Design a photovoltaic simulator system based on two-diode model with linear interpolation method

Received Jul 4, 2021 Revised Mar 2, 2022 Accepted Mar 28, 2021 For an effective study of photovoltaic (PV) systems, precise current-voltage (I-V), power – voltage (P-V) curves of photovoltaic modules are required. However, conducting experiment on real panels faces with many difficulties such as needing large space, high cost, objective conditions of the environment. Therefore, it is essential to research an emulator producing the I-V, P-V characteristics of a PV system the same as those conducted on a real PV panel. This paper presents a two–diode model simulation replacing a photovoltaic panel to export precise current-voltage (I-V), power – voltage (P-V) curves based on the linear interpolation method. The proposed simulator shows many advantages of subjecting to changes in radiation and temperature. The accuracy of the emulator has been not only verified by the simulation results on Matlab software, but also evaluated, compared with the experiment model. The simulation results have coincided with the experimental ones, the output error of less than 4% is shown in the experiment.


INTRODUCTION
In recent years, with the rapid depletion of fossil energy sources, serious environment pollution, exploiting alternative energy sources is getting a knotting issue to draw much attention from researchers [1]- [4]. Among renewable energy sources, solar energy plays an important role in the global sustainable energy source growth [5]- [9], especially, in countries with lots of sunshine like Vietnam. Solar energy can be used as an alternative energy source for electrical one without destroying the environment, little maintenance. However, applying the solar energy in practice has some disadvantage, for examples, performance of PV cell is low, the precision of the photovoltaic (PV) model is not high. Particularly, the accurate PV cell modeling helps significally to analyze PV system performance [9]. There are many models that have been introduced, such as single diode model including a current source in parallel to a diode which is simple but serious disadvantage when the temperature is various [10], and another model -dual diode model owning better accuracy at low irradiance levels which makes it easier for a more accurate prediction of PV system performance [11]. Therefore, to model the correct PV is mainly based on the correct determination of the parameters of the panels. In addition, the parameter identification is very necessary for simulating, evaluating performance [12], [13]. In addition, it has implications for application design in manufacturing and monitoring maximum  [14]- [20]. Since the importance of determining PV parameters is receiving increasing attention, a lot of research has been done to develop viable and practical methods to address this problem.
There are many proposed methods of determining the parameters of PV such as analytical methods using a series of complex mathematical equations to derive the parameters of PV [14], [21], [22]. However, these methods also reveal disadvantages such as large computational volume, complex calculations, requiring large computation time, especially when designing a real simulator model must have a microcontroller with extremely fast computational speed and processing time, which results in very expensive design costs [23]. This paper proposes to use the linear interpolation method on the basis of utilizing a DC-DC converter to output the signal to simulate characteristics of I-V, P-V in combination with communication, with the computer for the photovoltaic panel property simulator.

PV EMULATOR DESIGN 2.1. A dual-diode model of PV cell and I-V, P-V characteristic plot
Because the I-V, P-V characteristics of the diode match the I-V, P-V characteristics of PV cell module, the PV model is often based on the diode model. There are three PV cell models: Single diode model (SDM) [10], dual diode model (DDM) [22], and triple diode model (TDM) [23], [24]. SDM has simple control structure, low circuit cost, but I-V characteristic curve is less accurate, lack of stable performance under partial shading conditions, unstable to the low radiation region. DDM owns curve accuracy is higher; satisfactory performance under standard test conditions; implements hardware easily, but slightly high complexity and implementation cost. While TMD has got the highest I-V curve's accuracy, but modelling is quite complexity, the execution time is longest; implementing the hardware complicatedly. Therefore, the paper focuses on exploiting the dual diode model. The photovoltaic equivalent circuit in the dual diode model is characterized by an equivalent scheme as shown in Figure 1 consisting of a current source, two diodes, two resistors consisting of Rs and Rp. Rs is the equivalent series resistance of the PV array and Rp is the equivalent parallel resistance.  Figure 1 is calculated as follow [25]- [27]: Where: Plotting the I-V curve needs dealing with (1), but some unknown parameters , 01 , 02 , , require to be specified from equations: Convergence is achieved when Rs i+1 ≈ Rs i with an acceptable degree of error, and Rp is calculated as (8). Detecting

I-V curve linearization
In part 2.1, I-V, P-V characteristic curves of photovoltaic module have been plotted, but these curves are nonlinear owing to their highly dependent on T temperature and G solar radiation. Therefore, the practical implementation will be very complex because a number of points are very enormous, the memory of microcontroller is limited. To solve the above problems, the linear interpolation method is used by taking some special points shown in Figure 3 to design the controller for the power converter system in Figure 4. By implementing this method, the system uses less memory and doesn't spend much time searching for active points, but still ensures the accuracy of the system.
In Figure 3, the I-V curve can be analyzed into three regions: region A, region B and region C in which region B is the strong nonlinear region [29]. The linear interpolation method applied here to linearize the I-V curve is based on the segmentation principle. This method divides I-V curve into four linear intervals. Where:

THE PROPOSED SIMULATOR TOPOLOGY
To verify the correctness of the theoretical studies, in this section, the PV simulator model designed consists of 3 main parts [30] the first part is the PV model; the second part of the PV emulator is the control strategy; the third one of the PV emulator is power converter system, which shown in Figure 4. To control the photoelectric simulation system, using Atmega328p microcontroller has function of outputting control pulse with frequency of 50 kHz to Buck DC-DC converter and measuring the signal transmitted from the current sensor. Buck converter creates current characteristic, corresponding to load. Load uses a variable resistor to characterize the load. a microcontroller whose function is to measure output values of voltage or current, then calculate and give appropriate control signals for the DC-DC converter and communicate with computer to receive input parameters and output data as required by simulation system.

SIMULATION AND EXPERIMENT RESULTS
In order to verify theoretical research results, the experimental test bench of PV emulator system is demonstrated in Figure 5. In Figure 5(a) are devices used to build up the system, including PC, control board, display screen of current, voltage and load R. In Figure 5(b) is a detailed picture of the control board comprising of the pulse generator control circuit and the dc-dc converter . The system to conduct the  simulation test for the MSX60 solar arrays elected with the rating table from the manufacturer is shown in  Table 1.
From the parameters of MSX60 panels given by the manufacturer in Table 1, simulations on matlab software with the modeling of PV panel by double diode model have obtained I-V, P-V characteristic curves shown in Figures 6 and 7. When changing the temperature (250 ℃, 350 ℃, 450 ℃, 550 ℃, 650 ℃) and keeping the radiation constant (G=1000W/m 2 ), the I-V and P-V characteristic curves of the panel have demonstrated in Figure 6, and changing radiation characteristics: 100 W/m 2 , 200 W/m2, 300 W /m 2 , 400 W/m 2 , 500 W/m 2 , 600 W/m 2 , 700 W/m 2 , 800 W/m 2 , 1000 W/m 2 , keeping the temperature at 300 ℃, the I-V and P-V characteristic curves of the panel have demonstrated in Figure 7.  When connecting to the hardware to sample and change the loads by changing the variable resistor, we get the corresponding working points. The transmitted data is processed by the software and represented by pink points running on the I-V, P-V characteristics of the photovoltaic panel. The actual measured values of current I and voltage V of the resistive load R indicate that the working points in pink lie on the I-V, P-V characteristic curves of the simulated MSX60 panel shown Figures 8 and 9. The working points closely track the real curves, which proves that the simulator has accurately simulated the characteristics of real PV panels.

CONCLUSION
In the paper, a simulator is designed to simulate the I-V, P-V characteristics of PV panels. This study not only proposes a mathematical model of PV based on a double-diode model with high accuracy under low radiation conditions, but also designs a controller that applies linear interpolation method to control the Buck converter to output I -V, P-V characteristics like the output of the actual photovoltaic panel, and can communicate, control and analyze by software installed on the computer. The accuracy of the proposed system has been evaluated and compared with the actual data from the photovoltaic panel manufacturer MSX-60 with the output error ranging from 1 to 4% shown in the experiment. On the other hand, the simulator can adjust quickly and accurately, and can self-adjust by the I-V curve of the photovoltaic panels closely the actual conditions: radiation and temperature based on the capability of controller reprogrammable so that characteristic simulation can be applied to many different photovoltaic panels on the market today.