Performance Analysis of Series Z-Source
Four Switch Three Phase Inverter Fed
Induction Motor Drive 1R. Arivuselvi,
2T.K.S. Sathyanarayanan,
3A.V. Sindhuja and
4Srinivasan
1,2,3,4 Dept. of Electrical & Electronics Engineering,
Tagore Engineering College,
Rathinamangalam, Chennai, India.
Abstract This paper investigates the performance of a reduced switch three phase
series Z-source inverter fed cost effective induction motor (IM) drive
system. The objective of the paper is to minimize the THD and reduces the
overall cost of the system. This paper explores the series Z-source inverter
(SZSI) topology for induction motor (IM) with solar photovoltaic (PV) as
source in drive application. Series Z-source inverter has single stage power
conversion with buck-boost capability. Shoot through ratio is used for
boosting dc link voltage in series Z- source inverter. In this paper, for
enhancing the performance of SZSI improved shoot through envelops
technique along with sinusoidal pulse width modulation control technique
.The major benefits of modified boost control technique are current
reduction and harmonics reduction in output voltage as compared to
simple boost control scheme. The validity and feasibility of modified boost
control technique for shoot through envelop to control SZSI fed induction
motor is verified by simulation results.
Index Terms: Series z source inverter, four switch three phase inverter,
voltage sags.
International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 2945-2960ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
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1. Introduction
Series Z-Source Inverter (ZSI), shown in Fig. 1, has been proposed to overcome
the limitations of traditional voltage source inverter (VSI) and the traditional
current source inverter (CSI). In a traditional voltage source inverter, the two
switches of the same phase leg can never be gated on at the same time, due to
the reason of short circuit. SPV fed converter system requires buck-boost
capability to satisfy the load requirement. It requires two stage power
conversion. This two-stage power conversion increases volume, cost and
degrades the reliability of system. In series ZSI, LC-network and inverter bridge
are in series. This series combination is connected across dc source, which
shows the reduced voltage across both capacitors. which is one of the suitable
topology in photovoltaic system. The Z-source inverter beneficially infuses the
shoot through states to step up the dc bus voltage by gating on both the switches
of a same leg. Therefore, the series Z-source inverter can step up step down the
voltage to a desired output voltage that is greater than the given input dc bus
voltage. The reliability of the inverter is improved to protect the circuit. Thus it
offers high reliable, low-cost and single-stage structure for buck boost power
conversion. To reduce the cost of the inverter and to boost up the voltage, this
switched inductor z-source four switch inverter which gives the chopper
operation includes and provides the good solution. These switched inductors are
mainly used to high boosting the voltage operation and protect the switches
during the shoot through period. Since, modified boost control technique is
presented which gives high dc link voltage with lower THD.
Fig 1. Series Z source inverter
2. Drive System Modelling
The block diagram of the proposed system is shown in Fig 2. The drive system
consist of a solar panel, series Z source network, 3 phase four switch inverter , 3
phase induction motor and control circuits. DC is supply obtained from the solar
panel and it is given to the inverter where the pulse is generated by the
sinusoidal PWM generator. According to the switching pattern inverter switches
turned on. The output of FSTPI is fed to 3 phase induction motor. The whole
drive system modeling involves the modelling of the inverter, Induction motor
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and Z-source inverter, which are discussed in the following subsections,
Fig 2.Block diagram of series z source inverter
The above fig.2 shows the block diagram of 4 switch 3 phase inverter induction
motor drive. It consists of front end rectifier, Impedance network, Sinusoidal
PWM generator, 4 switch 3 phase inverter. In the conventional z-source inverter
contains two inductors and two capacitors and one split link capacitor leg for
the 3rd
phase with four switches. In the proposed scheme, the split link capacitor
in the 3rd
arm of the existing model is replaced by the z-source capacitor link.
A. Modelling of Photovoltaic Arrays
Photovoltaic’s is the direct conversion of light into electricity. Some materials
exhibit a property known as the photoelectric effect that causes them to absorb
photons of light and release electrons. Each individual solar energy cell
produces only 1-2 watts. To increase power output, cells are combined in a
weather-tight package called a solar module. The basic equation from the theory
of semiconductors that mathematically describes the I-V characteristics of the
ideal photovoltaic cell.
I=Iph –Ir(exp[ ]-1) – (1)
Fig 3. PV Equivalent Circuit
Where, ph is the current generated by the incident light (it is directly
proportional to the Sun irradiation), is the reverse saturation or leakage
current of the diode is the temperature of the p-n junction and “a” is the diode
ideality constant, “q” is the electron charge [1.60217646 * 10−19C], “k” is the
Boltzmann constant [1.3806503 *10−23J/K]. The equivalent circuit of a PV cell
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is as shown in Fig.3. A single cell has a rated voltage of 0.51V and rated power
of 0.3 W .In practical arrays, which are composed of several connected
photovoltaic cells. If the array is composed of Np parallel connections of cells
the photovoltaic and saturation currents may be expressed as
Ipv=Ipv,n+KI∆T( ) (2)
Where, pv,n is the light-generated current at the nominal condition (usually
25°C and 1000W/m2), T= T – Tn (being T and Tn the actual and nominal
temperatures [K]), G[W/m2] is the irradiation on the device surface and Gn is
the nominal irradiation.
B. Four Switch Three Phase Inverter Model
In the analysis, the inverter switches are considered as ideal power switch
q1,q2,q3,q4. The topology employs four switches and four diodes to generate
two line–line voltages, V13 and V23, whereas V12 is generated according to
Kirchhoff’s voltage law from a split-capacitor bank in the dc-link. Due to the
circuit configuration, the maximum obtainable peak value of the line–line
voltage equals Vdc/2.
Fig.4. Inverter switching state (0,0)
It is assumed that the conduction states of the power switches are associated
with binary variables q1 to q4. Therefore, a binary “1” will indicate a closed
switch, while “0” will indicate the open state. Pairs q1-q3 and q2-q4 are
complementary and as a consequence q3=1-q1 and q4=1-q2. It will assumed
that a stiff voltage is available across the two dc-link capacitor , and Vc1=Vc2=
Vdc/2, Vdc corresponds to a stiff dc-link voltage . Pole voltage V1,V2,V3
depend on the states of the power switches and its expressed in terms of the
binary variables q1 and q2 and the dc- link voltage as follows
V1= (2q1 -1) Vdc/2 (3)
V2= (2q2 -1) Vdc/2 (4)
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V3 =0 (5)
In the four switch configuration, there are four switching status such as (0, 0),
(0, 1), (1, 0), and (1, 1), in which. In the case of the six switch converter,
switching status (0, 0) and (1, 1) are regarded as zero-vectors, which the motor
load is replaced by a resistive load cannot supply the dc-link voltage to the load,
so that current cannot flow through the load. However, in the four switch
converter, one phase of the motor is always connected to the midpoint of the dc-
link capacitors, so that current is flowing even at the zero-vectors, as shown in
Fig.4. Moreover, in the case of (0, 1) and (1, 0), the phase which is connected to
the midpoint of dc-link capacitors is uncontrolled and only the resultant current
of the other two phases flow through this phase. If the load is ideally symmetric
and capacitors voltage are equal, there is no current in uncontrolled phase in the
(0, 1) and (1, 0) vectors. Large variations of the voltage across the two dc-link
capacitors caused by one phase current circulating through the capacitive bank,
will cause significant ripples, distortions, and unbalances in inverter output
currents. Two of the inverter switching states (1, 1),(0, 0) cause unequal loading
of the split dc-link capacitors. This causes one half of the link to discharge at a
faster rate than the other, resulting in the generation of a voltage imbalance. The
possible value of pole voltages V1 and V2, depend on the state of the switches
q1 and q2. The induction motor load is replaced by the resistive load for the
understanding the modes operation. There are four switching states with the
following pole voltages
V1 = V2 = , when q1 = q2 = 0 ;
V1 = , V2 = when q1=1, q2 = 0 ;
V1 = , V2 = when q1 =0, q2 = 1
V1 = V2 = , when q1 = q2 = 1
The phase to neutral voltage can be defined as
V01= V1- Vn0 (6)
V02= V2 - Vn0 (7)
V03= V3- Vn0 and V3= 0 (8)
where “n” is the centre point of split capacitors, “o” is the neutral point of IM
windings and Vno is the voltage between the centre point of split capacitors and
the neutral point of IM windings.
Normally the induction motor load phase voltage are balanced
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Van+Vbn+Vcn = 0
Vn0= 2q1+2q2-2) (9)
The phase to neutral voltage can be derived as follows
Substituting Equations (7) and (1) in (4)
V01= ( (4q1-2q2-1) (10)
V02= ( (4q2-2q1-1) (11)
V03= ( (-2q1-2q2+2) (12)
Table 1 : Switching function and output voltages from inverter
Switching Function
Switch ON
Output voltage
q1 q2 T1 =q1 T3=q2 V01 V02 V03
0 0 T2 T4
0 1 T2 T3
0
1 0 T1 T4
0
1 1 T1 T3
For better realization, the three phase quantities are transformed to αβ
quantities.
= 123 (13)
K= (14)
Where =[ , ]T
, 123 =[ 01 02 03]
The induction motor is assumed to be symmetric with its neutral wire
disconnected. The voltage components are given by
= (q1Vdc-( Vdc- ( )) (15)
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= ( ( q2Vdc-( ) Vdc) (16)
Table 2 : The combinations of switch states
Q1 Q2 V= +j
0
0
V1= ( )
1
0
V1= ( )
1
1
V1= ( )
0
1
V1= ( )
C. Induction Motor Model
The mathematical model of a three phase y connected induction motor and the
load is given by the following equations in the d-q synchronously rotating
reference frames as [6] .A change of variable that formulates a transformation
of the 3 phase variables of stationary circuit elements to the arbitrary reference
frame is expressed as
fqd0s
=Ks
fabcs
Where (fqd0s)T =[fqs fds f0s], (fabcs)
T =[fas fbs fcs]
The voltage equations in machine variable is expressed as
Vabcs=rsiabcs+p abcs (17)
Vabcr=rriabcr+p abcr (18)
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Te = (3P/4) Lm[iqs idr-ids iqr] (19)
Te = Jm(dωr/dt)+Bmωr+TL (20)
dθr/dt = ωr (21)
Where:
Vqs, Vds = q, d-axis stator voltages
iqs, ids = q, d axis stator current
Iqs, Ids = q, d axis rotor current
Rs, Rr = The stator and rotor resistances per phase
Ls, Lr = The self inductances of the stator and rotor respectively
Lm = The mutual inductance
Ωr = The rotor speed
p = The number of poles
p = The differential operator
Te = The electromagnetic developed torque
TL = The load torque
Jm = The rotor inertia
Bm = The rotor damping co-efficient
θ = The rotor position
D. Series Z Source Model
Fig.1 shows the main circuit of the proposed solar photovoltaic based series ZSI
fed induction motor drive system consist of inductors (L1, L2), capacitors
(C1,C2), diode D, decoupling capacitor Cp, feedback diode Ds and solar PV
source. SZSI utilises shoot through state for boosting dc voltage. Shoot through
is the state where upper and lower devices of the same phase leg of inverter are
turn on intentionally. In simple boost control, shoot through is achieved by
comparing dc reference line with triangular wave. By changing the level of dc
reference or line, shoot through duty ratio is changed which results in boosting
of dc link voltage. Shoot through can be achieved in seven different ways by
turning on two switches of the phase a or b or c or ab or bc or ca or abc.. The
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change in magnitude of Vt provides boosting of dc link voltage. In tradition
there are two control signals of Vt . i .e. Vt1 and Vt2 with positive magnitude and
negative magnitude. For reducing the size, cost of the PV panel and LC network
in series Z-source network, modified boost control with improved shoot envelop
technique is used. SZSI is operated in two modes: shoot through mode and
active mode (non shoot through mode)
Mode 1(shoot through mode):
In shoot through mode inductors charge and capacitors discharge, diode goes in
to reverse bias due to negative voltage appear across it. Fig.5(a) shows
equivalent circuit of SZSI in shoot through mode. The variables and their
direction of current are shown in the fig. 5(a)
Fig.5(a) Equivalent circuit of SZSI in shoots through mode
Mode 2 (non shoot through mode):
In non shoot through state inductors discharge and capacitors charge, diode
operates in forward bias mode. Fig. 5 (b) shows equivalent circuit of SZSI in
non shoot through mode. The variables and their direction of current are shown
in the fig. 5(b).
Fig.5(b) Equivalent circuit of SZSI in non shoots through mode
E. Analysis of the Z-source network
The Fig.1.Show equivalent circuit of the impedance source inverter. Assume the
inductor (L1, L2,L3 andL4) and capacitors (C1 and C2) have the same
inductance and capacitance values respectively. From the above equivalent
circuit:
Vc1=Vc2=Vc (22)
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VL1=VL2=VL (23)
VL=VC,Vd=2VC
Vi=0
During switching cycle T;
VL=V0-VC (24)
Vd=V0
Vi=VC-VL=VC-(V0-VC) (25)
Vi=2VC-V0
Where, V0 is the dc source voltage &
T=T0+T1 (26)
The average output voltage of the inductors over one switching period (T)
should be zero in steady state
VL=(T0/T)vc+(T1/T)(V0-VC)=0
VL=(T0VC+T1V0-T1VC)/T=0
(T0-T1)VC+T1V0=0
(T1-T0)VC=T1V0
VC/V0=T1/(T1-T0) (27)
Similarly the average dc link voltage across the inverter bridge can be found as
follows. From equation (25)
Vi=2Vc(T1/T)-V0(T1/T)=0 (28)
2VC(T1/T)=V0(T1/T)
2VC=VO
From equation (27)
VC=V0T1/ (T1-T0)
The peak dc link voltage across the inverter bridge,
Vi=2VC-V0
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Vi = ( / 1 − 0)V0
Vi=B.V0 (29)
Where B= T/(T1 –T0)≥1
B – Boost factor
The output peak phase voltage from the inverter
Vac=M(Vi/2) (30)
Where, M – Modulation index
Vac=M(BV0/2) (31)
The output voltage can be stepped up and down by choosing an appropriate
buck boost factor BB:
BB= B.M (it varies from 0 to α )
The capacitor voltage can be expressed as:
Vc1=Vc2=Vc=V0=(1-(T0/T))/(1-(2T0/T)) (32)
The boost factor BB is determined by the modulation index m and the boost
factor B. The boost factor B can be controlled by duty cycle of the shoot
through the zero state over the non-shoot through the states of the PWM
inverter. The shoot through zero state does not affect PWM control of the
inverter because it equivalently produces the same zero voltage to the load
terminal. The available shoot through period is limited by the zero state periods
that is determined by the modulation index.
3. Need of Inductors and Capacitors in Z Source Network
For the traditional voltage source inverter, the dc capacitor is the sole energy
storage and filtering element to suppress voltage ripple and serve temporary and
in the current source inverter the current ripples are suppressed. The series Z-
source network is a combination of four inductors and two capacitors. In this
combined circuit, the Z-source network is the energy storage/filtering element
for the series Z source inverter. This series Z-source network provides a second-
order filter and is more effective to suppress voltage and current ripples than
capacitor or inductor used alone in the traditional inverters. Therefore, the
smaller inductors and capacitors are required compare than the traditional
source inverters. Considering additional filtering and energy storage provided
by the inductors, the series Z source network should require less capacitance
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and smaller size compared with the traditional voltage source inverter.
Similarly, when the two capacitors (C1 and C2) are small and near to zero.
Considering additional filtering and energy storage by the capacitors, the Z-
source network should require less inductance and smaller size compared with
the conventional current source inverter.
4. Result and Discussions
The proposed system is verified and performance of the inverter configuration
and its control strategy is developed by Matlab software. IM current waveform
and voltage waveform of the four switch three phase series Z-source inverter are
identical conditions with traditional six switch three phase inverter. Peak value
of line – line voltage is 220 V is shown in fig.6 In simple boost control
technique for achieving peak line voltage as in proposed modified control
technique, shoot through ratio must be increased which results in reducing the
modulation index.
Fig. 6 Inverter output voltage with time (sec)
The starting phase current in the acceptable range. The steady state three phase
current waveform shown in fig.7 indicate almost balanced conditions
Fig. 7 Inverter output current with time (sec)
Performance curves response of induction motor for full load condition (Tm=
10.5 N-m). From the result , it can be observed that the speed reaches the steady
state value that is 1500 rpm with in 0.6 sec when the motor running at full rated
load condition . so when the motor is fed by z-source inverter then its speed
increases and settling time decrease .The Total Harmonic Distortion (THD) of
is found as 3.41 where as the THD of 6 switch three phase PWM inverter is
found as 6.61% shown in Fig. 12. It is found that the performance of the four
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switch three phase inverter based drive is much close to that of the traditional 6
switches three phase inverter. The analysis and simulation results show that this
inverter can dramatically reduce the complexity of the control algorithms and
cost.The waveform for current, speed, electromagnetic torque and THD are
shown in figures 8-12.
Fig 8 Stator Current with Time (sec)
Fig .9 Rotor Current with Time (sec)
Fig.10 Electromagnetic torque with Time (sec)
Fig.11 Speed with Time (sec)
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Fig.12 Harmonic Spectrum of the SZSI
5. Conclusion
This paper had been demonstrated that the reduced switch series Z-source
inverter topology is a good alternative technology to traditional inverter for
more efficient, more reliable and less cost conversion systems. The performance
parameters of three-phase induction motor such as stator current, rotor current,
rotor speed and electromagnetic torque was investigated for different load
conditions. In summary, the reduced switch series Z-source inverter ASD
system has several unique advantages that are very desirable for many
applications: It can produce any desirable output ac voltage, even greater than
the line voltage Reduces in-rush and harmonic current. Unique drive features
include buck-boost inversion by single power-conversion stage, improved
reliability, strong EMI immunity and low EMI.
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