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A Fast MPPT Algorithm For Single Stage
Grid-connected PV Inverter
GU Jun-yin
School of Electromechanical Engineering and Automation
Shanghai University
Shanghai, China
CHEN Guo-cheng
School of Electromechanical Engineering and Automation
Shanghai University
Shanghai, China
Abstract – In this paper, the power coupling relationship between
the PV array, the filtering capacitor, and the grid-connected PV
inverter was analyzed. The P/V characteristic was categorized
into three sections, the unstable area, the stable area, and the
sliding-mode stable area, a judging criterion was given. Through
theoretical and mathematical analysis, the periodic power
coupling can be reflected by the capacitor voltage and its change
in monotony. Based on the power decoupling of the capacitor in a
power cycle, by precisely calculating the required power
reference for the inverter in the following cycle, the MPPT
process can be optimized. The proposed method is especially
efficient during the MPPT dynamic process, i.e. during start-up
or when solar radiation changes sharply. An experimental 180W
prototype is designed for verification of the theoretical analysis.
Keywords – grid-connected PV inverter; MPPT; power
coupling; filtering capacitor
I. INTRODUCTION
PV grid-connected inverters can be placed into single and
double stage inverter based on their high-frequency power conversion stages. Since the single stage inverter has only one high-frequency power conversion stage, it has many significant advantages, i.e. high conversion efficiency, highutilization of photovoltaic components and high reliability [1-5]. As shown in Figure 1, a single stage grid-connected PV system includes the PV module, a grid-connected inverter and the filtering capacitors. The PV module’s output has approximately a constant power flow, however the inverter’soutput has periodic fluctuations due to its grid-connecting requirement. Therefore, filtering capacitors with large enough capacity are necessary to balance the transient power difference between the inverter and PV module. The filtering capacitors in turn cause power coupling between the PV module and the inverter.
The nonlinear relationship of the PV module’s output power and its output voltage is shown in Figure 2. In order to achieve maximum output power, the PV module needs to be “controlled” by using a maximum power point tracking (MPPT) method [5-13]. The MPPT method is generally
PVpinvp
cppvC
po
PV module AC Power
Single-stage
grid-connected
inverter
Figure1. Single stage grid-connected PV power system
implemented with a small perturbation in the output power of the PV module. This allows for the determination of the PV module’s output power changing trend, which will define the next step of the algorithm. The small perturbation method assumes that the characteristic of the PV module output is stable. However, light and temperature conditions or other external factors can significantly change the output characteristics of the PV module. Due to the filtering capacitors power coupling effect, the change of PV module output power cannot be reflected by the inverter’s output power in real time. For that reason, the MPPT based on the steady-state analysis cannot guarantee that the inverter’soutput power can follow the changes in the PV module’s output power in real time. In the worst case, the MPPT algorithm may fail, which will lead to a system crash.
References [5-6] state that by using a single stage photovoltaic inverter, the capacitor’s voltage fluctuation reflects the power relation between the PV module and the inverter. Current-sensor-less MPPT algorithms are analyzed,but no steady-state or dynamic performance analysis is given.Reference [7] analyzes the steady-state performance of the MPPT affected by the capacitor’s energy storage in singlestage inverter. However, it does not analyze the mutual relationship between the dynamic MPPT performance and the energy storage in the capacitor. Reference [9] analyzes the stability of the MPPT algorithm of a single stage inverter withthe introducing of a variable step algorithm to improve the dynamic performance, but it does not analyze the effect of the storage capacitor on the MPPT performance.
In this paper, the power coupling of the filtering capacitor in a single stage grid-connected inverter is studied. The output characteristic of the PV module is divided into a non-stable
960978-1-4577-2119-9/12/$26.00 c©2011 IEEE
area, a stable area, and a sliding mode area, with an identification criteria being given. If the output power of the
1A
0A
2A2B
0B
1B
p
u
pm
um
A Zone M Zone B Zone
Figure2. The P/V characteristic of the PV array
PV module changes abruptly, the filtering capacitor’s voltage changes and the power coupling relationship between the PV module, filtering capacitor, and grid-connected inverter can be used to accurately calculate the required power reference forthe inverter in the following cycle, by analytical calculations.Within one power cycle, the power of the PV module, filteringcapacitor, and inverter is decoupled so to optimize the tracking process of the MPPT and to improve its dynamic performance.
II. CAPACITOR VOLTAGE AND INSTANTANEOUS POWER
WAVEFORM
Architecture of single stage grid-connected PV system is shown in Figure 1. In this figure, pPV is the output power of PV module, pc is the filtering capacitor's power, and pinv and po
are the inverter's input and output power, respectively. If the inverter losses are ignored, both are approximately equal. According to instantaneous power balance:
c pv inv pv op p p p p
The inverter’s output power po is calculated by:
2ˆ sin , 100o op p t
ˆop is the peak output power of the inverter.
From equation (2) it can be seen that the inverter’s output power po has a large ripple in the DC component, while the PV module’s output power is approximately a constant DC flow. Between the PV module and the inverter, a capacitorwith large enough capacity is necessary to achieve power decoupling between both sides. In the single stage grid-connected inverter system, the capacitor voltage uc is equal tothe output voltage of the PV module. The slope of the capacitor voltage is decided by the power flow direction in the capacitor. From figure 2, equations (1) and (2), the time domain relationship of the voltage and power of the PV module can be obtained, as shown in Figure 3. By analyzing these elements, the graph area formed by pinv and pPV
waveforms reflects the power coupling in the system, while the slope of the capacitor’s voltage uc, reflects the system’s
operating zone, such as will be demonstrated in the next section.
A. Power coupling relationship analysis
( )t t
p
0
0
cu
pvp
invp
1 1( )t2 2( )t ( ) 3 3( )t 4 4( )t
( )t t
1N 2N
3N
4N
1L2L
1C
2C
IS
IIS
Figure3. The waveform of the capacitor voltage and instantaneous power
In figure 3, N1, N2 and N3 are the intersection pointsbetween the PV module’s output power pPV and the inverter’s output power po. L1 and L2 are the subsection of the pPV
waveform between N1 to N2 and N2 to N3, respectively. C1 and C2 are the subsections between N1 to N2 and N2 to N3 of the pinv waveform, respectively. SI is the area surrounded bythe C1 and L1 lines and SII is the area enclosed by the C2 and L2
lines.
The SI area shows that the inverter’s output power is greater than the PV module’s output power, so the capacitor discharges, and its voltage uc is decreasing. SII shows that theinverter’s output power is less than the PV module’s output power, so the capacitor is charging, and its voltage uc is increasing. If the area SI is equal to SII, the stable operating point is reached, the net power flow of the capacitor is zeroover one cycle of the grid’s power waveform. In that case, the inverter’s output power and the PV module output power, over one cycle, are decoupled.
B. Monotonic relationship analysis
When the system is working in zone A, pPV is rising with the increase in uc, while in zone B, pPV and uc are inversely proportional. If the system is working in zone M,corresponding to the N1 to N2 and N2 to N3 segments of Figure 3, the waveform is no longer monotonic, each section is convex, and the limit points on these sections correspond to the MPP. As the PV power’s waveform is approximately symmetric in the M region, the N1 to N2 and N2 to N3 segmentsof the waveform are also symmetric in the time domain.Therefore, according to the relationship between the p-t and u-t curves, we can determine which region the system is operating in.
From the above analysis, the peak/bottom points of the capacitor voltage waveform correspond to the intersectionpoints of the PV module and inverter output power waveforms.The angles of the intersection at these points reflect not only the system’s operating region but also, whether the capacitor’s
2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) 961
power is decoupled or not, meaning that the system is eitheroperating in the stable or unstable point.
In Figure 3, 1 is the corresponding angle at t1 and 2 is the corresponding angle at t2. When the system is in the linear region (zone A or B), from t1 to t2, the power variation is given by:
2 22 1ˆ (sin sin )op p
The capacitor’s voltage uc decreases monotonically if the inverter’s output power is more than the PV module’s output power, corresponding to the section between N1 and N2 in Figure 3.
If the PV module is operating in zone A the output power is decreasing monotonically, corresponding to the section N1
to N2 and 0p ; whereas in Zone B, 0p . Therefore, by
detecting the capacitor’s voltage behavior, the angles
1and 2 of the slope change can be obtained. Furthermore,
we can determine if p is negative or positive, which can
determine if the system’s operating point is in region A or B. In the M region, the PV module’s power waveform is
approximately symmetrical, so 1 2 , and p is
approximately zero. In figure 4(c) the L1 section is not monotonic, because the system rolled over the MPP. So the L1
section presents a convex shape.
Irrespective of which area the system is operating in, the pc
changes direction at every intersection of the inverter and PV module’s output power waveform.
III. STABILITY AND DECOUPLING CONDITION ANALYSIS
By the analysis decribed below, near the MPP the system shows a stable "variable structure sliding mode movement" with a small swing. Therefore, the power decoupling in the M zone constitutes a sufficient condition for stability of MPP.
A. Stability Analysis
In Figure 2, the system is assumed to be operating in the stable point either at A0 or B0. If there is a positive disturbance on the inverter’s output power po at A0 point, this will lead to reduction in voltage of the filtering capacitor. The PV module’s output power Ppv is correspondingly decreasing. The system moves from the A0 to A1; the decreasing of pPV means that thecapacitor is outputting power, thus uc further declines. The process of uc and pPV decrease constitutes a positive feedback, which will eventually lead to a system failure. If there is a negative po disturbance, uc will increase, the system will movefrom the A0 to A2 and pPV will increase, this means that the capacitor is absorbing energy. This movement will further increase uc, which also constitutes a positive feedback. This process will cause the system to go over the PV characteristic maximum point. Zone A is the unstable region, therefore operation in this area should be avoided.
At the B0 point, if the inverter’s output power po has a
positive disturbance, this will lead to a lower uc, which means
that pPV increases and the system moves from B0 to B2. The
increasing of pPV means that the capacitor is absorbing energy,
therefore uc rises and the system’s movement from the B0 to
B2 is suppressed automatically. Similarly, when there is a
negative disturbance in po, the movement from B0 to B1 is also
suppressed and the system will move back to point B0. These
two processes are both are negative feedback processes,
therefore zone B is a stable region.
In the M zone, the system is in a specially stable state, i.e.the system is oscillating between stable and unstable regions
due to the "variable structure sliding mode movement". The
system’s variable structure is the first necessary condition for
sliding movement occurrence. Whether the system is moving
from the stable zone to unstable zone or the opposite situation
is occurring, the monotonic change of PV module’s output
characteristics corresponds to the change of the system’s
structure. Therefore, the MPP represents the variable structure
changing point. The second necessary condition is the polarity
change of the control law. When the intersection between the
inverter power waveform and the PV output power waveform
occurs, the polarity of the power flow changes, which
corresponds to the polarity change of the control law.In that control mode, if the capacitor’s power is decoupled,
there will be no change in the voltage in a power cycle, the system rolls over the relative maximum points of the PV power waveform and then reversely slips back to the initial point. Therefore, the MPPT issue will be transferred intodecoupling issues in the capacitor’s power after the system enters into the M zone.
B. Analysis of power decoupling conditions
In Figure 3, if the system is operating either in zone A or B,
L1 and L2 are approximately straight lines. So C1 and C2 L1
and L2 can be, respectively, given by the following formulas:
2
1 1 2
2
2 2 1
1 2 1
1 1 2
1 2 1
2 2 1
2 2 1
2 2 1
: sin , ,
: sin , ,
: , ,
: , ,( )
o
o
C p t t
C p t t
p p p pL
p p p pL
From the integration below, SI and SII can be obtained:
2
1
2 2 22 1
2 1
2 1 2 1
2 22 1
2 1
ˆˆ sin ( ) (sin sin )2
sin 2 sin 2ˆˆ
2 4
ˆ (sin sin )2
I o o
o o
o
S p td t p
p p
p
962 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)
2 22 1
2 1
2 1 2 1
( )ˆ (sin sin )
2
( ) sin 2 sin 2ˆ ( )
2 4
II o
o
S p
p
Through the analysis above, if power decoupling is required,it is necessary to ensure that SI is equal to SII. If the SI is equal to SII, the following can be obtained:
2 21 2sin sin 1
From equation (7) following conclusions can be derived: If
the system is operating in a stable mode, then 2 1- / 2 . If
the system is operating in zone A, then 1 2
3
4 4;
likewise, in zone B, then 1 2
3
4 4.
In the M zone L1, L2 are not linear, the equations (4) to (7)
are an approximation, then we may let 1 2
3= = -
4 4+ ,
where is a very small value.
( )t t
p
cu
1 1( )t( )t t
2 2( )t ( ) 3 3( )t 4 4( )t
PVp
invp
0
0
1N
2N
3N
4N
(a) A ZONE
( )t t
p
cu
1 1( )t( )t t
2 2( )t ( ) 3 3( )t 4 4( )t
PVpinvp
0
0
1N
2N3N
4N
(b) B ZONE
( )t t
p
cu
1 1( )t( )t t
2 2( )t ( ) 3 3( )t 4 4( )t
invppvp
0
0
1N
2N
3N
4N
(c) M ZONE
Figure4. The waveform of the capacitor’s voltage and instantaneous
power in different area
IV. ACTIVE DECOUPLING FOR FAST MPPT
The purpose MPPT is to achieve maximum power generation. Therefore, the MPPT algorithm needs to assess two indicators: the time duration that the system takes to reach the MPP and the amplitude variation of power or voltage whenhaving reached the MPP.
Based on the foregoing analysis, if there is powerdecoupling of the capacitor at MPP, the "variable structure sliding mode movement" is automatically implemented within the system. However, if the system does not enter the M zone, power decoupling is not necessary, since whether in zone A or B, power decoupling means that the system is relatively stable at that point. Particularly when the system has started from the open circuit voltage, if the power decoupling occurs in zone B, the progress to the M zone will be slow. The fast MPPT should be able to track the PV module’s output power to pm in the quickest way, that also means the capacitor voltage, which is equal to PV module’s voltage, lowers to ucm in the same manner. That is inturn equivalent to that the inverter outputsmaximum power. After rising to pm, if decoupling is introduced, the system is stablized which means that the system enters intothe "variable structure sliding mode movement" state.
In figure 4 either in zone A or B, the midpoint of the L1
section is given by:
2 21 2 1 2sin sin
ˆ2 2
m inv
p pp p
If the system is decoupled, by using equation (7) and
equation (8), ˆ / 2m invp p is obtained. Therefore, if
ˆ 2inv mp p is given as power reference in the next power
cycle, the decoupling can be approximatly achieved.
The decoupling method above is especially suitable for system start-up and sharp radiation changes.
2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) 963
V. EXPERIMENTAL RESULTS
An experimental prototype was designed with the following parameters:
Tab. 1 Parameters of the experimental prototype
Parameter Value
Rated Power/VA 200
Input Voltage/V 30
Filtering Capacitor/uF 8800
Switching Frequency/kHz 151.2~448.9
Transformer’s Winding ratio 1 6
Primary Inductance/uH 6Output Inductance/uH 600
An in-house PV simulator was used to simulate the PV panel’s output characteristic. As the key issue in this paper is to further investigate the system’s dynamic performance, differnent MPPT algorithms can be tested. The perturb and observe (P&O) method is evaluated here.
Uc:10V/div
iinv:0.5A/div
t:400ms/div
(a) MPPT without decoupling control
Uc:10V/div
iinv:0.5A/div
t:400ms/div
(b) MPPT with decoupling control
Uc:10V/div
iinv:0.5A/div
t:20ms/div
(c) Expanded waveform of graph b
Figure5. Start-up waveforms
Uc:10V/div
iinv:0.5A/div
t:40ms/div
(a) MPPT without decoupling control
Uc:10V/div
iinv:0.5A/div
t:40ms/div
(b) MPPT with decoupling control
Figure6. Waveforms when PV module output power changed
In figure (5) and (6), uc is the filtering capacitor’s voltage,and iinv is the inverter’s output current waveform. From the comparison of figure 5 (a) and (b), by adding the decoupling algorithm, it can be seen that, the system’s start-up time isshorter than that without decoupling control. The start-up time can be reduced approximately by half. From Figure 5 (c) it can be seen that, by adding the decoupling algorithm, the system starts at maximum power. When the capacitor voltage reaches the maximum power point, the capacitor’s power coupling can be removed within a power cycle, to ensure the system to stay in M zone. Therefore, fast MPPT is achieved.
Figure 6 shows the experimental comparison of the waveforms before and after adding decoupling control when the power at MPP of the simulator drops from 160W to 90W.Figure 6 (a) is the experiment waveform without decouplingcontrol. It can be seen that at the moment in which the power drops abruptly, the system can not respond immediately in order to track the power change, resulting in an abrupt input voltage drop also. After this the voltage slowly rises again.Figure 6 (b) is the experiment waveform with the decouplingcontrol. At sharp change in PV module characteristics, the system can stabilize the capacitor’s voltage within a single cycle. Therefore the system is safe from a voltage collapse.
Fast tracking can be achieved and the stability of the system’s performance can be ensured from the above analysis.The experimental waveforms show the validity of the proposed decoupling control method.
VI. CONCLUSION
By analyzing the power coupling relationship between the single stage grid-connected inverter, the PV module andfiltering capacitor, the adverse effects of the filtering capacitor’s energy storage, in the process of maximum power tracking, are highlighted. Through theoretical analysis, a method for removing the power coupling of the filteringcapacitor and eliminating the adverse effects on the maximum
964 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)
power tracking, based on the regulation of the change in thefiltering capacitor voltage, was presented. The proposed method can eliminate the coupling relationship of the filteringcapacitor in a single power cycle. The method can improve the dynamic performance of the MPPT. The principle of activedecoupling presented in this paper, can be combined withdifferent MPPT methods in order to optimize the maximum power tracking process.
ACKNOWLEDGMENTS
The authors wish to thank the strong support fromINVOLAR Co. (Shanghai), and to express heartfelt gratitude toProf. Yan Xing, Dr. Li Zhang and Dr. Hongfei Wu from the Nanjing University of Aeronautics and Astronautics, for providing valuable discussions and materials.
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