parametric solution, the method that the present invention proposes is on existing function optimization method basis, consider photovoltaic cell output characteristic model and the maximum power point matching problem of Optimal Parameters under different operating condition thereof, construct the Nonlinear System of Equations by nonlinear iteration or Nonlinear least squares optimization Algorithm for Solving, by seven initial parameter values choosing methods and the optimizing of two-level nested Nonlinear System of Equations iteration of priori, obtain seven parameter sets under required standard condition, the physical significance that each parameter has it clear and definite, the basic data that parametric solution process only utilizes photovoltaic cell producer to provide, therefore dissimilar photovoltaic cell is applicable to.

Accompanying drawing explanation

The 5-parameter photovoltaic cell equivalent-circuit model schematic diagram that Fig. 1 provides for the embodiment of the present invention;

The implementation method of the photovoltaic cell output characteristic modeling that Fig. 2 provides for the embodiment of the present invention and parametric solution thereof;

The photovoltaic cell 7-parameter model equivalent parameters that Fig. 3 provides for the embodiment of the present invention solves process flow diagram;

The emulation fitting result of CRM220S156P-60 series photovoltaic battery panel output characteristics modeling and parameter extraction method that Fig. 4 provides for the embodiment of the present invention and the comparison diagram of measured data.

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the present invention will be further described:

Based on seven parameter photovoltaic cell output characteristic modeling methods of STFT operator, as shown in Figure 2,

Step 1: the equivalent electrical circuit initial model setting up photovoltaic cell output characteristic, provides the equivalence 5 parameter transcendental equation of its physical mathematics form then; Described parameter refers to photogenerated current I _ph, diode reverse saturation current I _o, equivalent series impedance R _s, equivalent parallel resistance value R _shand ideal factor a;

Step 2: theoretical according to Special Trans Function Theory (STFT), definition STFT operator, carries out decoupling zero by the photovoltaic cell 5 parameter transcendental equation model in step 1, obtains the decoupling zero explicit equation parameter model of photovoltaic cell;

Step 3: utilize the standard condition basic data that photovoltaic cell manufacturer provides, the decoupling parameter unknown-model parameter under standard condition is asked for by Solving Nonlinear Systems of Equations algorithm (as non-linear iterative or Nonlinear least squares optimization algorithm etc.), ask in process in parameter, introduce short-circuit current temperature coefficient modifying factor κ _scwith open-circuit voltage temperature coefficient modifying factor κ _oc, the described short-circuit current temperature coefficient at Optimized Matching maximum power point place and open-circuit voltage temperature coefficient, thus described photovoltaic cell output characteristic model is essentially 7 parameter equivalent models;

Step 4: in conjunction with described decoupling parameter unknown-model parameter transforming relationship, the standard condition unknown parameters ' value asked in integrating step 3 obtains the unknown parameters ' value of described decoupling parameter model under given operating mode;

Step 5: the unknown parameters ' value under described given operating mode is brought in described photovoltaic cell decoupling parameter model, obtains the photovoltaic cell model of the concentrated expression photovoltaic cell output characteristic under final given operating mode.

The data that producer provides comprise open-circuit voltage V under photovoltaic cell standard condition _{oc, ref}, short-circuit current I _{sc, ref}, maximum power point voltage V _{mpp, ref}, maximum power point electric current I _{mpp, ref}, the Series Sheet battery number N that comprises of photovoltaic cell component _ser, short-circuit current temperature coefficient α _scwith open-circuit voltage temperature coefficient β _oc.

Concrete grammar is as follows:

In step 1, the process asking for photovoltaic cell output characteristic equivalent electrical circuit initial model equivalent 7 parameter transcendental equations is accordingly:

According to photovoltaic cell equivalent-circuit model, the 5 parameter transcendental equation forms that can obtain photovoltaic cell output characteristic are:

$I_{\mathrm{PV}}=I_{\mathrm{ph}}-I_0(\exp \left(\frac{V_{\mathrm{PV}}+I_{\mathrm{PV}}{R}_s}{a}\right)-1)-\frac{V_{\mathrm{PV}}+I_{\mathrm{PV}}{R}_s}{R_{\mathrm{sh}}}---\left(1\right)$

Wherein: I _phfor photogenerated current; I ₀for flowing through the reverse saturation current of diode; A=nN _skT/q, N _sfor the monocell number that photovoltaic battery panel/array comprises, k is Boltzmann constant: k=1.38 × 10 ²³j/K, T are photovoltaic cell working temperature, and q is the unit quantity of electric charge, q=1.6 × 10 ¹⁹c; R _sand R _shbe respectively equivalent series resistance and equivalent parallel resistance; I _pVand V _pVbe respectively output current and the output voltage of photovoltaic battery panel/array.

In step 2, definition STFT operator, by photovoltaic cell 5 parameter transcendental equation model explicitization in step 1, the explicit analytical expressions obtaining photovoltaic cell equivalent model is:

$I_{\mathrm{PV}}=\left(\frac{(I_{\mathrm{ph}}+I_0)-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}}}{1+\frac{R_s}{R_{\mathrm{sh}}}}\right)(1-\frac{a(1+\frac{R_s}{R_{\mathrm{sh}}})}{R_s(I_0+I_{\mathrm{ph}}-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}})}{\mathrm{trans}}_{+}\left(D\right))---\left(2\right)$

Wherein, defining STFT operator D is

$D=\frac{I_0{R}_s\exp \left(\frac{V_{\mathrm{PV}}}{a}\right)\exp \left(\frac{R_s(I_0+I_{\mathrm{ph}}-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}})}{a(1+\frac{R_s}{R_{\mathrm{sh}}})}\right)}{a(1+\frac{R_s}{R_{\mathrm{sh}}})}---\left(3\right)$

Then transforming function transformation function trans ₊be defined as,

In step 3, the process of the decoupling parameter unknown-model parameter that the standard condition basic data utilizing photovoltaic cell manufacturer to provide is asked under standard condition is:

(ref, that is, irradiance 1000W/m under the standard condition that photovoltaic cell manufacturer provides ², panel working temperature 25 DEG C) underlying parameter comprise: photovoltaic cell short-circuit current I _{sc, ref}, open-circuit voltage V _{oc, ref}, maximum power point electric current I _{mpp, ref}, maximum power point voltage V _{mpp, ref}.Unknown parameter under standard condition to be solved comprises: photogenerated current I _ph, _ref, diode reverse saturation current I _{o, ref}, equivalent series impedance R _{s, ref}, equivalent parallel resistance value R _{sh, ref}and ideal factor a _ref; In addition, in order to the model accuracy at maximum power point place under the different operating mode of Optimized Matching, short-circuit current temperature coefficient modifying factor κ is introduced _scwith open-circuit voltage temperature coefficient modifying factor κ _oc.

Based on the underlying parameter that described photovoltaic cell manufacturer provides, according to the equivalent relation under different operating condition, obtain the equality constraint set solving described standard condition unknown parameter.

Equality constraint 1: according to the short circuiting work condition of photovoltaic cell, under standard condition, have

$I_{\mathrm{sc},\mathrm{ref}}=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(5\right)$

Equality constraint 2: according to the open-circuit working condition of photovoltaic cell, under standard condition, have

$0=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{V_{\mathrm{oc},\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{V_{\mathrm{oc},\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(6\right)$

Equality constraint 3: according to the maximum power point condition of work of photovoltaic cell, under standard condition, have

$I_{\mathrm{mpp},\mathrm{ref}}=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(7\right)$

Equality constraint 4: according to the power vs. voltage curve gradient dP/dV=0 of photovoltaic cell at maximum power point place, under standard condition, have

${\frac{\mathrm{dP}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}={\frac{\∂\left(\mathrm{VI}\right)}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}={I_{\mathrm{mpp},\mathrm{ref}}-V_{\mathrm{mpp},\mathrm{ref}}\frac{\mathrm{dI}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}---\left(8\right)$

Wherein,

${\frac{\mathrm{dI}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}=\frac{\frac{I_{0,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{1}{R_{\mathrm{sh},\mathrm{ref}}}}{1+\frac{I_{0,\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{R_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}}---\left(9\right)$

Equality constraint 5: in order to the model accuracy at maximum power point place under the different operating mode of Optimized Matching, introduce short-circuit current temperature coefficient modifying factor κ _scwith open-circuit voltage temperature coefficient modifying factor κ _oc, because temperature increment is not remarkable on the impact of photovoltaic cell output characteristic curve shape, get Δ T=5 DEG C, T'=T _ref+ Δ T, considers maximum power point condition, has

$I_{{\mathrm{mpp},T}^{\′}}=I_{{\mathrm{ph},T}^{\′}}-I_{{0,T}^{\′}}(\exp \left(\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}\right)-1)-\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}---\left(10\right)$

Due to I _{mpp, T '}be unknown dependent variable, therefore, be similar to and substitute maximum power point condition by open circuit voltage conditions, have

$0=I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(\exp \left(\frac{V_{\mathrm{oc},T^{\′}}}{a_{T^{\′}}}\right)-1)-\frac{V_{\mathrm{oc},T^{\′}}}{R_{\mathrm{sh},T^{\′}}}---\left(11\right)$

Wherein,

$I_{\mathrm{ph},T^{\′}}=\frac{G_{T^{\′}}}{G_{\mathrm{ref}}}\·\frac{\mathrm{AM}}{{\mathrm{AM}}_{\mathrm{ref}}}[I_{\mathrm{ph},\mathrm{ref}}+{\mathrm{\α}}_{\mathrm{sc}}(1-{\mathrm{\κ}}_{\mathrm{sc}}/100)\mathrm{\ΔT}]---\left(12\right)$

V _oc,T′≌V _oc,ref+β _oc(1+κ _oc/100)·ΔT (13)

The update equation of all the other nonstandard condition conditional parameters is,

$R_{\mathrm{sh},T^{\′}}\≅\frac{G_{\mathrm{ref}}}{G_{T^{\′}}}\·R_{\mathrm{sh},\mathrm{ref}}---\left(14\right)$

$a_{T^{\′}}\≅a_{\mathrm{ref}}\·\frac{T_{\mathrm{cell},T^{\′}}}{T_{\mathrm{cell},\mathrm{ref}}}---\left(15\right)$

$\left\{\begin{array}{c}{I}_{0,T^{\′}}=I_{0,\mathrm{ref}}\·{\left[\frac{T_{\mathrm{cell},T^{\′}}}{T_{\mathrm{cell}-\mathrm{ref}}}\right]}^3\·\exp \left(\frac{1}{k}\left({\frac{E_g}{T}|}_{T_{\mathrm{cell},\mathrm{ref}}}{-\frac{E_g}{T}|}_{T_{\mathrm{cell}},T^{\′}}\right)\right),k=8.617\×{10}^{-5}\mathrm{eV}\·K^{-1}\\ E_g\left(T\right)=E_g\left(0\right)-\frac{a\·T^2}{T+b},E_g\left(0\right)=1.166\mathrm{eV},a=4.73\×{10}^{-4}\mathrm{eV}\·K^{-1},b=636K\end{array}\right.---\left(16\right)$

Equality constraint 6: photovoltaic battery manufacturers can provide peak power temperature coefficient parameter γ usually _mpp, and the impact of this parameter of consideration all not yet in effect in existing photovoltaic cell output characteristic model parameter solution procedure.As everyone knows, in order to improve the utilization factor of the output power from photovoltaic cells, usual expectation carries out maximal power tracing control (MPPT) to photovoltaic battery panel/array, therefore, the maximum power output coupling of the photovoltaic cell output characteristic model set up under different operating mode has material impact for photovoltaic cell capable of generating power system and control strategy design thereof.Solve the unknown parameter obtained to need in conjunction with peak power temperature coefficient parameter γ _mppcarry out School Affairs to approach, make

γ _mpp＝γ _model(17)

Wherein, γ _modelfor combining the model peak power temperature coefficient parameter that the unknown parameter that solves obtains.Ask for γ _modelsubprocess be:

With standard condition work temperature _{cell, ref}=25 DEG C extend, at T for benchmark _cellin ∈ [-10 DEG C, 50 DEG C] scope, with Δ T _cell=3 DEG C is increment, carry out peak power at each temperature extension point T ' to resolve, the Nonlinear System of Equations be made up of at the update equation that temperature extends point formula (7) and formula (8) is solved, namely with nonlinear iteration or Nonlinear least squares optimization scheduling algorithm

$\left\{\begin{array}{c}{I}_{\mathrm{mpp},T^{\′}}=V_{\mathrm{mpp},T^{\′}}\·\frac{\frac{I_{0,T^{\′}}}{a_{T^{\′}}}{e}^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}+\frac{1}{R_{\mathrm{sh},T^{\′}}}}{1+\frac{I_{0,T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}{e}^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}+\frac{R_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}}\\ I_{\mathrm{mpp},T^{\′}}=I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(e^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}-1)-\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}\end{array}\right.---\left(18\right)$

Wherein, I _{0, T '}, a _{t '}and R _{sh, T '}22 revise by formula (14) ~ (16) respectively, and R _{s, T '}and I _{ph, T '}update equation be,

$\left\{\begin{array}{c}{R}_{s,T^{\′}}=R_{s,\mathrm{ref}}\\ I_{{\mathrm{ph},T}^{\′}}=\frac{G_{T^{\′}}}{G_{\mathrm{ref}}}\·\frac{{\mathrm{AM}}_{T^{\′}}}{{\mathrm{AM}}_{\mathrm{ref}}}(I_{\mathrm{ph},\mathrm{ref}}+{\mathrm{\α}}_{\mathrm{sc}}(1-{\mathrm{\κ}}_{\mathrm{sc}}/100)(T_{\mathrm{cell},T^{\′}}-T_{\mathrm{cell},\mathrm{ref}}))\end{array}\right.---\left(19\right)$

Bring formula (19) into formula (18) to solve and can obtain,

P _mpp,T′＝I _mpp,T′V _mpp,T′(20)

Then asked for the peak power temperature coefficient that peak power obtains can be expressed as by the adjacent temperature point that extends,

${\mathrm{\γ}}_{\mathrm{mpp},T_n^{\′}}\≅\frac{P_{\mathrm{mpp},T_{n-1}^{\′}}-P_{\mathrm{mpp},T_n^{\′}}}{T_{n-1}^{\′}-T_n^{\′}}---\left(21\right)$

To the peak power temperature coefficient handling averagely that each temperature extension knock type (21) is asked for, as the peak power temperature coefficient of photovoltaic cell output characteristic model, namely

${\mathrm{\γ}}_{\mathrm{mode}l}\≅\frac{1}{n}\·\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\γ}}_{\mathrm{mpp},T_i^{\′}}\right)---\left(22\right)$

Comprehensive above-mentioned constraint condition analysis, simultaneous formula (5) ~ formula (8), formula (11), formula (17), obtain Nonlinear System of Equations F (x):

$F\left(x\right)=\left\{\begin{array}{c}{I}_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}-I_{\mathrm{sc},\mathrm{ref}}\\ I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{V_{\mathrm{oc},\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{V_{\mathrm{oc},\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}\\ I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}-I_{\mathrm{mpp},\mathrm{ref}}\\ I_{\mathrm{mpp},\mathrm{ref}}-V_{\mathrm{mpp},\mathrm{ref}}\·\frac{\frac{I_{0,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{1}{R_{\mathrm{sh},\mathrm{ref}}}}{1+\frac{I_{0,\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{R_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}}\\ I_{{\mathrm{ph},T}^{\′}}-I_{{0,T}^{\′}}(e^{\frac{V_{\mathrm{oc},T^{\′}}}{a_{T^{\′}}}}-1)-\frac{V_{\mathrm{oc},T^{\′}}}{R_{\mathrm{sh},T^{\′}}}\\ {\mathrm{\γ}}_{\mathrm{mpp}}-{\mathrm{\γ}}_{\mathrm{mode}l}\end{array}\right.---\left(23\right)$

Wherein, variable vector x to be solved is,

x≌[I _ph,ref,I _0,ref,a _ref,R _s,ref,R _sh,ref,κ _oc,κ _sc] ^T(24)

The described Nonlinear System of Equations problem constructed by formula (23) ~ (25), and the Nonlinear System of Equations subproblem wherein constructed by formula (18), non-linear due to equation, and known variables number is no less than nonlinear equation number in system of equations, therefore, usual employing Iterative search algorithm, or the optimizing algorithm such as non-linear least square solves overall feasible solution (may not being optimum solution) so that system of equations error of sum square is minimum for objective function is chosen in conjunction with rational initial value.

The solution procedure of Nonlinear System of Equations F (x)=0 as shown in Figure 3.For non-linear iterative or Nonlinear least squares optimization algorithm, the convergence that in formula (24), the initial value of variables collection to be solved is chosen for the Nonlinear System of Equations iteration shown in formula (23) has material impact.The process of choosing of the initial value of described variables collection to be solved is:

When after the unknown parameter set (24) drawn standard condition by optimizing algorithm under, in conjunction with described decoupling parameter unknown-model parameter transforming relationship formula (12) ~ (16) (19), the standard condition unknown parameters ' value asked in integrating step 3 obtains the unknown parameters ' value of described decoupling parameter model under given operating mode.

Conversion process is solved by above-mentioned, unknown parameters ' value under described given operating mode is brought into described based in the photovoltaic cell transcendental equation Decoupled Model of STFT operator, obtain the photovoltaic cell model of the concentrated expression photovoltaic cell output characteristic under final given operating mode, emulate for photovoltaic cell capable of generating power system.

As the application of the embodiment of the present invention, according to photovoltaic cell output characteristic modeling proposed by the invention and seven parameter extracting methods, actual testing and emulation matching is carried out respectively to polysilicon photovoltaic cells panel CRM220S156P-60 series.Specific operation process is, utilizes programmable electronic load measure photovoltaic cell volt-ampere characteristic at standard conditions; Then, the photovoltaic cell output characteristic modeling proposed based on the embodiment of the present invention and seven parameter extracting methods set up seven parameter output characteristics models of CRM220S156P-60 series photovoltaic battery panel; Finally, based on the CRM220S156P-60 series photovoltaic battery panel volt-ampere characteristic under seven described parameter output characteristics model emulation fit standard situations.

Fig. 4 shows the emulation fitting result of the actual measurement data of CRM220S156P-60 series photovoltaic battery panel and the output characteristics modeling and parameter extraction method based on embodiment of the present invention proposition.Can find out from result and coincide very well, the unknown parameter set under the standard condition of extraction is: photogenerated current is 8.095A, and reverse saturation current is 8.23 × 10 ^-10a, ideal factor is 1.6002V, and equivalent parallel resistance is 305.10 Ω, and equivalent series resistance is 0.406 Ω.

The root-mean-square error of above-mentioned emulation fitting result is 0.0238A, the photovoltaic cell output characteristic modeling and seven parameter extracting methods that describe the present invention's proposition are correct, and thus the method also can be applied in the research of multiple photovoltaic cell modeling and parameter extraction technology up till now.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (9)

1., based on seven parameter photovoltaic cell output characteristic modeling methods of STFT operator, it is characterized in that, comprise the following steps:

Step 1: the equivalent electrical circuit initial model setting up photovoltaic cell output characteristic, and the equivalence 5 parameter transcendental equation providing photovoltaic cell output characteristic; Described 5 parameters comprise photogenerated current I _ph, diode reverse saturation current I _o, equivalent series impedance R _s, equivalent parallel resistance value R _shand ideal factor a;

Step 2: definition STFT operator, carries out decoupling zero according to STFT is theoretical to the photovoltaic cell equivalence 5 parameter transcendental equations in step 1, obtains the decoupling zero explicit equation parameter model of photovoltaic cell;

Step 3: utilize the standard condition basic data that photovoltaic cell manufacturer provides, according to the equivalent relation under different operating condition, the equality constraint set of Criterion operating mode decoupling zero explicit equation parameter model unknown parameter, set up Nonlinear System of Equations, ask for described unknown parameter by Solving Nonlinear Systems of Equations algorithm;

Ask in process in parameter, introduce short-circuit current temperature coefficient modifying factor κ _scwith open-circuit voltage temperature coefficient modifying factor κ _oc, the short-circuit current temperature coefficient at Optimized Matching maximum power point place and open-circuit voltage temperature coefficient;

Step 4: try to achieve the unknown parameters ' value of decoupling zero explicit equation parameter model under given operating mode according to the unknown parameters ' value of decoupling zero explicit equation parameter model under the standard condition asked in step 3;

Step 5: brought into by the unknown parameters ' value under described given operating mode in described photovoltaic cell decoupling zero explicit equation parameter model, obtains the photovoltaic cell model of concentrated expression photovoltaic cell output characteristic under final given operating mode.

2. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 1, it is characterized in that, in described step 1, the equivalence 5 parameter transcendental equation of photovoltaic cell output characteristic is specially:

$I_{\mathrm{PV}}=I_{\mathrm{ph}}-I_0(\exp \left(\frac{V_{\mathrm{PV}}+I_{\mathrm{PV}}{R}_s}{a}\right)-1)-\frac{V_{\mathrm{PV}}+I_{\mathrm{PV}}{R}_s}{R_{\mathrm{sh}}}---\left(1\right);$

Wherein, I _phfor photogenerated current; I ₀for flowing through the reverse saturation current of diode; A=nN _skT/q, n are ideal factor coefficient, characterization model nonlinearity; N _sfor the monocell number that photovoltaic battery panel/array comprises, k is Boltzmann constant: k=1.38 × 10 ²³j/K, T are photovoltaic cell working temperature, and q is the unit quantity of electric charge, q=1.6 × 10 ¹⁹c; R _sand R _shbe respectively equivalent series resistance and equivalent parallel resistance; I _pVand V _pVbe respectively output current and the output voltage of photovoltaic battery panel/array.

3. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 1, it is characterized in that, in described step 2, the decoupling zero explicit equation parameter model of photovoltaic cell is specially:

$I_{\mathrm{PV}}=\left(\frac{(I_{\mathrm{ph}}+I_0)-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}}}{1+\frac{R_s}{R_{\mathrm{sh}}}}\right)(1-\frac{a(1+\frac{R_s}{R_{\mathrm{sh}}})}{R_s(I_0+I_{\mathrm{ph}}-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}})}{\mathrm{trans}}_{+}\left(D\right))---\left(2\right);$

Wherein, D is STFT operator, $D=\frac{I_0{R}_s\exp \left(\frac{V_{\mathrm{PV}}}{a}\right)\exp \left(\frac{R_s(I_0+I_{\mathrm{ph}}-\frac{V_{\mathrm{PV}}}{R_{\mathrm{sh}}})}{a(1+\frac{R_s}{R_{\mathrm{sh}}})}\right)}{a(1+\frac{R_s}{R_{\mathrm{sh}}})}---\left(3\right);$

Transforming function transformation function trans ₊be defined as,

Wherein, x is accumulative frequency, determines transforming function transformation function trans ₊computational accuracy, m is the cumulative power level of transforming function transformation function.

4. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 1, it is characterized in that, the standard condition basic data that in described step 3, photovoltaic cell manufacturer provides comprises: open-circuit voltage V under photovoltaic cell standard condition _{oc, ref}, short-circuit current I _{sc, ref}, maximum power point voltage V _{mpp, ref}, maximum power point electric current I _{mpp, ref}, the Series Sheet battery number N that comprises of photovoltaic cell component _ser, short-circuit current temperature coefficient α _scand open-circuit voltage temperature coefficient β _oc;

Decoupling zero explicit equation parameter model unknown parameter under standard condition to be solved comprises: photogenerated current I _{ph, ref}, diode reverse saturation current I _{o, ref}, equivalent series impedance R _{s, ref}, equivalent parallel resistance value R _{sh, ref}and ideal factor a _ref.

5. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 1, it is characterized in that, the concrete grammar of the equality constraint set of described step 3 Plays operating mode decoupling zero explicit equation parameter model unknown parameter is:

Equality constraint 1: the short circuiting work condition according to photovoltaic cell can obtain:

$I_{\mathrm{sc},\mathrm{ref}}=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(5\right)$

Equality constraint 2: the open-circuit working condition according to photovoltaic cell can obtain:

$0=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{V_{\mathrm{oc},\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{V_{\mathrm{oc},\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(6\right)$

Equality constraint 3: the maximum power point condition of work according to photovoltaic cell can obtain:

$I_{\mathrm{mpp},\mathrm{ref}}=I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(\exp \left(\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}\right)-1)-\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}---\left(7\right)$

Equality constraint 4: can obtain according to the power vs. voltage curve gradient dP/dV=0 of photovoltaic cell at maximum power point place:

${\frac{\mathrm{dP}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}={\frac{\∂\left(\mathrm{VI}\right)}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}=I_{\mathrm{mpp},\mathrm{ref}}-V_{\mathrm{mpp},\mathrm{ref}}{\frac{\mathrm{dI}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}---\left(8\right)$

Wherein, ${\frac{\mathrm{dI}}{\mathrm{dV}}|}_{\mathrm{mpp},\mathrm{ref}}=\frac{\frac{I_{0,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{1}{R_{\mathrm{sh},\mathrm{ref}}}}{1+\frac{I_{0,\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{R_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}}---\left(9\right)$

Equality constraint 5: in order to the model accuracy at maximum power point place under the different operating mode of Optimized Matching, introduce short-circuit current temperature coefficient modifying factor κ _scwith open-circuit voltage temperature coefficient modifying factor κ _oc, because temperature increment is not remarkable on the impact of photovoltaic cell output characteristic curve shape, get Δ T=5 DEG C, T'=T _ref+ Δ T, considers maximum power point condition, has

$I_{\mathrm{mpp},T^{\′}}=I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(\exp \left(\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}\right)-1)-\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}---\left(10\right)$

Wherein, V _{oc, ref}, I _{sc, ref}, V _{mpp, ref}, I _{mpp, ref}open-circuit voltage, short-circuit current, maximum power point voltage, maximum power point electric current under photovoltaic cell standard condition; I _{ph, ref,}i _{0, ref}, R _{s, ref}, R _{sh, ref}, a _refbe respectively the photogenerated current of the decoupling zero explicit equation parameter model under standard condition, diode reverse saturation current, equivalent series impedance, equivalent parallel resistance value and ideal factor a _ref; I _{mpp, T'}, I _{ph, T'}, V _{mpp, T'}, R _{s, T'}, R _{sh, T'}, I _{0, T'}, a _t'be respectively the maximum power point electric current under delta temperature T', photogenerated current, maximum power point voltage, equivalent series resistance, equivalent parallel resistance, equivalent diode reverse saturation current and ideal factor;

Equality constraint 6: γ _mpp=γ _model(17)

Wherein, γ _mppfor peak power temperature coefficient parameter, γ _modelfor combining the model peak power temperature coefficient parameter that the unknown parameter that solves obtains.

6. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 1, is characterized in that, the Nonlinear System of Equations of the standard condition decoupling zero explicit equation parameter model unknown parameter set up in described step 3 is specially:

$F\left(x\right)=\left\{\begin{array}{c}{I}_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{I_{\mathrm{sc},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}-I_{\mathrm{sc},\mathrm{ref}}\\ I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{V_{\mathrm{oc},\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{V_{\mathrm{oc},\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}\\ I_{\mathrm{ph},\mathrm{ref}}-I_{0,\mathrm{ref}}(e^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}-1)-\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}-I_{\mathrm{mpp},\mathrm{ref}}\\ I_{\mathrm{mpp},\mathrm{ref}}-V_{\mathrm{mpp},\mathrm{ref}}\·\frac{\frac{I_{0,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{1}{R_{\mathrm{sh},\mathrm{ref}}}}{1+\frac{I_{0,\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}{e}^{\frac{V_{\mathrm{mpp},\mathrm{ref}}+I_{\mathrm{mpp},\mathrm{ref}}{R}_{s,\mathrm{ref}}}{a_{\mathrm{ref}}}}+\frac{R_{s,\mathrm{ref}}}{R_{\mathrm{sh},\mathrm{ref}}}}\\ I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(e^{\frac{V_{\mathrm{oc},T^{\′}}}{a_{T^{\′}}}}-1)-\frac{V_{\mathrm{oc},T^{\′}}}{R_{\mathrm{sh},T^{\′}}}\\ {\mathrm{\γ}}_{\mathrm{mpp}}-{\mathrm{\γ}}_{\mathrm{mode}l}\end{array}\right.---\left(23\right).$

7. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 6, it is characterized in that, the solution procedure of described Nonlinear System of Equations is specially:

Determine that variable vector x to be solved is,

$x\≅{[I_{\mathrm{ph},\mathrm{ref}},I_{0,\mathrm{ref}},a_{\mathrm{ref}},R_{s,\mathrm{ref}},R_{\mathrm{sh},\mathrm{ref}},{\mathrm{\κ}}_{\mathrm{oc}},{\mathrm{\κ}}_{\mathrm{sc}}]}^T---\left(24\right)$

Non-linear due to equation, and known variables number is no less than nonlinear equation number in system of equations, adopt Iterative search algorithm or non-linear least square optimizing algorithm minimum for objective function with system of equations error of sum square, choose rational initial value and solve overall feasible solution.

8. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 7, it is characterized in that, the process of choosing of described initial value is:

Wherein, a ₁and a ₂for ideal factor initial estimate coefficient, C _sfor equivalent series resistance initial estimate coefficient, C _shfor equivalent parallel resistance initial estimate coefficient.

9. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operator as claimed in claim 1, it is characterized in that, the concrete grammar of trying to achieve the unknown parameters ' value of decoupling zero explicit equation parameter model under given operating mode according to the unknown parameters ' value of decoupling zero explicit equation parameter model under the standard condition asked in step 4 is:

Substitute maximum power point condition by open circuit voltage conditions, have

$0=I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(\exp \left(\frac{V_{\mathrm{oc},T^{\′}}}{a_{T^{\′}}}\right)-1)-\frac{V_{\mathrm{oc},T^{\′}}}{R_{\mathrm{sh},T^{\′}}}---\left(11\right)$

Wherein,

$I_{\mathrm{ph},T^{\′}}=\frac{G_{T^{\′}}}{G_{\mathrm{ref}}}\·\frac{{\mathrm{AM}}_{T^{\′}}}{{\mathrm{AM}}_{\mathrm{ref}}}[I_{\mathrm{ph},\mathrm{ref}}+{\mathrm{\α}}_{\mathrm{sc}}(1-{\mathrm{\κ}}_{\mathrm{sc}}/100)\mathrm{\ΔT}]---\left(12\right)$

$V_{\mathrm{oc},T^{\′}}\≅V_{\mathrm{oc},\mathrm{ref}}+{\mathrm{\β}}_{\mathrm{oc}}(1+{\mathrm{\κ}}_{\mathrm{oc}}/100)\·\mathrm{\ΔT}---\left(13\right)$

Wherein, G _reffor the irradiance under standard condition; G _t'for the irradiance under delta temperature T'; AM _reffor the optical path factor under standard condition; AM _t'for the optical path factor under delta temperature T'; Δ T=5 DEG C;

The update equation of all the other nonstandard condition conditional parameters is,

$R_{\mathrm{sh},T^{\′}}\≅\frac{G_{\mathrm{ref}}}{G_{T^{\′}}}\·R_{\mathrm{sh},\mathrm{ref}}---\left(14\right)$

$a_{T^{\′}}\≅a_{\mathrm{ref}}\·\frac{T_{\mathrm{cell},T^{\′}}}{T_{\mathrm{cell},\mathrm{ref}}}---\left(15\right)$

$\left\{\begin{array}{c}{I}_{0,T^{\′}}=I_{0,\mathrm{ref}}\·{\left[\frac{T_{\mathrm{cell},T^{\′}}}{T_{\mathrm{cell}-\mathrm{ref}}}\right]}^3\·\exp \left(\frac{1}{k}({\frac{E_g}{T}|}_{T_{\mathrm{cell},\mathrm{ref}}}-{\frac{E_g}{T}|}_{T_{\mathrm{cell},T^{\′}}})\right),k=8.617\×{10}^{-5}\mathrm{eV}\·K^{-1}\\ E_g\left(T\right)=E_g\left(0\right)-\frac{a\·T^2}{T+b},E_g\left(0\right)=1.166\mathrm{eV},a=4.73\×{10}^{-4}\mathrm{eV}\·K^{-1},b=636K\end{array}\right.---\left(16\right)$

Ask for γ _modelsubprocess be:

With standard condition work temperature _{cell, ref}=25 DEG C extend, at T for benchmark _cellin ∈ [-10 DEG C, 50 DEG C] scope, with Δ T _cell=3 DEG C is increment, carry out peak power at each temperature extension point T ' to resolve, the Nonlinear System of Equations be made up of at the update equation that temperature extends point formula (7) and formula (8) is solved, namely with nonlinear iteration or Nonlinear least squares optimization scheduling algorithm

$\left\{\begin{array}{c}{I}_{\mathrm{mpp},T^{\′}}=V_{\mathrm{mpp},T^{\′}}\·\frac{\frac{I_{0,T^{\′}}}{a_{T^{\′}}}{e}^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}+\frac{1}{R_{\mathrm{sh},T^{\′}}}}}{1+\frac{I_{0,T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}{e}^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}+\frac{R_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}}\\ I_{\mathrm{mpp},T^{\′}}=I_{\mathrm{ph},T^{\′}}-I_{0,T^{\′}}(e^{\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{a_{T^{\′}}}}-1)-\frac{V_{\mathrm{mpp},T^{\′}}+I_{\mathrm{mpp},T^{\′}}{R}_{s,T^{\′}}}{R_{\mathrm{sh},T^{\′}}}\end{array}\right.---\left(18\right)$

Wherein, I _{0, T '}, a _{t '}and R _{sh, T '}revise by formula (14) ~ (16) respectively, and R _{s, T '}and I _{ph, T '}update equation be,

$\left\{\begin{array}{c}{R}_{s,T^{\′}}=R_{s,\mathrm{ref}}\\ I_{\mathrm{ph},T^{\′}}=\frac{G_{T^{\′}}}{G_{\mathrm{ref}}}\·\frac{{\mathrm{AM}}_{T^{\′}}}{{\mathrm{AM}}_{\mathrm{ref}}}(I_{\mathrm{ph},\mathrm{ref}}+{\mathrm{\α}}_{\mathrm{sc}}(1-{\mathrm{\κ}}_{\mathrm{sc}}/100)(T_{\mathrm{cell},T^{\′}}-T_{\mathrm{cell},\mathrm{ref}}))\end{array}\right.---\left(19\right)$

Bring formula (19) into formula (18) to solve and can obtain,

P _mpp,T′＝I _mpp,T′V _mpp,T′(20)

Then asked for the peak power temperature coefficient that peak power obtains can be expressed as by the adjacent temperature point that extends,

${\mathrm{\γ}}_{\mathrm{mpp},T_n^{\′}}\≅\frac{P_{\mathrm{mpp},T_{n-1}^{\′}}-P_{\mathrm{mpp},T_n^{\′}}}{T_{n-1}^{\′}-T_n^{\′}}---\left(21\right)$

Wherein, P _{mpp, T'n-1}and P _{mpp, T'n}be respectively the maximum power point power under the (n-1)th temperature extension point and the n-th temperature extension point; γ _{mpp, T'n}it is the maximum power point gradient under the n-th temperature extension point;

To the peak power temperature coefficient handling averagely that each temperature extension knock type (21) is asked for, as the peak power temperature coefficient γ of photovoltaic cell output characteristic model _model, namely

${\mathrm{\γ}}_{\mathrm{mode}l}\≅\frac{1}{n}\·\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\γ}}_{\mathrm{mpp},T_i^{\′}}\right)---\left(22\right).$