Simple and Fast Dynamic Photovoltaic Emulator based on a Physical Equivalent PV-cell Model

Photovoltaic emulators are a speciﬁc type of power electronics system to mimic the behaviour of a photovoltaic (PV) panel or array and facilitate the testing of energy systems. Existing solutions usually require sophisticated hardware design and fast computing. This paper presents a simple, reliable, and effective circuit-based photovoltaic (PV) emulator based on the equivalent PV stacked cells. The PV emulator can be used for solar system testing and analysis, such as maximum power point tracking (MPPT) and partial shading effect. The I – V and P – V characteristic curves of the emulator have been generated by using an LTspice simulator. It is experimentally investigated and compared with a real PV panel and existing emulator products. The experiment results show good agreement with the mimicked actual PV panel. The proposed PV emulator shows a better dynamic response and shorter settling time than several benchmarked commercial products. The enhancement in the time response is due to the simplicity of the emulator, where a few power diodes and some resisters are used. In addition to simplicity, the PV emulator is very cost-effective.


INTRODUCTION
Recently, owing to the increase in energy demand, environmental issues and scarcity of traditional energy sources, the world is moving towards using renewable energy sources such as wind energy and solar power. Power electronic systems are the enabling technology to interface with these sources and integrate them into the electricity grid. To facilitate the testing of these power electronic systems, energy emulators based on the power electronics system are developed. Solar photovoltaic (PV) emulators have been useful for indoor testing to provide a convenient tool to develop solar PV power systems and related products.
The PV emulator is used to produce the non-linear electrical characteristics of PV cells or panels [1,2]. The majority of the reported PV emulators use a power supply, either a switching power converter or a linear regulator. Many studies have been done in the literature on PV source emulators, most of them are based on the switched-mode power supply (SMPS) because SMPS is more effective than a linear regulator [3,4]. In [1], the authors used a two-switch non-inverting buckboost DC/DC converter topology as a PV emulator to mimic the real PV behaviour. The key idea is to use multiple linear equations to perform curve fitting of the actual I -V curve. The authors in [2] proposed a boost-buck DC/DC converter with dual-loop proportional-integral (PI) current control to mimic the PV system characteristic of series and parallel combinations and under dynamic operating conditions. The authors in [5] proposed a PV emulator by using a microcontroller and switched-mode buck DC/DC converter. A feedback compensator is designed in order to improve the speed response, and system stability, also to reduce the steady-state error. The proposed controller has been experimentally verified for a 115 W solar panel (Shell S115). In [4], a DC/DC push-pull forward (PPF) converter topology is used as a PV simulator. The feedback Takagi-Sugeno fuzzy PI controller based on the MATLAB/Simulink interface is used to achieve an acceptable dynamic and steady-state performance. The DC/DC buck converter based on the two-stage LC filter is proposed in [6] to extend the control bandwidth of the PV emulator. Nevertheless, the dynamic responses of these converter-based PV emulators with better control are still significantly slower than the real PV panel. Empirical model-based emulators with the assistance of more advanced and expensive digital controllers have also been introduced in [7] and [8]. The reconfigurable simulator for checking the partial shading effect was provided in [9]. The dual-mode controller was also introduced in [2,10], which works in both the current source and voltage source regions. However, it needs additional electronic hardware in addition to the basic converter and associated circuitry.
The authors in [11], proposed a low-cost PV emulator. It is used to test the maximum power point tracking (MPPT) for a PV system. However, it has an inaccurate P-V and I-V characteristic curves. PV emulators in the market are generally costly due to complex hardware design and implementation costs to reach high level of accuracy, mimic different environmental conditions, high power level and high efficiency [12]. Many MPPT techniques have been reported in recent years, such as fraction open-circuit voltage (FOC), hill climbing (HC), fraction shortcircuit current (FSC), perturb and observe (P&O), incremental conductance (InC), feedback voltage/current, and current sweep [13][14][15].
Based on the previous literature review, the PV emulator is even very hard to implement and required a high-performance controller or simple structure with inaccurate performance and slow dynamic response. Therefore, a simple structure based on a physical PV-cell model is used in this study. Since the electro-thermal property of the diode is similar to the PV cell, the PV emulators based on this type of circuit achieve better performance, both in the steady state and transient state. The authors in [16] have briefly described the aforementioned method; however, it is unclear how the diode string is designed to mimic the electrical characteristics of a commercial PV panel. In addition, the dynamic response, partial shading condition, and the electro-thermal property of the circuit have not been studied.
Here, first, a PV emulator using the physical PV-cell model has been built based on the key design equations. In addition to the work presented in [16], the thermal issue related to the diode string has been investigated and solved by adding a cooling system (variable speed fan). Second, the study includes investigating the effects of the partial shading (PS) of series combinations of PV cells and compare their maximum power points (MPPs). A boost DC/DC converter loaded with a perturbing and observe (P&O) algorithm is used to evaluate the proposed PV emulator platform [15,17]. The performance of the proposed emulator is also compared with a commercial 10 W PV panel and several commercial PV emulator products.
This work is organized as follows: The photovoltaic mathematical model and equivalent circuit design based on a one-diode photovoltaic representation are presented in Section 2. Section 3 illustrates and discusses the simulation and experimental results. Finally, Section 4 concludes the paper.

PHOTOVOLTAIC MATHEMATICAL MODEL AND EQUIVALENT CIRCUIT DESIGN BASED ON A ONE-DIODE PHOTOVOLTAIC REPRESENTATION
For the sake of simplicity and acceptable accuracy, the onediode PV model, as shown in Figure 1 [18,19] is used in this paper. The PV model is built by using DC current source, diode, series resistance (R s ), and parallel resistance (R p ). The DC current source I ph is used to represent the cell photo-current generated by the PV cell. I ph is a function of both solar radiation and cell temperature. The series resistance (R s ) is used to represent the total of several structural and contact resistance of the PV model. Last, the equivalent parallel resistance (R p ) is used to present the leakage current during the p-n junction that depends on the fabrication technology of the PV cell itself.
The mathematical representation for the series-connected PV cells shown in Figure 2 shows can be derived as follows [15,20]: where V d is the forward diode voltage (V), and I d is the diode forward current (A).
where I pv is the output current of PV (A). I ph and I o are the photovoltaic and saturation currents of the PV array, respectively. V pv is the output voltage of PV (V). V t is the thermal voltage of the PV system with several cells connected in series. R seq is the equivalent series resistance (Ω), and R peq is the equivalent parallel resistance (Ω). a is the diode ideality factor.
where K is the Boltzmann constant, and it is equal to . T is the actual temperature of the pn junction (Kelvin). q is the electron charge and it is equal to 1.60217646 × 10 − 19 C. N is the number of cells connected in series to increase the output voltage of the PV panel.
Here, a p-n junction power diode, resistors, and a constant current source are used to build a simple PV panel emulator as an equivalent physical PV cell/panel model, as shown in Figure 2. I ph of the PV emulator is represented by using a DC voltage source which operates at constant current mode. In order to clarify the proposed circuit clearly, Equation (1) is presented graphically in Figure 3.
In general, the manufacturers of PV panels supply limited information about electrical and thermal behaviour at the standard test conditions (STC). Usually, the photovoltaic datasheet contains details about the open-circuit voltage (V oc ), shortcircuit current (I sc ), the current and voltage at MPP (I mpp and V mpp ) [21]. This paper uses the datasheet of commercially available PV panel to work out the circuit parameters for the emula- The characteristic I -V curve of the photovoltaic cell. The net cell current I pv is composed of the light-generated current I ph , I Rpeq , and the diode current I d tor. By using three operating points, namely, short circuit, MPP, and open circuit, we are able to develop the model with four boundary conditions [22]. However, mathematically it is not sufficient to find the values of the five parameters of the PV emulator (R seq , R peq , N , I Ph , and diode ideality factor a) based on the four boundary conditions.
According to the semiconductor material used to fabricate diodes, the ideality factor is between 1 and 2 [22,23]. The diode ideality factor is estimated to be 1.85, according to the diode datasheet (1n5400) and (V oc -I sc ) curve method [24]. By using boundary conditions, the following equations can be produced [25].
By considering the value at short-circuit operation condition and substitute the value of the voltage and current (0, I sc ) , Equation (3) can be express as (5).
By substituting the voltage and current values at open-circuit condition (V oc , 0) in Equation (3), it can be re-written as: By considering the value at MPP operation condition and substitute the value of the voltage and current (V mpp , I mpp ), Equation (3) can be express as (7).
The derivative of (7) with respect to V mp at MPP is given by: Equation (8) can be simplified to find the values of the four parameters, as shown below: where N is the number of diodes required to build a PV emulator. where: and W −1 is the negative branch of the lambert W function.

Experimental circuit setup
In this study, the Powertech PV panel (ZM9054) is selected as the reference PV panel to be mimicked. The PV emulator consists of a DC voltage source (operating at constant current mode), a diode string, and two of the electrical resistance, as shown in Figure 2. The PV emulator components, such as R s , R p , N , and I ph , are selected based on MATLAB calculation of the mentioned mathematical equation of the real PV panel. The design component values are shown in Table 1. Equations (9), (10), (15), and (16) are used to calculate parameters required to build the emulator circuit. A selected power diode (1n5400), with reverse saturation current (5 × 10 −6 ), is used with I sc , V oc , I mp , and V mp values from the commercial datasheet, as shown in Table 2.
The number of power diodes (N) needed to mimic the real PV panel is different from one PV panel to another, and it can be calculated by using (9). The number of diodes for the proposed PV emulator is found below by considering the maximum operating temperature of the selected diode, which is equal to 150 • C based on its datasheet.

Steady-state response
The experiment results agree with the simulation results, as shown in Figure 5. Figure

Thermal behaviour based on cooling system
In order to evaluate the impact of using a variable speed cooling system (12 VDC 0.24 A 3 pin cooling fan PVA092G12M), the different speed scenarios starting from 0 up to full speed have been used. The fan speed is controlled by using a simple switching circuit and variable duty cycle.
Figure the thermal behaviour and the issues associated with using a single diode model to mimic the PV panel. The x-axis presents the duty cycle that controls the speed of the fan, where the y-axis shows the output resistive load connected with the PV emulator. In Figure 7, when moving from the left-to righthand side, the speed of the fan is increasing by increasing the duty cycle. When moving from bottom to top, the resistive load is increasing up to the point that the emulator reaches opencircuit operating condition. A thermal imaging camera (FLIR TG 167) is used to capture the temperature change once the current increases.
It is notable from the figure that the diode string temperature increases from 29.2 to 98.3 • C, without any cooling system (first column on the left). After that, the cooling system (fan) used at duty cycle D = 0.25, the diode string temperature increases from 29 to 85.5 • C. At D= 0.5, the diode string temperature increases from 28.1 to 76.5 • C. At D = 0.75, the diode string temperature increases from 27.2 to 68.9 • C, and finally, at D = 1.0, the diode string temperature increases from 26.4 to 56.7 • C. The cooling system is used to keep the diode string temperature at an acceptable value to minimize the high-temperature effects on the PV emulator characteristics.

Partial shading response
The series connection of the two groups of diode string by using a bypass diode to mimic the electric characteristic of the PV cell under PS condition is shown in Figure 8. Each diode string has its own current source (irradiation level), and the two current sources have different values. The first current source value is based on the current of the real PV panel under a certain irradiation level, where the other current source is based on the value of the generated current of the actual PV panel after partial shading. Figures 9 and 10 show a comparison between the I -V and P-V characteristic curves based on experiment and simulation results for the real PV panel, proposed PV emulator, and LTspice simulation under PS effect, respectively. It is clear from Figure 9 that the real PV panel will have two MPPs under partial shading conditions, that is, local value (6.7380 W) and global value (7.8721 W). Another shading scenario (irradiation level 760 W ∕m 2 at 27 • C) is shown in Figure 10. It is clear from the two figures that the proposed PV emulator mimics the real PV panel perfectly even under partial shading effect.

MPPT test using a boost DC/DC converter
In this section, another experimental work has been conducted to test and validate the proposed PV emulator during the dynamic MPPT test. Figure 11  A boost DC/DC converter with a P&O algorithm is used to test the proposed PV emulator. The experimental setup is shown in Figure 12. Figure 13 shows the performance of the proposed PV emulator during MPPT test. The top waveform presents the output voltage of the PVE side, followed by the output voltage of the boost converter side, followed by the output power, then the current of the PVE side. It is clear from the figure that the performance of the proposed PV emulator is not effected by the used MPPT system. On the other hand, the tracking system is able to track the MPPs, where the tracked current and voltage match with the one in Figure 11 at the same irradiation levels.

Dynamic characteristics
In Figure 14, the comparison of the dynamic behaviour between Powertech PV panel (ZM9054), PV emulator based on diode   Figure 14b, the PV emulator dynamic response lags around 3 ms with respect to the real Powertech PV panel (ZM9054). In addition, the programmable PV emulator (PPVE, model: EA-PSI 9360-15 2U) lags around 120 ms with respect to the real Powertech PV panel (ZM9054), as shown in Figure 14a. The PV emulator based on the diode string is simple, but it is very effective, and it has fast dynamic behaviour compare to both real PV panel and commercial PV emulator. The dynamic response of the proposed PV emulator also compared with some of the existing PV emulator platforms, as shown in Table 3. The proposed emulator shows the best response time compare with the existing solutions.

CONCLUSION
This paper presents a simple and cost-effective method to develop a PV emulator that can mimic a real PV panel by using a few power diodes and some resistors. The main problem of this design is the increase of diode string temperature, specifically at the open-circuit condition (i.e. maximum power dissipation), where the diode string temperature increases from 29.2 to 98.3 • C without any cooling system. This problem has been solved by adding a variable speed fan. The electro-thermal performances of series-connected PV cells have been studied. LTspice simulation program is used to build the electrical model of the solar panel. In addition to simulation work, a thermal camera is used to investigate and capture the effect of temperature on the diode string. The proposed PV emulator shows high performance, where the generated power was identical with a real PV panel and a commercial PV emulator. Furthermore, the dynamic response of the proposed PV emulator shows improvement by 117 ms compared to the commercial PV emulator device. To sum up, the proposed emulator has been tested by using one of the well-known MPPT methods (P&O), where the result was closed to the result when the real PV panel is used.