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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

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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

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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

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[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.

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[5] Eduardo I. Ortiz Rivera, Luis A. Rodríguez, “The Z-Source Converter as an

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