T-S fuzzy rule reduction modeling method of photovoltaic power generation system

Abstract

The invention discloses a T-S fuzzy rule reduction modeling method for a photovoltaic power generation system, and belongs to the technical field of new energy photovoltaic power generation system modeling. The modeling method comprises the following steps: constructing a nonlinear dynamic model of the photovoltaic power generation system; establishing a system state equation based on the dynamic model, and dividing non-linear terms in the equation into direct non-linear terms and indirect non-linear terms; defining a antecedent variable, a membership function and a fuzzy rule, performing fuzzy linearization on direct and indirect non-linear terms by using a sector non-linear method, and giving a T-S fuzzy model; and carrying out defuzzification to obtain a T-S fuzzy photovoltaic power generation system model. According to the method, the fuzzy coupling relation between the nonlinear terms of the system is reconstructed by using the method for dividing the nonlinear terms, the fuzzy rule of the T-S fuzzy photovoltaic power generation system model is effectively reduced, and the calculation complexity of a model-based algorithm in actual engineering can be remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of new energy photovoltaic power generation system modeling, and in particular to a TS fuzzy rule reduction modeling method for a photovoltaic power generation system. Background Art

[0002] Amidst the growing global demand for clean energy, solar energy, a renewable energy source with large storage capacity, widespread coverage, and no pollution, is becoming increasingly important in the supply of new energy. Photovoltaic (PV) power generation systems convert solar energy into electricity through photovoltaic (PV) panels, which in turn supplies power to loads. The development of PV, a new clean energy generation method, has significantly reduced environmental pollution caused by the use of non-renewable energy sources such as fossil fuels, and has also transformed the global energy structure. Therefore, the practical significance of PV power generation is significant.

[0003] In actual engineering, the working environment of photovoltaic power generation systems is complex and changeable. When the surrounding environment interferes, such as when the light intensity and temperature change significantly, the IV and PV characteristic curves of the photovoltaic panel will change significantly, making the photovoltaic power generation system dynamic exhibit strong nonlinear and coupled characteristics, and the maximum power output of the photovoltaic power generation system is also extremely unstable. The Takagi-Sugeno (TS) model, due to its powerful and high-precision approximation capabilities, can convert complex nonlinear systems into a series of linear subsystems connected by related membership functions. In recent years, the method of modeling DC / DC Buck circuits in photovoltaic power generation systems based on the TS fuzzy model has attracted attention, and the TS fuzzy photovoltaic power generation system has also been widely used.

[0004] While the introduction of the TS fuzzy modeling method can more accurately capture the dynamic characteristics of a photovoltaic system's DC / DC buck circuit under varying conditions, such as illumination and temperature, making system modeling more precise, the resulting TS fuzzy model, simply for the sake of improving modeling accuracy, has a large number of antecedent variables, and the number of fuzzy rules increases exponentially. This leads to excessive computational complexity, as each rule requires membership calculation, inference, and defuzzification. This excessive number of rules can lead to algorithmic delays, impacting the system's dynamic response speed. Several methods have been proposed to reduce fuzzy rules, but these methods are relatively complex. Summary of the Invention

[0005] The present invention provides a TS fuzzy rule reduction modeling method for a photovoltaic power generation system, aiming to solve the problems of a large number of fuzzy rules and high algorithm calculation complexity in the current photovoltaic power generation system modeling based on the TS fuzzy model.

[0006] In order to solve the above problems, the technical solution of the present invention is:

[0007] A TS fuzzy rule reduction modeling method for a photovoltaic power generation system comprises the following steps:

[0008] Construct a nonlinear dynamic model of photovoltaic power generation system;

[0009] Establish the system state equation based on the dynamic model and divide the nonlinear terms in the equation into direct nonlinear terms and indirect nonlinear terms;

[0010] Define antecedent variables, membership functions and fuzzy rules, use sector nonlinear method to fuzzy linearize direct and indirect nonlinear terms, and give TS fuzzy model;

[0011] The TS fuzzy photovoltaic power generation system model is obtained by defuzzification.

[0012] Furthermore, the photovoltaic power generation system consists of a photovoltaic array, a DC-DC Buck converter, and a load. The nonlinear dynamic model of the photovoltaic power generation system considered is as follows:

[0013]

[0014] Among them, v pv is the capacitance C a The PV array voltage on L and v b They are the current on the inductor L and the capacitance C in the DC-DC Buck converter circuit. b The voltage on the MOSFET, u is the duty cycle of the pulse duration modulation signal that controls the switching MOSFET, R b and R L They are respectively the capacitors C b and the internal resistance of the inductor L, V D is the forward voltage of the power diode, i o is the measurable load current, i pv is the output current of the photovoltaic array, which is calculated by the following expression:

[0015]

[0016] Among them, n p is the number of photovoltaic cells in parallel, n3 is the number of photovoltaic cells in series, I ph is the photocurrent, I rs is the reverse saturation current, the photocurrent and reverse saturation current depend on light and temperature, k pv is the photovoltaic cell temperature coefficient, I sc is the short-circuit current of the battery at reference temperature and light, K I (mA / K) is the short-circuit current temperature coefficient, T is the actual temperature of the photovoltaic array, T r is the reference temperature of the photovoltaic array, λ is the sunshine intensity, Irr is the reference temperature T r The reverse saturation current under the condition of electron charge q=1.6×10 -19 C,E gp =1.1eV is the band gap energy of the semiconductor that makes up the unit cell, the pn junction characteristic factor p is 1-5, and the Boltzmann constant K = 1.3805×10 -23 J / K;

[0017] Photovoltaic array power P pv and its corresponding photovoltaic array voltage v pv The partial derivative of

[0018]

[0019] When the system reaches the maximum power point, there is Therefore the controlled output is:

[0020]

[0021] Furthermore, the system state equation established based on the dynamic model is as follows:

[0022]

[0023]

[0024] Among them, I b =1-i o / i L ,G a =i pv / v pv ,d D =-V p / L,x=[i L v pv b ] T .

[0025] The nonlinear term in the system state equation is I b ,i L , v pv , G a , According to the coupling relationship between nonlinear terms, I b ,i L , v pv For the direct nonlinear term, select G a and is an indirect nonlinear term. The nonlinear sector range of the indirect nonlinear term can be determined by the nonlinear sector range of the direct nonlinear term. pv From the equation, we can see that when v pv When the maximum value ispv Minimum, v pv When the minimum pv Maximum, then through v pv The nonlinear sector range can determine the indirect nonlinear term i pv The nonlinear sector range of the indirect nonlinear term G can be further determined. a and Nonlinear sector range.

[0026] Furthermore, the specific process of defining antecedent variables, membership functions and fuzzy rules is as follows:

[0027] 1) Select the direct nonlinear term as the antecedent variable and define its range of variation as i L ∈[M2, M1], v pv ∈[N2, N1], I b ∈[J2, J1]; define the antecedent variable as z1(t)=i L , z2(t)=v pv , z3(t)=I b , whose maximum value is z 1max =M1,z 2max =N1,z 3max =J1; the minimum value is z 1min =M2,z 2min =N2,z 3min =J2;

[0028] 2) The membership function designed according to the bounds of the antecedent variables is:

[0029] For z1(t)=i L , its membership function is S a1 (z1(t)) and S b1 (z1(t)) are defined as follows:

[0030]

[0031] For z2(t)=v pv , its membership function S a2 (z2(t)) and S b2 (z2(t)) are defined as follows:

[0032]

[0033] For z3(t)=I b , its membership function S a3 (z3(t)) and S b3 (z3(t)) are defined as follows:

[0034]

[0035] 3) Define the following fuzzy rules based on the antecedent variables:

[0036] Rule 1: z1(t) is the maximum, z2(t) is the maximum, z3(t) is the maximum;

[0037] Rule 2: z1(t) is the maximum value, z2(t) is the maximum value, and z3(t) is the minimum value;

[0038] Rule 3: z1(t) is the maximum value, z2(t) is the minimum value, and z3(t) is the maximum value;

[0039] Rule 4: z1(t) is the maximum value, z2(t) is the minimum value, and z3(t) is the minimum value;

[0040] Rule 5: z1(t) is the minimum, z2(t) is the maximum, and z3(t) is the maximum.

[0041] Rule 6: z1(t) is the minimum value, z2(t) is the maximum value, and z3(t) is the minimum value;

[0042] Rule 7: z1(t) is the minimum value, z2(t) is the minimum value, and z3(t) is the maximum value;

[0043] Rule 8: z1(t) is the minimum, z2(t) is the minimum, and z3(t) is the minimum.

[0044] Furthermore, after fuzzy linearizing the direct and indirect nonlinear terms using the sector nonlinear method, the TS fuzzy model of the photovoltaic power generation system based on fuzzy rule i is:

[0045] Rule i: If z1(t) is z2(t) is z3(t) is So

[0046]

[0047] y(t)=C i x(t)

[0048] Where i = 1, 2, ..., 8, and is the fuzzy set of rules corresponding to the antecedent variables,

[0049]

[0050]

[0051] Furthermore, the TS fuzzy photovoltaic power generation system model obtained by defuzzification is:

[0052]

[0053]

[0054] where z(t) = [z1(t) z2(t) z3(t)] T is the antecedent variable vector, h i (z(t)) represents the normalized membership function and satisfies

[0055]

[0056] Among them, F ji (z j (t)) represents the antecedent variable z j (t) In the fuzzy set F ji The membership weight of .

[0057] Compared with the prior art, the present invention has the following advantages:

[0058] The present invention fully considers the coupling relationship between nonlinear terms in the nonlinear dynamic model of photovoltaic power generation system, separates the nonlinear terms into direct nonlinear terms and indirect nonlinear terms, solves the limitation of directly selecting nonlinear terms while ignoring the influence of coupling relationship on system dynamics in the prior art, and increases the flexibility of TS fuzzy modeling.

[0059] The present invention rationally selects direct nonlinear terms as antecedent variables, and based on the coupling relationship between nonlinear terms, calculates the nonlinear sector range of indirect nonlinear terms. The number of fuzzy rules of the TS fuzzy photovoltaic power generation system model constructed based on this method is significantly reduced compared with the existing modeling technology, which effectively reduces the computational complexity of the algorithm and expands the practical value of the relevant algorithm in practical application engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 1 is a flow chart of a TS fuzzy rule reduction modeling method for a photovoltaic power generation system according to an embodiment of the present invention;

[0061] Figure 2 Schematic diagram of the Buck topology circuit structure of the photovoltaic power generation system considered in the embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process. However, the protection scope of the present invention is not limited to the following embodiment.

[0063] This embodiment provides a technical solution: Based on the photovoltaic power generation system, a TS fuzzy rule reduction modeling method is proposed, such as Figure 1 As shown, the specific steps include:

[0064] Step S1: constructing a nonlinear dynamic model of a photovoltaic power generation system;

[0065] Step S2: Establishing a system state equation based on the dynamic model, dividing the nonlinear terms in the equation into direct nonlinear terms and indirect nonlinear terms;

[0066] Step S3: define antecedent variables, membership functions and fuzzy rules, use sector nonlinear method to fuzzy linearize direct and indirect nonlinear terms, and give TS fuzzy model;

[0067] Step S4: Defuzzification to obtain the TS fuzzy photovoltaic power generation system model.

[0068] In step S1, the structure of the photovoltaic power generation system is as follows: Figure 2 As shown in Figure 1, the photovoltaic power generation system consists of a photovoltaic array, a DC-DC Buck converter, and a load. Its nonlinear dynamic model is as follows:

[0069]

[0070] Among them, v pv is the capacitance C a The PV array voltage on L and v b They are the current on the inductor L and the capacitance C in the DC-DC Buck converter circuit respectively b The voltage on the MOSFET, u is the duty cycle of the pulse duration modulation signal that controls the switching MOSFET, R b and R L They are respectively the capacitor C b and the internal resistance of the inductor L, V D is the forward voltage of the power diode, i o is the measurable load current, i pv is the output current of the photovoltaic array, which is calculated by the following expression:

[0071]

[0072] Among them, n p is the number of photovoltaic cells in parallel, n s is the number of photovoltaic cells connected in series, I ph is the photocurrent, I rs is the reverse saturation current, the photocurrent and reverse saturation current depend on light and temperature, k pv is the photovoltaic cell temperature coefficient, I scis the short-circuit current of the battery at reference temperature and light, K I (mA / K) is the short-circuit current temperature coefficient, T is the actual temperature of the photovoltaic array, T r is the reference temperature of the photovoltaic array, λ is the sunshine intensity, I rr is the reference temperature T r The reverse saturation current under the condition of electron charge q=1.6×10 -19C ,E gp =1.1eV is the band gap energy of the semiconductor that makes up the unit cell, the pn junction characteristic factor p is 1-5, and the Boltzmann constant K = 1.3805×10 -23 J / K.

[0073] Photovoltaic array power P pv and its corresponding photovoltaic array voltage v pv The partial derivative of

[0074]

[0075] When the system reaches the maximum power point, there is Therefore the controlled output is:

[0076]

[0077] In step S2, the system state equation is established according to the dynamic model as follows:

[0078]

[0079]

[0080] Among them, I b =1-i o / i L , G a =i pv / v pv , d D =-V D / L ,x=[i L v pv v b ] T .

[0081] The nonlinear term in the system state equation is I b ,i L , v pv , G a , According to the coupling relationship between nonlinear terms, I b ,i L , v pv For the direct nonlinear term, select Ga and is an indirect nonlinear term. The nonlinear sector range of the indirect nonlinear term can be determined by the nonlinear sector range of the direct nonlinear term. pv From the equation, we can see that when v pv When the maximum value is pv Minimum, v pv When the minimum pv Maximum, then through v pv The nonlinear sector range can determine the indirect nonlinear term i pv The nonlinear sector range of the indirect nonlinear term G can be further determined. a and Nonlinear sector range.

[0082] In this example, the Siemens SP75 solar photovoltaic module is used, and its specifications are as follows:

[0083] SP75 Specifications of Considered PV Modules

[0084] parameter Numerical Number of series-parallel batteries (36，1) Maximum power 75 watts Rated current 4.4A Rated voltage 17 volts Short-circuit current 4.8A Open circuit voltage 21.7 volts Short-circuit current temperature coefficient 2.06 mA / °C Open circuit voltage temperature coefficient -0.077 V / °C

[0085] like Figure 2 As shown, the DC-DC Buck converter consists of IRFP460 power MOSFET, 150μH storage inductor L, 1000μF capacitor C a and C b And power rectifier diode MBR2045CT. Capacitor C b and the internal resistance R of the inductor L b and R L The forward voltage of the power rectifier diode is V D =0.57V, and the operating frequency of the converter is set to 100000Hz.

[0086] In step S3, the process of defining the antecedent variable and the membership function is as follows: the direct nonlinear term is selected as the antecedent variable, and its variation range is defined as i L ∈[M2, M1], v pv ∈[N2, N1], I b ∈[J2,J1]. Define the antecedent variable as z1(t)=i L , z2(t)=v pv , z3(t)=I b , whose maximum value is z 1max =M1=5,z 2max =N1=22,z 3max =J1=0.2. The minimum value is z 1min =M2=-5,z 2min =N2=8,z3min =J2=0.1.

[0087] The membership function designed according to the bounds of the antecedent variables is:

[0088] For z1(t)=i L , its membership function is S a1 (z1(t)) and S b1 (z1(t)) are defined as follows:

[0089]

[0090] For z2(t)=v pv , its membership function S a2 (z2(t)) and S b2 (z2(t)) are defined as follows:

[0091]

[0092] For z3(t)=I b , its membership function S a3 (z3(t)) and S b3 (z3(t)) are defined as follows:

[0093]

[0094] The fuzzy rules are defined as follows:

[0095] Rule 1: z1(t) is the maximum, z2(t) is the maximum, z3(t) is the maximum;

[0096] Rule 2: z1(t) is the maximum value, z2(t) is the maximum value, and z3(t) is the minimum value;

[0097] Rule 3: z1(t) is the maximum value, z2(t) is the minimum value, and z3(t) is the maximum value;

[0098] Rule 4: z1(t) is the maximum value, z2(t) is the minimum value, and z3(t) is the minimum value;

[0099] Rule 5: z1(t) is the minimum, z2(t) is the maximum, and z3(t) is the maximum.

[0100] Rule 6: z1(t) is the minimum value, z2(t) is the maximum value, and z3(t) is the minimum value;

[0101] Rule 7: z1(t) is the minimum value, z2(t) is the minimum value, and z3(t) is the maximum value;

[0102] Rule 8: z1(t) is the minimum, z2(t) is the minimum, and z3(t) is the minimum.

[0103] After fuzzy linearizing the direct and indirect nonlinear terms using the sector nonlinear method, the TS fuzzy model of the photovoltaic power generation system based on fuzzy rule i is:

[0104] Rule i: If z1(t) is z2(t) is z3(t) is So

[0105]

[0106] y(t)=C i x(t)

[0107] Where i = 1, 2, ..., 8, and is the fuzzy set of rules corresponding to the antecedent variables,

[0108]

[0109]

[0110] The TS fuzzy photovoltaic power generation system model obtained by defuzzification is:

[0111]

[0112]

[0113] where z(t) = [z1(t) z2(t) z3(t)] T is the antecedent variable vector, h i (z(t)) represents the normalized membership function and satisfies

[0114]

[0115] Among them, F ji (z j (t)) represents the antecedent variable z j (t) In the fuzzy set F ji The membership weight of .

[0116] The existing TS fuzzy modeling method of photovoltaic power generation system ignores the coupling relationship between nonlinear terms in the nonlinear dynamic model of photovoltaic power generation system and simply converts I b ,i L , v pv , G a and These five nonlinear terms are used as antecedent variables, which makes the TS fuzzy model of the photovoltaic power generation system have 32 fuzzy rules. The TS fuzzy modeling method proposed in the present invention separates the nonlinear terms in the nonlinear dynamic model of the photovoltaic power generation system into direct nonlinear terms and indirect nonlinear terms by finding the coupling relationship between the nonlinear terms. Based on the coupling relationship, the direct nonlinear terms I b ,i L , v pv As antecedent variables, this makes the TS fuzzy model of photovoltaic power generation system have 8 fuzzy rules. Compared with the TS fuzzy model of photovoltaic power generation system obtained by traditional TS fuzzy modeling method, the number of fuzzy rules is significantly reduced.

[0117] Comparison data table of the embodiment of the present invention and the existing modeling technology

[0118]

[0119] In summary, the TS fuzzy rule reduction modeling method for a photovoltaic power generation system described in the above embodiment can significantly reduce the number of fuzzy rules in the TS fuzzy photovoltaic power generation system model. The TS fuzzy model of a photovoltaic power generation system established using the modeling method provided by the present invention can effectively reduce the computational complexity of algorithms designed based on this model and improve the response speed of algorithm execution.

[0120] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A TS fuzzy rule reduction modeling method for photovoltaic power generation systems, characterized by: The following steps are involved: Construct a nonlinear dynamic model of photovoltaic power generation system; Establish the system state equation based on the dynamic model and divide the nonlinear terms in the equation into direct nonlinear terms and indirect nonlinear terms; Define antecedent variables, membership functions and fuzzy rules, use sector nonlinear method to fuzzy linearize direct and indirect nonlinear terms, and give TS fuzzy model; The TS fuzzy photovoltaic power generation system model is obtained by defuzzification.

2. The TS fuzzy rule reduction modeling method for a photovoltaic power generation system according to claim 1, characterized in that: The photovoltaic power generation system consists of a photovoltaic array, a DC-DC Buck converter and a load. Its nonlinear dynamic model is as follows: Among them, v pv is the capacitance C a The PV array voltage on L and v b They are the current on the inductor L and the capacitance C in the DC-DC Buck converter circuit respectively b The voltage on the MOSFET, u is the duty cycle of the pulse duration modulation signal that controls the switching MOSFET, R b and R L They are respectively the capacitor C b and the internal resistance of the inductor L, V D is the forward voltage of the power diode, i o is the measurable load current, i pv is the output current of the photovoltaic array, which is calculated by the following expression: Among them, n p is the number of photovoltaic cells in parallel, n s is the number of photovoltaic cells connected in series, I ph is the photocurrent, I rs is the reverse saturation current, the photocurrent and reverse saturation current depend on light and temperature, k pv is the photovoltaic cell temperature coefficient, I sc is the short-circuit current of the battery at reference temperature and light, K I (mA / K) is the short-circuit current temperature coefficient, T is the actual temperature of the photovoltaic array, T r is the reference temperature of the photovoltaic array, λ is the sunshine intensity, I rr is the reference temperature T r Reverse saturation current under Photovoltaic array power P pv and its corresponding photovoltaic array voltage v pv The partial derivative of is: When the system reaches the maximum power point, there is Therefore the controlled output is:

3. The TS fuzzy rule reduction modeling method for a photovoltaic power generation system according to claim 2, characterized in that: The system state equation established according to the dynamic model is as follows: Among them,I b =1st o / and L ,MR a =and p v / v pv ,d D =-V D / L, x=[i L in pv in b ] T ; The nonlinear term in the system state equation is I b 、i L 、v pv , G a 、 According to the coupling relationship between nonlinear terms, I b 、i L and v pv For the direct nonlinear term, select G a and is an indirect nonlinear term; the nonlinear sector range of the indirect nonlinear term can be determined by the nonlinear sector range of the direct nonlinear term; pv From the equation, we can see that when v pv When the maximum value is pv Minimum, v pv When the minimum pv Maximum, then through v pv The nonlinear sector range determines the indirect nonlinear term i pv The nonlinear sector range of the indirect nonlinear term G can be further determined. a and Nonlinear sector range.

4. The TS fuzzy rule reduction modeling method for a photovoltaic power generation system according to claim 3, characterized in that: The process of defining antecedent variables and membership functions is as follows: Select the direct nonlinear term as the antecedent variable and define its range of variation as i L ∈[M2, M1], v pv ∈[N2, N1], I b ∈[J2, J1]; define the antecedent variable as z1(t)=i L , z2(t)=v pv , z3(t)=I b , whose maximum value is z 1max =M1,z 2max =N1,z 3max =J1, the minimum value is z 1min =M2,z 2min =N2,z 3min =J2; The membership function designed according to the bounds of the antecedent variables is: For z1(t)=i L , its membership function is S a1 (z1(t)) and S b1 (z1(t)) are defined as follows: For z2(t)=v pv , its membership function S a2 (z2(t)) and S b2 (z2(t)) are defined as follows: For z3(t)=I b , its membership function S a3 (z3(t)) and S b3 (z3(t)) are defined as follows: The fuzzy rules are defined as follows: Rule 1: z1(t) is the maximum, z2(t) is the maximum, z3(t) is the maximum; Rule 2: z1(t) is the maximum value, z2(t) is the maximum value, and z3(t) is the minimum value; Rule 3: z1(t) is the maximum value, z2(t) is the minimum value, and z3(t) is the maximum value; Rule 4: z1(t) is the maximum value, z2(t) is the minimum value, and z3(t) is the minimum value; Rule 5: z1(t) is the minimum, z2(t) is the maximum, and z3(t) is the maximum. Rule 6: z1(t) is the minimum value, z2(t) is the maximum value, and z3(t) is the minimum value; Rule 7: z1(t) is the minimum value, z2(t) is the minimum value, and z3(t) is the maximum value; Rule 8: z1(t) is the minimum, z2(t) is the minimum, and z3(t) is the minimum.

5. The TS fuzzy rule reduction modeling method for a photovoltaic power generation system according to claim 4, characterized in that: After fuzzy linearizing the direct and indirect nonlinear terms using the sector nonlinear method, the TS fuzzy model of the photovoltaic power generation system based on fuzzy rule i is: Rule i: If z1(t) is z2(t) is z3(t) is So y(t)=C i x(t) Where i = 1, 2, ..., 8, and is the fuzzy set of rules corresponding to the antecedent variables, 6. The TS fuzzy rule reduction modeling method for a photovoltaic power generation system according to claim 5, characterized in that: The TS fuzzy photovoltaic power generation system model obtained by defuzzification is: where z(t) = [z1(t) z2(t) z3(t)] T is the antecedent variable vector, h i (z(t)) represents the normalized membership function and satisfies Among them, F ji (z j (t)) represents the antecedent variable z j (t) In the fuzzy set F ji The membership weight of .

7. The TS fuzzy rule reduction modeling method for a photovoltaic power generation system according to claim 2, characterized in that: i pv In the expression: electron charge q = 1.6×10 -19 C, E gp =1.1eV is the band gap energy of the semiconductor that makes up the unit cell, the pn junction characteristic factor p is 1-5, and the Boltzmann constant K = 1.3805×10 -23 J / K.

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