CN104362977A - Photovoltaic inverter two-peak dynamic/static MPP tracking efficiency test method - Google Patents

Abstract

The invention provides a photovoltaic inverter two-peak dynamic/static MPP tracking efficiency test method. The method includes the following steps that the maximum power point reached by photovoltaic arrays on the direct current side and the voltage range of an MPP of a photovoltaic inverter are determined; the photovoltaic arrays are selected and matched with the photovoltaic inverter; a single peak P-V curve of the photovoltaic arrays is determined; a two-peak MPP test efficiency P-V curve of the photovoltaic arrays is set and a photovoltaic inverter two-peak dynamic/static MPP tracking efficiency test is finished. According to the method, two-peak I-V curves of a direct current source under different powers and different blocking degrees are edited, the capability of the photovoltaic inverter for tracking the maximum power point of the two-peak I-V curves is tested and evaluated, and the gap in the aspect of tests and evaluation of two-peak I-V curve MPP tracking efficiency in the prior art is filled in.

Description

A testing method for dual-peak dynamic/static MPP tracking efficiency of photovoltaic inverters

technical field

The invention belongs to the detection field of photovoltaic inverters, and in particular relates to a method for testing the double-peak dynamic/static MPP tracking efficiency of photovoltaic inverters.

Background technique

In recent years, new energy represented by wind energy and solar energy has developed rapidly around the world. It is estimated that by 2020, the annual output of photovoltaic modules will reach 40GW. In this case, the power generation efficiency of the photovoltaic system is also receiving extensive attention. An important factor affecting the power generation efficiency of photovoltaic systems is the maximum power point tracking accuracy of photovoltaic inverters on the PV array P-V curve.

According to the characteristics of photovoltaic modules, its ideal P-V curve is a unimodal parabola. When the photovoltaic inverter performs maximum power point tracking, it only needs to track the top of its single peak. In actual operation, due to the influence of clouds, trees, buildings, and bird excrement, the photovoltaic array will be partially blocked. In this case, the solar irradiance received by the photovoltaic modules is quite different. The output characteristics of the strings will also change, and the P-V curve of the photovoltaic array will appear double-peaked or multi-peaked.

At present, conventional photovoltaic inverters only have single-peak MPP (Maximum Power Point) tracking. The development of MPPT control technology for photovoltaic inverters has gone through constant voltage control method ^[1] , short-circuit current proportional method ^[2] , etc., which are relatively simple but not sufficient. Accurate control methods; up to the widely used MPPT control methods such as disturbance observation method ^[3～7] , conductance incremental method ^[8][9] and intelligent processing methods based on fuzzy control, neural network and other nonlinear MPPT tracking method including control strategy.

Using the MPPT tracking method of the conventional photovoltaic inverter, it is impossible to track the bimodal IV curve of the photovoltaic array, resulting in the loss of power generation of the photovoltaic system. Attached Figure 1 shows that a photovoltaic array with a nominal installed capacity of 500kW is partially shaded, and when shaded, the irradiance of the shaded portion is about 50W/m ² . Under this shading degree, the PV curve of the photovoltaic array is shown in Fig. 2 . The working performance of the inverter is affected by shading. If the inverter has bimodal MPPT tracking capability, the maximum power P _array1 = 443.58kW that the inverter can achieve when being shading, and the power loss of the entire system is about 56.42kW. The percentage power loss is 11.28%. If the inverter does not have bimodal MPPT tracking capability, the inverter can reach the maximum power P _array2 =406.02kW when shaded, the power loss of the whole system is about 93.98kW, and the power loss percentage is 18.80%.

With the development of distributed photovoltaic systems, the application of distributed photovoltaic systems in cities will become more popular, which is characterized by complex surrounding environments and a greater probability of arrays being blocked by shadows. It can be foreseen that the photovoltaic inverter with bimodal MPPT control method will become one of the important indicators to measure the performance of the inverter.

At present, the methods for testing and evaluating the MPP tracking efficiency of photovoltaic inverters are mainly found in the European standard EN50530, which includes static MPP tracking efficiency testing, dynamic MPP tracking efficiency testing, and inverter startup and shutdown MPP tracking efficiency testing. Ideal unimodal P-V curve. In the actual use of photovoltaic arrays, affected by shadows, etc., its I-V curve will present multiple inflection points, resulting in a double-peak P-V curve of the photovoltaic array, which seriously affects the overall efficiency of the photovoltaic system. There are no reports on the testing standards and methods for bimodal MPPT efficiency.

references

[1] Yu Shijie, He Huiruo, Cao Renxian, etc. Control comparison of CVT and MPPT in photovoltaic water pump system [J] Solar Energy Sinica, 1998,19(4): 394-398.

[2] Zhou Lin, Wu Jian, et al. Review of Maximum Power Point Tracking Control Methods for Photovoltaic Arrays [J], High Voltage Technology, 2008(6)

[3]Femia N, Petrone G, Spagnuolo G, et al.Optimization of perturb and observe maximum powerpoint tracking method[J].IEEE Transactions on Power Electronics,2005,20(4):963-973

[4] Altas I H, Sharaf A M.A novel on-line MPP search algorithm for PV array [J] IEEE Transactions on Energy Conversion 1996,11(4):748-754

[5]Chee Wei Tan, Green T C, Hernandez-Aramburo C A.An improved maximum power pointtracking algorithm with current-mode control for photovoltaic applications[C]InternationalConference on Power Electronics and Drives Systems Kuala Lumpur,Malaysia 8 9-49 2005:

[6] Sun Wuben, Zeng Yi, Jiang Xiuchen, etc. Design and Implementation of Power System for Outdoor Online Monitoring Device [J] High Voltage Technology, 2007,33(8):178-182

[7]D’Souza N S, Lopes L A C, XueJun Liu.An intelligent maximum power point tracker using peak current control[C]IEEE 36th Conference on Power Electronics Specialists.Recife,Brazil:IEEE,2005:172-177]

[8] Hussein K H, Muta I Hoshino T, Osakada M. Maximum Photovoltaic power tracking: an algorithm for rapidly changing atmospheric conditions [J]. IEE Proceedings-Generation, Transmission and Distribution, 1995, 142(1): 59-64

[9]Yusof Y, Sayuti S H, Abdul Latif M, et al.Modeling and simulation of maximum power pointtracker for photovoltaic system[C]Proceedings of National Power and Energy conference.KualaLumpur,Malaysia,2004:88-93.

Contents of the invention

In order to overcome the above-mentioned deficiencies in the prior art, the present invention provides a method for testing the bimodal dynamic/static MPP tracking efficiency of photovoltaic inverters, by editing the bimodal I-V curves of the DC source under different power and different shading degrees, testing and evaluation The ability of the photovoltaic inverter to track the maximum power point of the double-peak I-V curve, this invention fills the gap in the current testing and evaluation of the MPP tracking efficiency of the double-peak I-V curve.

In order to realize the above-mentioned purpose of the invention, the present invention takes the following technical solutions:

The invention provides a photovoltaic inverter bimodal dynamic/static MPP tracking efficiency testing method, said method comprising the following steps:

Step 1: Determine the maximum power point that can be reached by the photovoltaic array on the DC side and the MPP voltage range of the photovoltaic inverter;

Step 2: Select the photovoltaic array and match it with the photovoltaic inverter;

Step 3: Determine the unimodal P-V curve of the photovoltaic module;

Step 4: Set the efficiency P-V curve of the photovoltaic array bimodal MPPT test, and complete the bimodal dynamic/static MPP tracking efficiency test of the photovoltaic inverter.

In the step 1, the maximum power that can be reached by the photovoltaic array on the DC side and the MPP voltage range of the photovoltaic inverter are determined according to the relevant parameters of the photovoltaic inverter operation; the relevant parameters of the photovoltaic inverter operation include the minimum MPP voltage U of the photovoltaic inverter _mppmin , the maximum MPP voltage U _mppmax , the optimum MPP working voltage and the nominal operating power of the PV inverter.

Determine the maximum power P ₀ that can be reached by the photovoltaic array on the DC side according to the nominal operating power of the photovoltaic inverter, and the maximum power of the set photovoltaic array bimodal PV curve does not exceed P ₀ ; according to the minimum MPP voltage U _mppmin of the photovoltaic inverter, The maximum MPP voltage U _mppmax and the optimal MPP operating voltage determine the MPP voltage range of the photovoltaic array. When setting the bimodal PV curve of the photovoltaic array, the operating voltages corresponding to all extreme points on the bimodal PV curve of the photovoltaic array are within the determined photovoltaic array. array MPP voltage range.

In the step 2, select a crystalline silicon photovoltaic array or a thin-film photovoltaic array according to the MPP voltage range of the photovoltaic inverter and the application occasion of the photovoltaic inverter, and match it with the photovoltaic inverter. Determine the number n of series connection of photovoltaic modules in the photovoltaic array and the number m of parallel connection of photovoltaic strings composed of series connection of photovoltaic modules.

In the step 3, the photovoltaic module mathematical model is used to determine the P-V curve of the single-peak MPPT efficiency test of the photovoltaic module. In the photovoltaic module mathematical model, there are:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; PV</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; sc</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; PV</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; oc</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; AQ</span>}}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, I _PV is the output current of the photovoltaic module, I _sc is the short-circuit current of the photovoltaic module, I ₀ is the saturation current of the diode, U _PV is the output voltage of the photovoltaic module, U _oc is the open circuit voltage of the photovoltaic module, and C _AQ is a constant, expressed as:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; AQ</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; FF</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; FF</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span>}$

Among them, FF _U is the voltage filling factor, which is 0.8 for the crystalline silicon components in the crystalline silicon photovoltaic array, and 0.72 for the thin-film components in the thin-film photovoltaic array; FF _I is the current filling factor, and for the crystal silicon components in the crystalline silicon photovoltaic array For silicon components, take 0.9, and for thin-film components in thin-film photovoltaic arrays, take 0.8;

When n pieces of photovoltaic modules are connected in series to form a photovoltaic string, and m photovoltaic series are connected in parallel to form a photovoltaic array, the open-circuit voltage and short-circuit current of the photovoltaic array are respectively expressed as:

U _{oc_a} = n U _oc

I _{sc_a} = mI _sc

Among them, U _{oc_a} is the open-circuit voltage of the photovoltaic array, and I _{sc_a} is the short-circuit current of the photovoltaic array.

In the step 4, the PV array bimodal MPPT test efficiency P-V curve is set according to the shading mode of the photovoltaic array and the shading degree of the shadow; the shading mode of the photovoltaic array includes shading of the entire column, shading of the entire row and shading of a single module;

It is set from the open-circuit voltage of the photovoltaic array to the voltage 0, the first maximum power extreme is the front peak, and the second maximum power extreme is the rear peak. When the photovoltaic inverter performs dual-peak dynamic/static MPPT tracking, it starts Search from the open circuit voltage to the direction of voltage drop;

1) If the front peak power value is greater than the rear peak power value, the maximum power point of the photovoltaic array can be found no matter whether the photovoltaic inverter has bimodal MPPT control function or not;

2) If the front peak power value is smaller than the rear peak power value, only the photovoltaic inverter with bimodal MPPT control function can search for the real maximum value of the photovoltaic array; The working condition looks for the maximum power point on the new P-V curve again.

Setting the efficiency P-V curve of the bimodal MPPT test of the photovoltaic array specifically includes setting the P-V curve of the bimodal static MPPT efficiency test and the P-V curve of the bimodal dynamic MPPT efficiency test.

When setting the bimodal static MPPT efficiency test PV curve, respectively set the photovoltaic array bimodal static MPPT efficiency test PV curve under high irradiance and low irradiance, and the bimodal static MPPT efficiency η _MPPT,stat of the photovoltaic inverter is expressed as:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPT</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; stat</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; MPP</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; PVS</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}$

Among them, ΔT is the sampling period, which is less than the minimum time interval of MPPT of the photovoltaic inverter; U _DC,i is the average value of the input voltage within the sampling period, I _DC,i is the average value of the input current within the sampling period, _PMPP,PVS is The photovoltaic array simulator actually outputs the maximum power value, z is the total number of sampling data points of the photovoltaic inverter, _TM is the detection time, and _TM = z×ΔT.

When setting the bimodal dynamic MPPT efficiency test PV curve, the bimodal dynamic MPPT efficiency test includes unimodal to bimodal conversion and bimodal to unimodal conversion; after the Nth test, the bimodal dynamic MPPT efficiency of the photovoltaic array is η _MPPTdyn,t Expressed as:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPTDyn</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPTdyn</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}$

Wherein, N is the total number of test times, and η _{MPPTdyn, k} is the bimodal dynamic MPPT efficiency of photovoltaic array in the k test, which is expressed as:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPTdyn</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; MPP</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; PVS</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}$

Among them, U _DC,i is the average value of the input voltage in the sampling period, I _DC,i is the average value of the input current in the sampling period, ΔT _i is the data sampling period of the DC side of the photovoltaic inverter in the k-th test, ΔT _j is the output power period of the photovoltaic array simulator in the k-th test, P _MPP,PVS,j is the maximum output power of the photovoltaic array simulator in the k-th test, and M is the total number of sampled data points of the photovoltaic array simulator .

Compared with prior art, the beneficial effect of the present invention is:

1) According to the shading condition of the photovoltaic array, the method sets the bimodal P-V curve cluster under low irradiance and high irradiance, so as to achieve the purpose of tracking the static bimodal MPPT under different working conditions of the inverter;

2) According to the change of shadow on site, set the change mode and change rate of the PV array P-V curve cluster under the change of shadow, so as to achieve the purpose of testing the dynamic bimodal MPPT efficiency of the inverter.

Description of drawings

Fig. 1 is a schematic diagram of a photovoltaic array being blocked by shadows in the prior art;

Fig. 2 is a P-V curve diagram when the photovoltaic array is shaded in the prior art;

Fig. 3 is the flow chart of bimodal MPPT efficiency test in the embodiment of the present invention;

Fig. 4 is the bimodal static MPPT efficiency test P-V curve figure in the embodiment of the present invention;

Fig. 5 is the bimodal dynamic MPPT efficiency test P-V curve figure in the embodiment of the present invention;

Fig. 6 is a schematic diagram of the change rate setting (test mode ①) of the photovoltaic array bimodal P-V curve in the embodiment of the present invention;

Fig. 7 is a schematic diagram of the change rate setting (test mode 2) of the photovoltaic array bimodal P-V curve in the embodiment of the present invention;

Fig. 8 is the I-V curve diagram of the photovoltaic module in the embodiment of the present invention;

Fig. 9 is the P-V curve diagram of the photovoltaic module in the embodiment of the present invention;

Fig. 10 is the bimodal P-V curve diagram of the photovoltaic array in the embodiment of the present invention;

Figure 11 is a schematic diagram of the test results of bimodal MPPT efficiency.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings.

As shown in Fig. 3, the present invention provides a kind of photovoltaic inverter bimodal dynamic/static MPP tracking efficiency testing method, and described method comprises the following steps:

Step 1: Determine the maximum power point that can be reached by the photovoltaic array on the DC side and the MPP voltage range of the photovoltaic inverter;

Step 2: Select the photovoltaic array and match it with the photovoltaic inverter;

Step 3: Determine the unimodal P-V curve of the photovoltaic module;

Step 4: Set the efficiency P-V curve of the photovoltaic array bimodal MPPT test, and complete the bimodal dynamic/static MPP tracking efficiency test of the photovoltaic inverter.

In the step 1, the maximum power that can be reached by the photovoltaic array on the DC side and the MPP voltage range of the photovoltaic inverter are determined according to the relevant parameters of the photovoltaic inverter operation; the relevant parameters of the photovoltaic inverter operation include the minimum MPP voltage U of the photovoltaic inverter _mppmin , the maximum MPP voltage U _mppmax , the optimum MPP working voltage and the nominal operating power of the PV inverter.

Determine the maximum power P ₀ that can be reached by the photovoltaic array on the DC side according to the nominal operating power of the photovoltaic inverter, and the maximum power of the set photovoltaic array bimodal PV curve does not exceed P ₀ ; according to the minimum MPP voltage U _mppmin of the photovoltaic inverter, The maximum MPP voltage U _mppmax and the optimal MPP operating voltage determine the MPP voltage range of the photovoltaic array. When setting the bimodal PV curve of the photovoltaic array, the operating voltages corresponding to all extreme points on the bimodal PV curve of the photovoltaic array are within the determined photovoltaic array. array MPP voltage range.

In the step 2, select a crystalline silicon photovoltaic array or a thin-film photovoltaic array according to the MPP voltage range of the photovoltaic inverter and the application occasion of the photovoltaic inverter, and match it with the photovoltaic inverter. Determine the number n of series connection of photovoltaic modules in the photovoltaic array and the number m of parallel connection of photovoltaic strings composed of series connection of photovoltaic modules.

In the step 3, the photovoltaic module mathematical model is used to determine the P-V curve of the single-peak MPPT efficiency test of the photovoltaic module. In the photovoltaic module mathematical model, there are:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; PV</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; sc</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; PV</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; oc</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; AQ</span>}}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, I _PV is the output current of the photovoltaic module, I _sc is the short-circuit current of the photovoltaic module, I ₀ is the saturation current of the diode, U _PV is the output voltage of the photovoltaic module, U _oc is the open circuit voltage of the photovoltaic module, and C _AQ is a constant, expressed as:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; AQ</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; FF</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; FF</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, FF _U is the voltage filling factor, which is 0.8 for the crystalline silicon components in the crystalline silicon photovoltaic array, and 0.72 for the thin-film components in the thin-film photovoltaic array; FF _I is the current filling factor, and for the crystal silicon components in the crystalline silicon photovoltaic array For silicon components, take 0.9, and for thin-film components in thin-film photovoltaic arrays, take 0.8;

When n pieces of photovoltaic modules are connected in series to form a photovoltaic string, and m photovoltaic series are connected in parallel to form a photovoltaic array, the open-circuit voltage and short-circuit current of the photovoltaic array are respectively expressed as:

U _{oc_a} = nU _oc (3)

I _{sc_a} = mI _sc (4)

Among them, U _{oc_a} is the open-circuit voltage of the photovoltaic array, and I _{sc_a} is the short-circuit current of the photovoltaic array.

In the step 4, the PV array bimodal MPPT test efficiency P-V curve is set according to the shading mode of the photovoltaic array and the shading degree of the shadow; the shading mode of the photovoltaic array includes shading of the entire column, shading of the entire row and shading of a single module;

It is set from the open-circuit voltage of the photovoltaic array to the voltage 0, the first maximum power extreme is the front peak, and the second maximum power extreme is the rear peak. When the photovoltaic inverter performs dual-peak dynamic/static MPPT tracking, it starts Search from the open circuit voltage to the direction of voltage drop;

1) If the front peak power value is greater than the rear peak power value, the maximum power point of the photovoltaic array can be found no matter whether the photovoltaic inverter has bimodal MPPT control function or not;

2) If the front peak power value is smaller than the rear peak power value, only the photovoltaic inverter with bimodal MPPT control function can search for the real maximum value of the photovoltaic array; The working condition looks for the maximum power point on the new P-V curve again.

Setting the efficiency P-V curve of the bimodal MPPT test of the photovoltaic array specifically includes setting the P-V curve of the bimodal static MPPT efficiency test and the P-V curve of the bimodal dynamic MPPT efficiency test.

(1) When setting the PV curves for the bimodal static MPPT efficiency test, set the PV array bimodal static MPPT efficiency test PV curves under high irradiance and low irradiance respectively. Each curve cluster includes the first peak greater than the rear peak, the first peak Slightly smaller than the back peak and the first peak is smaller than the back peak, as shown by C ₁ , C ₂ and C ₃ in Figure 4. Each curve is tested twice, each test is 10 minutes, and the test result is the average value of the two tests. When testing, for C1, the inverter should track P1 point, for C ₂ , the inverter should track P4 point to ensure that the inverter operating voltage is close to the optimal operating voltage, for C ₃ , the inverter should track P4 point . The bimodal static MPPT efficiency η _{MPPT,stat of} the photovoltaic inverter is expressed as:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPT</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; stat</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; MPP</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; PVS</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, ΔT is the sampling period, which is less than the minimum time interval of MPPT of the photovoltaic inverter; U _DC,i is the average value of the input voltage within the sampling period, I _DC,i is the average value of the input current within the sampling period, _PMPP,PVS is The photovoltaic array simulator actually outputs the maximum power value, z is the total number of sampling data points of the photovoltaic inverter, _TM is the detection time, and _TM = z×ΔT.

(2) Set the bimodal dynamic MPPT efficiency test P-V curve to verify the performance of the photovoltaic inverter tracking the true peak when the photovoltaic array is shaded by changes. When setting the P-V curve for bimodal dynamic MPPT efficiency test, the bimodal P-V curve should also include points where the front peak power value is greater than the rear peak power value, and the front peak power value is smaller than the rear peak power value, according to the same degree and shadow of the blocked components There are two test conditions set up:

2-1) The degree of occlusion changes;

The change of shading degree refers to the transformation of the P-V curve of the photovoltaic array between single peak and multi-peak during the process of shadow shading and shadow shading disappearing on the surface of the photovoltaic array. During the conversion process, the ability of the inverter to correctly find the true peak is investigated.

The bimodal dynamic MPPT efficiency test includes unimodal to bimodal conversion and bimodal to unimodal conversion; on the basis of the curve cluster in Figure 4, add a unimodal curve, denoted as C ₀ , where C0 corresponds to irradiance as S0, C1 corresponds to the irradiance under the shadow as S1, C2 corresponds to the irradiance under the shadow as S2, and C3 corresponds to the irradiance under the shadow as S3. The changing order of the multi-peak PV curve is: C ₀ →C ₁ →C ₀ →C ₂ →C ₀ →C ₃ , as shown in Figure 5. Under low irradiance and high irradiance, set the PV curve change rate and change times respectively, as shown in Figure 6. Under low irradiance and high irradiance, set the PV curve change rate respectively as shown in Figure 6, set the rising time from low irradiance to high irradiance (t0~t1), hold time (t1~t2) under high irradiance, and set the time from high irradiance to Low irradiance fall time (t2~t3) and low irradiance maintenance time (t3~t4). In this mode, N tests are performed. After the Nth test, the bimodal dynamic MPPT efficiency η _MPPTdyn,t of the photovoltaic array is expressed as:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPTDyn</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPTdyn</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}$

Wherein, N is the total number of test times, and η _{MPPTdyn, k} is the bimodal dynamic MPPT efficiency of photovoltaic array in the k test, which is expressed as:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; MPPTdyn</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; DC</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; MPP</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; PVS</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Among them, U _DC,i is the average value of the input voltage in the sampling period, I _DC,i is the average value of the input current in the sampling period, ΔT _i is the data sampling period of the DC side of the photovoltaic inverter in the k-th test, ΔT _j is the output power period of the photovoltaic array simulator in the k-th test, P _MPP,PVS,j is the maximum output power of the photovoltaic array simulator in the k-th test, and M is the total number of sampled data points of the photovoltaic array simulator .

2-2) The occlusion area remains unchanged, but the occlusion degree changes;

The shading area remains unchanged, and the shading degree change means that when the shading is fixed, the irradiance of the shaded part changes, from the first peak being larger than the second peak to the first peak being smaller than the second peak, as shown in the irradiance change S1→S3→S1 in Figure 5 , the corresponding multi-peak P-V change curve changes from C1→C3→C1. During the change process, when the irradiation curve changes, the inverter should be able to distinguish the maximum point and the maximum point on the double-peak P-V curve, and track the maximum power Points: P1, P5, P1. Set the change rate of the photovoltaic curve separately as shown in Figure 7, set the rising time from low irradiation to high irradiation (t0~t1), the holding time from high irradiation (t1~t2), and the falling time from high irradiation to low irradiation (t2~t3) As well as the low irradiance maintenance time (t3~t4), each test is repeated N times. In this mode, formula (6) and (7) are used to calculate the test efficiency of photovoltaic array MPPT.

Example

Analyze the loss of a 500kW photovoltaic array under different shading modes, and test the low-irradiance static MPPT efficiency. The array consists of 2000 pieces of Suntech 250W 25V Si-poly HiPerforma PLUTO. The combination of the array is 20 modules in series and 100 modules in parallel. The parameters of the photovoltaic modules are shown in Table 1, and the I-V curve and P-V curve of each photovoltaic module in the array are shown in Figure 8 and Figure 9.

Table 1

manufacturer Suntech model PLUTO250 component type Monocrystalline silicon short circuit current 8.63A open circuit voltage 37.4V Maximum power current 8.15A Maximum power voltage 30.7V Nominal power 250W conversion efficiency 15.55% Series resistance 0.152Ω Parallel resistance 500Ω Number of Bypass Diodes 3

In the case of light load (that is, the irradiance is 500W/m ² when there is no shadow shielding), the irradiance of the shielding area is set to 400W/m ² , 300W/m ² , 200W/m ² , 100W/m ² , The PV curve of the photovoltaic array in the case of 50W/m ² is shown in Figure 10. According to the setting principle 3), the irradiance under shading is selected as 400W/m ² , 300W/m ² and 50W/m ² curves for testing.

To test the bimodal MPPT efficiency of photovoltaic inverters under low irradiance, the photovoltaic array is partially shaded under the irradiation of 500W/m ² , and the surface irradiance of the shaded photovoltaic modules is 300W/m ² so that the PV curve of the array is a The bimodal curve has two extreme points, the maximum power point is at the rear peak of the PV curve, and the test time for each curve is the same as 10 minutes.

When the inverter does not have the multi-peak MPPT tracking mode, it can only track to the lower power extreme (first peak), as shown in the star tracking point shown in Figure 11. In this case, the PV inverter MPPT efficiency is 74.84%.

By changing the program instructions, the inverter has a simple multi-peak MPPT tracking capability. At this time, the inverter can track to the maximum power point (rear peak) of the photovoltaic array, as shown in the circular tracking point in Figure 11. In this case, the photovoltaic inverter MPPT efficiency is 99.55%.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Those of ordinary skill in the art can still modify or equivalently replace the specific implementation methods of the present invention with reference to the above embodiments. Any modification or equivalent replacement departing from the spirit and scope of the present invention is within the protection scope of the claims of the present invention pending application.

Claims (9)

1. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter follows the tracks of an Efficiency test method, it is characterized in that: said method comprising the steps of:

Step 1: determine the accessibility maximum power point of DC side photovoltaic array and photovoltaic DC-to-AC converter MPP voltage range;

Step 2: selective light photovoltaic array, and mate with photovoltaic DC-to-AC converter;

Step 3: determine the unimodal P-V curve of photovoltaic module;

Step 4: arrange photovoltaic array bimodal MPPT testing efficiency P-V curve, completes and follows the tracks of efficiency test to dynamically bimodal/static MPP of photovoltaic DC-to-AC converter.

2. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter according to claim 1 follows the tracks of Efficiency test method, it is characterized in that: in described step 1, run the relevant parameter determination accessibility maximum power of DC side photovoltaic array and photovoltaic DC-to-AC converter MPP voltage range according to photovoltaic DC-to-AC converter; Photovoltaic DC-to-AC converter runs the minimum MPP voltage U that relevant parameter comprises photovoltaic DC-to-AC converter _mppmin, maximum MPP voltage U _mppmax, best MPP operating voltage and photovoltaic DC-to-AC converter nominal operate power.

3. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter according to claim 2 follows the tracks of Efficiency test method, it is characterized in that: according to the accessibility maximum power P of photovoltaic DC-to-AC converter nominal operate power determination DC side photovoltaic array ₀, the photovoltaic array bimodal P-V curve maximum power of setting is no more than P ₀; According to the minimum MPP voltage U of photovoltaic DC-to-AC converter _mppmin, maximum MPP voltage U _mppmaxand best MPP operating voltage determination photovoltaic array MPP voltage range, when carrying out the bimodal P-V curve setting of photovoltaic array, the operating voltage that on photovoltaic array bimodal P-V curve, all extreme points are corresponding is all in the photovoltaic array MPP voltage range determined.

4. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter according to claim 1 follows the tracks of Efficiency test method, it is characterized in that: in described step 2, crystal silicon photovoltaic array or film photovoltaic array are selected in application scenario according to photovoltaic DC-to-AC converter MPP voltage range and photovoltaic DC-to-AC converter, and mate with photovoltaic DC-to-AC converter, simultaneously according to the serial number n of photovoltaic module in photovoltaic DC-to-AC converter MPP voltage range determination photovoltaic array and the quantity m in parallel of photovoltaic group string that is composed in series by photovoltaic module.

5. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter according to claim 1 follows the tracks of Efficiency test method, it is characterized in that: in described step 3, utilize photovoltaic module Mathematical Modeling determination photovoltaic module unimodal MPPT efficiency test P-V curve, in photovoltaic module Mathematical Modeling, have:

$I_{\mathrm{PV}}=I_{\mathrm{sc}}-I_0\left(\frac{U_{\mathrm{PV}}}{e^{U_{\mathrm{oc}}{C}_{\mathrm{AQ}}}-1}\right)$

Wherein, I _pVfor photovoltaic module output current, I _scfor photovoltaic module short circuit current, I ₀for diode saturation current, U _pVfor photovoltaic module output voltage, U _ocfor photovoltaic module open circuit voltage, C _aQfor constant, be expressed as:

$C_{\mathrm{AQ}}=\frac{{\mathrm{FF}}_U-1}{\ln (1-{\mathrm{FF}}_I)}$

Wherein, FF _ufor voltage activity coefficient, for the crystal silicon component in crystal silicon photovoltaic array, get 0.8, for the film assembly in film photovoltaic array, get 0.72; FF _ifor electric current activity coefficient, for the crystal silicon component in crystal silicon photovoltaic array, get 0.9, for the film assembly in film photovoltaic array, get 0.8;

N block photovoltaic module is connected into photovoltaic group string, and when simultaneously m photovoltaic group connection in series-parallel becomes photovoltaic array, photovoltaic array open circuit voltage and short circuit current are expressed as:

U _{oc_a}＝nU _oc

I _{sc_a}＝ml _sc

Wherein, U _{oc_a}for photovoltaic array open circuit voltage, I _{sc_a}for photovoltaic array short circuit current.

6. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter according to claim 1 follows the tracks of Efficiency test method, it is characterized in that: in described step 4, block pattern according to photovoltaic array and shade coverage extent arranges photovoltaic array bimodal MPPT testing efficiency P-V curve; The photovoltaic array pattern of blocking comprises that permutation is blocked, full line blocks and blocks with monolithic element;

Setting plays voltage 0 from photovoltaic array open circuit voltage, first maximum power extreme value is leading peak, second maximum power extreme value is postpeak, and photovoltaic DC-to-AC converter, when carrying out dynamically bimodal/static MPPT and following the tracks of, reduces direction towards voltage and searches for from open circuit voltage;

1) if when leading peak performance number is greater than postpeak performance number, no matter whether photovoltaic DC-to-AC converter possesses bimodal MPPT controlling functions, all can find the maximum power point of photovoltaic array;

2) if when leading peak performance number is less than postpeak performance number, the photovoltaic DC-to-AC converter possessing bimodal MPPT controlling functions is only had just can to search the true maximum of photovoltaic array; When on-the-spot shade changes, photovoltaic DC-to-AC converter finds the maximum power point on new P-V curve again according to current working.

7. dynamically bimodal/static MPP of the photovoltaic DC-to-AC converter according to claim 1 or 6 follows the tracks of Efficiency test method, it is characterized in that: arrange photovoltaic array bimodal MPPT testing efficiency P-V curve and specifically comprise and arrange bimodal static MPPT efficiency test P-V curve and bimodal dynamic MPPT efficiency test P-V curve.

8. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter according to claim 7 follows the tracks of Efficiency test method, it is characterized in that: when arranging bimodal static MPPT efficiency test P-V curve, the bimodal static MPPT efficiency test P-V curve of photovoltaic array under high irradiance and low irradiance is set respectively, the bimodal static MPPT efficiency eta of photovoltaic DC-to-AC converter _{mPPT, stat}be expressed as:

${\mathrm{\&eta;}}_{\mathrm{MPPT},\mathrm{stat}}=\frac{\underset{i=1}{\overset{z}{\mathrm{\&Sigma;}}}{U}_{\mathrm{DC},i}\&CenterDot;I_{\mathrm{DC},i}\&CenterDot;\mathrm{\&Delta;T}}{P_{\mathrm{MPP},\mathrm{PVS}}\&CenterDot;T_M}$

Wherein, Δ T is the sampling period, is less than photovoltaic DC-to-AC converter MPPT minimum interval; U _{dC, i}for the mean value of input voltage in the sampling period, I _{dC, i}for the mean value of input current in the sampling period, P _{mPP, PVS}for the actual Maximum Power Output value of photovoltaic arrays simulator, z is photovoltaic DC-to-AC converter sampled data points sum, T _mfor detection time, and there is T _m=z × Δ T.

9. dynamically bimodal/static MPP of photovoltaic DC-to-AC converter according to claim 7 follows the tracks of Efficiency test method, it is characterized in that: when arranging bimodal dynamic MPPT efficiency test P-V curve, bimodal dynamic MPPT efficiency test comprises unimodal to bimodal conversion and bimodal extremely unimodal conversion; The bimodal dynamic MPPT efficiency eta of photovoltaic array after the N time test _{mPPTdyn, t}be expressed as:

${\mathrm{\&eta;}}_{\mathrm{MPPTdyn},t}=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_{\mathrm{MPPTdyn},k}$

Wherein, N is testing time sum, η _{mPPTdyn, k}for the bimodal dynamic MPPT efficiency of photovoltaic array in kth time test, it is expressed as:

${\mathrm{\&eta;}}_{\mathrm{MPPTdyn}.k}=\frac{\underset{i=1}{\overset{z}{\mathrm{\&Sigma;}}}{U}_{\mathrm{DC},i}\&CenterDot;I_{\mathrm{DC},i}\&CenterDot;{\mathrm{\&Delta;T}}_i}{\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{P}_{\mathrm{MPP},\mathrm{PVS},j}\&CenterDot;{\mathrm{\&Delta;T}}_j}$

Wherein, U _{dC, i}for the mean value of input voltage in the sampling period, I _{dC, i}for the mean value of input current in the sampling period, Δ T _ifor photovoltaic DC-to-AC converter DC side data sampling period in kth time test, Δ T _jfor the photovoltaic arrays simulator power output cycle in kth time test, P _{mPP, PVS, j}for photovoltaic arrays simulator Maximum Power Output in kth time test, M is photovoltaic arrays simulator sampled data points sum.