Description of the dynamics of work of amorphous photovoltaic panels using process models

Abstract

The work investigates the dynamic parameters of an amorphous photovoltaic panel. The models were determined on the basis of actual meteorological data from the photovoltaic research stand located at the Institute of Mechanical Engineering at Warsaw University of Life Sciences. Models were developed using System Identification Toolbox (Matlab&Simulink Software). Presentation of the dynamic parameters was given by graphs of step responses and frequency characteristics. The results show that more complex model analyzes with the highest fit should be performed and the model structure changed.

Keywords

• 1 Photovoltaic panel
• system identification
• dynamic parameters
• process model

1. Introduction

2. Materials and methods

Research object and research method were presented in that paragraph. The main purpose of the study is identification of amorphous photovoltaic module dynamic properties. The result of those study could be implemented in the proper developing of control algorithm for photovoltaic system. 2.1.

Research object

For research purposes in this work, photovoltaic panels were used. The test stand, presented in Figure 1, is located at the Warsaw University of Life Sciences, at the Institute of Mechanical

Engineering. Also, the institute has its own meteorological station.

The subject of the research was the amorphous photovoltaic (PV) panel SCG62-HV-L, produced by the German manufacturer Sulfurcell. The PV panels are IEC certified; their parameters were described in Table 1. The unit power of the panel is 62,5 Wp. One panel was on the following structure (U2) and the second one was horizontally mounted on the ground (U4). 2.2.

Research method

To develop the model, the measurement of voltage [V] on the analyzed panel and the measurement of the irradiance [W/m2] were used. Measurement data were recorded every 15 seconds. The created xls files with daily measurements were input and output signals for the analyzed model. The Kipp & Zonen CM3 model pyranometer was used to measure the irradiance. The analyzed model is a singleinput single-output (SISO) model [ 8, 9 ]. The structure of the model is shown in Figure 2.

Irradiance

SISO model G(s)

Voltage

Based on the object identification in the Matlab & Simulink System Identification Toolbox, process models were developed [ 10-14 ]. The structure of a process model is a simple continuous-time transfer function that describes linear system dynamics in terms of one or more of the following elements:  gain factor k,  one or more time constants Ts,  possible time of delay Td before the system output responds to the input (dead time),  possible enforced integration [ 12 ].

The following model structure is a first-order continuous-time process model, where k is the static gain, Ts is a time constant, and Td is the input-to-output delay [ 12 ]: (s) =

∙ (s) = =

After verifying the fit of the models by mean square error (MSE higher than 80 %), the transfer function was obtained in the form:

Based on the obtained transfer function, the step and frequency characteristics of the analyzed amorphous panel were plotted. For step characteristics the following dynamic parameters were determined:  Gain factor k,  Time constant Ts,  Time of delay (if applicable) Td.

For frequency characteristics the following dynamic parameters were determined:

 Cut-off frequency ω0,  Period of signal change T.

The database contains measurements from several years. The most suitable models were selected for the article. In the following paragraphs the results for five days, 26/09/2019, 11/11/2019, 15/11/2019, 01/12/2019 and 07/12/2019, were described.

3. Results and discussion 3.1. Photovoltaic panel U2

Taking into account the day of 11/11/2019, the transfer function of subsequent models of the amorphous panel has the form:

The step characteristics of the model is inertial (Figure 3). When analyzing the frequency characteristics (Figure 4), the cut-off frequency (ω0) of the model at P1 was 2.2688 Hz, which corresponds to the period of signal change T was 0.441 sec, for P1DZ ω0=0.1167 and T=8.569sec, for P1Z ω0=0.5795 and T=1.726 sec. These are definitely too low values taking into account the nature of the work of the amorphous photovoltaic panel.

∗ 1 = .

∗

. ∗ , ∗ ,

The step characteristics of the model is also inertial (Figure 5). When analyzing the frequency characteristics (Figure 6), the cut-off frequency (ω0) of the model P1 was 26.9884 Hz, which corresponds to the period of signal change T equal to 0.037sec, for P1D ω0= 0.163, T=0.163 sec, for P2DZ ω0=379.74, T=0.0026 sec, for P3DZ ω0=0.0605, T=16.53 sec, for P2Z ω0=0.0705, T=14.184 sec. . ∗

. ∗ 3 / = , ∗ , . ∗ ∗ ,

The step characteristics of the model is also inertial (Figure 7). When analyzing the frequency characteristics (Figure 8), the cut-off frequency (ω0) of the model P2DZ15/11 was 0.109 Hz, which corresponds to the period of signal change T equal to 9.17 sec, for P2Z1/12 ω0=0.2595, T=3.85 sec, for P3Z1/12 ω0=9.8104, T=0.102 sec, for P2DZ7/12 ω0=0.176, T=5.682 sec, for P3Z7/12 ω0=22.9744, T=0.044 sec.

3.2. Photovoltaic panel U4

Taking into account the days 15/11/2019, 01/12/2019 and 07/12/2019, the transfer function of subsequent models of the amorphous panel has the form: (11) (12) (13) (14) (15) (16) 3.3.

Photovoltaic panel U2 and U4 dynamic parameters description Based on the step characteristics determined from the transfer function, the dynamic characteristics of the analyzed photovoltaic panels are described in the Table 2 and Table 3. 2.02 0.11 4.14 0.559

4. Conclusions

This report presents one of several examples of tests that have been carried out. The study shows that the process models, developed with the Matlab & Simulink System Identification Toolbox, made mostly really have high fits – over 80%. Most step characteristics of analyzed photovoltaic panels are an inertial type. There are different results for both panels on the following structure (U2) and for that horizontally mounted on the ground (U4). Both, the formulas of transfer functions and the dynamic parameters, are different.

For panel U2 the maximum value of Ts is 50.5 sec. For panel U2 the maximum value of Ts is about 9 sec. Time of the delay Td is short for two days in U2 panel modeling. For U4 panel modeling the time of delay is equal to 0. The reaction of the voltage of the photovoltaic panel to changes in the irradiance is really fast. The models analyzed in the paper and their detailed results seems to support this conclusion.

However, the parameters of the models, i.e. gain factor, time constant, cut-off frequency, do not best reflect the dynamics of the analyzed photovoltaic panels, as the common sources indicate [ 15 ]. Ultimately, it can be concluded that more complex analyzes of the models with the highest fit should be performed and the model structure should be changed, e.g. by adding another input or output parameter.

5. Acknowledgements

The article was written with the support of Polish National Agency for Academic Exchange (contract number PPN/BUA/2019/1/00179/U/00001).

6. References

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