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2016 China International Conference on Electricity Distribution (CICED 2016)
Xi’an, 10-13 Aug, 2016
Grid-connected PV system modeling and control based on
the variable step size of MPPT algorithm
Li Cuiping1, Zhuo Junwu1, Li Junhui1, Yao Zhizhong2
(1. School of Electrical Engineering, Northeast Dianli University, Jilin 132012, Jilin Province, China；2. Jilin
Electric Power Co.，Ltd.，Changchun 130021, China；)
observation (P&O), and incremental conductance(INC)
Abstract—Based on two kinds of maximum power point
tracking (MPPT), this paper proposed an improved
variable step size incremental conductance algorithm
which combined with constant voltage tracking. The
operating point of PV array is located near the maximum
power point (MPP) rapidly by using the fixed voltage
method, and the PV array is controlled to run at the MPP
quickly and accurately adopting different disturbance step.
Grid-connected inverter adopts the double closed-loop
control strategy of based on feed-forward decoupling to
realize the decoupling control of active and reactive power.
In PSCAD/EMTDC, the model of grid-connected
photovoltaic system (GCPS) has been implemented and
verified the effectiveness of the improved MPPT
algorithm.
Index Terms—Constant voltage tracking, Variable step
incremental conductance method, Modeling
gridconnected photovoltaic system,
feed-forward
decoupling, double closed-loop control
I. I NTRODUCTION
method. Due to these three methods have some
shortcomings, the improved MPPT control method are
often constructed at present. In [5], Xiong Yuansheng
combined CVT and P&O to solve the disadvantages of
CVT that ignores temperature change, and reduced the
oscillation near the MPP. In [6], Jiao Yang combined CVT
with INC of duty ratio perturbation MPPT algorithm
which improved the power tracking speed and precision,
and lowered power disturbance at the same time. In [7],
Chen Yaai proposed a gradient variable step size
perturbation and observation method which based on
gradient optimizing ideology. In the optimizing process,
the step size can be changed automatically with the slope
of P-U characteristic curve, therefore by increasing
optimizing efficiency.
The photovoltaic system simulation model is established
Solar energy is one of the most dominant renewable
in the PSCAD/EMTDC software. Based on the traditional
energy. By the end of 2015, total installed capacity of
INC, this paper proposed the method of combining the
Chinese photovoltaic generation is 43.18GW, of which
open circuit voltage with variable step INC, and verify the
distributed photovoltaic account for about 14%. During
effectiveness of the proposed method. Several dynamic
the 13th Five Year Plan, the installed targets of PV is
performance of photovoltaic power generation systems is
150GW, and distributed photovoltaic generation will
evaluated from the aspects of power control, current
break through 46% of the total. With the rapid
harmonic.
development
of
photovoltaic
power
generation,
II. MODELING AND CHARACTERISTIC
distributed photovoltaic power generation has a broad
RESEARCH OF PHOTOVOLTAIC PANELS
application prospect[1].
Due to the high cost of PV modules, we need to improve
A. The mathematical model of PV pane
the efficiency of the photovoltaic array as much as
Consider diode characteristics of PV panels, Fig. 1 can be
possible. The output voltage, current, power of PV array
used as equivalent circuit to describe. A series resistor Rs
which are influenced by the external environment show
and parallel resistor Rsh are used as being equivalent to the
nonlinear characteristics. So we need to adjust the load
loss of panels.
characteristics of the PV array to work at MPP in real time,
and the MPPT technology is the key to improve the
efficiency
of
photovoltaic
power
generation[2-3].
Conventional MPPT control methods mainly include:
constant voltage tracking(CVT)[4], perturbation and
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2016 China International Conference on Electricity Distribution (CICED 2016)
expressed
Rs
series
modules
(N S)
and
parallel
modules(NP) .
IL
Rsh
Id
Isc
by
Xi’an, 10-13 Aug, 2016




V

I L  N P I SC 1  C1 exp(
)  1 
N s C2VOC





V
(4)
When external irradiance and temperature changes, we
can calculate Isc、Voc、Im、Vm under the common condition
Fig.1 photovoltaic battery equivalent circuit
As shown in Fig.1, the I-V equation of photovoltaic panels
according to Isc，ref、Voc，ref、Im，ref、Vm，ref under the standard
may be written as Eq.(1)
condition.
I L  I SC

 q(V  I L Rs )   (V  I L Rs )
(1)
 I 0 exp 
  1 
AKT
Rsh

 

T  T  Tref
IL is the load current; V is the load voltage of the battery;
ISC is the excitation current
S 
which depends on solar
irradiance S and cell temperature t; I0 is the saturation
current of the PV panels without light; T is the absolute
temperature ; q is the electronic charge（1.6×10-19C）; K
  I sc，ref
I sc
is the Boltzmann’s constant （1.38×10-23J/K）; A is the
constant factor (when positive bias voltage is high, A is
equal to 1).
1
S
(1  aT )
Sref
(6)
(7)
(8)
S
I m  I m
(1  T )
Sref
(9)
Vm  Vm (1  T ) ln(1  S )
(10)
PV cells is very small and Rsh is big. Eq.(1) can be
simplified as Eq.(2) :
(2)
S ref
Voc  Voc (1  T ) ln(1  S )
Generally, (V+IL·Rs)/Rsh can be ignored because the Rs of

 q(V  I L Rs )  
I L  I SC  I 0 exp 
  1
AKT

 

S
(5)
The typical values of α、β、γ are α=0.0025/℃，β=0.5，
Eq. (2) ignored the Rsh, its deviation with real PV cell is
γ=0.00288/℃.
very small, so it can express the role of the irradiance and
Based on the Eq.(3)-(10), build the simulation model of
[8]
temperature in essence .
photovoltaic panels, its output as shown in Fig.2. Overall,
B. Engineering mathematics model of PV panels
photovoltaic panels are affected by the changes of
Above Eq.(1) and (2) belong to a transcendental equation
irradiance more than affected by temperature changes. At
and the solution of equation is very difficult. When we do
the same time the P-V curve shows that in a given
the actual engineering calculation, we make use of short
irradiance and temperature conditions, photovoltaic
circuit current Isc, open circuit voltage Voc, the current Im
panels have an unique MPP.
and the voltage Vm of MPP which are from photovoltaic
cell
manufacturer
tests
under
standard
condition(t=25 ℃ ,S=1000W/m ). So to simplify the
2
Eq.(2) :



V


I L  I SC 1  C1 exp(
)  1 
C
V


2 OC



(3)
Im
-Vm 
Im
Im -1
Where C1=1- ·exp
, C2= -1·ln(1- )
Isc 
 Isc
C2Voc
Isc  
PV array is consists of a series parallel modules. Based on
the Eq.(4) and Fig.1, the PV array output current IL can be
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2016 China International Conference on Electricity Distribution (CICED 2016)
10
Variable step conductance increment method is on the
300
1000W/m2
800W/m2
600W/m2
250
8
Xi’an, 10-13 Aug, 2016
basis of Eq. (13), to calculate the tangent slope absolute
200
I(A)
P(W)
6
4
1000W/m2
800W/m2
600W/m2
2
value (k = |A1*dP/dU|) of the working point, as a
150
100
coefficient of disturbance step. Far from the MPP, the
50
0
0
10
20
V(v)
30
0
0
40
(a)
300
8
250
30
40
disturbance step size are small also to enhance the tracking
precision. Specific work process is shown in Fig.3.
P(W)
150
15℃
25℃
35℃
4
100
2
value of the |dP/dU| and perturbation step length are big to
improve the tracking speed. Near the MPP, | dP/dU | and
200
t=15℃
t=25℃
t=35℃
I(A)
20
V(v)
t=25℃
10
6
10
Start
50
0
0
10
20
V(v)
30
40
0
0
10
20
V(v)
30
Sample T，V，I
Vref=0.79*Voc
40
Caculate
dT=T(k)-T(k-1)
(b) S=1000W/m2
Voc'=Voc-Voc*K*dT
Fig.2 The I-V and P-V curve of PV cells under different
Y
| T(k)-Tref |>ε
environmental conditions
N
III. VARIABLE STEP INCREMENTAL
Caculate
dV=V(k)-V(k-1)
dI=I(k)-I(k-1)
CONDUCTANCE METHOD OF MPPT CONTROL
k=|A1*dP/dU)|
STRATEGY
step=k*step
The photovoltaic cell P-V curves show that under different
environmental conditions, the VM of PV array is
approximately proportional to change when the Voc of PV
array change. Approximate linear relationship exists
between Vm and Voc, namely VM≈k1×Voc, in this paper
k1=0.78*Voc is affected by illumination change slightly
and is influenced by the temperature change strongly.
When the temperature change is big, Voc is updated by
online calculation. By adopting online open circuit
voltage correction method, Voc can be updated through
testing environment changes, and then multiply the
approximate proportionality factor, the VM can be
calculated roughly. According to Eq.(8), select the proper
temperature correction coefficient K. According to
Eq.(11), the Voc' can be calculated approximately under
the new environment.
Voc  Voc  Voc  K  T
(11)
Power curve is single peak function in the whole voltage
range. At the maximum power point voltage dP/dU = 0,
on both sides of the Vm are opposite, and the farther the
distance from MPP is, the greater the value of | dP/dU |
becomes.
At the MPP, dP/dV should be zero and the sign of dP/dV
may be identified by Eq. (12).
Y
Y
(12)
N
dI/dV=-I/V
I(k)-I(k-1)=0
N
dI/dV>-I/V
N
Y
Vref=Vref+step
Y
N
I(k)-I(k-1)>0
N
Y
Vref=Vref-step
Vref=Vref+step
Vref=Vref-step
Return
Fig.3 The flow chart of variable step conductance increment
method
Ⅳ. CONTROL STRATEGY OF INVERTER
The PV inverter consists of a diode, a dc-link capacitor, a
voltage source inverter (VSI) with a harmonic reduction
filter and a step-up transformer, as shown in Fig.5.
i2
ipv
S1
S3
S5
ic
+
Linv
udc
ia
ib
ic
Cdc
S4
O
dP
dI
 I U
0
dU
dU
V(k)-V(k-1)=0
S6
iga
igb
igc
S2
Cinv
Fig.5 Circuit model of a grid connection inverter
The design of the PV inverter control system uses double
In practical application, dI/dU is replaced by △I/△U, and
closed-loop control structure. The outer loop on the
compare the conductance of the working point (I/U) and
voltage of dc-link capacitor and reactive power control is
instantaneous value of conductance increment (△I/△U).
converted into the active current and reactive current
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2016 China International Conference on Electricity Distribution (CICED 2016)
Xi’an, 10-13 Aug, 2016
control. The inner loop current controller adopts the
Vq  Eq  LT
current feedback and voltage feed-forward decoupling
control strategy to realize the current fast tracking and
dI q
dt
  LT I d
(14)
outer loop controller is used for determining the current
In the synchronously rotating frame, ud and uq are the
reference value. The measurement and calculation
grid-side voltage, Vd and Vq are port voltage of the inverter
modules sense the three phase inverter current（ia、ib、
voltage, and ω is system angular frequency. Consider error
ic）, the three phase grid-side voltage （ua、ub、uc）and
is caused by the reactor and eliminated by PI controller Eq.
current and voltage of the three-phase static coordinate
(13) and (14) may be transformed into Eq. (15) and (16).
system are converted into two phase synchronous d-q
rotating frame. MPPT module monitors the PV array
Vd  Ed
N1
  LT I q  ud
N2
(15)
Vq  Eq
N1
  LT I d  uq
N2
(16)
current (IPV) and the dc-link voltage (Vdc) to use for
tracking the MPP of the PV array. The phase-locked-loop
(PLL) blocks and measures the phase of grid-side voltage
Esa to provide the reference phase angle used for d-q
transformation. In the synchronous rotating frame, the dc-
ud and uq can be expressed as Eq. (17) and (18)
link voltage and reactive power of the VSI can be
controlled separately by Iq and Id of the inverter. The input
ud  ( K p 
Ki *
)( I d  I d )
S
(17)
uq  ( K p 
Ki *
)( I q  I q )
S
(18)
of current controller is the output of outer loop, the output
of current controller are S1-S6 gate trigger signals which
are obtained from making a comparison between the
triangle wave and the reference of
VSI output port
voltage under synchronous d-q rotating frame, as shown
in Fig.6.
Ipv
L1
+
-
C1
Cdc
md
PCC
Detecting
currunt
and phase
SPWM
udc
L2
id iq
ud uq
idref iqref
Outer loop
controler
Eq
N1/N2
Vt.max
Detecting
voltage
and phase
θ ia,b,c
mq
Inner loop
controler
The Kp and Ki are the proportional and integral gains of
the PI controller. Based on above control equation, the
current controller may be implemented as shown in
Fig.7.
iqref
iq
θ ua,b,c
idref
park
+
+
-
id
-
PI
uq
- ++ Vq
ωLid
PI
ud - Vd
ωLiq
Vt
Vt=sqrt(Vtq2+Vtd2)
δ =tan-1(Vtq/Vtd)
Vt.min
δ
mq*
mq= Vt cosδ
md = Vt sinδ
md*
Q
Qref
Fig.7 Current controller of GPCS.
MPPT
udc，ref
udc
Ipv
Current controller compares the actual with reference
values of d-q rotating frame,and generates the reference
values Vd and Vq as the inverter voltage which are fed into
Fig.6 Control block diagram of GPCS
the terminal node. Through PWM the high frequency
The step-up transformer is equivalent to a reactor with
switching IGBT, m*d and m*q are transformed into actual
inductance LT ,and transformation ratio is N1–N2 .The AC
voltage Vd and Vq.
side voltage equation can be written as Eq. (13) and (14)
in the synchronously rotating frame[9].
dI
Vd  Ed  LT d   LT I q
dt
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Ⅴ. SIMULATION ANALYSIS
A. MPPT algorithm validation
PV array under standard conditions (25 ℃, 1000 W/m2)
(13)
parameters as: Voc,ref = 38.4 V, Isc = 8.37 A, Vm = 30.6 V,
Im = 8.17 A, NP = 6, Ns = 6.
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2016 China International Conference on Electricity Distribution (CICED 2016)
Table 1 Environment changing
Environment
Xi’an, 10-13 Aug, 2016
The output power of PV array and the change of gridconnected power as shown in Fig.9. When the
S/W/m2
t/℃
0~0.4s
800
25
conductance method tracks the MPP fast and realizes
0.4~0.8s
1000
25
transmission of active power from dc to ac smoothly.
0.8~1.2s
1000
35
Time
environment changes ， the variable step incremental
Set the changing environmental conditions according to
pin :pv output power
P: pv grid power
Table 1. As shown in Fig. 8, fixed step incremental
conductance method is adopted to track MPP. When
step=0.5V the dynamic response time is short, but the
oscillation of steady output voltage reference Vref is large.
When step=0.1V the oscillation of steady output voltage
reference Vref is small, but the dynamic response time is
pin :pv output power
P: pv grid power
long. Fixed step conductance incremental conductance
can’t meet the dynamic and static balance. The dynamic
response of variable step incremental conductance method
is faster than fixed step incremental conductance method
and oscillation of steady state voltage is smaller than
before and oscillation of steady state voltage is smaller
than before. The dynamic and steady state performance is
improved well.
Fig.9 The waveform of tracking power change
When double closed-loop control strategy is used,
assign in reference of reactive power Qref = 0, grid-side
of A phase voltage and current as shown in Fig.10,
which has realized the same phase angle of the phase
current and voltage, and the power factor approximates
to 1.
Voltage
△t=0.013s
△t=0.021s
Current
(a)
step=0.5V
Fig.10 Grid-connected current and voltage
△t=0.025s
When the irradiance changes from 800 W/m2 to 1000
W/m2, current amplitude changes from 46 A to 51 A
and output power increases. When S=1000W/m2,
t=25℃, we make the fast Fourier transform to A phase
current of which the harmonic content is 63 and
fundamental RMS is about 36.5A. As shown in Fig.11,
current harmonic distortion (THD) is 2.8%, meet the
requirements of grid-generation [10].
△t=0.05s
(b)
△t=0.003s
(c)
step=0.1V
△t=0.002s
Variable step
Fig.8 Voltage of MPP under different step
B.
Power control performance of the GCPS
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2016 China International Conference on Electricity Distribution (CICED 2016)
Fig.11 Grid-connected three phase current
[3]
Xi’an, 10-13 Aug, 2016
CHEN Wei, AI Xin，WU Tao, et al. Influence of grid-connected
photovoltaic system on power network[J]. Electric Power Automation Equipment, 2013, 33（2）：26-32, 39.
[4]
ZHOU Lin, Wu Jian, Li Qiuhua, et al. Survey of Maximum Power
Point Tracking Techniques for Photovoltaic Array[J]. High
Voltage Engineering, 2008, 34(6): 1145-1154.
[5]
Xiong Yuansheng, Yu Li, Xu Jianming. MPPT control of
photovoltaic generation system combining constant voltage
method
with
perturb-observe
method[J].
Electric
Power
Automation Equipment）, 2009, 29（6）：85-88.
[6]
Jiao Yang，Song Qiang，Liu Wenhua. Control strategy of gridconnected photovoltaic generation system based on modified
MPPT method[J].Electric Power Automation Equipment, 2010,
30（12）：92—96.
[7]
Chen Yaai, Zhou Jinghua, Li Jin, et al．Application of gradient
variable
step
size
MPPT
algorithm
in
photovoltaic
system[J]．Proceedings of the CSEE，2014，
34(19)：3156-3161．
[8]
Fig.12 Harmonic spectra of GCPS curren for S=1000W/m2
Rahman S A, Varma R K, Vanderheide T. Generalised model of a
photovoltaic panel [J]. Iet Renewable Power Generation, 2014,
Ⅵ.CONCLUSIONS
8(8):217-229.
On the basis of traditional incremental conductance
method, this paper proposed the method that combined
CVT with variable step length incremental conductance
method to make up for drawbacks of dynamic and
steady-state response of the traditional INC, and
reduced the power loss. The model and control method
of grid photovoltaic power generation system are
analyzed. Several dynamic performance of PV system
[9]
was evaluated including power control, grid current and
major in the motor operation control and new energy grid.
Zeng Q, Chang L, Song P. SVPWM-based current controller with
grid harmonic compensation for three-phase grid-connected
VSI[C]. IEEE PESC’04, 2004: 2494-2499.
[10] Technical requirements for connecting photovoltaic power station
to power system[S].
LI Cuiping(1982-): associate professor of Northeast Dianli University,
voltage, current harmonic. The simulation results show
that based on constant voltage tracking combined with
variable step length incremental conductance method of
photovoltaic power generation system can transmit the
power from dc to ac stably and to achieve operation with
unity power factor.
REFERENCES
[1]
ZHAO Zhengming，LEI Yi，HE Fanbo，et al. Overview of largescale grid-connected photovoltaic power plants[J]. Automation of
Electric Power Systems，2011，35（12）
：101-107.
[2]
DING Ming，WANG Weisheng，WANG Xiuli，et al. A review
on the effect of large-scale PV generation on power systems [J].
Proceedings of the CSEE，2014，34（1）：1-8.
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