Space vector modulated quasi z source inverter for photovoltaic application

Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
30-31, December, 2014, Ernakulam, India
100
SPACE VECTOR MODULATED QUASI Z-SOURCE
INVERTER FOR PHOTOVOLTAIC APPLICATION
JUBY JOSE1
, ARUNA T. A.2
1,2
Department of Electrical and Electronics Engineering, Sree Narayana Gurukulam College of Engineering,
Kolenchery, India,
ABSTRACT
The Z source Inverters (ZSI) overcomes the drawbacks of conventional Voltage Source and Current Source
Inverters. ZSI have the unique feature that its output can be controlled in both buck and boost mode in single stage
conversion. So ZSI is good choice for Photovoltaic applications. In this paper, a new topology of Z Source Inverter called
Quasi Z source Inverter is used for solar power applications, where both boosting and inverting of dc to ac power is
required. ZSI are capable of doing these in a single stage and so we can avoid the need of dc-dc booster. A novel
Maximum Boost control method based on Space Vector Pulse Width Modulation (SV PWM) is used here to control
Quasi ZSI output. Compared with traditional carrier based maximum boost control strategy, SVPWM has a wider linear
operating range and is easier for digital implementation. Also the number of switching transitions in each cycle is
reduced, which indicates less switching power losses. The simulation results in Matlab/Simulink platform are provided to
validate the theoretical study.
Keywords: Maximum Power Point Tracker (MPPT), PV cell, Quasi Z-Source Inverter (qZSI), Shoot-Through (ST),
Space Vector Pulse Width Modulation (SV PWM) , Z-Source Inverter (ZSI)
1. INTRODUCTION
IN recent years, the average rate of world primary power consumption has increased very much. Because of the
declining supply of petroleum, finding sustainable alternatives is becoming more and more urgent. Perhaps, the greatest
challenge is in devising a sustainable future, which relies on integration and control of renewable energy sources in grid
distributed generation. Generation of power locally at distribution voltage level by using non-conventional (or)
renewable energy sources like, solar photo voltaic cells, wind power, biogas, and fuel cell is known as Distributed
Generation(DG). Among the renewable energy sources, the worldwide-installed photovoltaic (PV) power capacity shows
nearly an exponential increase due to decreasing costs and improvements in solar energy technology.[6]The DC power
generated by solar array should be converted to suitable form to use it in different applications. For that, in solar power
conditioning systems, the interface converter system acts as the main component. Traditionally we had been using
Voltage Source Inverters (VSI) or Current Source Inverters (CSI) for applications of renewable sources. But these
inverters have many disadvantages like limited output, no immunity towards short circuits or open circuits and the need
of dead-time or overlap time in gate pulses to avoid short-circuits and open-circuits respectively in VSI and CSI. Also
when used with PV a dc-dc booster should be added (Fig.1), which increases the size and cost.
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
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ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 12, December (2014), pp. 100-110
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101
Figure1. Conventional solar power conditioning system
As a solution for these problems of VSI and CSI in 2002, F.Z. Peng [1] proposed a new topology for inverter
called Z-Source Inverters (ZSI) as shown in Fig. It is actually a combination of VSI and CSI consisting of a unique
impedance network with two capacitors and two inductors to couple the input source to the inverter bridge. ZSI has the
capability to give output in any range, i.e. buck or boost. The reason for all its advantages is the presence of an additional
switching state called Shoot-Through state where the load terminals are shorted. Later, to improve the performance of
ZSI, a new topology, Quasi ZSI (qZSI) was developed as shown in Fig.2. [2] Quasi ZSI has the advantages of lesser
value requirement impedance network components and continuous input current which avoids the input filter. In this
paper, Quasi ZSI is used for solar applications and the control of output is done by the newest scheme, Space Vector
Modulation. The block diagram of proposed system is in Fig.3. In the second chapter, ideas of PV cell its equivalent
circuit and modelling was discussed. Third chapter describes the MPPT used. Chapter 4 deals with analysis of qZSI and
chapter 5with Modified Space vector PWM for QZSI. Finally, the simulation results are given in chapter 6.
Figure 2. Voltage Fed Quasi ZSI
Figure 3. Block diagram of Solar powered qZSI

Proceedings of the International Conference on Emerging
2. PV CELL : EQUIVALENT CIRCUIT,
Solar cell is actually a PN junction,
of the solar cell are modelled as follows, see
proportional to the solar irradiation. This current (I
is termed as short circuit current (Isc). [7] [8]
The equations that describe I-V characteristics of the solar cell based on simple equivalent circuit are given below:
‫ܫ‬௅ ൌ ‫ܫ‬ௌ௛ ൅ ‫ܫ‬஽ ൅ ‫ ܫ‬ሺ1ሻ
‫ܫ‬௅ ൌ ‫ܫ‬ை ൬݁
೜ሺೇశ಺ೃೄሻ
಼೅ಲ െ 1൰ ሺ2ሻ
Hence, ‫ܫ‬ ൌ ‫ܫ‬௅ െ ‫ܫ‬ை ൬݁
೜൫ೇశ಺ೃೄ൯
಼೅ಲ െ 1൰ െ
௏ା
ோ
Where,
I is the cell current (A)
q is the charge of electron = 1.6x10-19
coloumbs
K is the Boltzmann constant (i.e. 1.38x10
T is the cell temperature (K)
IL is the light generated current (A)
Io is the diode saturation current (A)
RS, RSh are cell series and shunt resistance (ohms)
V is the cell output voltage (V)
A is an ideal factor depend on PV technology
The cells must be connected in series-parallel configuration on a module to produce enough hi
circuit for the solar module arranged in N
Figure
International Conference on Emerging Trends in Engineering and Management (ICETEM14)
102
PV CELL : EQUIVALENT CIRCUIT, MODELLING
Solar cell is actually a PN junction, and so it has similar characteristics as that of diodes
of the solar cell are modelled as follows, see Fig.4. The current source generates the photocurrent I
proportional to the solar irradiation. This current (IL) continue to flow without externally applied voltage and this current
[7] [8]
Figure 4. Equivalent circuit of PV Cell
V characteristics of the solar cell based on simple equivalent circuit are given below:
൰
ାூோೄ
ோೄ೓
ሺ3ሻ
coloumbs
K is the Boltzmann constant (i.e. 1.38x10-23 J/K)
are cell series and shunt resistance (ohms)
A is an ideal factor depend on PV technology
parallel configuration on a module to produce enough hi
circuit for the solar module arranged in NP parallel and NS series is shown in Fig.5. [7]
Figure 5. Generalized model of solar cell module
Trends in Engineering and Management (ICETEM14)
, December, 2014, Ernakulam, India
and so it has similar characteristics as that of diodes. The various parameters
generates the photocurrent IL, which is
) continue to flow without externally applied voltage and this current
V characteristics of the solar cell based on simple equivalent circuit are given below:
parallel configuration on a module to produce enough high power. The equivalent

103
Now equation (3) can be written as
‫ܫ‬ ൌ ܰ௉‫ܫ‬௅ െ ܰ௉‫ܫ‬ை ቌ݁
೜൬
ೇ
ಿೄ
శ
಺ೃೄ
ಿು
൰
಼೅ಲ െ 1ቍ െ
௏
ேೄ
൅
ூோೄ
ேು
ܴௌ௛
ሺ4ሻ
The typical current-voltage (I-V) and power-voltage (P-V) characteristic curves of a PV solar cell is shown in Fig 6.
.
Figure 6. P-V and I-V characteristics of solar cell
3. MAXIMUM POWER POINT TRACKING (MPPT)
The output power of PV cell depends mainly on the level of solar radiation and ambient temperature. To obtain
maximum efficiency of panel, the system must operate at or near the Maximum Power Point. To obtain this maximum
power from PV array, a Maximum Power Point Tracker is inserted in circuit. It varies the electrical operating point of the
PV panels so that they can deliver the maximum available power. In this paper, Perturb and Observe algorithm is used
due to the ease of implementation.
These technique is based on voltage reference adjustment to achieve maximum power point. In this algorithm a
small perturbation is introduced to the system. Due to this perturbation the power of the module changes. If the power
increases due to the perturbation then the perturbation is continued in that direction. After the peak power is reached the
power at the next instant decreases and hence after that the perturbation reverses. When the steady state is reached the
algorithm oscillates around the peak point. In order to keep the power variation small the perturbation size is kept very
small.[9] The flow chart of the algorithm is shown in the fig.8.
Figure 7. Sign of dP/dV at different positions on the power characteristic

Proceedings of the International Conference on Emerging
Figure 8
4. QUASI Z-SOURCE INVERTER
Like ZSI, Quasi ZSI has also nine switching
and a shoot-through zero state. The ST state can be made by shorting one or two or three legs of inverter. Thus total
seven combinations of ST states are there.
4.1 Mode 1: Non Shoot-Through Mode
In the non-shoot through mode, six active states and two conventional zero states
viewed from the DC side is equivalent to a current source
Figure 9. Equivalent circuit of QZSI in Active mode (Non Shoot
International Conference on Emerging Trends in Engineering and Management (ICETEM14)
104
Figure 8. Flowchart of P and O MPPT algorithm
SOURCE INVERTER
, Quasi ZSI has also nine switching states including six active states, two non shoot
. The ST state can be made by shorting one or two or three legs of inverter. Thus total
of ST states are there. We can divide working into two operational modes [
Through Mode
shoot through mode, six active states and two conventional zero states are there
viewed from the DC side is equivalent to a current source, as shown in Fig. 9
. Equivalent circuit of QZSI in Active mode (Non Shoot through
Trends in Engineering and Management (ICETEM14)
, December, 2014, Ernakulam, India
states including six active states, two non shoot-through zero states
. The ST state can be made by shorting one or two or three legs of inverter. Thus total
operational modes [2].
are there. The inverter bridge,
through State)

105
4.2 Mode 2: Shoot Through Mode
In the shoot through mode, both switches in at least one phase conduct simultaneously for a very short duration.
The DC link voltage during the shoot through states, is boosted by a boost factor, whose value depends on the shoot
through duty ratio. The equivalent circuits in shoot through state is shown in Fig.10
4.3 Circuit analysis
Assuming that during one switching cycle, T , the interval of the shoot through state is T0 ; the interval of non-
shoot-through states is T1 ; thus one has T = T0 + T1 and the shoot-through duty ratio, D= T0 /T .[1] [2] From Fig.9 which
is a representation of the inverter during the interval of the non-shoot-through states,T1, we get
‫ݒ‬௅ଵ ൌ ܸ௜௡ – ܸ஼ଵ , ‫ݒ‬௅ଶ ൌ െ ܸ஼ଶ (5)
‫ݒ‬௉ே ൌ ܸ஼ଵ െ ‫ݒ‬௅ଶ ൌ ܸ஼ଵ ൅ ܸ஼ଶ ; ‫ݒ‬ௗ௜௢ௗ௘ ൌ 0 (6)
During To , ‫ݒ‬௅ଵ=ܸ஼ଶ+ ܸ௜௡ ,‫ݒ‬௅ଶ =ܸ஼ଵ (7)
‫ݒ‬௉ே ൌ 0 ; ‫ݒ‬ௗ௜௢ௗ௘ ൌ ܸ஼ଵ ൅ ܸ஼ଶ (8)
At steady state, the average voltage of the inductors overdone switching cycle is zero
The peak dc-link voltage across the inverter bridge is
‫ݒ‬ො௉ே ൌ ܸ஼ଵ ൅ ܸ஼ଶ ൌ ‫ܸܤ‬௜௡ ሺ9ሻ
‫ܤ‬ ൌ
1
1 െ 2‫ܦ‬଴
ሺ10ሻ
Where B is the boost factor and Do is the Shoot-Through duty ratio of the qZSI. The output peak phase voltage, vac from
the inverter is derived in [1] [2] as:
‫ܿܽݒ‬ෞ ൌ ‫.ܯ‬ ‫ܤ‬
ܸ௜௡
2
ሺ11ሻ
M is the modulation index.
Figure 10. Equivalent circuit of QZSI in Shoot through state
5. MODIFIED SPACE VECTOR PWM FOR QUASI ZSI
Space vector modulation (SVM) for three-leg VSI is based on the representation of the three phase quantities as
vectors in a two-dimensional plane. The desired three phase voltages at the output of the inverter could be represented by
an equivalent vector Vref rotating in the counter clock wise direction as shown in Fig. 11. The magnitude of this vector is
related to the magnitude of the output voltage and the time this vector takes to complete one revolution is the same as the
fundamental time period of the output voltage. [10]

106
Figure 11. Switching Space Vectors
The traditional Space Vector Modulation Scheme can be modified by inserting shoot-through states in place of
non shoot-through zero states. This modified SV PWM can be used to control the quasi ZSI.[5] The boost can be
controlled by adjusting the time of shoot- through conduction.[3] The modified gate pulses for sector 1 is shown in fig.12
Figure 12. Switching patterns used for space vector modulation of ZSI
By abc-dq transformation given in equation (12) we can find component vectors for all the fifteen basic switching vectors
of qZSI, given in Fig.13
ܶ௔௕௖ିௗ௤ ൌ
‫ۏ‬
‫ێ‬
‫ێ‬
‫ۍ‬
2
√6
െ
1
√6
െ
1
√6
0
1
√2
െ
1
√2‫ے‬
‫ۑ‬
‫ۑ‬
‫ې‬
ሺ12ሻ
Figure 13. Space vector PWM switching vectors of ZSI

107
The objective of space vector PWM technique is to approximate the desired output voltage by setting proper
switching patterns of the power transistors. The required output voltage vector Vref can be approached using the linear
combinations of several of the fifteen basic space vectors according to the following equation (13)
ܸሬԦ௥௘௙ ൌ
ܶ௜
ܶ
ܸሬԦ௜ ൅
ܶ௝
ܶ
ܸሬԦ௝ ൅
ܶ଴
ܶ
൫ܸሬԦ଴, ܸሬԦ଻൯ ൅
ܶ௦௛
ܶ
ܸሬԦௌு௞ ሺ13ሻ
ሺ݅, ݆ ൌ 1~6, ݇ ൌ 1~7ሻ
Where, Vref represents the desired two dimensional phase voltage vectors in the d-q plane and Vn and Tn
represent one of the nine basic space vectors and the corresponding duration. T represents one switching period. The
reference voltage vector Vref of three-phase ZSI is obtained by mapping the desired three-phase voltages to the d-q plane
through the following equation:
ܸሬԦ௥௘௙ ൌ ൤
ܸௗ
ܸ௤
൨ ൌ ܶ௔௕௖ିௗ௤ ൥
ܸ௔
ܸ௕
ܸ௖
൩ ൌ
√6
2
ܸ෠௣௛ ൤
cosሺ߱‫ݐ‬ሻ
sinሺ߱‫ݐ‬ሻ
൨ ሺ14ሻ
In order to reduce the switching loss, the shoot-through states having two or three legs shorted will never be
chosen. In addition, the switching patterns should be symmetrical for the sake of a low total harmonic distortion and easy
implementation. The details of working out the duration of each vector and the switching patterns are discussed as
follows. The detailed calculation for sector 1 is given below [3].
For Sector 1: 0 ≤ ߠ ≤
గ
ଷ
. Therefore from fig.13 we can write
ܶ. ܸ‫݂݁ݎ‬ ቂ
cos ߠ
sin ߠ
ቃ ൌ ܶ4 . ܸ4 ቂ
ܿ‫ݏ݋‬ 0
‫݊݅ݏ‬ 0
ቃ ൅ ܶ6 . ܸ6 ൦
ܿ‫ݏ݋‬
ߨ
3
‫݊݅ݏ‬
ߨ
3
൪ ሺ15ሻ
And from, ܸ‫݂݁ݎ‬ ൌ
√଺
ଶ
ܸܽܿ ሺ16ሻ
ܸ‫݂݁ݎ‬ ൌ
√6
4
‫.ܯ‬ ܸ௉ே ሺ17ሻ
Solving we get
ܶ4 ൌ
√3
2
ܶ. ‫ ܯ‬ sin ቀ
ߨ
3
െ ߠቁ ሺ18ሻ
ܶ6 ൌ
√ଷ
ଶ
ܶ. ‫ ܯ‬ ‫݊݅ݏ‬ ߠ (19)
ܶ‫݋‬ ൅ ܶ‫ݏ‬ℎ ൌ ܶ െ ܶ‫݋‬ െ ܶ‫ݏ‬ℎ ሺ20ሻ
In the similar way we could derive the equations for all the six sectors.
6. SIMULATION RESULTS
PV cells are connected in series and parallel to get an average output voltage of 120 V. The inductor capacitor
values are designed as explained in [11]. The overall matlab model and the SV PWM subsystems are shown in Fig.15
and Fig.15.The parameters of the simulated system are as follows:
Switching frequency, fs = 10 KHz
Modulation Index, M = 0.8
Boost factor, B = 1.6
Inductances, L1=L2= 1 mH
Capacitances, C1=C2= 1.3µF

108
Figure 14. Matlab model of proposed system
Figure 15. Matlab model of Space Vector PWM
The output line and phase voltages are in Fig.16 and Fig.17. From the waveforms it is clear that the qZSI is able
to give boosted output. We give an input voltage of 120 V and obtained a line voltage peak of 170 V. The FFT analysis
done (Fig. 18) shows very lesser THD value. A graph is plotted between Voltage gain and modulation index for different
methods of PWM, Fig.19. Comparing with other traditional methods voltage gain is also good for SV PWM.
Figure 16. Output phase voltage of Quasi ZSI

109
Figure 17. Output Line Voltage of Quasi ZSI
Figure 18. FFT analysis of qZSI with SV PWM
Figure 19. Voltage gain, G Vs Modulation Index, M

110
7. CONCLUSION
The scope of solar applications is increasing now-a-days. ZSI is a good choice for applications of photovoltaic
energy systems where both buck and boost output are required. Improved topology of ZSI called Quasi Z source inverter
is used in this project which reduces the required capacitance to a great extent and make the input current continuous. In
SV PWM, switching patterns are designed to reduce the Switching losses and to get a symmetric waveform to reduce
total harmonic distortion. For the same Modulation Index, voltage gain of SVPWM is found to be maximum. Compared
with the traditional carrier-based maximum boost control strategy, the proposed Space Vector technique has a wider
linear operation range and is easier for digital implementation. Also the number of switching transition in each switching
cycle is reduced, which indicates less switching power losses. It will be beneficial for the further industrial applications
of the ZSIs. Matlab simulations validates the theoretical analysis.
REFERENCES
[1] Fang Zheng Peng, Z-Source Inverter, IEEE Transactions on Industry Applications, March/April 2002,
vol.39,no.2.
[2] Joel Anderson and F.Z.Peng, Four Quasi-Z-Source Inverters, Power Electronics Specialist Conference PESC’39th
IEEE, 15-19 June 2008,pp 2743-2749.
[3] Kun Yu, Fang Lin Luo, Miao Zhu, Space Vector Pulse Width Modulation Based Maximum Boost Control of Z
Source Inverters,IEEE Transactions on Industry Applications,2012
[4] F. Z. Peng, Miaosen Shen, Zhaoming Qian, Maximum Boost Control of Z-Source Inverters, in Proc. IEEE PESC
2004
[5] P. C. Loh, D. M. Vilathgamuwa, Y. S. Lai, G.T Chua, Y. Li, Pulse Width Modulation of Z Source Inverters, 2004
IEEE Industry Application Conferences,pp.148-155
[6] Bialasiewicz T, Renewable Energy Systems with Photovoltaic Power Generators: Operation And Modelling, July
2008, IEEE Transactions on Industrial Electronics, vol.55,no.7,pp.2752-2758.
[7] Zameer Ahmed,S.N.Singh, Extraction of Internal Parameters of Solar Photovoltaic Module by developing
Matlab/Simulink Based Model, ISSN 2012,vol.7,no.11
[8] Sonal Panwar, R. P. Saini, Development and Simulation of Solar Photovoltaic model using Matlab /Simulink and
its parameter extraction, International Conference on Computing and Control Engineering, April 2012
[9] Samer Alsadi, Basim Alsayid, Maximum Power Point Tracking Simulation for Photovoltaic Systems using
Perturb and Observe Algorithm, IJEIT ,December 2012, vol.2,pp.80-85.
[10] O. Ogasawara, H. Akagi, and A. Nabel, A novel PWM scheme of voltage source inverters based on space vector
theory, in Proc. EPE European Conf. Power Electronics and Applications, 1989, pp. 1197–1202.
[11] M. Hanif, M. Basu, K. Gaughan, Understanding the operation of a Z-source inverter for photovoltaic application
with a design example, IET Power Electronics, 2011 vol.4, Iss.3,pp. 278-287.
[12] Minakshi DebBarma, Sumita Deb, Champa Nandi, Sumita, “Maximum Photovoltaic Power Tracking Using
Perturb & Observe Algorithm In Matlab/Simulink Environment” International Journal of Electrical Engineering &
Technology (IJEET), Volume 1, Issue 1, 2010, pp. 71 - 84, ISSN Print : 0976-6545, ISSN Online: 0976-6553.

Space vector modulated quasi z source inverter for photovoltaic application

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