This paper presents the design and realization of a digital PV simulator with a PushPull Forward (PPF) circuit based on the principle of modular hardware and configurable software. A PPF circuit is chosen as the main circuit to restrain the magnetic biasing of the core for a DCDC converter and to reduce the spike of the turnoff voltage across every switch. Control and I/O interface based on a personal computer (PC) and multifunction data acquisition card, can conveniently achieve the data acquisition and configuration of the control algorithm and interface due to the abundant software resources of computers. In addition, the control program developed in Matlab/Simulink can conveniently construct and adjust both the models and parameters. It can also run in realtime under the external mode of Simulink by loading the modules of the RealTime Windows Target. The mathematic models of the PushPull Forward circuit and the digital PV simulator are established in this paper by the statespace averaging method. The polezero cancellation technique is employed and then its controller parameters are systematically designed based on the performance analysis of the root loci of the closed current loop with
k_{i}
and
R_{L}
as variables. A fuzzy PI controller based on the TakagiSugeno fuzzy model is applied to regulate the controller parameters selfadaptively according to the change of
R_{L}
and the operating point of the PV simulator to match the controller parameters with
R_{L}
. The stationary and dynamic performances of the PV simulator are tested by experiments, and the experimental results show that the PV simulator has the merits of a wide effective working range, high steadystate accuracy and good dynamic performances.
I. INTRODUCTION
In recent years, due to the serious problems of energy shortages, environmental pollution and energy security throughout the world, the development and utilization of clean renewable energy is becoming an important way to improve the energy structure, reduce environment pollution and persistently ensure the energy supply all over the world
[1]
,
[2]
. The worldwide interest in renewable energy has greatly promoted the development of PV generation technology and industry
[3]

[5]
.
In the research and development of PV generation systems, if a real PV array is used to test and verify the correctness and performance of the power electronic equipment and control systems, it would be both costly and timeconsuming. Therefore, the output characteristics of a PV array under various operating conditions are always simulated by a PV simulator, which can be made by an analog circuit, a digital circuit or an analog and digital hybrid circuit. There are several methods to implement a PV simulator, including:

1) amplifying the output of the current and voltage of a sample PV cell or photosensor diode with a controlled light source imitating sunlight or an LED light emission circuit to simulate variations in sunshine intensity[6],[7]

2) constructing a PV array by taking a PV cell equivalent circuit with analog circuits as a basic unit[8]

3) using a DC power supply controlled by a personal computer (PC) with a data acquisition card or a special real time digital simulator (such as RTLAB)[9],[10]

4) adopting a unidirectional DCDC converter with a basic topology controlled by a DSP, a PC, a microprocessor, a microcontroller, or some other digital control technology as the main circuit of the digital PV simulator to simulate the output characteristics of the PV array, where the DC input voltage is supplied by a DC power supply or an uncontrolled diode rectifier[11][14]

5) adopting the topology of a PWM rectifier with a bidirectional compound DC/DC converter controlled by a DSP or a PC[15]

6) using multiple multiphase DC/DC converters controlled by a PC or a DSP as the main circuit of the PV simulator[16],[17]

7) selecting a high frequency PWM rectifier for a threephase voltage source controlled by the host computer as the main circuit of the PV simulator[18].
Despite achieving adequate simulative effects, most of the PV simulators still exhibit some problems, such as a limited effective working range, bigger ripples of the output voltage and current, lack of systematic modeling and design methods for the controller parameters, lower development efficiency, and so on.
Considering the above drawbacks, the digital PV simulator presented in this paper adopts modular hardware, configurable software, systematic modeling and design methods for the controller parameters so as to obtain the merits of a wide effective working range, high steadystate accuracy, good control performances, high reliability and development efficiency. A comparison of the characteristics of the different methods for PV simulators is listed in
Table I
.
CHARACTERISTICS COMPARISON OF DIFFERENT METHODS FOR PV SIMULATOR
CHARACTERISTICS COMPARISON OF DIFFERENT METHODS FOR PV SIMULATOR
II. CONFIGURATION AND WORKING PRINCIPLE OF THE DIGITAL PV SIMULATOR
The overall configuration of the digital PV simulator is shown in
Fig. 1
. It mainly consists of a DC power supply, a DCDC converter, a digital controller, a PWM signal generation circuit, a measuring and signal conditioning circuit, a driving and isolating circuit, and so on. The main operation principle is as follows: the DC power supply provides a steady DC input voltage for the DCDC converter. According to the output voltage measured in realtime, the digital controller calculates the reference current signal by the IV characteristic model and then calculates the duty ratio of the converters’ PWM signals by a current closedloop regulator. After signal conversion, the duty ratio is converted into a signallevel control voltage which is sent to the PWM signal generation circuit to generate PWM signals. The PWM signals control the states of the power switches so as to adjust the converter’s output voltage and current after signal isolation and power driving. Finally, the PV simulator can always work at a certain operational point at which the output voltage and output current of the converter can satisfy both the load characteristics and the IV curve of the PV array. Thus, the output characteristics of the PV array can be easily simulated by the digital PV simulator.
Overall configuration of the digital PV simulator.
III. WORKING MECHANISM OF THE PUSHPULL FORWARD CIRCUIT
 A. Circuit Structure
The main circuit of the DCDC converter adopts a PushPull Forward (PPF) circuit in the PV simulator. A fullwave rectifier is applied in the secondary windings of the high frequency transformer so as to reduce the conduction losses of the rectifying diodes with a lowoutput voltage and a highoutput current. An LC filter is used to provide a continuous load current and to reduce harmonics.
Fig. 2
shows the topological structure of the DCDC converter. It can be seen from the figure that the PPF circuit is different from a conventional PushPull converter in that a clamping capacitor is connected in series between the two primary windings of the high frequency transformer and between the two power switches. As a result, it has the advantages of both the PushPull converter and Forward converter, and it can restrain the magnetic biasing of the core for the DCDC converter, magnetize the magnetic core bidirectionally and reduce the spike in the turnoff voltage across each switch. Therefore, the PPF circuit is becoming a kind of preponderant circuit topology for low voltage and high current output applications.
Diagram of PushPull Forward circuit.
 B. Analysis of the Operating Modes
In steady state, the PPF circuit has 8 operating modes in a switch cycle. Each power switch matches with the 4 operating modes of one cycle. In the following analysis, it is assumed that all of the power switches and diodes are ideal components and that the onstate voltage drops for all of the power electronic components are negligible
[19]
. The equivalent circuits of the former four operating modes are shown in
Fig.3
.
Equivalent circuits of the former four operating modes in a switch cycle.
1) Mode [t_{0}t_{1}]:
Prior to
t_{0}
, the power switches S
_{1}
and S
_{2}
are off. The primary current freewheels through
U_{in(+)}
→
N_{p2}
→
C_{b}
→
N_{p1}
→
U_{in()}
and forms a circular current which is
I_{a}
=
i_{p1}
=
i_{p2}
. During this period, the rectifying diodes of the secondary windings turn on simultaneously, and the current through each of the rectifying diodes is
i_{DR1}
=
i_{DR2}
=
I_{o}
/2. At
t_{0}
, the filtering inductor current runs down to the minimum value
I_{Lfmin}
.
At
t_{0}
, S
_{1}
turns on.
U_{in}
and
u_{cb}
are applied to the leakage inductances
L_{σ}
of
N_{p1}
and
N_{p2}
, respectively.
i_{p1}
increases rapidly due to
U_{in}
being in the same direction as
i_{p1}
, and
i_{p2}
decreases rapidly due to
u_{cb}
being in the opposite direction as
i_{p2}
. Corresponding with
i_{p1}
and
i_{p2}
,
i_{DR1}
and
i_{DR2}
increase and decreases respectively because of the affection of the magnetic circuit. During this period, the filtering inductor current increases gradually from
I_{Lfmin}
. This mode ends when
i_{DR1}
is equal to the load current, both
i_{p2}
and
i_{DR2}
are decreased to 0 and the commutation process ends. The voltage across S
_{1}
is always 2
U_{in}
during this period.
2) Mode [t_{1}t_{2}]:
In this mode,
U_{in}
and
u_{cb}
are applied to the magnetizing inductor
L_{m}
and the primary reduced inductance of the filtering inductances
L_{f}
of
N_{p1}
and
N_{p2}
, respectively. Each half of the changing rate of the magnetizing current and load current is shared by the primary winding.
i_{p1}
continues to increase in the original direction defined as the reference direction whereas
i_{p2}
increases gradually from 0 in the opposite direction. This mode lasts from
t_{1}
to
t_{2}
and S
_{1}
turns off at
t_{2}
. Because the circuit works like two forward converters in parallel, the circuit is called PushPull Forward circuit or converter. At the instant of S
_{1}
turning off,
i_{p1}
runs up to the maximum value, because both the magnetizing current and primary reduced current of the load current flow through S
_{1}
. The filtering inductor current also runs up to the maximum value accordingly. The voltage across S
_{1}
is also 2
U_{in}
during this period.
3) Mode [t_{2}t_{3}]:
After S
_{1}
turns off, the body diode
D_{S2}
of S
_{2}
is forced to turn on to continue the leakage inductance current because
i_{p1}
is always larger than
i_{p2}
before
t_{2}
. The energy of the leakage inductance is released to charge the clamping capacitor
C_{b}
through the low impedance loop
N_{p1}
→
D_{S2}
→
C_{b}
.
U_{in}
and
u_{cb}
are applied to the leakage inductances of
N_{p2}
and
N_{p1}
, respectively.
i_{p1}
decreases rapidly, and
i_{p2}
reduces to 0 gradually and then changes direction to increase rapidly in the reference direction.
i_{DR1}
and
i_{DR2}
decrease and increase, respectively. When
i_{DR1}
and
i_{DR2}
reach the same value
I_{a}
at
t_{3}
, this mode ends. During this period, the load current decreases gradually from
I_{Lfmax}
.
4) Mode [t_{3}t_{4}]:
During this period, both S
_{1}
and S
_{2}
are off, and the leakage inductance current is freewheeling through
U_{in(+)}
→
N_{p2}
→
C_{b}
→
N_{p1}
→
U_{in()}
and forms a circular current in the primary windings. Due to the two primary windings being seriesopposing connections, the voltages across them are both 0 and the voltages across the power switches are both
U_{in}
. At the same time, magnetizing current also forms a circular current in the secondary side of the high frequency transformer. This mode ends when S
_{2}
turns on at
t_{4}
.
5) Mode [t_{4}t_{5}][t_{5}t_{6}][t_{6}t_{7}][t_{7}t_{8}]:
At
t_{4}
, S
_{2}
turns on and the circuit goes into the second half of a switch cycle. The modes [
t_{4}t_{5}
], [
t_{5}t_{6}
], [
t_{6}t_{7}
] and [
t_{7}t_{8}
] in the second half of a switch cycle correspond to [
t_{0}t_{1}
], [
t_{1}t_{2}
], [
t_{2}t_{3}
] and [
t_{3}t_{4}
], respectively. The operating principle of the second half of a switch cycle works in the same way as the first half, except that the magnetizing currents of the two half cycles are opposite in direction. During the second half of a switch cycle, demagnetization of the high frequency transformer is completed.
The key operating waveforms are shown in
Fig.4
.
Key waveforms of PushPull Forward circuit.
 C. InputOutput Relationship
Suppose the primary winding turn of the transformer is
N_{P1}
=
N_{P2}
=
w_{1}
and its secondary winding turn is
N_{s1}
=
N_{s2}
=
w_{2}
, then the turns ratio of the secondary to primary is
n
=
w_{2}
/
w_{1}
. The duty ratio D is defined as 2
T_{on}
/
T_{s}
, where
T_{on}
is the on duration of each power switch (S
_{1}
or S
_{2}
) and
T_{s}
is the switch time period which is equal to the reciprocal of the switching frequency
f_{s}
.
During steadystate operation, the filtering inductor current is of the triangle waveform, and it varies periodically between
I_{Lfmin}
and
I_{Lmaxf}
. The inductor current increase Δ
I_{Lf(+)}
, during the on duration of S
_{1}
or S
_{2}
, is equal to its decrease Δ
I_{Lf()}
while S
_{1}
and S
_{2}
are both off. The relationship between them can be expressed as:
Thus:
That is:
where
U_{in}
and
U_{o}
are the average input voltage and output voltage, respectively.
If the power losses of the circuit are neglected, the average input current can be expressed as :
where
I_{o}
is the average load current,
I_{o}
=(
I_{Lfmin}
+
I_{Lfmax}
)/2.
IV. MODELING OF THE DIGITAL PV SIMULATOR
Fig. 5
shows a control block diagram of the digital PV simulator. There are two control loops in it: the outerreference loop and the innercurrent loop. The former measures the output voltage
u_{o}
of the PV simulator and feeds it back to the IV characteristic mode so as to generate the reference current
i_{ref}
; while the latter controls the filtering inductor current
i_{Lf}
.
R_{L}
represents the equivalent load resistance of the PV simulator’s load characteristics;
G
(
s
) is the transfer function of the duty ratio to the filtering inductor current;
G_{c}
(
s
) is the transfer function of the PI controller,
G_{c}
(
s
)=
k_{p}
+
k_{i}
/
s
;
G_{fi}
(
s
) is the equivalent transfer function of the current measuring, conditioning and filtering,
G_{fi}
(
s
)=1/(
T_{f1}s
+1); and
G_{fu}
(
s
) is the equivalent transfer function of the voltage measuring, conditioning and filtering,
G_{fu}
(
s
)=1/(
T_{f2}s
+1). The IV characteristics can be described from an engineering analytical model of the PV array. Because the changing rate of the filtering capacitance voltage
u_{Cf}
is very small in steadystate operation, the current
i_{Cf}
of the filtering capacitor branch is negligibly small and
i_{Lf}
is almost equal to
i_{o}
. Thus,
i_{Lf}
replaces
i_{o}
for use as the feed current in the actual control system. The modeling and controller parameter design of the PV simulator are carried out mainly based on the innercurrent loop.
Control block diagram of the digital PV simulator.
According to the working principle and the inputoutput relationship of the PPF circuit, when S
_{1}
(or S
_{2}
) is on, the relationship between the primary and secondary is:
where
i_{in}
,
i_{Lf}
and
u_{F}
correspond to the instantaneous value of input current, the filtering inductor current and the pulse voltage rectified by the rectifying diodes, respectively.
When S
_{1}
and S
_{2}
are both off, the relationship is:
By the above relationship and Kirchhoff’s voltage and current laws, considering the effect of the inductance parasitic resistor
R_{f}
, the statevariable equations of the PPF circuit with S
_{1}
(or S
_{2}
) being on are:
where
T_{on}
=
t_{02}
or
T_{on}
=
t_{46}
,
t_{02}
is the duration from
t_{0}
to
t_{2}
for each switch cycle, and
t_{46}
is the duration from
t_{4}
to
t_{6}
for each switch cycle. The defining methods for the following similar variable are similar to
t_{02}
and
t_{46}
.
Similarly, the statevariable equations of the PPF circuit when S
_{1}
and S
_{2}
are both off are:
where
T_{off}
=
t_{24}
or
T_{off}
=
t_{68}
.
Combining the above two switch statuses and according to the working mechanism of the simulator, the state space averaging equations of the PPF circuit in a switch time period are:
Due to
T_{on}
+
T_{off}
=
T_{s}
/2, D=2
T_{on}
/
T_{s}
, the above equations can be rewritten in state space expression as:
Assuming that the initial conditions are zero, the transfer function of the duty ratio to the filtering inductor current by Laplace transforms of equation (10) can be obtained as:
V. CONTROLLER PARAMETER DESIGN OF THE DIGITAL PV SIMULATOR
 A. Ideas of the Controller Parameter Design
The open loop transfer function of the current loop is:
There are two parameters (
k_{p}
and
k_{i}
) that need to be determined in equation (12).
k_{p}
and
k_{i}
are usually designed to match with the transfer function
G
(
s
). However,
G
(
s
) varies with
R_{L}
, and
R_{L}
varies with the operating point and has a wide variation range. As a result, together with the high dimension of
G_{ok}
(
s
), it is very difficult to determine the two controller parameters. If the pole of
G_{fi}
(
s
) is cancelled by the zero of the PI controller, namely,
k_{p}
/
k_{i}
=
T_{f1}
, the design difficulty will be reduced to a certain extent. However,
k_{i}
remains difficult to determine due to the uncertainty of
R_{L}
.
Under the condition of
k_{p}
/
k_{i}
=
T_{f1}
, the performances of the root loci with
k_{i}
and
R_{L}
as variables are analyzed for designing the controller parameters. On the basis of the analytical method, several sets of PI controller parameters matched with different
R_{L}
are designed. In order to match the controller parameters with
R_{L}
, a fuzzy PI controller based on the TakagiSugeno fuzzy model is applied to selfadaptively regulate the controller parameters so as to satisfy the control demands as the operating point changes.
 B. Performance Analysis of the Root Loci with ki
The open loop transfer function of the current loop with
k_{i}
as a variable is:
The root loci of the current loop with
k_{i}
as a variable for different values of
R_{L}
are a family of curves. It is found by analyzing the root loci that the root loci show three different types of motion curves with
R_{L}
=1.287Ω and
R_{L}
=1.403Ω as cutoff points. The typical root loci are shown in
Fig. 6
. It can be seen from the figure that the system is always stable no matter how
R_{L}
changes. However, the locations of the zeros and poles vary with
R_{L}
. For different locations of the zeros and poles, the performances of the current loop show large differences. At a given
R_{L}
, different closedloop poles have different values of
k_{i}
and performance indexes, such as the damping ratio
ζ
and the overshot. It is obvious that the value of
k_{i}
determines the location of the closedloop poles and the performances of the system.
Root loci of the current loop with k_{i} as variable( (a) R_{L}=1Ω, (b) R_{L}=1.3Ω, and (c) R_{L}=50Ω).
 C. Performance Analysis of the Root Loci with RL
According to the characteristic equations of the closed current loop system, its open loop transfer function with
R_{L}
as a variable is rewritten as:
The root loci of the current loop with
R_{L}
as a variable for different values of
k_{i}
are also a family of curves. Although the locations of the zeros and poles change with
k_{i}
, the form of the root loci is basically the same. Typical root loci are shown in
Fig. 7
.
Root loci of the current loop with R_{L} as variable.
It can be seen from the figure that the system is always stable no matter how
k_{i}
changes. When
k_{i}
kept constant, different values of
R_{L}
have different performance indexes. Apparently,
R_{L}
is also a key factor to influence the system’s performances.
 D. Design of Controller Parameters
From the analysis presented above, it can be seen that only suitable values of
k_{i}
matched with
R_{L}
can satisfy the performance requirements of the system because
R_{L}
varies with the operating point.
For this purpose, by combining the time domain performance indexes of the equivalent 2order system with the output characteristics of the PV array, typical operating points of the segmented operating ranges are selected to determine the closedloop dominant poles and the corresponding
k_{i}
based on the root loci analysis. The closedloop dominant poles are selected close to an imaginary axis and the absolute values of the real parts for the other closeloop poles and zeros are three times more than those of the closedloop dominant poles. Once the closedloop dominant poles are decided, the corresponding values of
k_{i}
can be calculated. For the given
T_{f1}
=0.01s, the value of
k_{p}
can be obtained according to the relationship
k_{p}
/
k_{i}
=
T_{f1}
. The PI controller parameters of the typical operating points in each of the segmented operating ranges are listed in
Table I
of the Appendix.
 E. Selfadaptive Regulation of the Controller Parameters
It can be seen from the above analysis that the controller parameters must be regulated timely and appropriately according to
R_{L}
in order to obtain satisfactory dynamic and stationary performances. For these reasons, a fuzzy PI controller based on the TakagiSugeno fuzzy model is applied to regulate the controller parameters according to the change of the operating point of the PV simulator. The structure of the fuzzy PI controller is shown in
Fig. 8
.
Structure of fuzzy PI controller.
In this paper,
R_{L}
is selected as the reference factor of the input variable, the input space is divided into four fuzzy subspaces based on the above design results of the controller parameter and every fuzzy subspace corresponds to the linear PI controller designed above. The models of the linear PI controllers are joined together smoothly by membership functions. With overlapping among the other inference rules, the TakagiSugeno fuzzy model achieves the nonlinear global mapping and makes the PI controller parameters of each rule have a different weighting factor. Therefore, with the fuzzy inference of the TakagiSugeno fuzzy model, the PI controller parameters can selfadaptively regulate according to the change of the operating point and
R_{L}
. The value of R
^{i}
_{c}
of the TakagiSugeno fuzzy model’s fuzzy implication relationship has the following form
[20]
:

ifRLisAithenkp=kip,ki=kii,i=1, 2, …,m
where,
i
is the
i
th rule;
m
is the number of fuzzy subspaces,
m
=4;
A^{i}
is the fuzzy subsets of the
i
th rule; and
k^{i}_{p}
and
k^{i}_{i}
are the outputs of the
i
th rule.
The total output of the fuzzy implication relation is given by:
where,
μ_{Ai}
(
R_{L}
) is the membership function of
R_{L}
and the application degree of the
i
th rule and is decided by the membership degree for all of the input subsets in the rule.
The membership function of
R_{L}
is the Gaussian type and it is shown in
Fig. 9
.
Membership function of R_{L}.
VI. HARDWARE AND SOFTWARE DESIGN OF THE DIGITAL PV SIMULATOR
 A. PushPull Forward Circuit
The design parameters of the PV simulator are shown in
Table II
of the Appendix. According to the above design requirements, the duty ratio of the PPF circuit and the turns ratio of the secondary to the primary are confirmed firstly. Considered the extreme case where the maximum output voltage prescribed by the design indexes can be obtained under the minimum input voltage and the effective duty ratio is increased as much as possible in order to decrease the turns ratio of the secondary to the primary, the turns ratio of the secondary to the primary can be calculated by:
where
D_{max}
is the maximum duty ratio of the PPF circuit,
D_{max}
=0.9.
The other parameters of the highfrequency transformer are calculated by using the Area Product method. According to the working mechanism of the PPF circuit and considered a certain safety margin, 1MBH60D100 IGBT modules and MUR3040PT diodes are selected as the power switches and output rectifying diodes, respectively.
According to the working mechanism of the PPF circuit, the averaging voltage of the clamping capacitor is equal to
U_{in}
. Due to the finite value of the clamping capacitor, there is a certain pulsating quantity of voltage Δ
u_{cb}
, and it can be expressed as:
Based on the estimation of the above formula and experimental research, a 10
μF
highfrequency noninductive capacitor is selected as the clamping capacitor.
The key parameters of the PPF circuit are listed in
Table III
of the Appendix.
 B. PWM Signal Generation, Driving and Isolating Circuit
In the PV simulator, a SG3525 is adopted as the pulse width modulation chip to generate two pushpull PWM signals according to the input control voltage. The two PWM signals generated by the SG3525 are amplified by two EXB840 modules to drive the power switches. The output signal of the EXB840’s pin5 is sent to pin10 of the SG3525 by photocoupler so as to shut down the PWM signals for protecting the power switches when an overcurrent occurs. In order to prevent the power switches from turning on simultaneously, the two PWM signals are interlocked in the driving circuit so as to enhance the reliability of the system. A diagram of the PWM signal generation, driving and isolating circuit is shown in
Fig.10
.
Diagram of PWM signal generation, driving and isolating circuit.
 C. Signal Measuring and Conditioning Circuit
The output voltage and inductor current are measured and converted into 0~2.5V voltage signals by Hall sensors. The signals are converted into 0~10V voltage signals by a signal conditioning circuit and then sent into a data acquisition card for A/D conversion. Taking the voltage measuring as an example, a diagram of the signal measuring and conditioning circuit is shown in
Fig. 11
.
Diagram of signal measuring and conditioning circuit.
 D. Control and I/O Interface
The control and I/O interface of the PV simulator, which consists of a personal computer and a PCI1710 multifunction data acquisition card, can conveniently achieve the data acquisition and configuration of the control algorithm and interface by the abundant software resources of the computer.
 E. Control Software Design
The modules of the RealTime Windows Target are loaded to become a seamless integration of the Simulink environment and the external equipment under the external mode of Simulink, which can make Simulink become a realtime configuration development environment and a graphical control platform. In order to construct and adjust the models and parameters of the PV array, sunshine intensity, PV array’s temperature and controller conveniently and to improve the software development efficiency and reliability, the control software of the PV simulator is designed and developed based on this configuration environment and control platform.
A diagram of the realtime configuration and control program for the PV simulator is shown in
Fig. 12
. To increase the readability of the program, models of the IV characteristics and the PI controller are both encapsulated into subsystems. Sampleddata control in equal intervals of time is adopted in the system and its sampling period is 1ms.
Block diagram of realtime configuration and control program for digital PV simulator.
In order to solve the PV model conveniently, the engineering analytical model of the PV array, which can accurately describe the output characteristics of the PV array with only several electrical parameters under the standard test conditions provided by the manufactures and is convenient for engineering applications, is adopted to build the IV characteristics subsystem in the MATLAB/Simulink environment. The engineering analytical model of the PV array can be expressed as
[21]
:
where:
DT
=
T

T_{ref}
,
V_{OC}
is the opencircuit voltage,
I_{SC}
is the shortcircuit current,
V_{m}
is the optimum operating voltage and
I_{m}
is the optimum operating current, which gives the maximum power at that time.
R_{s}
is the series internal resistor,
Q
and
Q_{ref}
are actual sunshine intensity and the reference sunshine intensity of 1000
W/m^{2}
, respectively.
T
and
T_{ref}
are the actual module temperature and the reference temperature of 25
℃
, respectively.
α
and
β
are the current and voltage temperature coefficients under the reference sunshine intensity, respectively.
A diagram of the IV characteristic subsystem is shown in
Fig.13
. It can be seen from the diagram that the models and parameters of the sunshine intensity, the PV array’s temperature, etc. can be built and adjusted conveniently.
Subsystem of IV characteristics.
A diagram of the fuzzy PI controller subsystem is shown in
Fig.14
. In order to ensure real time control, the TakagiSugeno fuzzy model is realized with the Embedded MATLAB Function block of Simulink in the subsystem. The block can achieve complicated function flexibility with the MATLAB programming language and it can execute simulations and generate code for a Realtime Workshop target.
Subsystem of fuzzy PI controller.
VII. EXPERIMENT RESULTS AND ANALYSIS
 A. System Implementation
Based on the principle of modular hardware and configurable software, the functional modules of the PV simulator’s hardware which consists of the PPF circuit, the PWM signal generation, the driving and isolating circuit, the measuring and signal conditioning circuit, the control and I/O interface, and so on, are all implemented and tested. After the module level test, all of the functional modules are connected with software to form a complete system and then tested in a whole system. In this paper, a DC programmable electronic load of IT8516C by ITECH is adopted to simulate the load characteristics. The whole system is shown in
Fig. 15
, and the parameters of the PV array used to verify the performance of the PV simulator are listed in
Table IV
of the Appendix.
Experimental setup of PV simulator.
 B. Steadystate Experiment
In the experiment, the load mutation test is done to verify the steadystate performances of the different operating points. The typical waveforms of the output voltage and filtering inductor current are shown in
Fig. 16
. In the test,
R_{L}
is changed suddenly from 20Ω to 5Ω and then changed suddenly from 5Ω to 20Ω after remaining a 5Ω for some time. The experimental waveforms indicate that the ripples of the voltage and current are both very small and that the system can work steadily at the operating point corresponding with
R_{L}
. The PV simulator has a fast dynamic response and a high steadystate accuracy.
Waveforms of output voltage and filtering inductor current.
Based on the above results, the static output characteristics of the PV simulator are simulated under 25℃ and different sunshine intensities as well as 1000W/m
^{2}
sunshine intensity and different temperatures. Due to limitations on the length of this paper, only the static output characteristics under 25℃ and different sunshine intensities are given. The experimental results are shown in
Fig.17
.
Static output characteristics of PV simulator under 25℃ and different sunshine intensities ((a) Currentvoltage characteristics and (b) Powervoltage characteristics).
The steadystate experimental results show that the output voltage and current of the PV simulator have a wide adjusting range, and that its currentvoltage characteristics and powervoltage characteristics comply well with the theoretical output characteristics.
 C. Dynamic Experiment
Due to variations of the operating point of the PV simulator with a load, the test of the power variation of the PV simulator with the sunshine intensity changed under natural conditions is done to verify the dynamic characteristic of the PV simulator. In the test, the sunshine intensity change under natural conditions is simulated by a combination of the positive and negative ramp function, and the other models. A DC programmable electronic load is selected in the constantvoltage mode to maintain a constant output voltage of the PV simulator so as to measure its output power. The curves of the sunshine intensity change and the output power for the PV simulator are shown in
Fig. 18
. The test result shows that the power of the PV simulator varies linearly with the sunshine intensity change and it has a good dynamic response.
Dynamic output characteristics of PV simulator ( (a) curve of sunshine intensity change and (b) curve of output power of PV simulator).
 D. System Efficiency
The PV simulator’s efficiency as a function of different output voltages under 1000W/m
^{2}
sunshine intensity is measured. The efficiency curve is shown in
Fig. 19
. The efficiency curve shows that the PV simulator has a high working efficiency within a wide operating range and that it can satisfy the design requirements.
Efficiency curve of the PV simulator in 1000W/m^{2} sunshine intensity.
VIII. CONCLUSIONS
In this paper, the hardware of a digital PV simulator is designed and implemented based on the principle of modular hardware. The control structure of the system is based on a PC and a multifunction data acquisition card. A PPF circuit is adopted as the main circuit of the PV simulator to restrain the magnetic biasing of the core for the DCDC converter and to reduce the spike of the turnoff voltage across every switch. Based on an analysis of the operating mode and the inputoutput relationship of the PPF circuit, mathematic models of the PPF circuit and PV simulator are built by the statespace averaging method. Aiming at the problem where the load resistance
R_{L}
changing with the operating point of the PV simulator leads to the difficult controller parameter design, the inertial element of the equivalent transfer function of current measuring, conditioning and filtering is cancelled by the polezero cancellation technique so as to reduce the design difficulty of the controller parameters. Then the controller parameters are systematically designed based on the performance analysis of the root loci of the closed current loop with
k_{i}
and
R_{L}
as variables. In order to match the controller parameters with
R_{L}
, a fuzzy PI controller based on the TakagiSugeno fuzzy model is applied to selfadaptively regulate the controller parameters.
The realtime configuration and the control program for the digital PV simulator are developed in the realtime environment of Matlab/Simulink which loads the modules of the RealTime Windows Target and works under the external mode of Simulink so that the models and parameters of the system can be adjusted conveniently and the system can run in realtime. Lastly, the stationary and dynamic performances of the PV simulator are tested by experiments. The experimental results show that when the controller parameters designed in this paper according to the statespace averaging model are applied to the PV simulator, satisfactory dynamic and stationary performances are obtained. This makes it have the merits of a wide effective working range, a high steadystate accuracy and good dynamic performances. Therefore, it can be seen that the modeling and controller parameter design of the digital PV simulator based on the PPF circuit proposed in this paper is correct and reasonable. It also has a significant reference value for the modeling and controller parameter design of many other types of PV simulators and converters.
BIO
Jike Zhang was born in Hohhot, China. He received his B.S. and M.S. degrees in Control Science and Engineering from the Inner Mongolia University of Technology, Hohhot, China, in 2000 and 2003, respectively. He is presently working toward his Ph.D. degree at the Inner Mongolia University of Technology. Since 2005, he has been a Lecturer in the Department of Automation, Inner Mongolia University of Technology. His current research interests include power electronics and control in renewable energy.
Shengtie Wang was born in Hohhot, China. He received his B.S. and M.S. degrees in Control Science and Engineering from the Chengdu University of Science and Technology, Chengdu, China, in 1985 and 1988, respectively. He received his Ph.D. degree in Electrical Engineering from the Huazhong University of Science and Technology, Wuhan, China, in 1999. Since 2000, he has been a Professor in the Department of Automation, Inner Mongolia University of Technology, Hohhot, China. From September to December of 2003, he was a Researcher at Mie University, Tsu, Japan, where he was engaged in research on the control of small wind turbines. From 2007 to 2008, he worked as a Visiting Scholar at the Norwegian University of Science and Technology (NTNU), Trondheim, Norway, where he was engaged in research on the control of large wind turbines. His current research interests include power electronics and control in renewable energy, intelligent control and applications.
Zhihe Wang was born in Baotou, China. He received his B.S. and M.S. degrees in Control Science and Engineering from Chongqing University, Chongqing, China, in 1985 and 1988, respectively. From 1991 to 1996, he worked for the Automation Research Institute, Inner Mongolia University of Technology, Hohhot, China, where he was engaged in research on electric drives, motion control, and power quality control. Since 2003, he has been a Professor in the Department of Automation, Inner Mongolia University of Technology. His current research interests include power electronics and converter control.
Lixin Tian was born in Baotou, China. He received his B.S. degree in Electronic Science and Technology from Inner Mongolia University, Hohhot, China, in 1989. From 1992 to 1996, he worked for the Automation Research Institute, Inner Mongolia University of Technology, Hohhot, China, where he was engaged in research on power electronics and power quality control. Since 2001, he has been a Assistant Professor in the Department of Electric Power, Inner Mongolia University of Technology. His current research interests include power electronics and energy conversion.
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