Design of quasi Z-Source AC/AC converter using MATLAB/SIMULINK
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Transcript of Design of quasi Z-Source AC/AC converter using MATLAB/SIMULINK
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1. INTRODUCTION
1.1 Introduction
In many industrial applications it is required to convert variable voltage into fixed
voltage or vice versa. An AC/AC converter converts an AC waveform such as the mains
supply, to another AC waveform, where the output voltage and frequency can be set
arbitrarily.
The most popular power conversion topologies for AC/AC conversion are
Matrix converter.
Indirect converter.
Direct converter.
For AC-AC conversion today typically converter systems with voltage or current a
DC-link is employed. For the voltage DC-link, the mains coupling could be implemented
by a diode bridge.
In order to achieve higher power density and reliability, it makes sense to consider
Matrix Converters that achieve three-phase AC/AC conversion without any intermediate
energy storage element. Conventional Direct Matrix Converters perform voltage and
current conversion in one single stage.
The power converter consists of two types of topologies; they are Voltage Source and
Current Source based converters. It is used in different occasions, and there exist some
limitations and drawbacks in traditional power converter:
1. The Voltage Source Converter (VSC) can be destroyed by shoot-through
states results from Electro Magnetic Interference, while Current Source Converter (CSC)
has the same problem of getting hurt by open-circuit.
2. The Voltage Source Rectifier (VSR) and Current Source Inverter (CSI) are a
boost converter, and Current Source Rectifier (CSR) and Voltage Source Inverter (VSI)
has a buck characteristic, it does not achieve a buck/boost feature.
The recently developed Z-Source inverter has some special characteristics due to the
extra topology. This dissertation focuses on the points (advantages and problems) which
appeared in the practical applications. It concludes the advantages and presents the
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methods for existing problems. The proposed Z-Source inverter achieved some merits,
such as buck/boost voltage at the same time and improved reliability of the inverter
without adding any other circuits concerning the X-type Z-source network (conventional
Z-source network). The application of Adjustable Speed Drives (ASD) in commercial and
industrial facilities is increasing due to improved efficiency, energy saving, and process
control. Voltage sags can interrupt an ASD system, thus shutting down critical loads and
processes. The Z-Source inverter ASD system can provide ride-through during the voltage
sags without any additional circuits. Concerning the ASD’s light-load condition, a bi-
directional Z-Source inverter ASD system has been proposed, which avoid the abnormal
operation mode.
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2. SINGLE PHASE Z-SOURCE PWM AC-AC CONVERTER
2.1 Introduction
As discussed earlier in chapter one for AC-AC power conversion that normally
requires variable output voltage and variable frequency, the most popular topology is
voltage source inverter with a DC link, i.e., a Pulse Width Modulation (PWM) inverter
with a diode rectifier front end and DC capacitor link. However, for applications where
only voltage regulation is needed a direct PWM AC-AC converter is a better choice to
achieve a smaller size and lower cost.
AC-AC converters can also perform line conditioning, isolating, and filtering of the
incoming power in addition to voltage regulation. However, in AC-AC power conversion
conventionally the thyristors (SCR) were used as a switch which affects the power factor
and increases the distortion. Moreover it requires extra circuit for its commutation
resulting in unreliability.
There have been tremendous advances in power semiconductor devices. The latest
advancements in power transistors or choppers has a feature of self-commutation,
replacing conventional SCR. Use of self-commuted switches with PWM control can
significantly improve the performance of AC-AC converters.
2.2 Z-Source AC-AC Converter Topology
Fig. 2.1 shows the single phase Z-source AC-AC converter (ZSAC), PWM voltage
fed, buck boost converter. This converter utilizes only two active devices (S1 and S2),
each combined with a full diode bridge for bi directional voltage blocking and bi
directional current paths. All the inductors and capacitors used in the ZSAC are of low
value because to filter switching ripples. The symmetrical Z-source network, which is the
combination of two inductors and two capacitors, is the energy storing element and also
acts as a filter for the ZSAC. Z source network when the source is taken of acts as a source
for the AC-AC converter. Since the switching frequency is much higher than the AC
source (or line) frequency, the inductor and capacitor requirements should be low because
charging and discharging of energy storing elements in Z-source are as much faster as
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switching frequency so that buck/boost operation is obtained simultaneously based on the
duty ratio control of bi directional switches.
ZSAC can operate with PWM duty ratio control in exactly the same way for convent-
-ional DC-DC converters.
Fig 2.1 Single phase Z-source AC-AC converter
2.2.1 Bi-directional switching of MOSFET
Since the switches used in ZSAC are MOSFETs, which is a unidirectional switch
which means it is capable of blocking voltage and conducting current in a single direction
i.e., conducting in a single quadrant, but the switch required for AC-AC converter should
be a bi-directional one. By definition a bi-directional switch, in literature also named
bilateral switch or AC-switch or 4Q-switch (Q stands for quadrant), has to be capable of
conducting currents and blocking voltages of both polarities, depending on control actual
signal.
Fig 2.2 Single Phase Z-source AC-AC converter with bidirectional switch
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Even though the research activity on the design and fabrication of a true bi-directional
switch is keep going either in the academy or in the power semiconductor industry, so far
no true bi-directional switches are available on the power electronics market.
Consequently, bi-directional switches have to be realized with discrete unidirectional
semiconductor devices variously arranged.
(a) (b)
Fig. 2.3 Direction of current during (a) Positive half cycle (b) Negative half cycle
Bidirectional switching analogy for ZSAC is shown above in fig. 2(a) and 2(b) for
positive and negative cycles of supply voltage respectively, Here we can see that in
negative half cycle the direction of current is exactly opposite to that of positive half cycle
current direction which can be interpreted as instead of negative current flowing in
opposite direction to that of positive half cycle current direction, a negative current
direction can be reversed and assumed to be positive current. In this way a MOSFET
which is a unidirectional switch can be made bidirectional by Diode Bridge.
2.2.2 Duty Ratio Control Strategy
As said earlier PWM control strategy for ZSAC is exactly same way as for
conventional DC-DC converters, i.e., referring to Fig.2.1 switches S1 and S2 are turned on
and off in complement. Since the switching frequency is higher as mentioned, a small
Snubber circuit may be needed for each switch to suppress switching surges and to
provide commutation path.
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Fig 2.4 Duty ratio control of ZSAC
2.3 Analysis of Z-Source Network
Fig. 2.5 Z-Source network
The above shown network is analyzed and the corresponding equations are obtained
as follows.
𝑉𝐿1 = 𝐿1
𝑑𝑖𝐿1
𝑑𝑡,𝑉𝐿2 = 𝐿2
𝑑𝑖𝐿2
𝑑𝑡
𝑖𝐶1 = 𝐶1
𝑑𝑉𝐶1
𝑑𝑡, 𝑖𝐶2 = 𝐶2
𝑑𝑉𝐶2
𝑑𝑡
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Voltage across Inductors 𝐿1,𝐿2 can be written as
𝑉𝑖𝑛 = 𝑉𝐶1 + 𝑉𝐿2 = 𝑉𝐿1 + 𝑉𝐶2 ( 2.1 )
⇒ 𝑉𝐿2 = 𝑉𝑖𝑛 − 𝑉𝐶1
⇒ 𝑉𝐿1 = 𝑉𝑖𝑛 − 𝑉𝐶2
𝑉𝑂 = 𝑉𝐶1 − 𝑉𝐿1
⇒ 𝑉𝐿1 = 𝑉𝐶1 − 𝑉𝑂
But 𝑉𝐶1 = 𝑉𝑖𝑛 − 𝑉𝐿2
⇒ 𝑉𝑖𝑛 = 𝑉𝑂 + 𝑉𝐿1 + 𝑉𝐿2 ( 2.2 )
Similarly, 𝑉𝑖𝑛 = 𝑉𝐶1 + 𝑉𝐶2 − 𝑉𝑂
Current through capacitor, 𝐶1 can be written as
𝑖𝑖𝑛 = 𝑖𝐶1 + 𝑖𝐿1
⇒ 𝑖𝐶1 = 𝑖𝑖𝑛 − 𝑖𝐿1&
𝑖𝐶1 = 𝑖𝐿2−𝑖𝑂
⇒ 𝑖𝐿2−𝑖𝑂 = 𝑖𝑖𝑛 − 𝑖𝐿1
⇒ 𝑖𝑖𝑛 = 𝑖𝐿1 + 𝑖𝐿2 − 𝑖𝑂 ( 2.3 )
Similarly, 𝑖𝑖𝑛 = 𝑖𝑂 + 𝑖𝐶1 + 𝑖𝐶2
2.4 Analysis of ZSAC
For the Z-source PWM AC-AC converters the control scheme described in fig 2.2 is
simple and easy to implement. The voltage fed, Z-source AC-AC converter shown in fig
2.1 is analyzed. The switches S1 and S2 as said earlier are gated on and off in complement
shown in fig 2.3. Two states exist in this circuit fig.2.4 (a) and fig.2.4 (b) show their
equivalent circuits. Since the inductors and capacitors of the Z-Source network have the
same inductances (L) and capacitances (C) in fig.2.4 (a) and fig.2.4 (b) respectively, the Z-
Source network becomes symmetrical.
Considering the currents through inductors L1 and L2 to be same since the Z-Source
network is assumed to be symmetrical.
Therefore we have,
𝑖𝐿1 = 𝑖𝐿2 = 𝑖𝐿 = 𝐼𝐿 𝑠𝑖𝑛(𝜔𝑡 + 𝜙𝐿)
𝑣𝐶1 = 𝑣𝐶2 = 𝑣𝐶 = 𝑉𝐶 𝑠𝑖𝑛(𝜔𝑡 + 𝜙𝐶)
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𝑖𝐶1 = 𝑖𝐿1 = 𝑖𝐶 = 𝜔𝐶𝑉𝐶 𝑠𝑖𝑛(𝜔𝑡 + 𝜙𝐶 + 90𝑜)
The input and output voltages are, and
𝑣𝑖 = 𝑉𝑖 𝑠𝑖𝑛(𝜔𝑡),𝑣𝑂 = 𝑉𝑂 𝑠𝑖𝑛(𝜔𝑡 + 𝜙0)
Where 𝜙𝐿, 𝜙𝐶 , 𝜙0 , are phase angles of the Z-network inductor current, Z-network
capacitor voltage, and output voltage respectively.
(a) (b)
Fig.2.6 Switching Operations (a) state 1: S2 is on and S1 is off. (b) State 2: S2 is off and S1 is on.
In state 1, the bidirectional switch S1 is turned off and S2 turned on. The AC source
charges the Z-network capacitors, while the inductors discharge and the transfers the
energy to the load. The interval of the converter operating in this state is (1-D) T, where D
is the duty ratio of switch S1, and T is the switching cycle, as shown in Fig 2.3 (a). As a
result, one has,
𝑣𝐶 = 𝑣𝑖 − 𝑣𝐿, 𝑣𝑂 = 𝑣𝑖 − 2𝑣𝐿 ( 2.4 )
In state 2, the bidirectional switch S1 is turned on and S2 turned off. The discharging
of the Z-network capacitors takes place, while the inductors charge and stores energy. The
interval of the converter operating in this state is DT, as shown in Fig 2.3 (b). Thus
𝑣𝐶 = 𝑣𝐿, 𝑣𝑂 = 0 ( 2.5 )
The average voltage of the inductors over one ac line period in steady state should be
zero, ignoring the fundamental voltage drop.
Thus from equations we have
𝑉𝐿 = 𝑣 𝐿 = 𝑣𝐶 .𝐷𝑇 + 𝑣𝑖 − 𝑣𝐶 . 1 − 𝐷 𝑇 𝑑𝑡 = 0
⇒ 𝑉𝐶 .𝐷 + 𝑉𝑖 − 𝑉𝐶 . 1 − 𝐷 = 0
⇒ 𝑉𝐶 .𝐷 = 𝑉𝐶 − 𝑉𝑖 . (1 − 𝐷)
⇒ 𝑉𝐶 . 1 − 2𝐷 = 𝑉𝑖 . (1 − 𝐷)
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⇒𝑉𝐶𝑉𝑖
= 1 −𝐷
1 − 2𝐷 ( 2.6 )
When D<0.5, 𝜙𝐶 = 0; and when D>0.5, 𝜙𝐶 = 𝜋
Assuming that the filter inductor and the inductor in the Z-network are very small and
there is no line frequency voltage drop across the inductor, the voltage across the load
should equal𝑉𝐶, the voltage across the capacitor of the Z-network, that is
𝑉𝑂𝑉𝑖
= 1 − 𝐷
1 − 2𝐷 ( 2.7 )
𝜙𝑂 = 0 For D<0.5 and 𝜙𝑂 = 𝜋 for D>0.5
Therefore from above equation it is evident that by controlling the duty ratio D, the
output voltage of the proposed AC-AC converter can bucked or boosted. In addition the
output voltage can be in-phase or out-of-phase with input voltage depending on operating
regions of the duty cycle. This is the unique feature of ZSAC.
In ZSAC the assumption was that the impedance source is assumed to be symmetrical
by making inductor and capacitors values equal.
i.e., 𝐿1 = 𝐿2 and𝐶1 = 𝐶2 this implies 𝑉𝐶1 = 𝑉𝐶2
⇒ 𝑉𝐶1 = 𝑉𝐶2 = 1 − 𝐷
1 − 2𝐷 .𝑉𝑖
( 2.8 )
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3. SINGLEPHASE AC-AC CONVERTER BASED ON
QUASI Z-SOURCE TOPOLOGY
3.1 Introduction
In AC-AC power conversion, for applications, where only voltage regulation is
needed, the direct PWM AC-AC converters are used to perform as ac choppers or power
line conditioners with the following features: the provision of a better power factor and
efficiency, low harmonic current in line, single-stage conversion, simple topology, and
ease of control, smaller size, and lower cost.
The AC-AC conversions or AC-AC line conditioners can also perform conditioning,
isolating, and filtering of the incoming power in addition to voltage regulation. The direct
PWM AC-AC converters can be derived from the DC-DC topologies, where all the
unidirectional switches are substituted by bidirectional devices.
The traditional direct PWM AC-AC converters are implemented by AC thyristor
power controllers, which use phase angle or integral cycle control of the AC supply to
obtain the desired output voltage. However, they have some significant disadvantages,
such as high total harmonic distortion(THD) in the source current, low power factor, and
poor power transfer efficiency. In order to achieve simple topologies, a family of single-
phase PWM AC-AC power converters has recently been proposed in. These are the Buck
converter, Boost converter, Buck-Boost converter, and Cuk converter. However, each
topology has its disadvantages: the increase of the output voltage above the input voltage
is not possible for Buck topology; the decrease of the output voltage below the input
voltage is not possible for Boost topology, the Buck-Boost, and Cuk topology can provide
for the output voltage to be both lower or higher than the input voltage with a reversible
phase angle. However, there are discontinuous input and output currents in the former
case. Multilevel or multi cell AC-AC converters in are step-down multilevel circuits based
on the concept of flying capacitors to reduce voltage stress on switches and improve the
quality of the output voltage. For isolated AC-AC topologies, the current-mode AC-AC
converters with high-frequency ac links have been proposed.
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The direct PWM AC-AC converters can be used to overcome voltage sags, swells, or
compensate static VAR in power systems. Recently, Z-source converters applied to DC-
AC inverters and AC-AC converters have been proposed. The work on Z-source DC-AC
inverters has been focused on modelling and control, the PWM strategy, applications, and
other Z-network topologies.
The Z-source AC-AC converters focus on single-phase topologies and three-phase
topologies. In order to overcome the inconvenience of the traditional Z-source inverter, a
class of quasi Z-source DC-AC inverters and quasi Z-source DC-DC converters has been
presented. The quasi Z-source inverters have some advantages, such as reducing passive
component ratings and improving input profiles. For DC-AC power conversion, the quasi
Z-source inverters when compared to the traditional Z-source inverter, feature lower DC
voltage on the capacitor as well as continuous input current. An improvement of the Z-
source inverter topology presented in with a reduced Z-source capacitor, reduced voltage
stress, and soft start capability can be considered as a class of quasi-Z-source inverters.
The quasi Z-source inverters for Photo Voltaic (PV)applications are presented in. When
the quasi Z-source inverter applies to DC-DC converters, a family of Z-source and quasi
Z-source DC-DC converters is proposed in with a minimal number of switches and
passive devices.
Traditional single-phase Z-source PWM AC-AC converters proposed have the
following features: the output voltage can be bucked-boosted and both in-phase/out-of-
phase with the input voltage. However, the conventional Z-source PWM AC-AC
converters in have a significant drawback: in that the input voltage and output voltage
does not share the same ground, thus the feature that the output voltage reverses or
maintains its phase angle relative to the input voltage is not supported well. Another
drawback is that the input current of the conventional single-phase Z-source PWM AC-
AC converters in is operated in the discontinuous current mode (DCM). When the input
current operates in DCM, its waveform is non-sinusoidal, which increases the input
current THD. Moreover, the peak of the input current in the DCM is higher than it is in the
continuous current mode (CCM).
The proposed converter called the single-phase quasi-Z-source AC-AC converter
inherits all the advantages of the traditional single-phase Z-source AC-AC converter,
which can realize Buck-Boost, reversal, or maintenance of the phase angle. Moreover, the
proposed single-phase quasi Z-source AC-AC converter has a number of the unique
advantages as follows: the input voltage and output voltage shares the same ground, thus
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the feature that the output voltage reverses or maintains phase angle with the input voltage
is supported well; the converter operates in CCM with special features, such as reducing
in-rush, a harmonic current, and improved power factor. The operating principles and
simulation results in comparison to those of conventional single-phase Z-source AC–AC
converter are presented.
3.2 Single Phase Quasi Z-Source AC-AC Converter Topology
Fig 3.1 shows the conventional single phase Z-Source AC-AC converter with input
and output not sharing same ground, operating in DCM.
Fig 3.1 Conventional Single-Phase Z-source AC–AC Converter Topology
Fig 3.2 Single-Phase Quasi Z-Source AC–AC Converter Topology
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Fig 3.2 shows the modified form Z-Source AC-AC converter which is single phase
quasi Z-Source AC-AC converterin which the components used are the same as those
shown in Fig. 3.1. It consists of a quasi-Z-source network with two inductors L1 and L2,
two capacitors C1 and C2, two bidirectional switches S1 and S2.
As already discussed in previous chapter that bidirectional are realized using
unidirectional switches. Fig. 3.3 shows the different configurations for bidirectional
switching.
(a) (b)
Fig. 3.3 Bidirectional Switching (a) Diode Bridge with single IGBT (b) Two anti-Parallel IGBT
The diode bridge switch has been the first configuration shown in Fig. 3.3(a). This
configuration has the advantage of requiring only one active device per switch with its
associated driver circuitry. But it has the relevant disadvantage that three devices are
conducting whenever the switch conducts, giving rise to relatively high conduction losses.
On the other hand the configuration shown in Fig. 3.3(b) uses two switches,
nevertheless conduction loss is comparatively low considering the configuration shown in
Fig. 3.3(a). Moreover in second configuration a freewheeling diode comes into action as
soon as if there are any sudden voltage spikes because of inductances present in the
converter.
Therefore, in Q-ZSAC switches S1 and S2 are implemented as shown in second
configuration i.e., Fig. 3.3 (a)
3.2.1 Duty Ratio Control Strategy
The duty ratio control of Q-ZSAC is same as that of implemented in ZSAC, i.e., a
reference waveform is compared with a saw tooth waveform in order to generate PWM
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signals on switches. As shown in Fig. 3.4, D is an equivalent duty ratio and T is a
switching period.
Fig 3.4 Duty Ratio Control Of Switches
In the same manner as the conventional single-phase Z-Source ac–ac converter, the
quasi Z-Source AC-AC converter has two types of operational state: state 1 and state 2.
The equivalent circuits of the two states are shown in Fig. 3.5(a) and (b). According to the
quasi Z-source topology shown in Fig. 3.2, the output shares the same ground with the
input. In addition, the input current is continuous due to the connection of the inductor L1
directly to the input.
(a) (b)
Fig.3.5 Equivalent circuit of the Q-ZSAC (a) State 1 (b) State 2
Therefore, the main differences between the conventional single-phase Z-Source AC–
AC converter and the single phase quasi Z-Source AC–AC converter are
1. The input voltage and the output voltage shares the same ground and
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2. The single phase quasi Z-Source converter draws a continuous ac current from
the source or input side, while the conventional single-phase Z-Source AC–AC converter
draws a discontinuous ac current.
In general, the peak of input current in DCM is higher than that in the CCM.
Moreover, the waveform of the input current in the CCM is more Sinusoidal than that in
the DCM.
3.3 Circuit analysis
Circuit analysis of the proposed single-phase quasi Z-Source AC–AC converter
begins with the following assumptions:
1. All capacitors and switches are ideal and lossless.
2. The converter is operating in the continuous conduction mode and
3. The switching frequency is more than the cut-off frequency of the output filter
and the frequency of the input and output voltages.
The Q-ZSAC has two operating states in one switching period: state 1 and state 2 as
shown in Figs. 3.5 (a) and 3.5 (b),respectively. In state I as shown in Fig. 3.5 (a), the time
interval in this state is (1-D) T; T is the switching period as shown in Fig. 3.4. In state 2 as
shown in Fig. 3.5 (b), the time interval in this state is DT. In state 1,SI is turned on and S2
is turned off as shown in Fig. 3.5 (a).
The time interval in this state is (1-D)T. We get with reference to fig 3.5 (a).
At node 1 (i.e., towards source side) voltage is 𝑉𝐶1
At node 2 (i.e., towards load side) voltage is 𝑉𝐶1 + 𝑉𝐶2
Now,
𝑉𝐿1 = 𝑉𝑖 − 𝑉𝐶1
𝐿1
𝑑𝑖𝐿1
𝑑𝑡= 𝑉𝑖 − 𝑉𝐶1
𝑉𝐿2 = 𝑉𝐶1 − 𝑉𝐶1 − 𝑉𝐶2 ( 3.1 )
⇒ 𝑉𝐿2 = −𝑉𝐶2
𝐿2
𝑑𝑖𝐿2
𝑑𝑡= −𝑉𝐶2
𝑉𝐿𝑓 = 𝑉𝐶1 + 𝑉𝐶2 − 𝑉𝑂
16
𝐿𝑓𝑑𝑖𝐿𝑓
𝑑𝑡= (𝑉𝐶1 + 𝑉𝐶2) − 𝑉𝑂
In state 2, S1 is turned OFF and S2 is turned ON, as shown in Fig. 3.5(b). The time
interval in this state is DT. Therefore,
At node 1 (i.e., towards source side) voltage is -𝑉𝐶2.
At node 2 (i.e., towards load side) voltage is0.
Now,
𝑉𝐿1 = 𝑉𝑖 − −𝑉𝐶2
⇒ 𝑉𝐿1 = 𝑉𝑖 + 𝑉𝐶2
i. e. , 𝐿1
𝑑𝑖𝐿1
𝑑𝑡= 𝑉𝑖 + 𝑉𝐶2
𝑉𝐿2 = 𝑉𝐶1 − 0
⇒ 𝑉𝐿2 = 𝑉𝐶1 ( 3.2)
i. e. , 𝐿2
𝑑𝑖𝐿2
𝑑𝑡= 𝑉𝐶1
𝑉𝐿𝑓 = 0 − 𝑉𝑂
⇒ 𝑉𝐿𝑓 = −𝑉𝑂
i. e. , 𝐿𝑓𝑑𝑖𝐿𝑓
𝑑𝑡= −𝑉𝑂
From Equations (3.1) and (3.2), we then obtain the averaged equations as follows
𝐿1
𝑑𝑖𝐿1
𝑑𝑡= 1 − 𝐷 . 𝑉𝑖 − 𝑉𝐶1 + 𝐷 . (𝑉𝑖 + 𝑉𝐶2)
𝐿2
𝑑𝑖𝐿2
𝑑𝑡= 1 −𝐷 . −𝑉𝐶2 + 𝐷 . (𝑉𝐶1) ( 3.3)
𝐿𝑓𝑑𝑖𝐿𝑓
𝑑𝑡= 1 − 𝐷 . 𝑉𝐶1+𝑉𝐶2 − 𝑉𝑂 + 𝐷 . (−𝑉𝑂)
In steady state,
𝐿1
𝑑𝑖𝐿1
𝑑𝑡= 𝐿2
𝑑𝑖𝐿2
𝑑𝑡= 𝐿𝑓
𝑑𝑖𝐿𝑓
𝑑𝑡= 0
17
From the above steady state equations
𝐿1
𝑑𝑖𝐿1
𝑑𝑡= 1 − 𝐷 . 𝑉𝑖 − 𝑉𝐶1 + 𝐷 . 𝑉𝑖 + 𝑉𝐶2 = 0
𝐿2
𝑑𝑖𝐿2
𝑑𝑡= 1 − 𝐷 . −𝑉𝐶2 + 𝐷 . 𝑉𝐶1 = 0 ( 3.4)
𝐿𝑓𝑑𝑖𝐿𝑓
𝑑𝑡= 1 − 𝐷 . 𝑉𝐶1+𝑉𝐶2 − 𝑉𝑂 + 𝐷 . −𝑉𝑂 = 0
Considering the voltage across inductor 𝐿2we have
1 − 𝐷 . −𝑉𝐶2 + 𝐷 . 𝑉𝐶1 = 0
1 − 𝐷 . 𝑉𝐶2 = 𝐷 . (𝑉𝐶1) ( 3.5 )
𝑉𝐶2 = 𝐷
1 −𝐷 . 𝑉𝐶1
We obtained 𝑉𝐶2 in terms of 𝑉𝐶1,by substituting the value of 𝑉𝐶2 in 𝑉𝐿1 to get 𝑉𝐶1in
terms of 𝑉𝑖 .
Therefore we get,
1 − 𝐷 . 𝑉𝑖 − 𝑉𝐶1 + 𝐷 . 𝑉𝑖 + 𝑉𝐶2 = 0
𝐷 . 𝑉𝑖 + 𝑉𝐶2 = 1 − 𝐷 . 𝑉𝐶1 − 𝑉𝑖 ( 3.6 )
𝐷 . 𝑉𝑖 + 𝐷
1 − 𝐷 . (𝑉𝐶1) = 1 − 𝐷 . 𝑉𝐶1 − 𝑉𝑖
By separating 𝑉𝐶1 terms on one side and 𝑉𝑖 terms on another side we get
𝐷2
1 − 𝐷 .𝑉𝐶1 − 1 − 𝐷 .𝑉𝐶1 = − 1 − 𝐷 .𝑉𝑖 − 𝐷.𝑉𝑖
𝐷2
1 − 𝐷− 1 − 𝐷 .𝑉𝐶1 = (−1 + 𝐷 − 𝐷).𝑉𝑖
𝐷2 − 1 − 𝐷 2
1 − 𝐷 .𝑉𝐶1 = −𝑉𝑖
2𝐷 − 1
1 − 𝐷 .𝑉𝐶1 = −𝑉𝑖
𝑉𝐶1 = 1 − 𝐷
1 − 2𝐷 .𝑉𝑖
𝑉𝐶1
𝑉𝑖=
1 − 𝐷
1 − 2𝐷 ( 3.8)
18
By substituting the value of 𝑉𝐶1to get the value of 𝑉𝐶2
𝑉𝐶2 = 𝐷
1 −𝐷 . 𝑉𝐶1
𝑉𝐶2 = 𝐷
1 − 𝐷 .
1 − 𝐷
1 − 2𝐷 .𝑉𝑖
𝑉𝐶2 = 𝐷
1 − 2𝐷 .𝑉𝑖
𝑉𝐶2
𝑉𝑖=
𝐷
1 − 2𝐷 ( 3.9 )
The obtained values of 𝑉𝐶1and 𝑉𝐶2to
1 − 𝐷 . 𝑉𝐶1+𝑉𝐶2 − 𝑉𝑂 + 𝐷 . −𝑉𝑂 = 0
1 − 𝐷 . 𝑉𝐶1+𝑉𝐶2 = 1 − 𝐷 + 𝐷 . 𝑉𝑂
1 − 𝐷 . 1 − D
1 − 2D . Vi +
𝐷
1 − 2𝐷 .𝑉𝑖 = 1 − 𝐷 + 𝐷 . 𝑉𝑂
𝑉𝑂 = 1 − 𝐷 . 1 − D + D
1 − 2D .𝑉𝑖
𝑉𝑂 = 1 − 𝐷
1 − 2𝐷 .𝑉𝑖
𝑉𝑂𝑉𝑖
= 1 − 𝐷
1 − 2𝐷 ( 3.10 )
The voltage gains can be defined as
𝐾𝐶1 =𝑉𝐶1
𝑉𝑖=
1 − 𝐷
1 − 2𝐷
𝐾𝐶2 =𝑉𝐶1
𝑉𝑖=
𝐷
1 − 2𝐷
𝐾𝑂 =𝑉𝑂𝑉𝑖
= 1 − 𝐷
1 − 2𝐷
19
Comparing voltage gains of conventional ZSAC and Q-ZSAC
Voltage gain Conventional ZSAC Q-ZSAC
𝐾𝐶1 =𝑉𝐶1
𝑉𝑖
1 − 𝐷
1 − 2𝐷
1 − 𝐷
1 − 2𝐷
𝐾𝐶2 =𝑉𝐶1
𝑉𝑖
1 − 𝐷
1 − 2𝐷
𝐷
1 − 2𝐷
𝐾𝑂 =𝑉𝑂𝑉𝑖
1 − 𝐷
1 − 2𝐷
1 − 𝐷
1 − 2𝐷
Table 3.1 Comparison of Voltage gains of Conventional ZSAC and Q-ZSAC
The plot between Voltage gain and Duty ratio is shown below.
Fig 3.6 Voltage gain variation curve form the corresponding Duty ratio
From Fig 3.6 it is clear that a smooth variation in voltage gain is obtained
corresponding to the change in Duty ratio which justifies the converter as Solid State
Transformer with continuously variable turn’s ratio.
20
4. MODELLING AND SIMULATION
4.1 Modeling of Z-Source PWM AC-AC Converter
ZSAC has been modeled using MATLAB/SIMULINK software for the below
mentioned Parameter values. corresponding block model is shown below in Fig. 4.1. the
output voltage, input current, and corresponding Capacitors voltages are shown.
4.1.1 Simulation Parameters
Input Voltage, Vi 100 Volts
MOSFET/DIODE RON =0.1Ω, RDIODE =0.01Ω
RSNUBBER =1e5, CSNUBBER =inf
L1 = L2 0.8 mH
C1 = C2 3.3 µF
Filter components, Lf&Cf 1.5 mH & 15µF
Load, R 20Ω
Switching Frequency, T 10KHz
Table 4.1 Simulation Parameters for ZSAC
4.1.2 Model Design
Fig. 4.1 Power Model of Z-Source PWM AC-AC Converter
21
Fig. 4.2 PWM Control Strategy
(a)
(b)
Fig. 4.3 Modulated Pulses for (a) D=0.25 (b) D=0.7
22
4.2 Modeling of Quasi Z-Source AC-AC Converter
Q-ZSAC has been modeled for the below mentioned Parameter values. corresponding
block model is shown below in Fig. 4.4. the output voltage, input current, and
corresponding Capacitors voltages are shown compared with that of conventional ZSAC.
4.2.1 Simulation Parameters
Input Voltage, Vi 100 Volts
IGBT/DIODE RON =0.001Ω,
RSNUBBER =1e5, CSNUBBER =inf
L1 = L2 1 mH
C1 = C2 6.8 µF
Filter components, Lf&Cf 1.4 mH & 10µF
Load, R 20Ω
Switching Frequency, T 20KHz
Table 4.2 Simulation Parameters for Q-ZSAC
4.2.2 Model Design
Fig. 4.4 Power Model Quasi Z-Source AC-AC Converter
23
4.3 Simulation Results
Simulation of above shown models i.e., Fig. 4.1 for ZSAC and that of Fig. 4.4 for Q-
ZSAC are simulated for the above mentioned parameter values and results are as shown
below.
PWM Control Strategy for the converters is implemented as shown in Fig. 4.2.
corresponding graphs are obtained for Duty ratios D=0.25 & D=0.7.
Fig.4.7 Input Voltage Waveform
However, the input voltage remains same so that ZSAC and Q-ZSAC can easily be
compared.
24
For D=0.25, Output Voltage of ZSAC is
(a)
(b)
Fig. 4.8 (a) Output Voltage of Conventional ZSAC (b) Corresponding THD analysis
Fig 4.8(a) shows the output voltage waveform of ZSAC and its corresponding FFT
analysis, which shows that the THD in output voltage waveform is very low implying the
output wave is nearly sinusoidal.
25
For D=0.25, Output Voltage of quasi ZSAC is
(a)
(b)
Fig. 4.9 (a) Output Voltage of Q-ZSAC (b) Corresponding THD analysis
Fig 4.9(a) shows the output voltage waveform of Q-ZSAC and its corresponding FFT
analysis, which shows that the THD in output voltage waveform is very much low
compared to the output voltage of conventional ZSAC.
26
Input Current for ZSAC for a Duty Ratio of 0.25 is
(a)
(b)
Fig. 4.10 (a) Input Current of Conventional ZSAC (b) Corresponding THD analysis
Fig. 4.10(a) shows the Input current wave of conventional ZSAC and whose FFT analysis
shows a high THD since the input current is operating DCM.
27
Input Current for quasi ZSAC for a Duty Ratio of 0.25 is
(a)
(b)
Fig. 4.11 (a) Input Current of Conventional Q-ZSAC (b) Corresponding THD analysis
Fig. 4.11(a) shows the Input current wave of Q-ZSAC and whose FFT analysis shows a very
low THD compared to that of conventional ZSAC input current THD since the input current is
operating DCM.
28
Voltages across capacitors in Z-Source network for conventional ZSAC when D=0.25
(a)
(b)
Fig. 4.12 Voltage across elements in ZSAC (a) Capacitor, C1 (b) Capacitor, C2
29
Voltages across capacitors in Z-Source network for quasi ZSAC when D=0.25
(a)
(b)
Fig. 4.13 Voltage across elements in Q-ZSAC (a) Capacitor, C1 (b) Capacitor, C2
30
One of the advantages of Z-Source converter is that having a phase reversing feature
depending on Duty ratio control of the switches.
Fig.4.14 Input Voltage Waveform
The input voltage remains same so that ZSAC and q-ZSAC can easily be compared.
31
For D=0.7, Corresponding results obtained are
(a)
(b)
Fig. 4.15 (a) Output Voltage of Conventional ZSAC (b) Corresponding THD analysis
Fig 4.15(a) shows the output voltage waveform of ZSAC and its corresponding FFT
analysis, which shows that the THD in output voltage waveform is very low implying the
output wave is nearly sinusoidal. But as we know the input and output are not sharing the
same ground thus phase reversing feature is not well supported in case of ZSAC.
32
For D=0.7, Output Voltage of quasi ZSAC is
(a)
(b)
Fig. 4.16 (a) Output Voltage of Q-ZSAC (b) Corresponding THD analysis
Fig 4.16(a) shows the output voltage waveform of ZSAC and its corresponding FFT
analysis, which shows that the THD in output voltage waveform is very low implying the
output wave is nearly sinusoidal and in case Q-ZSAC, since input and output sharing same
ground phase reversing feature can be well used.
33
Input Current for ZSAC for a Duty Ratio of 0.7 is
(a)
(b)
Fig. 4.18 (a) Input Current of Conventional ZSAC (b) Corresponding THD analysis
Fig. 4.18(a) shows the Input current wave of conventional ZSAC and whose FFT analysis
shows a very high THD which is not acceptable since the input current is operating DCM
switching stresses are very high as switching frequency is as high as 10 kHz.
34
Input Current for quasi ZSAC for a Duty Ratio of 0.7 is
(a)
(b)
Fig. 4.19 (a) Input Current of Conventional Q-ZSAC (b) Corresponding THD analysis
Fig. 4.19(a) shows the Input current wave of conventional ZSAC and whose FFT
analysis shows a low THD comparing to the THD of input current of ZSAC which is
acceptable since the input current is operating CCM switching stresses are very low.
35
Voltages across capacitors in Z-Source network for conventional ZSAC when D=0.7
(a)
(b)
Fig. 4.20 Voltage across elements in ZSAC (a) Capacitor, C1 (b) Capacitor, C2
36
Voltages across capacitors in Z-Source network for quasi ZSAC when D=0.7
(a)
(b)
Fig. 4.21 Voltage across elements in Q-ZSAC (a) Capacitor, C1 (b) Capacitor, C2
37
Comparison of Output Voltage and Input Current THD of both Conventional ZSAC
and Q-ZSAC
THD Conventional ZSAC
[%]
Quasi ZSAC
[%]
When D=0.7 3.66 0.51
When D=0.25 2.00 0.18
Table 4.3 Output Voltage THD of both Conventional ZSAC and Q-ZSAC
THD Conventional ZSAC
[%]
Quasi ZSAC
[%]
When D=0.7 156.72 25.80
When D=0.25 66.66 4.81
Table 4.4 Input Current THD of both Conventional ZSAC and Q-ZSAC
From above comparisons it is clear that Q-ZSAC conversion topology is far improved
than the conventional ZSAC which makes it to the usage in Power line conditioning.
38
CONCLUSION
A new family of simple topologies of single-phase Z-source AC-AC converters
(ZSAC) was presented in this dissertation. It is seen that, by duty-ratio control, the Z-
source AC–AC converters become “Solid State Transformers” with a continuously
variable turn’s ratio. The ZSAC converter employ only two active devices, they can
reduce cost and improve reliability. Steady-state analysis, simulation results were
illustrated using the buck-boost converter as an example. The unique phase-inversing
feature teaches us that inverter circuits can be easily derived by replacing both switch-
diode bridges with a traditional voltage-source inverter phase-leg switch (i.e., a
combination of switch and anti-parallel diode).
Although the conventional ZSAC has many features as mentioned, nevertheless the
input current is in Discontinuous Current Mode (DCM), so a new kind of quasi-Z-source
converter for AC–AC power conversion has been presented. Q-ZSAC inherits all the
advantages of the traditional single-phase Z-source AC–AC converter, which can realize
buck–boost as well as reversal or maintenance phase angle. In addition, the proposed
single-phase Q-ZSAC has unique advantages in that the input voltage and output voltages
share the same ground and the operation of the input current is in CCM. Comparison of
the principles of operation and the simulation results with those for the conventional
ZSAC are presented. The simulation results show that the proposed single-phase quasi-Z-
source ac–ac converter has a high efficiency, lower input current THD, lower output
voltage THD and higher input power factor in comparison with the conventional single-
phase Z-source AC–AC converter.
FUTURE SCOPE:
As we have seen the THD of input and output parameters of Q-ZSAC are very low
compared to conventional ZSAC. Hence, Q-ZSAC can be used as a Dynamic Voltage
Restorer (DVR) in order to compensate for voltage sags and swells in the AC–AC line
conditioning. The feature that the output voltage is boosted and in-phase with the input
voltage is used for voltage sag compensation; the feature that the output voltage is
bucked/boosted and out-of phase with the input voltage is used for voltage swell
compensation. Therefore, the DVR system, which employs the proposed converter, does
not require any battery energy-storage devices.
39
REFERENCES
[1] F.Z. Peng, L. Chen, and F. Zhang, “Simple topologies of PWM AC-AC converters,”
IEEE Power Electronics Letters, vol. 1, no. 1, pp. 10–13, March 2003.
[2] Fang Zheng Peng, Senior Member, IEEE, “Z-Source Inverter,” IEEE transactions on
industry applications, vol. 39, no. 2, March/April 2003.
[3] X.P. Fang, Z.M. Qian, and F.Z. Peng, “Single-phase Z-source PWM AC-AC
converters,” IEEE Power Electronics Letters, Vol. 3, No.4, pp. 121-124,2005.
[4] Minh-Khai Nguyen, Young-Gook Jung, and Young-Cheol Lim, “Single-Phase AC-
AC Converter based on Quasi Z-Source Topology,” IEEE International Symposium
on Industrial Electronics (ISIE 2009)Seoul Olympic Parktel, Seoul, Korea July 5-8,
2009.
[5] Eduardo I. Ortiz Rivera, Luis A. Rodríguez, “The Z-Source Converter as an
Introduction to Power Electronics and Undergraduate Research,”
[6] Babak Farhangi, shahrokh Farhangi, “Applications of Z-Source Converter in
Photovoltaic Grid-Connected Transformer-less Inverter,” Electrical Power Quality
and Utilisation, Journal Vol. XII, No. 2, 2006.
[7] Fang Lin Luo, Hong Ye, “Power Electronics-Advanced Conversion Technologies,”
© 2010, LLC CRC Press is an imprint of Taylor & Francis Group.
[8] Marian p. Kazmierkowski, Frede Blaabjerg, Ramu Krishnan, “Control in Power
Electronics,” © 2002, Elsevier Science, Academic Press.