A FLYING CAPACITOR BASED II LEVEL GRID

CONNECTED INVERTER FOR TRANSFORMER LESS PV

SYSTEMS

ABSTRACT- This paper presents a grid-connected single-phase

Transformer less photovoltaic converter based on two cascaded full bridges

with different dc-link voltages. The converter can synthesize up to eleven

voltage levels with a single dc bus, since one of the full bridges is supplied by a

flying capacitor. Harmonic distortion and electromagnetic interference (EMI)

can be reduced in the multilevel output. The switching strategy is employed

such that to regulate the flying-capacitor voltage, improves the efficiency for

most devices switch at the frequency and will minimize the minimum the

common-mode leakage cuurent with the help of a novel dedicated circuit.

Simulation results confirm the feasibility and good performance of the

proposed converter.

Index Terms—pulse width modulation (PWM) inverters, photovoltaic (PV)

systems, leakage current, multilevel systems.

CHAPTER-1

INTRODUCTION

GRID connected PV systems provides best solution for small-scale and

domestic applications. . While classical designs of PV converters feature a grid

frequency transformer, which is a typically heavy and costly component, at the

interface between the converter and the electrical grid, researchers are now

considering Transformerless architectures in order to reduce costs and weight and

improve efficiency. With the removal of grid frequency transformer involves all

benefits but worsens the output power quality and increases ground leakage current

Though fossil fuel resources are limited and depleting at an alarming rate, the

global demand for oil has increased significantly in recent years. Energy consumed

and demanded by transportation sector has risen exponentially due to increasing

number of vehicles. Transportation accounts for above 20% of the total energy-

related emissions .Today most of the world’s vehicles are dependent on

conventional energy sources. In this regard, alternative solutions for “sustainable

and green mobility” are being researched and implemented by researchers,

industries as well as policy makers.

The active parts of PV modules might be electrically insulated from the

ground-connected mounting frame; a path for ac ground leakage currents generally

exists due to a parasitic capacitance between the modules and the frame and to the

connection between the neutral wire and the ground, usually realized at the low-

voltage/medium-voltage (LV/MV) transformer [3]. In addition to deteriorating

power quality, the ground leakage current increases the generation of

electromagnetic interference and can represent a safety hazard, so that international

regulations pose strict limits to its magnitude.

This issue must be confronted in all transformer less PV converters, regardless of

architecture. In particular, in full-bridge-based topologies, the ground leakage

current is mainly due to high frequency variations of the common-mode voltage at

the output of the power converter [4]. Several solutions can be found in literature

aiming at the reduction of the common-mode voltage harmonic content [5]–[7].

Once the grid frequency transformer is removed from a PV converter, the bulkiest

wound and reactive components that remain are those that form the output filter

used to clean the output voltage and current from high frequency switching

components.

Further reduction in cost and weight and improvement in efficiency can be

achieved by reducing the filter size, and this is the goal of multilevel converters.

For years multilevel converters have been investigated [8], but only recently have

the results of such researches found their way to commercial PV converters.

Multilevel converters outperform conventional two- and three-level converters in

terms of harmonic distortion since they can synthesize the output voltages using

more levels the input voltage among several power devices, allowing for the use of

more efficient devices.

Fig.1 expected 11-level output Moreover, multilevel converters subdivid

Multilevel converters were initially employed in high-voltage industrial

and power train applications. They were first introduced in renewable energy

converters inside utility-scale plants, in which they are still largely employed [9].

Recently, they have found their way to residential-scale single-phase PV

converters; currently represent a hot research topic Single-phase multilevel

converters can be roughly divided into three categories based on design: neutral

point clamped (NPC), cascaded full bridge (CFB), and custom. In NPC topologies,

the electrical potential between the PV cells and the ground is fixed by connecting

the neutral wire of the grid to a constant potential, resulting from a dc-link

capacitive divider .

A huge advantage is that single-phase NPC converters are virtually immune from

ground leakage currents, although the same is not true for three-phase NPC

converters A recent paper has proposed an interesting NPC design for exploiting

next-generation devices such as super junction or SiC MOSFETs [16]. The main

drawback of NPC designs is that they need twice the dc-link voltage, with respect

to full bridge. CFBs make for highly modular designs. Usually, each full bridge

inside a CFB converter needs an insulated power supply, matching well with multi-

string PV fields [16].

Full bridges are sequentially permuted can be used to evenly share the power

among the parts and to mitigate the effects of the partial shading [17]. As an

alternative, only one power supply can be used if the output voltage is obtained

through a transformer [18].CFB can also be used for stand-alone application which

provides many degrees of freedom the control strategy to the developers. With

aforementioned sequential permutation with phase shifting [19], artificial neural

networks [20] and predictive control have been proposed to minimize harmonic

distortion and achieve maximum power point tracking (MPPT). When the supply

voltage is the same for each full bridge CFB can synthesize 2n+1 voltage levels

when CFB made up of n full bridges (and at least 4n power switches).

Custom architectures can generally provide more output levels with a given

number of active devices, and custom converters generally need custom pulse-

width modulation (PWM) and control schemes, although unified control schemes

for different types of multilevel converters can be implemented. In addition to

using fewer switches, custom architectures can be devised so that some of the

switches commutate at the grid frequency, thus improving the efficiency.

Reduction in the switches-per-output voltage-level ratio can be achieved in CFB

structures if different supply voltages are chosen for each full bridge (asymmetrical

CFBs). The topology proposed in this paper consists of two asymmetrical CFBs,

generating eleven output voltage levels.

In the proposed converter, one full bridge is supplied by dc source whereas a

flying capacitor supplies other one. Different sets of output voltages can be

obtained by suitably controlling the ratio between the two voltages, the flying

capacitor used as a secondary energy source allows for limited voltage boosting, as

it will result clear in the following section.

The number of output levels per switch (ten switches, eleven levels) is comparable

to what can be achieved using custom architectures. In order to reduce the ground

leakage current two additional very low power switches and a line frequency

switching device [transient circuit (TC)] were included in the final topology. The

custom converter proposed in [25] generates five levels with six switches but has

no intrinsic boosting capability. In [24], Rahimet al.used three dc-bus capacitors in

series together with two bidirectional switches (diode bridge+ unidirectional

switch) and an H-bridge to generate seven output levels; however, they give no

explanations on how they keep the capacitor voltages balanced. In [26], five

switches, four diodes, and two dc-bus capacitors in series are used to generate five

levels with boosting capability. Again, no mention is made about how the

capacitors are kept balanced.

Fig. 2. CFB with a flying capacitor.

For PV applications, the output voltage has to be controlled regardless of the

voltage ratio, Even though the PV field dc voltage is constantly changing due to

variations of solar radiation and to MPPT algorithm. Measuring the separate full-

bridge voltages and computing online the duty cycles needed to balance the

different voltages, and analyzing also the power balance between the separate cells.

A similar approach is followed in this paper. The developed PWM strategy, in

addition to controlling the flying capacitor voltage, with the help of the specific TC

illustrated in Section IV, minimizes the ground leakage current.

Finally, it is important to put in evidence that the proposed converter can work at

any power factor as reported in Section III, while not all the alternative proposals

can continuously supply reactive power. The proposed topology was presented by

the authors in a previous paper [27]. With respect to the previous work, this paper

was rewritten for 11-level output and presents a better organization and a new set

of simulation.

This paper is organized as follows: Section II presents converter topology with

PWM control strategy chosen in order to maximize the performance. Section III

discusses about CFB topology for the regulation of flying capacitor used to supply

the second full bridge. Section IV describes the principle of operation of the

additional components to reduce the ground leakage current. Section V shows the

simulation results, Whereas Section VI reports the concluding remarks.

CHAPTER 2

ELEVEN-LEVEL CONVERTER AND PWM CONTROL STRATEGY

The proposed converter is composed of two CFBs, one of which is supplied by a

flying capacitor (see Fig. 2). This basic topology is well known. In this paper, in

order to allow grid-connected operation with no galvanic isolation (transformerless

solution) different PWM strategy was developed for this basic topology. Using

PWM strategy alone is not going to maintain a low ground leakage current, other

components were added which will be discussed in next section. As it will be

described in the following, the proposed PWM strategy stretches the efficiency by

using, for the two legs where PWM frequency switching does not occur, devices

with extremely low voltage drop, such as MOSFETs lacking a fast recovery diode.

In fact, the low commutation frequency of those two legs allows, even in a reverse

conduction state the conduction in the channel instead of the body diode (i.e.,

active rectification). Insulated-gate bipolar transistors (IGBTs) with fast anti-

parallel diodes are required in the legs where high-frequency hard switching

commutations occur. For grid-connected operation, one full-bridge leg is directly

connected to the grid neutral wire, whereas the phase wire is connected to the

converter through an LC filter. Flying-capacitor

The full bridge supplied by the dc link is called the high-voltage full bridge

(HVFB), whereas the one with the flying capacitor is the low-voltage full-bridge

(LVFB). CFB can also be used for stand-alone application which provides many

degrees of freedom the control strategy, so that different PWM schemes can be

considered. However, the chosen solution needs to satisfy the following

requirements.

1)To limit the switching losses, most commutations must take place in the LVFB.

2) To reduce the ground leakage current, the neutral-connected leg of the

HVFB needs to switch at grid frequency

3) To control the flying-capacitor voltage the redundant states of the converter

must be properly used.

4) The driving signals must be obtained from a single carrier for a low-cost to

be used as a controller.

The switching pattern described in Table I was developed starting from the above

requirements. Requirement 2), in particular, is due to the aforementioned parasitic

capacitive coupling between the PV panels and their frames, usually connected to

the earth. Capacitive coupling provides the common-mode current inversely

proportional to the switching frequency of the neutral-connected leg. The converter

can operate in different output voltage zones, where the output voltage switches

between two specific levels. The operating zone boundaries vary according to the

dc-link and flying-capacitor voltages, and adjacent zones can overlap (see Fig. 3).

In zones A, the contribution of the flying-capacitor voltage to the converter output

voltage is positive (+ve), whereas it is negative (-ve) in B zones. Constructive

cascading of the two full bridges can, therefore, result in limited output voltage

boosting.

The operation of the converter does not differ much in the two cases. If two

overlapping operating zones can supply the same output voltage, the regulation of

will determine the operating zone, will be described in section III. the duty cycles

are calculated on-line by a simple equation, similarly to the approach presented in.

The instantaneous fundamental component of output voltage ∗ and switches

pattern.

Fig. 3. Operating zones under different ranges

CHAPTER 3

REGULATION OF FLYING-CAPACITOR VOLTAGE

Controlling the voltage of the flying capacitor voltage is critical when a grid-

connected PV converter is transferring the active power to the electrical grid. By

suitably choosing the operating zone flying-capacitor voltage is regulated

depending on the instantaneous output voltage request. Depending on the operating

zone of the converter (see Fig. 3), can be added to (A zones) or subtracted from (B

zones) the HVFB output voltage, charging or discharging the flying capacitor. In

accordance, considering a positive value of the current injected into the grid, the

flying capacitor is discharged in a zone and charged in B zone. Since a number of

redundant switch configurations can be used to synthesize the same output voltage

waveform, it is possible to control the voltage of the flying capacitor, forcing the

converter to operate more in A zones when the flying-capacitor voltage is higher

than a reference value or more in B zones when it is lower than a reference value.

Similar

(a). Flying-capacitor charge

Due to MPPT strategy, the DC-link voltage can go through sudden variations, it is

important that

the converter is able to work in any [ , ] condition. Through on-line duty cycle

computation, the distortion of the output voltage is minimized. It is important to

estimate the capability of the converter to regulate the flying-capacitor voltage

under different operating conditions. The ability to control flying-capacitor voltage

through proposed PWM strategy has been studied in simulation by average

sinusoidal with amplitude of 230√2V in simulations.

The white area and cannot be controllable in the gray and black regions. In

detail, cannot be decreased in the black region, whereas in gray region, it cannot be

increased. The safe operating area for the converter is the white region located

between the gray and black ones for stable operation. If failed in controlling , it can

be a constraint that ensuring flying capacitor cannot be over charged nor

completely discharged inside the white region.

CHAPTER 4

TRANSFORMERLESS PV CONVERTER

The commutation pattern of Table 1 is that T3 and T4 switch at grid frequency,

will commutate at every zero crossing of . If negative derivative with zero crossing

is considered.T3 closes and T4 opens, changing the neutral wire voltage (and thus

the voltage across the parasitic capacitance of the PV field) from zero to .because

of this reason the commutation can cause a large surge of leakage current which

will decrease the power quality and damage the PV modules.

Proper TC must be designed to decrease these surge currents. The proposed

converter topology constitute two-cell CFB described in Fig 2 with the addition of

TC components. For better understand of TC, the distributed parasitic capacitance

of the PV source was modeled with equivalent simple capacitance i.e., between

negative pole and the ground. The TC is formed from two low-power MOSFETs

M1 and M2,

Volume 3, Issue 1 JULY 2015 bidirectional switch T9, and resistor .

When converter enters operating zone 1, the HVFB output voltage must be zero by

switching T1 and T3 or T2 and T4 on. Nevertheless, to operate the TC, when

entering zone 1, T1, T2, T3, and T4 are all kept off, while T9 is on which

maintains neutral point floating and voltage on the parasitic capacitor stays

constant.

. (a) TC topology.

(a) TC operation

(c) TC waveforms.

Fig. 5. Ground leakage current limitation circuit topology and behavior.

One of M1 and M2 is turned on (M1 if the slope of the zero crossing is negative

and M2 if positive). At the same time is charged through with a first-order

transient, limiting the surge current. Whereas the TC introduces additional

components, they can be selected with current ratings much lower than the devices

of the CFB considering the power loss in the additional resistor is negligible.

.

Fig. 7. Simulation results with VDC = 300 V

In grid-connected operation, the output voltage is very close to the grid voltage

will not going to affect the power factor in the operation of TC. For correct

operation of the TC requires the grid voltage instantaneous angle obtained from a

grid voltage through phase locked loop (PLL) [20].

CHAPTER 5

MATLAB

MATLAB is a high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where

problems and solutions are expressed in familiar mathematical notation. Typical

uses include

Math and computation

Algorithm development

Data acquisition

Modeling, simulation, and prototyping

Data analysis, exploration, and visualization

Scientific and engineering graphics

MATLAB is an interactive system whose basic data element is an array that does

not require dimensioning. This allows solving many technical computing problems,

especially those with matrix and vector formulations, in a fraction of the time it

would take to write a program in a scalar non-interactive language such as C or

FORTRAN.

The MATLAB system consists of six main parts:

(a)Development Environment.

This is the set of tools and facilities that help to use MATLAB functions and files.

Many of these tools are graphical user interfaces. It includes the MATLAB desktop

and Command Window, a command history, an editor and debugger, and browsers

for viewing help, the workspace, files, and the search path.

(b) The MATLAB Mathematical Function Library.

This is a vast collection of computational algorithms ranging from elementary

functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated

functions like matrix inverse, matrix Eigen values, Bessel functions, and fast

Fourier transforms.

(c)The MATLAB Language.

This is a high-level matrix/array language with control flow statements, functions,

data structures, input/output, and object-oriented programming features. It allows

both "programming in the small" to rapidly create quick and dirty throw-away

programs, and "pro

gramming in the large" to create large and complex application programs.

(d) Graphics.

MATLAB has extensive facilities for displaying vectors and matrices as graphs, as

well as annotating and printing these graphs. It includes high-level functions for

two-dimensional and three-dimensional data visualization, image processing,

animation, and presentation graphics. It also includes low-level functions that allow

to fully customize the appearance of graphics as well as to build complete graphical

user interfaces on MATLAB applications.

(e)The MATLAB Application Program Interface (API). This is a library that

allows writing in C and FORTRAN programs that interact with MATLAB. It

includes facilities for calling routines from MATLAB (dynamic linking), calling

MATLAB as a computational engine, and for reading and writing MAT-files.

(f) MATLAB Documentation

MATLAB provides extensive documentation, in both printed and online

format, to help to learn about and use all of its features. It covers all the primary

MATLAB features at a high level, including many examples. The MATLAB online

help provides task-oriented and reference information about MATLAB features.

MATLAB documentation is also available in printed form and in PDF format.

MATLAB TOOLS :-

(g) Three phase source

The Three-Phase Source block implements a balanced three-phase voltage source

with an internal R-L impedance. The three voltage sources are connected in Y with

a neutral connection that can be internally grounded or made accessible. You can

specify the source internal resistance and inductance either directly by entering R

and L values or indirectly by specifying the source inductive short-circuit level and

X/R ratio.

(h) Universal bridge

The Universal Bridge block implements a universal three-phase power converter

that consists of up to six power switches connected in a bridge configuration. The

type of power switch and converter configuration are selectable from the dialog

box.

The Universal Bridge block allows simulation of converters using both naturally

commutated (or line-commutated) power electronic devices (diodes or thyristors)

and forced-commutated devices (GTO, IGBT, MOSFET).

The Universal Bridge block is the basic block for building two-level voltage-

sourced converters (VSC).

(i)current measurement block

The Current Measurement block is used to measure the instantaneous current

flowing in any electrical block or connection line. The Simulink output provides a

Simulink signal that can be used by other Simulink blocks.

(j) rate transition

The Rate Transition block transfers data from the output of a block operating at one

rate to the input of another block operating at a different rate. The Rate Transition

block's parameters allows you to specify options that trade data integrity and

deterministic transfer for faster response and/or lower memory requirements.

(k)multi port switch

The Multiport Switch block chooses between a number of inputs. The first (top)

input is called the control input, while the rest of the inputs are called data inputs.

The value of the control input determines which data input is passed through to the

output port.

If the control input is an integer value, then the specified data input is passed

through to the output. For example, suppose the Use zero-based indexing parameter

is not selected. If the control input is 1, then the first data input is passed through to

the output. If the control input is 2, then the second data input is passed through to

the output, and so on.

If the control input is not an integer value, the block first truncates the value to an

integer by rounding to floor. If the truncated control input is less than 1 or greater

than the number of input ports, an out-of-bounds error is returned.

You specify the number of data inputs with the Number of input ports parameter.

The data inputs can be scalar or vector. The block output is determined by these

rules: If you specify only one data input and that input is a vector, the block

behaves as an "index selector," and not as a multi-port switch. The block output is

the vector element that corresponds to the value of the control input. If you specify

more than one data input, the block behaves like a multi-port switch. The block

output is the data input that corresponds to the value of the control input. If at least

one of the data inputs is a vector, the block output is a vector. Any scalar inputs are

expanded to vectors. If the inputs are scalar, the output is a scalar.

The Index Vector block, also in the Signal Routing library, is another

implementation of the Multiport Switch block that has different default parameter

settings.

(l) direct look up table

The Direct Lookup Table (n-D) block uses its block inputs as zero-based indices

into an n-D table. The number of inputs varies with the shape of the output desired.

The output can be a scalar, a vector, or a 2-D matrix. The lookup table uses zero-

based indexing, so integer data types can fully address their range. For example, a

table dimension using the uint8 data type can address all 256 elements.

You define a set of output values as the Table data parameter. You specify what the

output shape is: a scalar, a vector, or a 2-D matrix. The first input specifies the

zero-based index to the first dimension higher than the number of dimensions in the

output, the second input specifies the index to the next table dimension, and so on,

as shown by this figure

(j)Zero-Order Hold

The Zero-Order Hold block samples and holds its input for the specified sample

period. The block accepts one input and generates one output, both of which can be

scalar or vector. If the input is a vector, all elements of the vector are held for the

same sample period.

You specify the time between samples with the Sample time parameter. A setting

of -1 means the Sample time is inherited.

This block provides a mechanism for discretizing one or more signals in time, or

resampling the signal at a different rate. If your model contains multirate

transitions, you must add Zero-Order Hold blocks between the fast-to-slow

transitions. The sample rate of the Zero-Order Hold must be set to that of the

slower block. For slow-to-fast transitions, use the Unit Delay block. For more

information about multirate transitions, refer to the Simulink or the Real-Time

Workshop documentation.

(k)Sum

The Sum block performs addition or subtraction on its inputs. This block can add or

subtract scalar, vector, or matrix inputs. It can also collapse the elements of a single

input vector.

You specify the operations of the block with the List of Signs parameter. Plus (+),

minus (-), and spacer (|) characters indicate the operations to be performed on the

inputs: If there are two or more inputs, then the number of characters must equal

the number of inputs.

For example, "+-+" requires three inputs and configures the block to subtract the

second (middle) input from the first (top) input, and then add the third (bottom)

input.

All nonscalar inputs must have the same dimensions. Scalar inputs will be

expanded to have the same dimensions as the other inputs. A spacer character

creates extra space between ports on the block's icon. If only addition of all inputs

is required, then a numeric parameter value equal to the number of inputs can be

supplied instead of "+" characters. If only one vector is input, then a single "+" or

"-" will collapse the vector using the specified operation.

The Sum block first converts the input data type(s) to the output data type using the

specified rounding and overflow modes, and then performs the specified

operations.

(l) Demux

The Demux block extracts the components of an input signal and outputs the

components as separate signals. The block accepts either vector (1-D array) signals

or bus signals (see Signal Buses in the Using Simulink documentation for more

information). The Number of outputs parameter allows you to specify the number

and, optionally, the dimensionality of each output port. If you do not specify the

dimensionality of the outputs, the block determines the dimensionality of the

outputs for you.

The Demux block operates in either vector or bus selection mode, depending on

whether you selected the Bus selection mode parameter. The two modes differ in

the types of signals they accept. Vector mode accepts only a vector-like signal, that

is, either a scalar (one-element array), vector (1-D array), or a column or row vector

(one row or one column 2-D array). Bus selection mode accepts only the output of

a Mux block or another Demux block.

The Demux block's Number of outputs parameter determines the number and

dimensionality of the block's outputs, depending on the mode in which the block

operates.

(m)Gain

The Gain block multiplies the input by a constant value (gain). The input and the

gain can each be a scalar, vector, or matrix.

You specify the value of the gain in the Gain parameter. The Multiplication

parameter lets you specify element-wise or matrix multiplication. For matrix

multiplication, this parameter also lets you indicate the order of the multiplicands.

The gain is converted from doubles to the data specified in the block mask offline

using round-to-nearest and saturation. The input and gain are then multiplied, and

the result is converted to the output data type using the specified rounding and

overflow modes.

(n) Outport

Outport blocks are the links from a system to a destination outside the system.

Simulink assigns Outport block port numbers according to these rules: It

automatically numbers the Outport blocks within a top-level system or subsystem

sequentially, starting with 1. If you add an Outport block, it is assigned the next

available number. If you delete an Outport block, other port numbers are

automatically renumbered to ensure that the Outport blocks are in sequence and

that no numbers are omitted. If you copy an Outport block into a system, its port

number is not renumbered unless its current number conflicts with an Outport block

already in the system. If the copied Outport block port number is not in sequence,

you must renumber the block or you will get an error message when you run the

simulation or update the block diagram.

(o)Real-Imag to Complex

The Real-Imag to Complex block converts real and/or imaginary inputs to a

complex-valued output signal.

The inputs can both be arrays (vectors or matrices) of equal dimensions, or one

input can be an array and the other a scalar. If the block has an array input, the

output is a complex array of the same dimensions. The elements of the real input

are mapped to the real parts of the corresponding complex output elements. The

imaginary input is similarly mapped to the imaginary parts of the complex output

signals. If one input is a scalar, it is mapped to the corresponding component (real

or imaginary) of all the complex output signals.

The input signals and real or imaginary output parameter can be of any data type

supported by Simulink, except Boolean. The Real-Imag to Complex block supports

fixed-point data types. The output is of the same type as the input or parameter that

determines the output.

For a discussion on the data types supported by Simulink, refer to Data Types

Supported by Simulink in the Using Simulink documentation.

(p)Complex to Magnitude-Angle

The Complex to Magnitude-Angle block accepts a complex-valued signal of type

double. It outputs the magnitude and/or phase angle of the input signal, depending

on the setting of the Output parameter.

The outputs are real values of type double. The input can be an array of complex

signals, in which case the output signals are also arrays. The magnitude signal array

contains the magnitudes of the corresponding complex input elements. The angle

output similarly contains the angles of the input elements.

(q)Relay

The Relay block allows its output to switch between two specified values. When

the relay is on, it remains on until the input drops below the value of the Switch off

point parameter.

When the relay is off, it remains off until the input exceeds the value of the Switch

on point parameter. The block accepts one input and generates one output.

The Switch on point value must be greater than or equal to the Switch off point.

Specifying a Switch on point value greater than the Switch off point value models

hysteresis, whereas specifying equal values models a switch with a threshold at that

value.

(r)Saturation

The Saturation block imposes upper and lower bounds on a signal. When the input

signal is within the range specified by the Lower limit and Upper limit parameters,

the input signal passes through unchanged. When the input signal is outside these

bounds, the signal is clipped to the upper or lower bound.

When the Lower limit and Upper limit parameters are set to the same value, the

block outputs that value

(s)Relational Operator

The Relational Operator block performs the specified comparison of its two inputs.

You select the relational operator connecting the two inputs with the Relational

Operator parameter. The block updates to display the selected operator. The

supported operations are given below.

You can specify inputs as scalars, arrays, or a combination of a scalar and an array:

For scalar inputs, the output is a scalar. For array inputs, the output is an array of

the same dimensions, where each element is the result of an element-by-element

comparison of the input arrays. For mixed scalar/array inputs, the output is an

array, where each element is the result of a comparison between the scalar and the

corresponding array element.

The input with the smaller positive range is converted to the data type of the other

input offline using round-to-nearest and saturation. This conversion is performed

prior to comparison.

The output data type is specified with the Output data type mode and Output data

type parameters. The output equals 1 for TRUE and 0 for FALSE.

(t)Lookup Table (2-D)

The Lookup Table (2-D) block computes an approximation to some function

z=f(x,y) given x, y, z data points.

The Row index input values parameter is a 1-by-m vector of x data points, the

Column index input values parameter is a 1-by-n vector of y data points, and the

Matrix of output values parameter is an m-by-n matrix of z data points. Both the

row and column vectors

must be monotonically increasing. These vectors must be strictly monotonically

increasing in the following cases: The input and output data types are both fixed-

point. The input and output data types are different. The lookup method is not

Interpolation-Extrapolation. The matrix of output values is complex. Minimum,

maximum, and overflow logging is on.

The block generates output based on the input values using one of these methods

selected from the Look-up method parameter list: Interpolation-Extrapolation--This

is the default method; it performs linear interpolation and extrapolation of the

inputs. If the inputs match row and column parameter values, the output is the value

at the intersection of the row and column. If the inputs do not match row and

column parameter values, then the block generates output by linearly interpolating

between the appropriate row and column values.

If either or both block inputs are less than the first or greater than the last row or

column values, the block extrapolates using the first two or last two points.

Interpolation-Use End Values--This method performs linear interpolation as

described above but does not extrapolate outside the end points of x and y. Instead,

the end-point values are used. Use Input Nearest--This method does not interpolate

or extrapolate. Instead, the elements in x and y nearest the current inputs are found

The corresponding element in z is then used as the output. Use Input Below--This

method does not interpolate or extrapolate. Instead, the elements in x and y nearest

and below the current inputs are found. The corresponding element in z is then used

as the output. If there are no elements in x or y below the current inputs, then the

nearest elements are found. Use Input Above--This method does not interpolate or

extrapolate. Instead, the elements in x and y nearest and above the current inputs

are found.

The corresponding element in z is then used as the output. If there are no elements

in x or y above the current inputs, then the nearest elements are found.

CHAPTER 6

SIMULATION RESULTS

Under MATLAB/Simulink, The simulations cover entire range of active and

reactive power

injected into the grid, Dc-link voltage= 300v was used in the simulations.

The PWM frequency was =20 kHz, and the flying capacitor had a capacitance

of = 500μF. Surge limiting resistance was selected as 1.5 kΩ. With feedforward

through proportional-integral regulator plus feed forward at =8.5A rms. The

instantaneous commutations and the injection of both active and reactive power

was simulated the entire performance will not depend on the power factor. As

outputs are independent of power factor simulations are done for unity power

factor only. As grid voltage angle information is available. So, PLL is needed.

With the DC voltage ratio the THD of the grid currents increases, being 2.7%, 3%

and 3.3%, respectively.

Fig. 8. TC behavior with a 200 nF parasitic capacitor

fig. 6. Block scheme of the delay-based PLL

TABLE I

DESCRIPTION OF THE CONVERTER OPERATING

ZONES

Fig. 9. Vfc step variation response.

CHAPTER 7

CONCLUSION

This paper has proposed a novel eleven-level grid connected transformerless

PV converter with full bridges with CFB topology, one of which is supplied by a

floating capacitor, in order to improve the efficiency a suitable PWM strategy was

developed (at low frequency most devices commutate) and with the help of

specific TC, the ground leakage current is minimized. The proposed PWM strategy

can regulate the voltage across the flying capacitor. Simulations were performed to

assess the ability to regulate the flying capacitor voltage in wide range of operating

conditions. Extensive simulations and experiments confirm the results of the

theoretical analysis and show the good performance of the converter as far as

Harmonic distortion and ground leakage current are concerned. The proposed

converter can continuously operate at arbitrary power factors, has limited boosting

capability and can produce eleven output voltage levels.

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