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 fullrange 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 zeroemission and renewable electricity harvesting method. PV panels gained worldwide acceptance and extensive application because it has a long lifetime operation and no moving parts; PV panels are environmentfriendly and nearly maintenancefree
[1]

[3]
. PV modules possess nonlinear VI 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 VI 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 VI 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 highperformance microcontrollers. The VI 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 converterbased 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 highperformance 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 nonlinear VI 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.
Commerciallyavailable 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
V_{in}
. The power converter is designed such that the output voltage
V_{o}
and inductor current
i_{L}
follows the VI curve. The host computer configures a customized curve and computes an array table.
System structure.
Output voltage,
V_{o}
, is identified and used as input to the simulating core. After generating a table lookup, a current reference value
I_{ref}
is produced according to the VI curve. The calculation result of the simulating core
I_{ref}
together with the maximum output voltage of actual PV module (simulation target)
V_{max}
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 deadtime 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 nonlinear PV characteristic. If the parameters of the PV array are detailed enough, a circuit model is drawn and the output VI equation is calculated considering environmental factors (e.g. temperature and illumination)
[19]
. A set of formulas are commonly derived to describe the nonlinear VI characteristic, and this calculation method only requires four parameters
[4
,
20]
. Maximum power point voltage (
V_{mp}
), maximum power point current (
I_{mp}
), open circuit voltage (
V_{oc}
), and short circuit current (
I_{sc}
) are four available parameters of commercial PV module products. In the proposed design, a 100W PV module is used as the simulation target, and
V_{mp}
(18V),
I_{mp}
(5.55A),
V_{oc}
(21.6V) and
I_{sc}
(6.11A) are measured at 25℃ and 1000W/m
^{2}
irradiance. With the VI equation set, a VI curve under a specific condition (assuming it is under 25 ℃ and 1000W/m
^{2}
irradiance) is drawn in
Fig. 2
. For digital use, array elements that indicate operation points of the curve are calculated from VI 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 VI curve. However, it is impractical to save hundreds of elements into the controller to match every practical value of
V_{o}
. In this design, a 30point, twodimensional table is used with concentrated data near the expected maximum power points.
VI curve and piecewise linear interpolation method.
To get the theoretical output reference value
I_{ref}
from the twodimensional table with practical voltage
V_{o}
, 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
V_{o}
is used as an index for lookup and interpolation calculation. Assuming that the VI 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,
V_{o}
is equal to
a
or
c
, thus the lookup 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,
V_{o}
is equal to
x
, and
I_{ref}
should be
f
. For the linear interpolation method, line segment AB represents curve segment AFB. The equation of line segment AB is
When
V_{o}
is
x
, a mathematical calculation value
e
is obtained from Equation (1) because point E is the matching point in segment AB. Consequently,
I_{ref}
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 VI 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
V_{in}
of 30V. Input capacitor
C_{in}
is used to reduce the input current ripple. For Q1 and Q2, a 500ns deadtime is introduced in the PWM generator to prevent cross conduction. The inductor current
I_{L}
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 16bit digital signal controller (DSC) dsPIC33FJ64GS606 which runs at 40MHz. Linear current sensor ACS711 of Allegro MicroSystems is used to measure
I_{L}
, and two ADCs of the DSC are configured to measure
V_{o}
and
I_{L}
. The converter operates at a 100 kHzswitching frequency and 20 kHzsampling frequency. The DC resistance of inductor
R_{L}
and ESR of output capacitor
R_{ESER}
are also taken into consideration.
The designed system parameters are shown in
Table I
.
PARAMETERS OF THE CIRCUIT ELEMENTS
PARAMETERS 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
I_{ref}
is generated by the simulating core based on the realtime output voltage
V_{o}
. It is compared with the measured inductor current
I_{L}
. The plant represents the buck converter and
G_{id}(s)
is the small signal transfer function between the inductor current and duty cycle in Equation (4).
Block diagram of the inductor current control system.
In Equation (4),
R
is the load of the converter and
G_{id}
is only changed with load. Short circuit (SC,
R
=0), maximum power point output (MPP,
R
=
V_{mp}
/
I_{mp}
), 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,
G_{id}(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).
Transfer function of G_{id}. (a) Bode plot of G_{id}. from Equation (4). (b) Bode plot of G_{id}. from the simulation.
H_{i}
(
s
) is the transfer function of the current sensor ACS711. According to the characteristic performance of ACS711, timedomain parameters are calculated. The transfer function with a time delay factor
H_{i}
(
s
) is derived by
The bode plot of current sensor ACS711 is shown in
Fig. 5
.
Bode plot of H_{i}.
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
.
Bode plot of the compensated current control system.
A discretetime 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 highvoltage 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 lookingup. 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
V_{oc}
(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
.
V_{max}
is a digital value indicating the maximum voltage of the simulation target (
V_{oc}
).
V_{max}
is the chosen reference value of the voltage loop to keep the output voltage equal to
V_{oc}
. The plant represents the buck converter, and
G_{vd}
(
s
) is the small signal transfer function between output voltage and duty cycle and is obtained by
Block diagram of output voltage control system.
R
is the load of the converter and
G_{vd}
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.
G_{vd}
, 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).
Bode plot of G_{vd}. (a) Bode plot of G_{vd} from Equation (6). (b) Bode plot of G_{vd} from the simulation.
A compensator,
C_{v}
(
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
V_{oc}
during the voltage control loop working.
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
d_{i}
and
d_{v}
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,
d_{v}
and
d_{i}
, 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
Block diagram of the cross tackling control algorithm.
There is always a fixed duty cycle corresponding to the
V_{oc}
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 VI curve effectively, including the SC and OC points, and a continuous transition is achieved.
VI curve with a constant voltage load.
The voltagepower (VP) 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 IV curve can be obtained with this simulator control strategy.
VP 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.
Waveform of simulator under the SC state.
Waveform of simulator under the OC state.
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.
Acknowledgements
This work is sponsored by the National Natural Science Foundation of China (grant number 51207135), Jiangsu Natural Science Foundation (grant number BK2012266), and YZUYangzhou City Joint Fund (grant number 201203810) , CSC No. 201409300007.
BIO
Shuren Wang was born in Yantai, China, in 1990. He received his BSEE degree from the School of Energy and Power Engineering, Yangzhou University, Yangzhou, China in 2013. He is currently working on his M.S. degree in Electrical Engineering at Yangzhou University. He is engaged in research on power electronics and control, including electronic load, DC/DC converters, matrix converters, and the application of power electronics in renewable energy systems. DC motor control is also one of his interests.
Wei Jiang was born in Yangzhou, China, in 1980. He received his B.S. degree from Southwest Jiaotong University, Chengdu, China, in 2003, and M.S. and Ph.D. degrees in Electrical Engineering from the University of Texas at Arlington, Texas, Arlington in 2006 and 2009, respectively. From 2007 to 2008, he worked in EF Technologies L.L.C. as a senior design engineer. In 2010, he joined Yangzhou University as a lecturer and founded Smart Energy Laboratory, where he is an associate professor. Currently, he is on sabbatical leave in the University of Strathclyde, Glasgow, UK, as a visiting professor. His current research interests include digitalized power conditioning to renewable energy and energy storage devices and microscopic analysis of electromechanical energy conversion.
Zhengyu Lin was born in China in 1976. He received his B.Sc. and M.Sc. degrees from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 1998 and 2001, respectively, and t Ph.D. degree from HeriotWatt University, Edinburgh, UK in 2005. He is currently a Lecturer with Electrical, Electronic and Power Engineering, Aston University, Birmingham, UK. He was a Research Associate at the University of Sheffield, Sheffield, UK, from 2004 to 2006, R&D Engineer in Emerson Industrial Automation, Control Techniques PLC, from 2006 to 2011, Senior Research Scientist in Sharp Laboratories of Europe Ltd. from 2011 to 2012, and lecturer at Coventry University, Coventry, UK, from 2013 to 2014. His research interests include power electronics and its applications in renewable energy, energy storage, motor drives, and power systems.
Tariq A.
,
Asgha M.S. J.
“Development of an analog maximum power point tracer for photovoltaic panel,”
in Proc. IEEE Power Electronics and Drives Systems
2005
Vol. 1
251 
255
Mekki H.
,
Mellit A.
,
Salhi H.
,
Khaled B.
“Modeling and simulation of photovoltaic panel based on artificial neural networks and VHDLlanguage,”
in Proc. 14th IEEE Int. Conf. Electron., Circuits Syst. (ICECS)
2007
58 
61
Khouzam K.
,
Khoon Ly C.
,
Koh C.
,
Ng P. Y.
“Simulation and realtime modelling of space photovoltaic systems,”
in Proc. IEEE 1st World Conf. Photovoltaic Energy Convers., Conf. Record 24th IEEE Photovoltaic Spec. Conf.
1994
Vol. 2
2038 
2041
Zeng Q.
,
Song P.
,
Chang L.
“A photovoltaic simulator based on dc chopper,”
in Proc. IEEE CCECE Conf.
2002
Vol. 1
257 
261
Ldloyd S.
,
Smith G.
,
Infield D.
“Design and construction of a modular electronic photovoltaic simulator,”
in Proc. Inst. Electr. Eng. Power Electr. Variable Speed Drives Conf.
2000
120 
123
Armstrong S.
,
Lee C.
,
Hurley W.
“Investigation of the harmonic response of a photovoltaic system with a solar emulator,”
in Proc. Eur. Conf. Power Electron. Appl.
2005
1 
8
Midtgard O.
“A simple photovoltaic simulator for testing of power electronics,”
in Proc. Eur. Conf. Power Electron. Appl.
2007
1 
10
Koran A.
,
Sano K.
,
Kim R.
,
Lai J.
2010
“Design of a photovoltaic simulator with a novel reference signal generator and twostage LC output filter,”
IEEE Trans. Power Electron.
25
(5)
1331 
1338
DOI : 10.1109/TPEL.2009.2037501
Ollila J.
“A medium power PVarray simulator with a robust control strategy,”
in Proc. IEEE Conf. Control Appl.
1995
40 
45
Yongdong L.
,
Jianye R.
,
Min S.
“Design and implementation of a solar array simulator,”
in Proc. ICEMS Int. Conf.
2004
2633 
2636
Schofield D.M.K.
,
Foster M.P.
,
Stone D.A.
2011
“Lowcost solar emulator for evaluation of maximum power point tracking methods,”
Electronics Letters
47
(3)
208 
209
DOI : 10.1049/el.2010.2930
Koran A.
,
LaBella T.
,
Lai J.
2014
“High Efficiency Photovoltaic Source Simulator with Fast Response Time for Solar Power Conditioning Systems Evaluation,”
IEEE Trans. Power Electron.
29
(3)
1285 
1297
DOI : 10.1109/TPEL.2013.2262297
Zhao J.
,
Kimball J. W.
“A Digitally Implemented Photovoltaic Simulator with a double current mode controller,”
in Proc. Appl. Power Electron. Conf. (APEC)
Feb. 2012
53 
58
Koutroulis E.
,
Kalaitzakis K.
,
Voulgaris N.
2001
“Development of a microcontrollerbased, photovoltaic maximum power point tracking control system,”
IEEE Trans. Power Electron.
16
(1)
46 
54
DOI : 10.1109/63.903988
Chen Y.
,
Smedley K.
2004
“A costeffective singlestage inverter with maximum power point tracking,”
IEEE Trans. Power Electron.
19
(5)
1289 
1294
DOI : 10.1109/TPEL.2004.833458
Fortunato M.
,
Giustiniani A.
,
Petrone G.
,
Spagnuolo G.
,
Vitelli M.
2008
“Maximum power point tracking in a onecyclecontrolled singlestage photovoltaic inverter,”
IEEE Trans. Ind. Electron.
55
(7)
2684 
2693
DOI : 10.1109/TIE.2008.918463
Hua C.
,
Lin J.
,
Shen C.
1998
“Implementation of a DSPcontrolled photovoltaic system with peak power tracking,”
IEEE Trans. Ind. Electron.
45
(1)
99 
107
DOI : 10.1109/41.661310
Villalva M. G.
,
Gazoli J. R.
,
Filho E. R.
2009
“Comprehensive approach to modeling and simulation of photovoltaic arrays,”
IEEE Trans. Power Electron.
24
(5)
1198 
1208
DOI : 10.1109/TPEL.2009.2013862