CN104778352B

CN104778352B - The seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators

Info

Publication number: CN104778352B
Application number: CN201510149180.4A
Authority: CN
Inventors: 彭飞; 陈玉峰; 辜超; 朱文兵; 周加斌; 朱孟照; 杜修明; 朱庆东; 王建; 任敬国; 李�杰; 白德盟
Original assignee: State Grid Corp of China SGCC; Electric Power Research Institute of State Grid Shandong Electric Power Co Ltd
Current assignee: State Grid Corp of China SGCC; Electric Power Research Institute of State Grid Shandong Electric Power Co Ltd
Priority date: 2015-03-31
Filing date: 2015-03-31
Publication date: 2017-12-12
Anticipated expiration: 2035-03-31
Also published as: CN104778352A

Abstract

The invention discloses a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators, including：Establish the equivalent circuit initial model of photovoltaic cell output characteristic；STFT operators are defined, obtain the decoupling explicit equation parameter model of photovoltaic cell；The standard condition basic data provided using photovoltaic cell manufacturer, establishes Nonlinear System of Equations, derivation algorithm asks for the unknown parameter；Try to achieve unknown parameters ' value of the decoupling explicit equation parameter model under given operating mode；Unknown parameters ' value under the given operating mode is brought into the photovoltaic cell decoupling explicit equation parameter model, obtains the photovoltaic cell model of concentrated expression photovoltaic cell output characteristic under final given operating mode.Beneficial effect of the present invention：STFT operators do not have domain limitation used by model decoupling, and can be arranged as required to desired STFT decouplings operator computational accuracy, and application is more flexible.

Description

The seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators

Technical field

The invention belongs to technical field of photovoltaic power generation, more particularly to a kind of seven parameter photovoltaic cells based on STFT operators are defeated Go out characteristics modeling method.

Background technology

With the continuous social and economic development, the situation in short supply of fossil energy and problem of environmental pollution become increasingly conspicuous, people Higher and higher requirement is proposed to the energy, finding new energy turns into the urgent problem that current mankind faces, and development and utilization can The renewable sources of energy are extremely urgent.Wherein, solar energy is as a kind of one of regenerative resource for cleaning, having large-scale development prospect, In home-use small-sized solar power generation system, the grid-connected power station of large-sized photovoltaic, architecture-integral photovoltaic glass curtain wall, sun energy circuit The fields such as lamp, wind-photovoltaic complementary power supply system receive significant attention and furtherd investigate.

Solar energy power generating is that solar energy is converted into electric energy using solar cell.Photovoltaic generating system master To be made up of photovoltaic battery array, energy-storage system of accumulator, controller and inverter, wherein photovoltaic battery array is photovoltaic generation The key component of system, direct current energy is converted solar energy into by photovoltaic battery array, turned direct current energy by inverter Turn to the AC energy feed-in power network with frequency with phase with power network.Due to the difficulty or ease journey of photovoltaic cell modeling accuracy and its realization degree Degree is controlled rear class system design and control strategy research and development such as maximal power tracing (MPPT), and inverter control etc. has weight Influence, it is therefore, significant to the accurate High Efficiency Modeling of photovoltaic cell output characteristic.

The power output of photovoltaic battery array and incident irradiance degree, photovoltaic cell operating temperature, incident light inclination angle and Load impedance etc. is related.Photovoltaic cell manufacturer generally only provides limited photovoltaic battery panel operational factor, such 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 generally under standard rated condition (SRC, i.e. irradiation level 1000W/m², 25 DEG C of panel operating temperature, except NOCT test conditions are：Irradiation level 800W/m², environment temperature 20 degrees Celsius DEG C) measure.The power output of photovoltaic battery panel is maximum under above-mentioned standard rated condition, but in photovoltaic cell face It is extremely difficult in the actual moving process of plate.Therefore, though the above-mentioned environmental factor of the power output of photovoltaic cell and itself work are joined Several change and change, its output characteristics is characterized as multigroup non-linear I-V characteristic curve under the conditions of different operational factors.

The output characteristics of photovoltaic cell can be described by the equivalent-circuit model being widely used at present, as shown in Figure 1.Should Equivalent circuit includes a photogenerated current source, a backward dioded in parallel with the photogenerated current source, one and reverse two pole Pipe equivalent parallel resistance and series resistance in parallel.Above-mentioned equivalent-circuit model includes 5 unknown parameters, i.e. photoproduction electricity Flow I_ph, diode reverse saturation current I_o, equivalent series impedance R_s, equivalent parallel resistance value R_shAnd ideal factor a.Due to Modeling accuracy is high, and above-mentioned 5 parameter model is widely used in photovoltaic cell modeling and simulating.But due to above-mentioned equivalent electric The mathematical form of road model has intrinsic transcendental equation characteristic, i.e., exists between equivalent backward dioded its voltage and electric current Iteration couples, thus initial value iteration and unstable phenomenon occur in system emulation, is particularly imitated in the circuit based on SPICE In the photovoltaic generating system modeling and simulating of true analysis software.Therefore, how to overcome the transcendental equation of above-mentioned equivalent-circuit model special Property and effectively using producer provide data the unknown parameter in model is accurately solved, become photovoltaic cell output characteristic Model problem urgently to be resolved hurrily.

At present, the decoupling method based on Lambert-W functions can be used to transcendental equation, but Lambert-W functions have There is strict (- 1/e ,+) domain limitation, and its computational accuracy and computational efficiency have much room for improvement.

And in existing photovoltaic cell equivalent-circuit model unknown parameter method for solving, it is conventional by fixed ideal factor Method and function optimization method.Wherein, fixed ideal factor method is assumed under the conditions of constant ideal factor, utilizes the number such as iterative method Value calculating method solves to remaining 4 parameter, but secures 1 parameter, can accurately produce shadow to the overall modeling of model Ring.

And for function optimization class method, generally it is mostly the open circuit bar based on the photovoltaic cell equivalent-circuit model at present Part, short circuit condition, maximum power point condition and maximum power point gradient condition are to the reason under the standard condition in 5 parameter Think factor a, equivalent series resistance R_sWith equivalent parallel resistance R_pSolution is optimized Deng for target variable, and is obtained by optimization A, R_sAnd R_pDiode reverse saturation current I under standard condition is solved by open-circuit condition₀, and assume under standard condition Photogenerated current is approximately the short circuit current under standard condition, and this have lost the computational accuracy of model to a certain extent.In addition, light Volt array operating point is usually the maximum power point under different operating conditions, effectively to utilize the defeated of photovoltaic battery array Go out efficiency, therefore, constructed photovoltaic cell output characteristic model and its Optimal Parameters are also desirable that can have at maximum power point Preferable model accuracy, the short circuit current at peak power temperature coefficient parameter and maximum power point as matched manufacturer's offer The amendment of temperature coefficient and open-circuit voltage temperature coefficient, and in current photovoltaic cell output characteristic modeling and parametric solution Do not imitate the influence for considering above-mentioned factor.

The content of the invention

The purpose of the present invention is exactly to solve the above problems, it is proposed that a kind of seven parameter photovoltaic electrics based on STFT operators Pond output characteristics modeling method, this method realize quick essence while output characteristics unknown-model parameter matching and optimization is realized True output characteristics decoupling computation, improve the emulation of the photovoltaic cell capable of generating power system based on the photovoltaic cell output characteristic model Computational efficiency, accurate efficient model basis is provided for the control strategy design of photovoltaic cell capable of generating power system.

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

A kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators, comprise the following steps：

Step 1：The equivalent circuit initial model of photovoltaic cell output characteristic is established, and provides photovoltaic cell output characteristic Equivalent 5 parameter transcendental equation；5 parameter includes 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：STFT operators are defined, the equivalent 5 parameter transcendental equation of photovoltaic cell in step 1 is entered according to STFT theories Row decoupling, obtains the decoupling explicit equation parameter model of photovoltaic cell；

Step 3：Using photovoltaic cell manufacturer provide standard condition basic data, according under the conditions of different operating etc. Effect relation, the equality constraint set of standard condition decoupling explicit equation parameter model unknown parameter is established, establishes nonlinear equation Group, the unknown parameter is asked for by Solving Nonlinear Systems of Equations algorithm；

During parameter is asked for, short circuit current temperature coefficient modifying factor κ is introduced_scWith open-circuit voltage temperature coefficient amendment Factor κ_oc, short circuit current temperature coefficient and open-circuit voltage temperature coefficient at Optimized Matching maximum power point；

Step 4：Unknown parameters ' value according to explicit equation parameter model is decoupled under the standard condition asked in step 3 is tried to achieve Decouple unknown parameters ' value of the explicit equation parameter model under given operating mode；

Step 5：Bring the unknown parameters ' value under the given operating mode into the photovoltaic cell decoupling explicit equation parameter mould In type, the photovoltaic cell model of concentrated expression photovoltaic cell output characteristic under final given operating mode is obtained.

The equivalent 5 parameter transcendental equation of photovoltaic cell output characteristic is specially in the step 1：

Wherein, I_phFor photogenerated current；I₀To flow through the reverse saturation current of diode；A=nN_sKT/q, n are ideal factor Coefficient, characterization model nonlinearity；N_sThe monocell number included by photovoltaic battery panel/array, k are Boltzmann constant：k =1.38 × 10²³J/K, T are photovoltaic cell operating temperature, and q is the unit quantity of electric charge, q=1.6 × 10¹⁹C；R_sAnd R_shRespectively etc. Imitate series resistance and equivalent parallel resistance；I_PVAnd V_PVThe respectively output current and output voltage of photovoltaic battery panel/array.

The decoupling explicit equation parameter model of photovoltaic cell is specially in the step 2：

Wherein, D is STFT operators,

Transforming function transformation function trans₊It is defined as,

Wherein, x is accumulative frequency, determines transforming function transformation function trans₊Computational accuracy, m be transforming function transformation function cumulative power Level.

The standard condition basic data that photovoltaic cell manufacturer provides in the step 3 includes：Photovoltaic cell standard condition Lower open-circuit voltage V_oc,ref, short circuit current I_sc,ref, maximum power point voltage V_mpp,ref, maximum power point electric current I_mpp,ref, photovoltaic electric The series connection monocell number N that pond component is included_ser, short circuit current temperature coefficient α_scAnd open-circuit voltage temperature coefficient β_oc；

Decoupling explicit equation parameter model unknown parameter under standard condition to be solved includes：Photogenerated current I_ph,ref, two Pole pipe reverse saturation current I_o,ref, equivalent series impedance R_s,ref, equivalent parallel resistance value R_sh,refAnd ideal factor a_ref。

The specific side of the equality constraint set of the step 3 Plays operating mode decoupling explicit equation parameter model unknown parameter Method is：

Equality constraint 1：It can be obtained according to the short circuiting work condition of photovoltaic cell：

Equality constraint 2：It can be obtained according to the open-circuit working condition of photovoltaic cell：

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

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

Wherein,

Equality constraint 5：For the model accuracy under Optimized Matching difference operating mode at maximum power point, short circuit current temperature is introduced Spend coefficient modifying factor κ_scWith open-circuit voltage temperature coefficient modifying factor κ_oc, because temperature increment is to photovoltaic cell output characteristic The influence of curve shape is not notable, takes T=5 DEG C of Δ, T'=T_ref+ Δ T, consider maximum power point condition, have

Wherein, V_oc,ref、I_sc,ref、V_mpp,ref、I_mpp,refOpen-circuit voltage, short circuit current, maximum under photovoltaic cell standard condition Power point voltage, maximum power point electric current；I_ph,ref、I_0,ref、R_s,ref、R_sh,ref、a_refDecoupling respectively under standard condition shows The photogenerated current of formula equation parameter model, 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'Maximum power point under respectively delta temperature T' Electric current, 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_modelThe model that the unknown parameter solved for combination obtains is most High-power temperature coefficient parameter.

The Nonlinear System of Equations tool for the standard condition decoupling explicit equation parameter model unknown parameter established in the step 3 Body is：

The solution procedure of the 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)

It is non-linear due to equation, and known variables number is no less than nonlinear equation number in equation group, using repeatedly For searching algorithm or non-linear least square optimizing algorithm with the minimum object function of equation group error of sum square, choose rational Initial value solves global feasible solution.

The selection process of the initial value is：

Wherein, a₁And a₂For ideal factor initial estimate coefficient, C_sFor equivalent series resistance initial estimate coefficient, C_shFor etc. Parallel resistance initial estimate coefficient is imitated, the int in parameter refers to the initial value of relevant parameter.

It is aobvious that unknown parameters ' value according to explicit equation parameter model is decoupled under the standard condition asked in step 4 tries to achieve decoupling The specific method of unknown parameters ' value of the formula equation parameter model under given operating mode is：

Maximum power point condition is substituted by open circuit voltage conditions, is had

Wherein,

V_oc,T′≌V_oc,ref+β_oc(1+κ_oc/100)·ΔT (13)

Wherein, G_refFor the irradiation level under standard condition；G_T'For the irradiation level under delta temperature T'；AM_refFor standard condition Under optical path factor；AM_T'For the optical path factor under delta temperature T'；T=5 DEG C of Δ；

The update equation of remaining nonstandard condition conditional parameter is,

Ask for γ_modelSubprocess be：

With standard condition work temperature_cell,refExtended on the basis of=25 DEG C, in T_cell∈ [- 10 DEG C, 50 DEG C] scope It is interior, with Δ T_cell=3 DEG C are increment, peak power resolving are carried out in each temperature extension point T ', with nonlinear iteration or non-thread Property Least-squares minimization scheduling algorithm solve and extended the nonlinear equation that the update equation put forms in temperature by formula (7) and formula (8) Group, i.e.,

Wherein, I_0,T’、a_T’And R_sh,T’Corrected respectively by formula (14)~(16), and R_s,T’And I_ph,T’Update equation be,

Formula (19) is brought 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 by the adjacent temperature point that extends and be represented by,

Wherein, P_mpp,T'n-1And P_mpp,T'nThe peak power that respectively the (n-1)th temperature extends under point and the n-th temperature extension point Point power；γ_mpp,T'nFor the maximum power point gradient under the n-th temperature extension point；

The peak power temperature coefficient handling averagely asked for each temperature extension knock type (21), as photovoltaic cell The peak power temperature coefficient γ of output characteristics model_model, i.e.,

The beneficial effects of the invention are as follows：

Compared to prior art, the seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators proposed In, STFT operators have no intrinsic (- 1/e ,+) the domain limitation of Lambert-W functions used by model decoupling, and can be with Desired STFT decouplings operator computational accuracy is arranged as required to, application is more flexible, and can easily build SPICE netlists will The electric output characteristics model of the photovoltaic panel is effectively encapsulated, and the circuit-level for photovoltaic cell system emulates.In addition, in light In terms of lying prostrate battery output characteristics unknown-model parametric solution, method proposed by the present invention is comprehensive on the basis of existing function optimization method Close the maximum power point matching problem for considering photovoltaic cell output characteristic model and its Optimal Parameters under different operating conditions, structure Seven ginsengs of priori can be passed through by the Nonlinear System of Equations of nonlinear iteration or Nonlinear least squares optimization Algorithm for Solving by having built Number Initialization Algorithms and two-level nested Nonlinear System of Equations iteration optimizing, obtain seven parameter sets under required standard condition To close, each parameter has its clear and definite physical significance, the basic data that parametric solution process provides merely with photovoltaic cell producer, Therefore it is applied to different types of photovoltaic cell.

Brief description of the drawings

Fig. 1 is 5- parameters photovoltaic cell equivalent-circuit model schematic diagram provided in an embodiment of the present invention；

Fig. 2 is the implementation of photovoltaic cell output characteristic provided in an embodiment of the present invention modeling and its parametric solution；

Fig. 3 is that photovoltaic cell 7- parameter models equivalent parameters provided in an embodiment of the present invention solves flow chart；

Fig. 4 is that CRM220S156P-60 series photovoltaics battery panel output characteristics provided in an embodiment of the present invention is modeled and joined The emulation fitting result of number extracting method and the comparison diagram of measured data.

Embodiment：

The present invention will be further described with embodiment below in conjunction with the accompanying drawings：

A kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators, as shown in Fig. 2

Step 1：The equivalent circuit initial model of photovoltaic cell output characteristic is established, then provides its physical mathematics form Equivalent 5 parameter transcendental equation；The 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：It is theoretical according to Special Trans Function Theory (STFT), STFT operators are defined, by step The parameter transcendental equation model of photovoltaic cell 5 in 1 is decoupled, and obtains the decoupling explicit equation parameter model of photovoltaic cell；

Step 3：The standard condition basic data provided using photovoltaic cell manufacturer, is calculated by Solving Nonlinear Systems of Equations Method (such as non-linear iterative or Nonlinear least squares optimization algorithm) asks for decoupling parameter model under standard condition not Know parameter, during parameter is asked for, introduce short circuit current temperature coefficient modifying factor κ_scWith open-circuit voltage temperature coefficient amendment Factor κ_oc, the short circuit current temperature coefficient and open-circuit voltage temperature coefficient at Optimized Matching maximum power point, thus it is described Photovoltaic cell output characteristic model is essentially 7 parameter equivalent models；

Step 4：With reference to the decoupling parameter unknown-model parameter transforming relationship, with reference to the standard condition asked in step 3 Unknown parameter is worth to unknown parameters ' value of the decoupling parameter model under given operating mode；

Step 5：Unknown parameters ' value under the given operating mode is brought into the photovoltaic cell decoupling parameter model, obtained The photovoltaic cell model of concentrated expression photovoltaic cell output characteristic under final given operating mode.

The data that producer provides include open-circuit voltage V under photovoltaic cell standard condition_oc,ref, short circuit current I_sc,ref, it is maximum Power point voltage V_mpp,ref, maximum power point electric current I_mpp,ref, the series connection monocell number N that is included of photovoltaic cell component_ser, it is short Road current temperature coefficient α_scWith open-circuit voltage temperature coefficient β_oc。

Specific method is as follows：

In step 1, the corresponding equivalent 7 parameter transcendental equation of photovoltaic cell output characteristic equivalent circuit initial model is asked for Process is：

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

Wherein：I_phFor photogenerated current；I₀To flow through the reverse saturation current of diode；A=nN_sKT/q, N_sFor photovoltaic cell The monocell number that panel/array is included, k are Boltzmann constant：K=1.38 × 10²³J/K, T are photovoltaic cell work temperature Degree, q are the unit quantity of electric charge, q=1.6 × 10¹⁹C；R_sAnd R_shRespectively equivalent series resistance and equivalent parallel resistance；I_PVAnd V_PV The respectively output current and output voltage of photovoltaic battery panel/array.

In step 2, STFT operators are defined, the parameter transcendental equation model of photovoltaic cell 5 in step 1 is explicitly changed, obtained The explicit analytical expressions of photovoltaic cell equivalent model are：

Wherein, defining STFT operators D is

Then transforming function transformation function trans₊It is defined as,

In step 3, the standard condition basic data provided using photovoltaic cell manufacturer asks for the decoupling under standard condition The process of parameter model unknown parameter is：

(ref, i.e. irradiation level 1000W/m under the standard condition that photovoltaic cell manufacturer provides², panel operating temperature 25 DEG C) underlying parameter include：Photovoltaic cell short circuit current I_sc,ref, open-circuit voltage V_oc,ref, maximum power point electric current I_mpp,ref, most High-power voltage V_mpp,ref.Unknown parameter under standard condition to be solved includes：Photogenerated current I_ph,_ref, diode reverse Saturation current I_o,ref, equivalent series impedance R_s,ref, equivalent parallel resistance value R_sh,refAnd ideal factor a_ref；In addition, in order to Model accuracy under Optimized Matching difference operating mode at maximum power point, introduce short circuit current temperature coefficient modifying factor κ_scAnd open circuit Voltage temperature coefficient modifying factor κ_oc。

The underlying parameter provided based on the photovoltaic cell manufacturer, according to the equivalent relation under the conditions of different operating, is obtained To the equality constraint set for solving the standard condition unknown parameter.

Equality constraint 1：It can be seen from the short circuiting work condition of photovoltaic cell, under standard condition, have

Equality constraint 2：It can be seen from the open-circuit working condition of photovoltaic cell, under standard condition, have

Equality constraint 3：It can be seen from the maximum power point condition of work of photovoltaic cell, under standard condition, have

Equality constraint 4：It can be seen from power vs. voltage curve gradient dP/dV=0 of the photovoltaic cell at maximum power point, Under standard condition, have

Wherein,

Due to I_mpp,T’It is unknown dependent variable, it is therefore, approximate to substitute maximum power point condition by open circuit voltage conditions, have

Wherein,

V_oc,T′≌V_oc,ref+β_oc(1+κ_oc/100)·ΔT (13)

Equality constraint 6：Usual photovoltaic cell manufacturer can provide peak power temperature coefficient parameter γ_mpp, and existing light Lie prostrate the influence not yet in effect for considering the parameter in battery output characteristics model parameter solution procedure.It is well known that in order to improve light Lie prostrate the utilization rate of cell output, it is usually desirable to maximal power tracing control (MPPT) is carried out to photovoltaic battery panel/array, Therefore, maximum power output matching of the photovoltaic cell output characteristic model established under different operating modes is sent out for photovoltaic cell Electric system and its control strategy design have material impact.Solving obtained unknown parameter needs to combine peak power temperature coefficient Parameter γ_mppVerified and approached so that

γ_mpp=γ_model (17)

Wherein, γ_modelTo combine the model peak power temperature coefficient parameter that the unknown parameter solved obtains.Ask for γ_modelSubprocess be：

Wherein, I_0,T’、a_T’And R_sh,T’22 corrected respectively by formula (14)~(16), and R_s,T’And I_ph,T’Update equation be,

Formula (19) is brought into formula (18) to solve and can obtain,

P_mpp,T′=I_mpp,T′V_mpp,T′ (20)

The peak power temperature coefficient handling averagely asked for each temperature extension knock type (21), as photovoltaic cell The peak power temperature coefficient of output characteristics model, i.e.,

Summary constraints is analyzed, and simultaneous formula (5)~formula (8), formula (11), formula (17), obtains Nonlinear System of Equations F (x)：

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 Nonlinear System of Equations problem constructed by formula (23)~(25), and wherein by the non-linear of formula (18) construction Equation group subproblem, it is non-linear due to equation, and known variables number is no less than nonlinear equation number in equation group, because This, generally use Iterative search algorithm, or the optimizing algorithm such as non-linear least square is with the minimum mesh of equation group error of sum square Scalar functions combine rational initial value and choose the global feasible solution of solution (possible and non-optimal solution).

The solution procedure of Nonlinear System of Equations F (x)=0 is as shown in Figure 3.For non-linear iterative or non-linear minimum Two multiply optimized algorithm, and the initial value of variables collection to be solved chooses the Nonlinear System of Equations iteration shown in for formula (23) in formula (24) Convergence there is material impact.The selection process of the initial value of the variables collection to be solved is：

After unknown parameter set (24) under standard condition are drawn by optimizing algorithm, with reference to the decoupling parameter model Unknown parameter transforming relationship formula (12)~(16) (19), with reference to described in being worth to the standard condition unknown parameter asked in step 3 Unknown parameters ' value of the decoupling parameter model under given operating mode.

By above-mentioned solution conversion process, the unknown parameters ' value under the given operating mode is brought into and described is based on STFT operators Photovoltaic cell transcendental equation Decoupled Model in, obtain concentrated expression photovoltaic cell output characteristic under final given operating mode Photovoltaic cell model, emulated for photovoltaic cell capable of generating power system design.

As the application of the embodiment of the present invention, according to photovoltaic cell output characteristic modeling proposed by the invention and seven ginsengs Number extracting method, actual test is carried out to polysilicon photovoltaic cells panel CRM220S156P-60 series respectively and emulation is fitted. Specific operation process is to utilize the VA characteristic curve of programmable electronic load measure photovoltaic cell at standard conditions；Then, CRM220S156P- is established in the photovoltaic cell output characteristic modeling and seven parameter extracting methods proposed based on the embodiment of the present invention Seven parameter output characteristics models of 60 series photovoltaic battery panels；Finally, based on seven described parameter output characteristics model emulations CRM220S156P-60 series photovoltaic battery panel VA characteristic curves under fit standard situation.

Fig. 4 is shown the actual measurement data of CRM220S156P-60 series photovoltaic battery panels and implemented based on the present invention The emulation fitting result for the output characteristics modeling and parameter extraction method that example proposes.It coincide fine, carries as can be seen from the results Unknown parameter collection under the standard condition taken is combined into：Photogenerated current is 8.095A, and reverse saturation current is 8.23 × 10^-10A, reason It is 1.6002V to think the factor, 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, illustrates photovoltaic cell output proposed by the present invention Characteristic models and seven parameter extracting methods are correct, thus this method can also promote the use of current a variety of photovoltaic cells In the research of modeling and parameter extraction technology.

Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, model not is protected to the present invention The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need to pay various modifications or deformation that creative work can make still within protection scope of the present invention.

Claims

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

Step 1：The equivalent circuit initial model of photovoltaic cell output characteristic is established, and provides the equivalent of photovoltaic cell output characteristic 5 parameter transcendental equations；5 parameter includes photogenerated current I_ph, diode reverse saturation current I₀, equivalent series impedance R_s、 Equivalent parallel resistance value R_shAnd ideal factor a；

Step 2：STFT operators are defined, the equivalent 5 parameter transcendental equation of photovoltaic cell in step 1 is solved according to STFT theories Coupling, obtain the decoupling explicit equation parameter model of photovoltaic cell；

Step 3：The standard condition basic data provided using photovoltaic cell manufacturer, according to the equivalent pass under the conditions of different operating System, the equality constraint set of standard condition decoupling explicit equation parameter model unknown parameter is established, establishes Nonlinear System of Equations, is led to Cross Solving Nonlinear Systems of Equations algorithm and ask for the unknown parameter；

During parameter is asked for, short circuit current temperature coefficient modifying factor κ is introduced_scWith open-circuit voltage temperature coefficient modifying factor κ_oc, short circuit current temperature coefficient and open-circuit voltage temperature coefficient at Optimized Matching maximum power point；

Step 4：Unknown parameters ' value according to explicit equation parameter model is decoupled under the standard condition asked in step 3 tries to achieve decoupling Unknown parameters ' value of the explicit equation parameter model under given operating mode；

Step 5：Unknown parameters ' value under the given operating mode is brought into the photovoltaic cell decoupling explicit equation parameter model, Obtain the photovoltaic cell model of concentrated expression photovoltaic cell output characteristic under final given operating mode；

The standard condition basic data that photovoltaic cell manufacturer provides in the step 3 includes：Opened under photovoltaic cell standard condition Road voltage V_oc,ref, short circuit current I_sc,ref, maximum power point voltage V_mpp,ref, maximum power point electric current I_mpp,ref, photovoltaic cell group The series connection monocell number N that part is included_ser, short circuit current temperature coefficient α_scAnd open-circuit voltage temperature coefficient β_oc；

Decoupling explicit equation parameter model unknown parameter under standard condition to be solved includes：Photogenerated current I_ph,ref, diode Reverse saturation current I_0,ref, equivalent series impedance R_s,ref, equivalent parallel resistance value R_sh,refAnd ideal factor a_ref；

The specific method of the equality constraint set of the step 3 Plays operating mode decoupling explicit equation parameter model unknown parameter For：

<mrow> <mfrac> <mrow> <mi>d</mi> <mi>P</mi> </mrow> <mrow> <mi>d</mi> <mi>V</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&part;</mo> <mrow> <mo>(</mo> <mi>V</mi> <mi>I</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>V</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mfrac> <mrow> <mi>d</mi> <mi>I</mi> </mrow> <mrow> <mi>d</mi> <mi>V</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> 1

Wherein,

Equality constraint 5：For the model accuracy under Optimized Matching difference operating mode at maximum power point, short circuit current temperature system is introduced Number modifying factor κ_scWith open-circuit voltage temperature coefficient modifying factor κ_oc, because temperature increment is to photovoltaic cell output characteristic curve The influence of shape is not notable, takes T=5 DEG C of Δ, T'=T_ref+ Δ T, consider maximum power point condition, have

<mrow> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>exp</mi> <mo>(</mo> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> <mo>)</mo> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

Wherein, V_oc,ref、I_sc,ref、V_mpp,ref、I_mpp,refOpen-circuit voltage, short circuit current, peak power under photovoltaic cell standard condition Point voltage, maximum power point electric current；I_ph,ref、I_0,ref、R_s,ref、R_sh,ref、a_refDecoupling respectively under standard condition is explicitly square Photogenerated current, diode reverse saturation current, equivalent series impedance, equivalent parallel resistance value and the ideal of journey parameter model Factor a_ref；I_mpp,T'、I_ph,T'、V_mpp,T'、R_s,T'、R_sh,T'、I_0,T'、a_T'Maximum power point electric current under respectively 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 (7)

Wherein, γ_mppFor peak power temperature coefficient parameter, γ_modelTo combine the model maximum work that the unknown parameter solved obtains Rate temperature coefficient parameter.

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

Wherein, I_phFor photogenerated current；I₀To flow through the reverse saturation current of diode；A=nN_sKT/q, n are ideal factor coefficient, Characterization model nonlinearity；N_sThe monocell number included by photovoltaic battery panel/array, k are Boltzmann constant：K= 1.38×10²³J/K, T are photovoltaic cell operating temperature, and q is the unit quantity of electric charge, q=1.6 × 10¹⁹C；R_sAnd R_shIt is respectively equivalent Series resistance and equivalent parallel resistance；I_PVAnd V_PVThe respectively output current and output voltage of photovoltaic battery panel/array.

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

<mrow> <msub> <mi>I</mi> <mrow> <mi>P</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <mo>(</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mo>)</mo> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mrow> <mi>P</mi> <mi>V</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mfrac> </mrow> </mfrac> <mo>)</mo> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>I</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> </mrow> </msub> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mrow> <mi>P</mi> <mi>V</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mi>trans</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> 2

Wherein, D is STFT operators,

Transforming function transformation function trans₊It is defined as,

4. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators as claimed in claim 1, it is special Sign is that the Nonlinear System of Equations for the standard condition decoupling explicit equation parameter model unknown parameter established in the step 3 is specific For：

<mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>e</mi> <mfrac> <mrow> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mi>c</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mi>c</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mi>c</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>e</mi> <mfrac> <msub> <mi>V</mi> <mrow> <mi>o</mi> <mi>c</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mrow> <mi>o</mi> <mi>c</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>e</mi> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mfrac> <mrow> <mfrac> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </msup> <mo>+</mo> <mfrac> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>e</mi> <mfrac> <msub> <mi>V</mi> <mrow> <mi>o</mi> <mi>c</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mrow> <mi>o</mi> <mi>c</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&gamma;</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mrow> <mi>mod</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

5. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators as claimed in claim 4, it is special Sign is that the solution procedure of the Nonlinear System of Equations is specially：

Determine that variable vector x to be solved is,

<mrow> <mi>x</mi> <mo>&cong;</mo> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&kappa;</mi> <mrow> <mi>o</mi> <mi>c</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&kappa;</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

It is non-linear due to equation, and known variables number is no less than nonlinear equation number in equation group, is searched using iteration Rope algorithm or non-linear least square optimizing algorithm choose rational initial value with the minimum object function of equation group error of sum square Solve global feasible solution.

6. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators as claimed in claim 5, it is special Sign is that the selection process of the initial value is：

Wherein, a₁And a₂For ideal factor initial estimate coefficient, C_sFor equivalent series resistance initial estimate coefficient, C_shFor it is equivalent simultaneously Join resistance initial estimate coefficient.

7. a kind of seven parameter photovoltaic cell output characteristic modeling methods based on STFT operators as claimed in claim 1, it is special Sign is that it is explicit to try to achieve decoupling according to the unknown parameters ' value that explicit equation parameter model is decoupled under the standard condition asked in step 4 The specific method of unknown parameters ' value of the equation parameter model under given operating mode is：

<mrow> <mn>0</mn> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>exp</mi> <mo>(</mo> <mfrac> <msub> <mi>V</mi> <mrow> <mi>o</mi> <mi>c</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> <mo>)</mo> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mrow> <mi>o</mi> <mi>c</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

Wherein,

<mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>G</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> <msub> <mi>G</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <mo>&CenterDot;</mo> <mfrac> <mrow> <msub> <mi>AM</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mrow> <mrow> <msub> <mi>AM</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </mfrac> <mo>&lsqb;</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&alpha;</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&kappa;</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>100</mn> <mo>)</mo> </mrow> <mi>&Delta;</mi> <mi>T</mi> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>V</mi> <msup> <mrow> <mi>oc</mi> <mo>,</mo> <mi>T</mi> </mrow> <mo>&prime;</mo> </msup> </msub> <mo>&cong;</mo> <msub> <mi>V</mi> <mrow> <mi>oc</mi> <mo>,</mo> <mi>ref</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&beta;</mi> <mi>oc</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>&kappa;</mi> <mi>oc</mi> </msub> <mo>/</mo> <mn>100</mn> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <mi>&Delta;T</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> 4

Wherein, G_refFor the irradiation level under standard condition；G_T'For the irradiation level under delta temperature T'；AM_refFor under standard condition Optical path factor；AM_T'For the optical path factor under delta temperature T'；T=5 DEG C of Δ；

<mrow> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>&cong;</mo> <mfrac> <msub> <mi>G</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>G</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> <mo>&CenterDot;</mo> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> <mo>&cong;</mo> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mfrac> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>&CenterDot;</mo> <msup> <mrow> <mo>&lsqb;</mo> <mfrac> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <mo>&rsqb;</mo> </mrow> <mn>3</mn> </msup> <mo>&CenterDot;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mi>k</mi> </mfrac> <mo>(</mo> <mrow> <mfrac> <msub> <mi>E</mi> <mi>g</mi> </msub> <mi>T</mi> </mfrac> <msub> <mo>|</mo> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </msub> <mo>-</mo> <mfrac> <msub> <mi>E</mi> <mi>g</mi> </msub> <mi>T</mi> </mfrac> <msub> <mo>|</mo> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>k</mi> <mo>=</mo> <mn>8.617</mn> <mo>&times;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> <mi>e</mi> <mi>V</mi> <mo>&CenterDot;</mo> <msup> <mi>K</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mi>g</mi> </msub> <mrow> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>E</mi> <mi>g</mi> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <mi>a</mi> <mo>&CenterDot;</mo> <msup> <mi>T</mi> <mn>2</mn> </msup> </mrow> <mrow> <mi>T</mi> <mo>+</mo> <mi>b</mi> </mrow> </mfrac> <mo>,</mo> <msub> <mi>E</mi> <mi>g</mi> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>1.166</mn> <mi>e</mi> <mi>V</mi> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>a</mi> <mo>=</mo> <mn>4.73</mn> <mo>&times;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> <mi>e</mi> <mi>V</mi> <mo>&CenterDot;</mo> <msup> <mi>K</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> <mi>b</mi> <mo>=</mo> <mn>636</mn> <mi>K</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>

Ask for γ_modelSubprocess be：

With standard condition work temperature_cell,refExtended on the basis of=25 DEG C, in T_cellIn the range of ∈ [- 10 DEG C, 50 DEG C], With Δ T_cell=3 DEG C are increment, are extended point T ' progress peak power resolving in each temperature, with nonlinear iteration or it is non-linear most A young waiter in a wineshop or an inn multiplies optimized algorithm and solves the Nonlinear System of Equations being made up of formula (3) and formula (4) in the update equation of temperature extension point, i.e.,

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>&CenterDot;</mo> <mfrac> <mrow> <mfrac> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> </msup> <mo>+</mo> <mfrac> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mfrac> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>e</mi> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <msub> <mi>a</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mfrac> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>

Wherein, I_0,T’、a_T’And R_sh,T’Corrected respectively by formula (18)~(20), and R_s,T’And I_ph,T’Update equation be,

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>G</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> <msub> <mi>G</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mfrac> <mo>&CenterDot;</mo> <mfrac> <mrow> <msub> <mi>AM</mi> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </msub> </mrow> <mrow> <msub> <mi>AM</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>p</mi> <mi>h</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&alpha;</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>&kappa;</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>100</mn> </mrow> <mo>)</mo> <mo>(</mo> <mrow> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <msup> <mi>T</mi> <mo>&prime;</mo> </msup> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow>

Formula (22) is brought into formula (21) to solve and can obtain,

P_mpp,T′=I_mpp,T′V_mpp,T′ (23)

<mrow> <msub> <mi>&gamma;</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msubsup> <mi>T</mi> <mi>n</mi> <mo>&prime;</mo> </msubsup> </mrow> </msub> <mo>&cong;</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msubsup> <mi>T</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> </mrow> </msub> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msubsup> <mi>T</mi> <mi>n</mi> <mo>&prime;</mo> </msubsup> </mrow> </msub> </mrow> <mrow> <msubsup> <mi>T</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>T</mi> <mi>n</mi> <mo>&prime;</mo> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>

Wherein, P_mpp,T'n-1And P_mpp,T'nThe maximum power point work(that respectively the (n-1)th temperature extends under point and the n-th temperature extension point Rate；γ_mpp,T'nFor the peak power temperature coefficient under the n-th temperature extension point；

The peak power temperature coefficient handling averagely asked for each temperature extension knock type (24), exported as photovoltaic cell The peak power temperature coefficient γ of characteristic model_model, i.e.,

<mrow> <msub> <mi>&gamma;</mi> <mrow> <mi>mod</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>&cong;</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&gamma;</mi> <mrow> <mi>m</mi> <mi>p</mi> <mi>p</mi> <mo>,</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mo>&prime;</mo> </msubsup> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> 6