Practical Photovoltaic Simulator with a Cross Tackling Control Strategy Based on the First-hand Duty Cycle Processing

Abstract

This paper proposes a methodological scheme for the photovoltaic (PV) simulator design. With the advantages of a digital controller system, linear interpolation is proposed for precise fitting with higher computational efficiency. A novel control strategy that directly tackles two different duty cycles is proposed and implemented to achieve a full-range operation including short circuit (SC) and open circuit (OC) conditions. Systematic design procedures for both hardware and algorithm are explained, and a prototype is built. Experimental results confirm an accurate steady state performance under different load conditions, including SC and OC. This low power apparatus can be adopted for PV education and research with a limited budget.

I. INTRODUCTION

People around the world are confronted with the shortage of conventional energy resources and environmental problems caused by the excessive reliance on fossil fuels. Photovoltaic (PV) systems enable a zero-emission and renewable electricity harvesting method. PV panels gained worldwide acceptance and extensive application because it has a long life-time operation and no moving parts; PV panels are environment-friendly and nearly maintenance-free [1]-[3]. PV modules possess non-linear V-I output characteristics with several factors (e.g. temperature and irradiance), hence interfacing conditioners with maximum power point tracking (MPPT) are required to get energy from PV panels with improved efficiency. A number of MPPT algorithms were studied theoretically and experimentally in the past decade. However, field tests with real PV panels are sometimes unpredictable because of various factors [4], [5]. With a PV simulator that emulates the V-I output characteristic of an actual PV module, testing the PV powered system became repeatable and durable; testing can be conducted at any time and under any weather condition [6].

A PV simulator conceptually consists of a simulating core to produce the V-I characteristic standard value, power amplifying stages, and local controller. In the literature, three main approaches are chosen to design a simulating core. One of the approaches is the use of actual mini PV cells or photo diodes with a controllable illuminant [7]-[9]. Apparently, this method changes the irradiant condition such as partial shading or different sunlight. However, determining the influence of other factors (e.g. temperature) on the output characteristic is difficult and expensive. Another method uses mixed circuits that are patterned after a PV cell [10]-[14]. In the mixed circuit design, output characteristics can manually toggled by triggering functional blocks in the circuits. The digital implementation of the simulating core is becoming popular because it has more high-performance microcontrollers. The V-I output reference value can be directly calculated from the physical equations in the running program. A lookup table can also be made beforehand. Furthermore, the online modification can be achieved using data communication with a computer. In this paper, a DC/DC converter-based PV simulator is designed that enables the customization of the output characteristic of the PV simulator according to the target PV modules and its operation conditions.

Most conventional designs fail to consider short circuit (SC) and open circuit (OC) operation states in the literature, even though SC and OC are two common operation states for PV modules in practical missions. A high-performance PV simulator can work in both SC and OC states. To ensure the ideal working points for a PV simulator under SC and OC cases, a cross tackling control strategy is proposed.

For PV simulator testing, resistive loads are commonly chosen to verify whether the simulator follows the non-linear V-I curve of the real PV modules. Constant current loads are also used [8], [15]. However, most practical MPPT technologies force the voltage of input power source to be constant in steady states [16]-[18]. In this paper, a constant voltage load is used to run the functional test.

Commercially-available PV simulators are expensive because of the high power rating [13]. Affordable PV simulators with a low power rating are also essential for the MPPT algorithm verification with limited budget. The proposed design is useful for some research activities in small laboratories and teaching exercises in schools.

 

II. SYSTEM DESCRIPTION

As shown in Fig. 1, the proposed system is mainly composed of three sections: DC/DC power converter, microcontroller system, and host computer. A synchronous buck topology is used for enhanced efficiency, thus the converter produces voltage ranging from 0 to Vin. The power converter is designed such that the output voltage Vo and inductor current iL follows the V-I curve. The host computer configures a customized curve and computes an array table.

Fig. 1.System structure.

Output voltage, Vo, is identified and used as input to the simulating core. After generating a table look-up, a current reference value Iref is produced according to the V-I curve. The calculation result of the simulating core Iref together with the maximum output voltage of actual PV module (simulation target) Vmax are used as reference values for the current control subsystem and voltage control subsystem, respectively. The output is processed by the crossing tackling control system.

A detailed control strategy will be discussed in Section V. A corresponding duty cycle is calculated by the controller; two complementary PWM signals with a dead-time are generated to drive Q1 and Q2.

 

III. IMPLEMENTATION OF SIMULATING CORE

To follow the actual PV output characteristic, a mathematical model of the PV output characteristic is introduced and an algorithm is presented.

Different mathematical models are proposed to present the non-linear PV characteristic. If the parameters of the PV array are detailed enough, a circuit model is drawn and the output V-I equation is calculated considering environmental factors (e.g. temperature and illumination) [19]. A set of formulas are commonly derived to describe the non-linear V-I characteristic, and this calculation method only requires four parameters [4,20]. Maximum power point voltage (Vmp), maximum power point current (Imp), open circuit voltage (Voc), and short circuit current (Isc) are four available parameters of commercial PV module products. In the proposed design, a 100W PV module is used as the simulation target, and Vmp (18V), Imp (5.55A), Voc (21.6V) and Isc (6.11A) are measured at 25℃ and 1000W/m2 irradiance. With the V-I equation set, a V-I curve under a specific condition (assuming it is under 25 ℃ and 1000W/m2 irradiance) is drawn in Fig. 2. For digital use, array elements that indicate operation points of the curve are calculated from V-I equations using the computer and saved in the microcontroller. Different PV modules or one under different generating conditions are calculated and simulated by digitizing the curve data without exceeding the power rating. Using more data points results in a finer V-I curve. However, it is impractical to save hundreds of elements into the controller to match every practical value of Vo. In this design, a 30-point, two-dimensional table is used with concentrated data near the expected maximum power points.

Fig. 2.V-I curve and piecewise linear interpolation method.

To get the theoretical output reference value Iref from the two-dimensional table with practical voltage Vo, a table lookup method combined with the piecewise linear interpolation is designed. Piecewise interpolation entails curve fitting using different polynomials in various curve segments. Linear polynomials are preferred because of reduced computation load. In the simulating core, the digital value of the output voltage Vo is used as an index for look-up and interpolation calculation. Assuming that the V-I curve in Fig. 2 is divided into five segments by six points (A, B, C, D, S and O)., point A (a, b) and point B (c, d) are two adjacent fixed points. Two possible cases should be discussed. In one case, Vo is equal to a or c, thus the look-up program can directly find the result from the array and corresponding data b or d that indicate the theoretical current reference value will be obtained. Accordingly, the simulator is working at point A or B. In other instances, Vo is equal to x, and Iref should be f. For the linear interpolation method, line segment AB represents curve segment AFB. The equation of line segment AB is

When Vo is x, a mathematical calculation value e is obtained from Equation (1) because point E is the matching point in segment AB. Consequently, Iref is equal to e that is the approximate value of f. After the processing the control, the simulator works at point E instead of the ideal power point F. Apparently, an error exists when piecewise linearization is used for the nonlinear V-I curve. The concentrated data point near the maximum power point reduces the error substantially.

 

IV. SYSTEM DESIGN AND CONTROL STRATEGY

A. Hardware Design

Circuit elements and their values are prepared for a prototype design. As shown in Fig. 1, the power stage of the system is a buck converter with an input voltage Vin of 30V. Input capacitor Cin is used to reduce the input current ripple. For Q1 and Q2, a 500ns dead-time is introduced in the PWM generator to prevent cross conduction. The inductor current IL is always continuous because the negative current is allowed for the synchronous buck. Hence inductor value L is calculated by

Capacitor C is used to smoothen the output voltage by absorbing the current ripple. The LPF formed by L and C is essential for the design, and C is calculated by

The microcontroller system in Fig. 1 mainly consists of a microchip 16-bit digital signal controller (DSC) dsPIC33FJ64GS606 which runs at 40MHz. Linear current sensor ACS711 of Allegro MicroSystems is used to measure IL, and two ADCs of the DSC are configured to measure Vo and IL. The converter operates at a 100 kHz-switching frequency and 20 kHz-sampling frequency. The DC resistance of inductor RL and ESR of output capacitor RESER are also taken into consideration.

The designed system parameters are shown in Table I.

TABLE IPARAMETERS OF THE CIRCUIT ELEMENTS

B. Current Mode Control

Current mode control is a major part of this simulator. It forces the power circuit to produce a controllable current based on the output voltage. To ensure a controllable output current, inductor current control is designed. The converter, current sensor, and ADC are analyzed for control precision.

The inductor current control system block diagram is shown in Fig. 3. In a current control loop, the digital value Iref is generated by the simulating core based on the real-time output voltage Vo. It is compared with the measured inductor current IL. The plant represents the buck converter and Gid(s) is the small signal transfer function between the inductor current and duty cycle in Equation (4).

Fig. 3.Block diagram of the inductor current control system.

In Equation (4), R is the load of the converter and Gid is only changed with load. Short circuit (SC, R=0), maximum power point output (MPP, R=Vmp/Imp), and open circuit (OC, R=∞) are three especial operation states in system operation. However, working under OC state (point O in Fig. 2) is not feasible for current mode control because of the insignificant current. The control mode under OC state will be discussed in detail. Load R is assumed to be 0.01Ω at the SC condition that facilitates the control system analysis. After substituting the values of the circuit parameters, Gid(s) under these two states (SC and MPP) are calculated and bode plots of the transfer function in Equation (4) are shown in Fig. 4(a). A PSPICE simulation is used to verify Equation (4). Taking advantage of AC sweep, the gain from the duty cycle to the inductor current is illustrated in Fig. 4(b).

Fig. 4.Transfer function of Gid. (a) Bode plot of Gid. from Equation (4). (b) Bode plot of Gid. from the simulation.

Hi(s) is the transfer function of the current sensor ACS711. According to the characteristic performance of ACS711, time-domain parameters are calculated. The transfer function with a time delay factor Hi(s) is derived by

The bode plot of current sensor ACS711 is shown in Fig. 5.

Fig. 5.Bode plot of Hi.

Considering both stability and quick response, a Type 3 amplifier is designed. A bode plot of the compensated current system in SC and MPP states are shown in Fig. 6.

Fig. 6.Bode plot of the compensated current control system.

A discrete-time equivalent is obtained using the Tustin method. With the digital current compensator, a stable current control system is obtained. Consequently, the current mode control is capable of operating on both states except in points near the OC state.

C. Cross Tackling Control Strategy

The PV module acts like a constant voltage source in a high-voltage region (e.g. curve segment DO in Fig. 2). In fact, PV output voltage also slightly varies in this region. Fortunately, current mode control still works in this region as long as more dots are used for the table looking-up. Hence, in most cases, the regulated output voltage is generated by an output current control instead of a direct output voltage control. A current mode subsystem is sufficient for a routine simulating state.

However, if the load is significantly light and acts as a constant voltage that is larger than Voc (21.6V for this simulating target), current mode control is not a good choice because error during sampling may destabilize the control effort. A single current mode control cannot guarantee good tracking performance in a light load region. Therefore, an improved control strategy involving the voltage control loop is needed.

The output voltage control subsystem block diagram is shown in Fig. 7. Vmax is a digital value indicating the maximum voltage of the simulation target (Voc). Vmax is the chosen reference value of the voltage loop to keep the output voltage equal to Voc. The plant represents the buck converter, and Gvd(s) is the small signal transfer function between output voltage and duty cycle and is obtained by

Fig. 7.Block diagram of output voltage control system.

R is the load of the converter and Gvd is changed alone with R. The voltage mode control is designed for an OC state or other light load states; hence R=1000 Ω is calculated using Equation (6) for an approximate analysis. Gvd, under light load state (R=1000Ω) is calculated and bode plots of the transfer function Equation (6) are shown in Fig. 8(a). A PSPICE simulation work is performed to verify the model in Equation (6). Taking advantage of the AC sweep, the gain from duty cycle to the inductor current is illustrated in Fig. 8(b).

Fig. 8.Bode plot of Gvd. (a) Bode plot of Gvd from Equation (6). (b) Bode plot of Gvd from the simulation.

A compensator, Cv(s), is designed based on the system characteristic. The bode plot of the compensated voltage control loop at OC is shown in Fig. 9. As a result, the output voltage remains as Voc during the voltage control loop working.

Fig. 9.Bode plot of the compensated voltage control system.

With the current control loop and voltage control loop, a cross tackling control strategy that runs the simulator in every practical load case is proposed. The algorithm that directly deals with the duty cycle is shown on Fig. 10. Variables di and dv are the calculated results of the current control loop and voltage control loop, respectively. Variable d is the final duty cycle that is used by the PWM generator. The converter first handles two output duty cycles, dv and di, and chooses the minimum value for final use. Instead of using a convenient double loop control algorithm, the proposed strategy tackles both voltage mode control and current mode control by choosing a duty cycle. Switching from one mode to the other is sustained, depending on the load state during that particular moment. Conceptually, the output voltage of the buck converter is directly proportional to the duty cycle D based on the equation

Fig. 10.Block diagram of the cross tackling control algorithm.

There is always a fixed duty cycle corresponding to the Voc for a certain PV module. The voltage control loop provides an amplitude restriction for each simulation target.

 

V. EXPERIMENTAL RESULTS

A power source prototype is built based on the methods discussed earlier. An electronic load which was chosen as the load works at a constant voltage mode, and the voltage increases from 0V to 24V with a step size of 0.4V per second. Every operation point of this process is recorded by the oscilloscope, as shown in Fig. 11. The horizontal axis is the output voltage and vertical axis indicates the output current. As the voltage generated by the electronic load changes, the simulator tracks the ideal V-I curve effectively, including the SC and OC points, and a continuous transition is achieved.

Fig. 11.V-I curve with a constant voltage load.

The voltage-power (V-P) curve of the simulator is shown in Fig. 12. The maximum power is achieved at 100W at the MPP condition. Two 0W points are also achieved in the SC and OC points. These results prove that a more practical and ideal I-V curve can be obtained with this simulator control strategy.

Fig. 12.V-P curve with a constant voltage load.

The simulator performance under the SC and OC states are shown in Fig. 13 and Fig. 14. The excellent waveforms are produced under SC and OC. Fig 15 illustrates the transient from the current mode to the voltage mode that works at the OC state. A continuous process is achieved because an increasing duty cycle is applied.

Fig. 13.Waveform of simulator under the SC state.

Fig. 14.Waveform of simulator under the OC state.

Fig. 15.Transition from the current mode to voltage mode.

 

VI. CONCLUSIONS

A digital PV simulator is proposed and the design procedure is described in this paper. The interpolation method is introduced for the inner curve fitting of the simulating core instead of the single table lookup method. A prototype is built based on the control system analysis. A cross tackling control strategy that depends on both current control loop and voltage control loop is proposed for every operation state, including two extreme working states (OC and SC).

Experimental results illustrate minimal difference between the ideal PV and the simulated output characteristic. Constant current during SC and constant voltage during OC are successfully achieved.

PV simulators are useful apparatuses with the development of the PV industry. More reliable, available, and effective products are in demand. With a novel design scheme, this simulator proven to be suitable for teaching and laboratory research applications.