CN114818574A - Parameter identification method for photovoltaic array double-diode seven-parameter model - Google Patents

Parameter identification method for photovoltaic array double-diode seven-parameter model Download PDF

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CN114818574A
CN114818574A CN202210235761.XA CN202210235761A CN114818574A CN 114818574 A CN114818574 A CN 114818574A CN 202210235761 A CN202210235761 A CN 202210235761A CN 114818574 A CN114818574 A CN 114818574A
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张国玉
王宏华
路天航
王成亮
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Hohai University HHU
Jiangsu Fangtian Power Technology Co Ltd
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Jiangsu Fangtian Power Technology Co Ltd
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Abstract

The invention discloses a photovoltaic array double-diode seven-parameter model parameter identification method. Based on the application of combining an improved particle swarm algorithm and an analytical method, the ideal factors and the series equivalent resistance of the two diodes are optimized and solved, and then the photo-generated current, the parallel equivalent resistance and the reverse saturation current of the two diodes are solved by the analytical method. In order to improve the performance of the algorithm, a double fitness function is provided, and adaptive evolution learning and adaptive mutation operators are introduced. The method solves the problems that the photovoltaic array double-diode seven-parameter model parameter is difficult to solve and the single-diode model parameter is low in solving precision.

Description

Parameter identification method for photovoltaic array double-diode seven-parameter model
Technical Field
The invention relates to a photovoltaic array double-diode seven-parameter model parameter identification method, and belongs to the new technical field of photovoltaic power generation systems.
Background
At present, models for describing the output characteristics of the photovoltaic array mainly include a single-diode five-parameter model and a double-diode seven-parameter model. The single diode model has become a main model used in engineering due to few parameters and simple calculation. However, the two-diode seven-parameter model is relatively more accurate, especially in low light conditions. This is mainly because the single diode model ignores the complex saturation current of the PN junction depletion region.
The method for identifying the parameters of the photovoltaic array double-diode seven-parameter model mainly comprises an analytical method, a numerical solution method and an intelligent algorithm. The analytic method needs to make certain assumptions or neglect some parameters, and the solution is simple and rapid, but the precision is relatively low. The numerical solution generally needs to introduce new parameters, such as voltage/current temperature coefficient, series equivalent resistance at open-circuit voltage, and parallel equivalent resistance at short-circuit current, to construct a new equation, which is sensitive to an initial value during solution, and is easy to fall into local optimum or even fail to solve a numerical value. The intelligent algorithm is widely applied to photovoltaic array modeling due to the universal global search capability and the effectiveness of processing nonlinear functions. The currently commonly used intelligent algorithms include a particle swarm algorithm, a genetic algorithm, a neural network, a simulated annealing algorithm and the like, the random algorithm is generally unstable in convergence and slow in convergence speed, seven parameters of the double-diode seven-parameter model are extracted directly by using the intelligent algorithm, and the algorithm is large in calculation amount and relatively complex.
Therefore, how to simply, conveniently and accurately extract seven parameters of the photovoltaic array double-diode seven-parameter model has important significance for the research and development of photovoltaic power generation systems.
Disclosure of Invention
The invention provides a photovoltaic array double-diode seven-parameter model parameter identification method, which combines an improved particle swarm algorithm with an analytic method, improves the solving precision and reduces the algorithm complexity.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention provides a photovoltaic array double-diode seven-parameter model parameter identification method, wherein seven parameters of a double-diode seven-parameter model comprise: two diode ideality factors, a series equivalent resistor, a photo-generated current, a parallel equivalent resistor and two diode reverse saturation currents;
the method comprises the following steps:
1) establishing a photovoltaic array double-diode seven-parameter model;
2) extracting two diode ideality factors and series equivalent resistance in the photovoltaic array double-diode seven-parameter model by adopting an improved particle swarm algorithm;
3) and solving the photo-generated current, the parallel equivalent resistance and the reverse saturation current of the two diodes in the photovoltaic array double-diode seven-parameter model by using an analytical method based on the extracted two diode ideal factors and the series equivalent resistance.
Further, the method for establishing the photovoltaic array double-diode seven-parameter model comprises the following steps:
1-1) the current output equation of the photovoltaic array double-diode seven-parameter model is as follows:
Figure BDA0003539941370000021
wherein I is the output current of the photovoltaic array, V is the output voltage of the photovoltaic array, I ph Is a photo-generated current, I o1 And I o2 Is a reverse saturation current of two diodes, a 1 And a 2 Is the ideal factor of a diode, N s For the number of cells connected in series, R s And R p A series equivalent resistance and a parallel equivalent resistance, respectively, and q is an electron charge amount (1.6 e) -19 C) K is Boltzmann constant (1.38 e) -23 J/K), T is the absolute temperature of the photovoltaic array;
1-2) integrating a in seven parameters of a photovoltaic array double-diode seven-parameter model 1 、a 2 And R s As the parameters to be optimized of the algorithm, the other four parameters I ph 、R p 、I o1 And I o2 Can be represented as a 1 、a 2 And R s A function of (a);
for the simplicity of formula expression when the subsequent current output equation is substituted into three states of short-circuit current, open-circuit voltage and maximum power point, the order is as follows:
Figure BDA0003539941370000031
Figure BDA0003539941370000032
Figure BDA0003539941370000033
in the formula I sc For short-circuit current, V oc Is an open circuit voltage, V m Is the maximum power point voltage, I m Maximum power point current;
under the short-circuit state, the short-circuit current point (0, I) sc ) Substituting the formula (1) to obtain:
Figure BDA0003539941370000034
under the open circuit state, the open circuit voltage point (V) oc 0) substitution of formula (1) to give:
Figure BDA0003539941370000035
under the state of maximum power point, the maximum power point (V) is set m ，I m ) Substituting the formula (1) to obtain:
Figure BDA0003539941370000036
at maximum power point, the derivative of the voltage derivative is 0, i.e.:
Figure BDA0003539941370000037
the derivation is carried out on the formula (1) and is substituted by the formula (8) to obtain:
Figure BDA0003539941370000041
the equations can be obtained from the simultaneous equations of formula (5), formula (6), formula (7) and formula (9):
Figure BDA0003539941370000042
Figure BDA0003539941370000043
Figure BDA0003539941370000044
Figure BDA0003539941370000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003539941370000046
Figure BDA0003539941370000047
Figure BDA0003539941370000048
D＝l m V oc -V m I sc (14)
in the formula, A i ,B i C, D are variables of alternative formulae, I ph Is photo-generated current，Io 1 And Io 2 Is reverse saturation current of two diodes, R p Is a parallel equivalent resistor;
1-3) short-circuit current I under different illumination and temperature sc Maximum power point current I m Open circuit voltage V oc Maximum power point voltage V m The parameter update formula of (1) is:
Figure BDA0003539941370000049
Figure BDA00035399413700000410
Figure BDA00035399413700000411
Figure BDA00035399413700000412
in the formula I scref 、I mref 、V ocref 、V mref 、S ref And T ref Respectively short-circuit current, maximum power point current, open-circuit voltage, maximum power point voltage, illumination intensity and absolute temperature of the photovoltaic array under the standard working condition, K i Is the temperature coefficient of current, K, of the photovoltaic array v The voltage temperature coefficient of the photovoltaic array is shown, alpha is the voltage illumination correction coefficient of the photovoltaic array, and S is the actual illumination intensity of the photovoltaic array;
furthermore, the parameters of the photovoltaic array double-diode seven-parameter model have certain constraint conditions, which can be described as follows:
g j (x)≤0，j＝1，2，...，J (19)
wherein x is ═ a 1 ,a 2 ,R s ]And J is the number of inequality constraints.
Further, a dual-fitness value comparison method is adopted when the ideal factors of the two diodes and the series equivalent resistance are extracted, and the objective function is separated from the constraint condition; adopting standardization processing for each constraint condition; the two fitness functions are respectively:
Figure BDA0003539941370000051
Figure BDA0003539941370000052
in the formula, x i Representing the ith particle, the fit function corresponding to the objective function value, the Root Mean Square Error (RMSE) of the calculated current value and the actual measured current value for the model, the vio function corresponding to the constraint, the degree of constraint violation for the particle, n the number of sets of measured data, I cl Calculating output current value for model corresponding to the l-th group of measured voltages, I el For the l-th set of actual measured current values,
Figure BDA0003539941370000053
Figure BDA0003539941370000054
and N is the number of population particles.
Further, an improved particle swarm algorithm is adopted to extract two diode ideality factors and series equivalent resistance in seven parameters of a photovoltaic array double-diode seven-parameter model, and the method comprises the following steps:
2-1) setting values of algorithm parameters, operation condition parameters, photovoltaic array parameters and seven parameters in a double-diode seven-parameter model;
randomly initializing the positions and the speeds of N particles in a value range; updating the short-circuit current I under different working conditions according to the formulas (15) to (18) sc Maximum power point current I m Open circuit voltage V oc And maximum power point voltage V m ；
Solving the remaining four parameter values of the photovoltaic array two-diode seven-parameter model according to the equations (10) to (13): photo-generated current I ph Parallel connection equivalentResistance R p Two diodes reverse saturation current I o1 And I o2 (ii) a Discarding an infeasible solution from the initial population particles to ensure that seven parameters of the photovoltaic array double-diode seven-parameter model are all in a feasible solution range;
2-2) solving a model output current approximate solution corresponding to the measured voltage by using a Newton iteration method, calculating a particle objective function value, solving an individual optimal position pbest and a global optimal position gbest, and setting the particle violation degree to be 0;
2-3) updating the position and the speed of the particle according to an adaptive evolution learning mode:
Figure BDA0003539941370000061
Figure BDA0003539941370000062
Figure BDA0003539941370000063
Figure BDA0003539941370000064
where ω is the inertia factor, ω max 、ω min Respectively representing the maximum and minimum values, fit min And fit avg Respectively representing minimum and average objective function values, h function corresponding to the adaptive evolutionary learning factor of the particle, t being the current iteration number, c 1 And c 2 Are an individual learning factor and a social learning factor, r 1 And r 2 Is [0,1 ]]Random number of inner, v i ,x i ,pbest i Respectively representing the speed, the position and the individual optimal position of the ith particle, wherein the gbest is the global optimal position;
after the positions and the speeds of the particles are updated, carrying out-of-limit processing on unreasonable particles, and taking the position and speed values as the maximum values if the position and speed values exceed the maximum values and taking the position and speed values as the minimum values if the position and speed values exceed the minimum values;
2-4) solving the remaining four parameter values of the photovoltaic array double-diode seven-parameter model according to the formula (10) to the formula (13): photo-generated current I ph Parallel equivalent resistance R p Two diodes reverse saturation current I o1 And I o2 (ii) a Calculating a particle dual fitness function value according to the formula (20) and the formula (21);
2-5) the formula for calculating the t-th generation particle concentration degree delta is as follows:
Figure BDA0003539941370000071
in the formula (I), the compound is shown in the specification,
Figure BDA0003539941370000072
respectively an average value, a maximum value and a minimum value of the t-th generation particle objective function value,
Figure BDA0003539941370000073
is t generation particle x i The objective function value of (1);
the probability of variation for each generation of particles is dynamically adjusted based on the degree of aggregation δ:
Figure BDA0003539941370000074
in the formula, beta is a constant and is used for adjusting the variation speed of the variation probability, and the value range is [2,4 ];
[0,1]random number r generated within the range is less than the variation probability
Figure BDA0003539941370000075
In the process, the optimal position of each particle individual is varied by adopting Cauchy distribution, and after the variation operation, the double fitness function value of the individual optimal particle is recalculated:
pbest＝pbest(1+0.5tan(π(rand-0.5))) (28)
2-6) updating pbest according to the particle comparison principle, comprising:
a) when two particles x i And x j When all the functions are feasible, the particles with small fit function values are excellent;
b) when two particles x i And x j When the function values are not feasible, the particles with small vio function values are excellent;
c) when the particle x i Feasible and x j If not feasible, if particle x j If the value of vio is less than a predetermined smaller positive number epsilon, then the particle with the smaller fit function value is superior, otherwise particle x is superior i The quality is excellent;
updating the gbest according to the particle comparison principle comprises the following steps:
a) when two particles x i And x j When all the functions are feasible, the particles with small fit function values are excellent;
b) when the particle x i Feasible and x j When not feasible, particle x i The product is superior.
2-7) repeating the steps 2-3-2-6 until the following relation is continuously established for M times or the algorithm is operated to the maximum iteration time, and outputting two ideal factors a of the diodes 1 、a 2 And a series equivalent resistance R s The optimal solution of (2);
fit(gbest t-1 )-fit(gbest t )＜e min (29)
in the formula, e min For accuracy, fit (gbest) t ) The objective function value of the t-th generation global optimum particle gbest is obtained.
Further, based on the extracted two diode ideality factors and the series equivalent resistance, the method for solving the photo-generated current, the parallel equivalent resistance and the two diode reverse saturation currents in the photovoltaic array double-diode seven-parameter model by using the analytic method comprises the following steps of:
solving the remaining four parameter values I of the photovoltaic array double-diode model according to the following formula ph 、R p 、I o1 And I o2 ；
Figure BDA0003539941370000081
Figure BDA0003539941370000082
Figure BDA0003539941370000083
Figure BDA0003539941370000084
In the formula (I), the compound is shown in the specification,
Figure BDA0003539941370000085
Figure BDA0003539941370000086
Figure BDA0003539941370000087
D＝I m V oc -V m I sc (14)
in the formula, A i ,B i C, D are variables of alternative formulae, I ph Is a photo-generated current, I o1 And I o2 Is reverse saturation current of two diodes, R p Is a parallel equivalent resistor.
Compared with the prior art, the invention has the following beneficial effects:
the method combines the improved particle swarm algorithm with the analytic method, solves the problems that the double-diode seven-parameter model parameter of the photovoltaic array is difficult to solve and the single-diode model parameter is low in solving precision, and provides a new way for identifying the parameters of the photovoltaic array.
After the self-adaptive evolution learning is introduced, the search capability of the constraint boundary can be improved, and the convergence speed can be accelerated.
After the self-adaptive Gaussian mutation operator is introduced, the diversity of the population can be improved, and the phenomenon of premature can be prevented.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is an equivalent circuit of a photovoltaic array dual-diode seven-parameter model;
FIG. 3 shows measured data and simulated I-V output characteristic curves of a photovoltaic array under different illumination and temperature conditions.
Detailed Description
The method for identifying parameters of a photovoltaic array dual-diode seven-parameter model provided by the invention is described in detail below with reference to the accompanying drawings.
The present embodiment provides a method for identifying parameters of a photovoltaic array dual-diode seven-parameter model, as shown in fig. 1, including the following steps:
1) establishing a photovoltaic array double-diode seven-parameter model;
2) extracting two diode ideal factors and series equivalent resistance in seven parameters of a photovoltaic array double-diode seven-parameter model by adopting an improved particle swarm algorithm;
3) and solving the photo-generated current, the parallel equivalent resistance and the reverse saturation current of the two diodes in the seven parameters of the photovoltaic array double-diode seven-parameter model by using an analytical method based on the extracted two diode ideal factors and the series equivalent resistance.
In the step 1), a photovoltaic array double-diode seven-parameter model is established, and the method comprises the following steps:
1-1) FIG. 2 is an equivalent circuit of a photovoltaic array double-diode seven-parameter model, which can be obtained according to the Hall-Koff current law:
Figure BDA0003539941370000101
wherein I is the output current of the photovoltaic array, V is the output voltage of the photovoltaic array, I ph Is a photo-generated current, I o1 And I o2 Is a reverse saturation current of two diodes, a 1 And a 2 Is ideal for diodeN of s For the number of cells connected in series, R s And R p A series equivalent resistance and a parallel equivalent resistance, respectively, and q is an electron charge amount (1.6 e) -19 C) K is Boltzmann constant (1.38 e) -23 J/K), T is the absolute temperature of the photovoltaic array;
1-2) integrating a in seven parameters of a photovoltaic array double-diode seven-parameter model 1 、a 2 And R s As the parameters to be optimized of the algorithm, the other four parameters I ph 、R p 、I o1 And I o2 Can be represented as a 1 、a 2 And R s A function of (a);
for the simplicity of formula expression when the subsequent current output equation is substituted into three states of short-circuit current, open-circuit voltage and maximum power point, the order is as follows:
Figure BDA0003539941370000102
Figure BDA0003539941370000103
Figure BDA0003539941370000104
in the formula I sc For short-circuit current, V oc Is an open circuit voltage, V m Is the maximum power point voltage, I m Maximum power point current;
under the short-circuit state, the short-circuit current point (0, I) sc ) Substituting the formula (1) to obtain:
Figure BDA0003539941370000111
under the open circuit state, the open circuit voltage point (V) oc 0) substitution of formula (1) to give:
Figure BDA0003539941370000112
under the state of maximum power point, the maximum power point (V) is set m ，I m ) Substituting the formula (1) to obtain:
Figure BDA0003539941370000113
at maximum power point, the derivative of the voltage derivative is 0, i.e.:
Figure BDA0003539941370000114
the derivation is carried out on the formula (1) and is substituted by the formula (8) to obtain:
Figure BDA0003539941370000115
the equations can be obtained from the simultaneous equations of formula (5), formula (6), formula (7) and formula (9):
Figure BDA0003539941370000116
Figure BDA0003539941370000117
Figure BDA0003539941370000118
Figure BDA0003539941370000119
in the formula (I), the compound is shown in the specification,
Figure BDA00035399413700001110
Figure BDA00035399413700001111
Figure BDA00035399413700001112
D＝l m V oc -V m I sc (14)
in the formula, A i ,B i C, D are variables of alternative formulae, I ph Is a photo-generated current, I o1 And I o2 Is reverse saturation current of two diodes, R p Is a parallel equivalent resistor;
1-3) short-circuit current I under different illumination and temperature sc Maximum power point current I m Open circuit voltage V oc Maximum power point voltage V m The parameter update formula of (1) is:
Figure BDA0003539941370000121
Figure BDA0003539941370000122
Figure BDA0003539941370000123
Figure BDA0003539941370000124
in the formula I scref 、I mref 、V ocref 、V mref 、S ref And T ref Respectively short-circuit current, maximum power point current, open-circuit voltage, maximum power point voltage, illumination intensity and absolute temperature of the photovoltaic array under the standard working condition, K i Electricity being a photovoltaic arrayCoefficient of flow temperature, K v The voltage temperature coefficient of the photovoltaic array is shown, alpha is the voltage illumination correction coefficient of the photovoltaic array, and S is the actual illumination intensity of the photovoltaic array;
1-4) two diode ideality factors a in photovoltaic array double-diode seven-parameter model parameters 1 、a 2 And a series equivalent resistance R s The method is always in a feasible solution range, namely the model only needs to process constraint conditions on the other four parameters, and the constraint conditions of the model can be described as follows:
g j (x)≤0，j＝1，2，...，J (19)
wherein x is ═ a 1 ,a 2 ,R s ]J is the number of inequality constraints;
1-5) separating a target function from a constraint condition by adopting a double-fitness value comparison method when extracting two ideal factors of the diode and a series equivalent resistor; in addition, in order to weaken the difference of each constraint condition, standardization processing is adopted for each constraint condition; the two fitness functions are respectively:
Figure BDA0003539941370000125
Figure BDA0003539941370000131
in the formula, x i Representing the ith particle, the fit function corresponding to the objective function value, the Root Mean Square Error (RMSE) of the calculated current value and the actual measured current value for the model, the vio function corresponding to the constraint, the degree of constraint violation for the particle, n the number of sets of measured data, I cl Calculating an output current value for a model corresponding to the l-th set of measured voltages, I el For the l-th set of actual measured current values,
Figure BDA0003539941370000132
Figure BDA0003539941370000133
and N is the number of population particles.
In the step 2), two diode ideality factors and series equivalent resistance in seven parameters of a photovoltaic array double-diode seven-parameter model are extracted by adopting an improved particle swarm algorithm, and the method comprises the following steps:
2-1) setting algorithm parameters and learning factor c 1 And c 2 2, population size 20, maximum number of iterations 1000, maximum and minimum inertia factors 0.9 and 0.4, respectively, parameter a 1 、a 2 And R s Are 0.1, 0.2 and 0.1 respectively, and the algorithm precision e min 1e-5, times M is 50; setting operating condition parameters and photovoltaic array parameters; setting a 1 And a 2 The value range is [1,2 ]]And [1, 4]]，I ph The value range is [0.95I ] sc ,1.05I sc ]，I o1 The value range is [0, I o2 ]，I o2 The value range is [0,0.1I sc ]，R s And R p The value range is [0.01,3 ]]And [50,5000]；
Randomly initializing the positions and the speeds of N particles in a value range; updating the short-circuit current I under different working conditions according to the formulas (15) to (18) sc Maximum power point current I m Open circuit voltage V oc And maximum power point voltage V m ；
Solving the remaining four parameter values of the photovoltaic array two-diode seven-parameter model according to the equations (10) to (13): photo-generated current I ph Parallel equivalent resistance R p Two diodes reverse saturation current I o1 And I o2 (ii) a Discarding an infeasible solution of the initial population particles, namely ensuring that seven parameters of the photovoltaic array double-diode seven-parameter model are in a feasible solution range;
2-2) solving a model output current approximate solution corresponding to the measured voltage by using a Newton iteration method, calculating a particle objective function value, solving an individual optimal position pbest and a global optimal position gbest, and setting the particle violation degree to be 0;
2-3) updating the position and the speed of the particle according to an adaptive evolution learning mode:
Figure BDA0003539941370000141
Figure BDA0003539941370000142
Figure BDA0003539941370000143
Figure BDA0003539941370000144
where ω is the inertia factor, ω max 、ω min Respectively representing the maximum and minimum values, fit min And fit avg Respectively representing minimum and average objective function values, h function corresponding to the adaptive evolutionary learning factor of the particle, t being the current iteration number, c 1 And c 2 Are an individual learning factor and a social learning factor, r 1 And r 2 Is [0,1 ]]Random number of inner, v i ,x i ,pbest i Respectively representing the speed, the position and the individual optimal position of the ith particle, wherein the gbest is the global optimal position; after the self-adaptive evolution learning is introduced, the search capability of the constraint boundary can be improved, and the convergence speed can be accelerated;
after the positions and the speeds of the particles are updated, carrying out-of-limit processing on unreasonable particles, and taking the position and speed values as the maximum values if the position and speed values exceed the maximum values and taking the position and speed values as the minimum values if the position and speed values exceed the minimum values;
2-4) solving the remaining four parameter values of the photovoltaic array double-diode seven-parameter model according to the formula (10) to the formula (13): photo-generated current I ph Parallel equivalent resistance R p Two diodes reverse saturation current I o1 And I o2 (ii) a Calculating a particle dual fitness function value according to the formula (20) and the formula (21);
2-5) the formula for calculating the t-th generation particle concentration delta is as follows:
Figure BDA0003539941370000151
in the formula (I), the compound is shown in the specification,
Figure BDA0003539941370000152
respectively an average value, a maximum value and a minimum value of the t-th generation particle objective function value,
Figure BDA0003539941370000153
is t generation particle x i The objective function value of (1);
the probability of variation for each generation of particles is dynamically adjusted based on the degree of aggregation δ:
Figure BDA0003539941370000154
in the formula, beta is a constant and is used for adjusting the variation speed of the variation probability, and the value range is [2,4 ];
[0,1]random number r generated within the range is less than the variation probability
Figure BDA0003539941370000155
In the process, the optimal position of each particle individual is varied by adopting Cauchy distribution, and after the variation operation, the double fitness function value of the individual optimal particle is recalculated:
pbest＝pbest(1+0.5tan(π(rand-0.5))) (28)
2-6) updating pbest according to the particle comparison principle, specifically comprising:
a) when two particles x i And x j When both are feasible, the particles with small fit function values are excellent;
b) when two particles x i And x j When the function values are not feasible, the particles with small vio function values are excellent;
c) when the particle x i Feasible and x j If not feasible, if particle x j If the value of vio is less than a predetermined smaller positive number epsilon, then the particle with the smaller fit function value is superior, otherwise particle x is superior i The quality is excellent;
updating the gbest according to the particle comparison principle, specifically as follows:
a) when two particles x i And x j When all the functions are feasible, the particles with small fit function values are excellent;
b) when the particle x i Feasible and x j When not feasible, particle x i The quality is excellent;
2-7) repeating the steps 2-3-2-6 until the following relation is continuously established for M times or the algorithm is operated to the maximum iteration number, and outputting a 1 、a 2 And R s The optimal solution of (2);
fit(gbest t-1 )-fit(gbest t )＜e min (29)
in the formula, e min For accuracy, fit (gbest) t ) The objective function value of the t-th generation global optimum particle gbest is obtained.
In step 3), based on the extracted two ideal factors a of the diode 1 、a 2 And a series equivalent resistance R s Solving the rest four parameter values of the photovoltaic array double-diode seven-parameter model according to the equations (10) to (13): photo-generated current I ph Parallel equivalent resistance R p Two diodes reverse saturation current I o1 And I o2 . So far, the seven parameters in the double-diode seven-parameter model are extracted through the steps.
This example estimates the I-V output characteristics of a photovoltaic array (CSUN 340-72M). The characteristic parameters of the photovoltaic array under the standard working condition are shown in table 1:
TABLE 1 characteristic parameters of CSUN340-72M photovoltaic arrays
Parameter(s) Parameter value Parameter(s) Parameter value
I sc (A) 9.62 K i (％/℃) 0.039
U oc (V) 47.6 K v (％/℃) -0.307
I m (A) 8.89 N s 72
U m (V) 37.9 α 0.005
TABLE 2 root mean square error between measured current and simulated current of photovoltaic array
Number of groups Irradiance (W/m) 2 ) Back plate temperature (. degree. C.) RMSE(A)
1 872 38.5 0.0741
2 677 30.5 0.1234
3 758 34.8 0.0976
4 826 40.3 0.0872
5 492 27.5 0.1108
FIG. 3 shows measured data and simulated I-V output characteristic curves of a photovoltaic array under different illumination and temperature conditions. Table 2 corresponds to the root mean square error of the measured current and the simulated current at different illumination and temperatures in fig. 3.
As can be seen from Table 2, the RMSE of the measured current and the simulated current of the photovoltaic array does not exceed 0.13A, and the invention better simulates the I-V output characteristics of the CSUN340-72M photovoltaic array.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, it is possible to make various improvements and modifications without departing from the technical principle of the present invention, and those improvements and modifications should be considered as the protection scope of the present invention.

Claims (6)

1. A parameter identification method for a photovoltaic array double-diode seven-parameter model is characterized in that seven parameters of the double-diode seven-parameter model comprise: two diode ideality factors, a series equivalent resistor, a photo-generated current, a parallel equivalent resistor and two diode reverse saturation currents;
the method comprises the following steps:
establishing a photovoltaic array double-diode seven-parameter model;
extracting two diode ideality factors and series equivalent resistance in the photovoltaic array double-diode seven-parameter model by adopting an improved particle swarm algorithm;
and solving the photo-generated current, the parallel equivalent resistance and the reverse saturation current of the two diodes in the photovoltaic array double-diode seven-parameter model by using an analytical method based on the extracted two diode ideal factors and the series equivalent resistance.
2. The method for identifying parameters of a seven-parameter model according to claim 1, wherein the method for establishing the photovoltaic array two-diode seven-parameter model comprises the following steps: two diode ideality factors and series equivalent resistance in seven parameters of the photovoltaic array double-diode seven-parameter model are used as parameters to be optimized in the algorithm, and the rest four parameters are as follows: the method comprises the following steps of generating a photo current, connecting an equivalent resistor in parallel and connecting two diodes with reverse saturation current as a function of parameters to be optimized:
1-1) the current output equation of the photovoltaic array double-diode seven-parameter model is as follows:
Figure FDA0003539941360000011
wherein I is the output current of the photovoltaic array, V is the output voltage of the photovoltaic array, I ph Is a photo-generated current, I o1 And I o2 Is a reverse saturation current of two diodes, a 1 And a 2 Is the ideal factor of a diode, N s For the number of cells connected in series, R s And R p The resistance values are respectively a series equivalent resistance and a parallel equivalent resistance, q is the electronic charge quantity, k is a Boltzmann constant, and T is the absolute temperature of the photovoltaic array;
1-2) order:
Figure FDA0003539941360000021
Figure FDA0003539941360000022
Figure FDA0003539941360000023
in the formula I sc For short-circuit current, V oc Is an open circuit voltage, V m Is the maximum power point voltage, I m Maximum power point current;
under the short-circuit state, the short-circuit current point (0, I) sc ) Substituting the formula (1) to obtain:
Figure FDA0003539941360000024
under the open circuit state, the open circuit voltage point (V) oc 0) substitution of formula (1) to give:
Figure FDA0003539941360000025
under the state of maximum power point, the maximum power point (V) is set m ，I m ) Substituting the formula (1) to obtain:
Figure FDA0003539941360000026
at maximum power point, the derivative of the voltage derivative is 0, i.e.:
Figure FDA0003539941360000027
the derivation is carried out on the formula (1) and is substituted by the formula (8) to obtain:
Figure FDA0003539941360000028
the equations can be obtained from the simultaneous equations of formula (5), formula (6), formula (7) and formula (9):
Figure FDA0003539941360000029
Figure FDA00035399413600000210
Figure FDA0003539941360000031
Figure FDA0003539941360000032
in the formula (I), the compound is shown in the specification,
Figure FDA0003539941360000033
Figure FDA0003539941360000034
Figure FDA0003539941360000035
D＝I m V oc -V m I sc (14)
in the formula, A i ,B i C, D are variables of alternative formulae, I ph Is a photo-generated current, I o1 And I o2 Is reverse saturation current of two diodes, R p Is a parallel equivalent resistor;
1-3) short-circuit current I under different illumination and temperature sc Maximum power point current I m Open circuit voltage V oc Maximum power point voltage V m The parameter update formula of (1) is:
Figure FDA0003539941360000036
Figure FDA0003539941360000037
Figure FDA0003539941360000038
Figure FDA0003539941360000039
in the formula I scref 、I mref 、V ocref 、V mref 、S ref And T ref Respectively short-circuit current, maximum power point current, open-circuit voltage, maximum power point voltage, illumination intensity and absolute temperature of the photovoltaic array under the standard working condition, K i Is the current temperature coefficient, K, of the photovoltaic array v Is the voltage temperature coefficient of the photovoltaic array, alpha isAnd (4) voltage illumination correction coefficient of the photovoltaic array, wherein S is actual illumination intensity of the photovoltaic array.
3. The seven-parameter model parameter identification method according to claim 2, wherein the photovoltaic array two-diode seven-parameter model parameters all have certain constraint conditions and are described as follows:
g j (x)≤0，j＝1，2，...，J (19)
wherein x is ═ a 1 ,a 2 ,R s ]J is the number of inequality constraints, a 1 And a 2 Is the ideal factor of a diode, R s Is a series equivalent resistance.
4. The method for identifying parameters of a seven-parameter model according to claim 2, wherein the method for establishing the photovoltaic array two-diode seven-parameter model further comprises: separating a target function and a constraint condition when two diode ideal factors and a series equivalent resistor are extracted by adopting a double-fitness value comparison method; adopting standardization processing for each constraint condition; the two fitness functions are respectively:
Figure FDA0003539941360000041
Figure FDA0003539941360000042
in the formula, x i Representing the ith particle, the fit function corresponding to the objective function value, the root mean square error of the calculated current value and the actual measured current value for the model, the vio function corresponding to the constraint condition, the degree of constraint violation for the particle, n the number of sets of measured data, I cl Calculating output current value for model corresponding to the l-th group of measured voltages, I el For the l-th set of actual measured current values,
Figure FDA0003539941360000043
Figure FDA0003539941360000044
and N is the number of population particles.
5. The seven-parameter model parameter identification method according to claim 4, wherein two diode ideality factors and series equivalent resistance in the seven parameters of the photovoltaic array two-diode seven-parameter model are extracted by adopting an improved particle swarm optimization, and the method comprises the following steps:
2-1) setting value ranges of algorithm parameters, operation condition parameters, photovoltaic array parameters and seven parameters in a double-diode seven-parameter model;
randomly initializing the positions and the speeds of N particles in a value range; updating the short-circuit current I under different working conditions according to the formulas (15) to (18) sc Maximum power point current I m Open circuit voltage V oc And maximum power point voltage V m ；
Solving the remaining four parameter values of the photovoltaic array two-diode seven-parameter model according to the equations (10) to (13): photo-generated current I ph Parallel equivalent resistance R p Two diodes reverse saturation current I o1 And I o2 (ii) a Discarding infeasible solutions by the initial population particles to ensure that seven parameters of the photovoltaic array double-diode seven-parameter model are in a feasible solution range;
2-2) solving a model output current approximate solution corresponding to the measured voltage by using a Newton iteration method, calculating a particle objective function value, solving an individual optimal position pbest and a global optimal position gbest, and setting the particle violation degree to be 0;
2-3) updating the position and the speed of the particle according to an adaptive evolution learning mode:
Figure FDA0003539941360000051
Figure FDA0003539941360000052
Figure FDA0003539941360000053
Figure FDA0003539941360000054
where ω is the inertia factor, ω max 、ω min Respectively representing the maximum and minimum values, fit min And fit avg Respectively representing minimum and average objective function values, h function corresponding to the adaptive evolutionary learning factor of the particle, t being the current iteration number, c 1 And c 2 Are an individual learning factor and a social learning factor, r 1 And r 2 Is [0,1 ]]Random number of inner, v i ,x i ,pbest i Respectively representing the speed, the position and the individual optimal position of the ith particle, wherein the gbest is the global optimal position;
after the positions and the speeds of the particles are updated, carrying out-of-limit processing on unreasonable particles, and taking the position and speed values as the maximum values if the position and speed values exceed the maximum values and taking the position and speed values as the minimum values if the position and speed values exceed the minimum values;
2-4) solving the remaining four parameter values of the photovoltaic array double-diode seven-parameter model according to the formula (10) to the formula (13): photo-generated current I ph Parallel equivalent resistance R p Two diodes reverse saturation current I o1 And I o2 (ii) a Calculating a particle dual fitness function value according to the formula (20) and the formula (21);
2-5) the formula for calculating the t-th generation particle concentration degree delta is as follows:
Figure FDA0003539941360000061
in the formula (I), the compound is shown in the specification,
Figure FDA0003539941360000062
are respectively the t generationThe average, maximum and minimum values of the particle objective function values,
Figure FDA0003539941360000063
is t generation particle x i The objective function value of (1);
the probability of variation for each generation of particles is dynamically adjusted based on the degree of aggregation δ:
Figure FDA0003539941360000064
in the formula, beta is a constant and is used for adjusting the variation speed of the variation probability, and the value range is [2,4 ];
[0,1]random number r generated within the range is less than the variation probability
Figure FDA0003539941360000065
In the process, the optimal position of each particle individual is varied by adopting Cauchy distribution, and after the variation operation, the double fitness function value of the individual optimal particle is recalculated:
pbest＝pbest(1t0.5tan(π(rand-0.5))) (28)
2-6) updating pbest according to the particle comparison principle, wherein the updating comprises the following steps:
a) when two particles x i And x j When all the functions are feasible, the particles with small fit function values are excellent;
b) when two particles x i And x j When the function values are not feasible, the particles with small vio function values are excellent;
c) when the particle x i Feasible and x j If not feasible, if particle x j If the value of vio is less than a predetermined smaller positive number epsilon, then the particle with the smaller fit function value is superior, otherwise particle x is superior i The quality is excellent;
updating the gbest according to the particle comparison principle comprises the following steps:
a) when two particles x i And x j When all the functions are feasible, the particles with small fit function values are excellent;
b) when the particle x i Feasible and x j When not feasible, particle x i Is superior.
2-7) repeating the steps 2-3-2-6 until the following relation is continuously established for M times or the algorithm is operated to the maximum iteration time, and outputting two ideal factors a of the diodes 1 、a 2 And a series equivalent resistance R s The optimal solution of (2);
fit(gbest t-1 )-fit(gbest t )＜e min (29)
in the formula, e min For accuracy, fit (gbest) t ) The objective function value of the t-th generation global optimum particle gbest is obtained.
6. The seven-parameter model parameter identification method according to claim 1, wherein the method for solving the photo-generated current, the parallel equivalent resistance and the two diode reverse saturation currents in the photovoltaic array two-diode seven-parameter model by using an analytic method based on the extracted two diode ideality factors and the series equivalent resistance comprises the following steps:
solving the remaining four parameter values I of the photovoltaic array double-diode model according to the following formula ph 、R p 、I o1 And I o2 ；
Figure FDA0003539941360000071
Figure FDA0003539941360000072
Figure FDA0003539941360000073
Figure FDA0003539941360000074
In the formula (I), the compound is shown in the specification,
Figure FDA0003539941360000075
Figure FDA0003539941360000076
Figure FDA0003539941360000077
D＝I m V oc -V m I sc (14)
in the formula, A i ,B i C, D are variables of alternative formulae, I ph Is a photo-generated current, I o1 And I o2 Is reverse saturation current of two diodes, R p Is a parallel equivalent resistor.
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CN115828818A (en) * 2023-02-02 2023-03-21 湖北工业大学 Photovoltaic cell parameter identification method and storage medium
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CN115828818A (en) * 2023-02-02 2023-03-21 湖北工业大学 Photovoltaic cell parameter identification method and storage medium
CN115828818B (en) * 2023-02-02 2023-05-16 湖北工业大学 Photovoltaic cell parameter identification method and storage medium
CN116466571A (en) * 2023-06-12 2023-07-21 中国科学技术大学先进技术研究院 PID parameter self-tuning control chip and system
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