Hammed Project

8/6/2019 Hammed Project

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NEWCASTLE UNIVERSITY

SCHOOL OF ELECTRICAL, ELECRTONIC AND COMPUTERENGINEERING

I, HAMMED AWAD ALANZI , confirm that this report and the work presented in it are my

own achievement.

I have read and understand the penalties associated with plagiarism.

Singed: …………………………………………………..Date: ……………………………………………………..



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Abstract

Nowadays, wind energy is attracting wide attention as an environment-friendly renewable

energy source for supplying the global electrical energy consumption due to high prices of oil,

global warming, fast increasing of energy demand and rapid development of renewable

energy source. Among different types of topologies for connecting wind turbine to the grid,

variable speed system which connects a permanent magnet synchronous generator to the grid

by a back to back voltage source converter has achieved more attention because of power

control ability and high efficiency. Due to power control ability impact of this system the

improvement of the control strategies become a new challenge in order to satisfy the grid

interconnection requirements.

The main aim of this project is to focus on the current control of the grid side converter which

let the full controllability of the DC-link voltage and the reactive power delivered to the grid.

The vector control theory will be the base of the controller which will be modelled. It will be

attempted that the controllers will have a rapid response time in the all operation area during

normal operation. The controllers will be designed and analyzed using Matlab/Simulink.



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ACKNOWLEDGEMENTS

To my father..

To my mother..

To my wonderful wife

To my daughter Elaf

To those who were lamps enlightening my way, supporting and encouraging me, to my dear

brothers and sisters.

Thanks are also due to those who helped to complete this project; special thanks to Dr. David

Atkinson.



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Contents

Abstract ................................................................................................................................ ii ACKNOWLEDGEMENTS.................................................................................................. iii List of Figures ...................................................................................................................... vi List of Tables ..................................................................................................................... viii CHAPTER1 Introduction ...................................................................................................... 1

1.1 Background ............................................................................................................... 1 1.2 Project objective .......................................................................................................... 1 1.3 Dissertation outline ...................................................................................................... 1

CHAPTER 2 Wind Energy ................................................................................................... 2 2.1 Wind Energy Background .......................................................................................... 2 2.2 Constant speed wind turbines ..................................................................................... 3 2.3 Variable Speed Turbine ............................................................................................. 4 2.4 Variable Speed Turbine Generators .............................................................................. 4 2.5 Back-To-Back Voltage Source Converter.................................................................... 7

2.5.1 Machine-Side Converter Control ........................................................................... 7 2.5.2 Line-Side Converter Control .................................................................................. 7

2.6 Control Schemes .......................................................................................................... 8 2.6.1 Current Control (CC) ............................................................................................. 9 2.6.2 Space-Vector (VS) Control .................................................................................... 9 2.6.3 Direct Power Control (DPC) ................................................................................ 11

Chapter 3 Simulation of the system ..................................................................................... 13 3.1 Simulation of sine-wave PWM control....................................................................... 13 3.2 Simulation of third harmonic injection PWM ............................................................ 16 3.3 Simulation of Space Vector Modulation (SVM) ......................................................... 19 3.4 Simulation of Phase Locked loop (PLL)..................................................................... 19

Chapter 4 control of the system ........................................................................................... 23 4.1 Introduction ............................................................................................................... 23 4.2 The PI controller ........................................................................................................ 29 4.3 The reference frame transform ................................................................................... 29 4.4 Voltage source converter connected to the resistive load ............................................ 33 4.5 Voltage source converter connected to the resistive load with control loop................. 35 4.6 Voltage source converter connected to the grid with controller .................................. 39



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Chapter 5 Conclusion .......................................................................................................... 41 References .......................................................................................................................... 42



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List of Figures

Figure 1: Simple Wind Turbine Energy Generation System ........................................… 2

Figure 2: Power transmitted to the hub shaft at different wind speeds ………........…… 3

Figure 3: PMSG Converters topologies ………………………..................................…. 6

Figure 4: Power flow through line side and machine side converter.…….……......…... 8

Figure 5: Basic Block Diagram of CC-PWM Converter..................................................9

Figure 6: Three-phase SV control ……..…………….………………….………..….... 11

Figure 7: Direct Power control ………………………………..................................… 12

Figure 8:A three phase voltage source inverter and the controller unit .....................… 13

Figure 9: Simulation model of sine-wave PWM control scheme ….............................. 14

Figure 10: Output waveforms of the sine-wave PWM scheme.................................…. 15

Figure 11: Simulation of third harmonic PWM scheme —the controller unit...……..... 17

Figure 12: Output waveforms of third harmonic PWM scheme......................................18

Figure 13: Simulation of 3s/2s…...........................................……………...............….. 20

Figure 14: Figure 14. Simulation of 2s/2r…………………………...........................… 20

Figure 15: Simulation of natural reference frame into rotation reference frame........… 21

Figure 16. The output waveform of the rotation reference f rame....................….......… 21

Figure 17: Voltage source converter which is connected to the grid ........................…. 23

Figure 18: The simulation block of the three phase two level of voltage source

converter......................................................................................................................... 24

Figure 19: The output voltage of the simulated voltage source converter........................25

Figure 20: single phase equivalent circuit ……..…………….…...………………...….. 25

Figure 21: The transfer function model of back to back voltage source connected to the

grid.................................................................................................................................... 26

Figure 22: The current of inductor when modulation index is unity.............................…27

Figure 23: The current of inductor when the modulation index is 0 .5…..........................28

Figure 24: transform block from abc reference frame to αβ reference frame...................30



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Figure 25: The output signal from abc to αβ transform....................................................31

Figure 26: Block diagram for transforming the αβ reference frame to the dq referenceframe.....................................................................................................................................31

Figure 27.: The output of the dq reference frame block...................................................... 32

Figure 28: Block in matlab/simulink for transforming from the dq to abc reference

frame................................................................................................................................… 32

Figure 29: An equivalent circuit of the voltage source converter with load.....................…33

Figure 30: The transfer function model of the voltage source converter with the load.…...34

Figure 31: The converter current with unity modulation index …….............................…. 35

Figure 32: The current of the inverter when modulation index is 0.5……..…..............…...35

Figure 33: The voltage source converter connected to the load with the controller..............37

Figure 34: The voltage source converter current waveform ……...................……..….….. 38

Figure 35: The actual value and the demanded value in the q axis ..................................… 38

Figure 36: The actual value and the demanded value in the d axis.............................……... 38

Figure 37: The transfer function model of the grid connected voltage source converter…... 39

Figure 38: The currents (iq & i∗q) waveform of voltage source converter with the grid....…. 40

Figure 39: The currents (id& i∗d ) waveform of voltage source converter with the grid..........40



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List of Tables

Table 1: VSC switching states..........................................................................................10

Table 2: Switching table for direct power........................................................................12

Table 3: The value of different parameters in project without load.................................27

Table 4: Value of parameters when VSC connected to the grid and load……………...34

Table 5: The value of controller parameters for load …………...………...……..….…37

Table 6: The value of controller parameters for grid ....................................................40



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CHAPTER1 Introduction

1.1 Background

In terms of percentage of early growth of installed capacity per technology source, the wind

energy was the fastest growing energy technology in the 90s [1]. Hence, this growing results

in significant proportion of consumer’s electrical power demands from wind energy [2]. For

example, “ The UK is the windiest country in Europe, with over 40% of the available

resources, and improvements in technology have resulted in the cost of wind power falling to

close to those of conventional sources of electricity” [3].

In recent years, several power converter topologies have been developed to incorporate with

the electrical grid, which allow variable speed operation of the wind turbine, and enhanced

power extraction as well. For this reason, designing variable speed turbine has the following

considerations: a control methods should be designed to extract the maximum power from the

turbine and provide a constant grid voltage and frequency [4].

In the sequel, enormous attentions, in terms of cost and complexity, have been moved

towards controlling techniques. This project investigates the Back-To-Back voltage source

converter (B-T-B VSC). Different topologies of B-T-B VSC generators, their advantages and

drawbacks, are studied. In addition, several control methods that have been used for both

Line-Side and Machine-Side converters are explained

1.2 Project objective

The main purpose of the project is the controlling of the grid current via the use of an appropriate scheme, afterwards the simulation of the voltage source converter between DC

link voltage and the grid is given more consideration.

1.3 Dissertation outline

The dissertation is divided into five chapters. First chapter covers the basic information about

importance wind energy. The second chapter reviews the wind turbine energy system along

with constant and variable speed turbines along with constant and variable speed turbines.

Chapter three outlines simulate of sine-wave PWM control, third harmonic injection PWM,

Space Vector Modulation (SVM) and Phase Locked loop (PLL). By the Proportional-

Integral (PI) controller, the DC link capacitor and the grid, is implemented and controlled in

chapter four. The fifth chapter conclude the project, the main conclusions is provided.



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CHAPTER 2 Wind Energy

2.1 Wind Energy Background

The Wind energy can be defined as the use of the wind to generate electricity. In other words,

wind energy system transforms moving energy of the wind into electrical energy that can beapplied for practical use. Occasionally, it can be more reasonable to obtain new power by

building a wind farm than by building a coal, natural gas, or other type of power plant,

particularly, in areas where an excellent wind can be founded. That is why recently wind

energy is considered to be a clean, safe, and renewable (inexhaustible) power resource [5].

The windmills have been used for hundreds of years in order to harness the wind’s energy.

On the contrary, nowadays wind turbines are efficient technology much more than windmills,

and usually, the horizontal-axis is used for this turbines [6].

Figure 1 shows simple wind energy generation system. The main elements that constitute

turbine are a rotor, hub, nacelle and tower. In order to generate the electrical energy, the wind

turns the three rotor’s blades around a central hub. As the nacelle houses the drive -train and

power converter, the electrical energy is generated by converting Kinetic energy into

electrical energy [5], [7].

To transmit the electrical current to the grid ensuring maximum productivity, in modern

system, mechanical drive systems cooperated with advanced generator. This generator

responsible to convert energy produced by mechanical parts into an electricity [4]. However,

different types of generator require different control methods, which dominate the flow of

energy form the wind turbine to the connected grid.

Furthermore, in term of turbine speed, two types, fixed and variable turbine speed have been

used. Next section explains the energy capturing, advantages and limitations for each turbine

type.

Fig.1. Simple Wind Turbine Energy Generation System [8]



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2.2 Constant speed wind turbines

In the past, the induction generator has been widely used for constant speed wind turbine.

However, according to [9], “as the rating of the wind turbines are getting higher and more

widespread, a couple of problems with the constant speed wind turbine occurs, which make

variable speed constant frequency systems more attractive”. These problems are briefly

described in the following.

Selection of wind speed upon which the wind turbine produces its rated power was an

important issue concerning the design of a constant speed wind turbine. In general the power

transmitted to the hub shaft of the wind turbine is expressed as [6]

=

1

2

3

(1)

where is the turbine power, is the air density, A is the swept turbine area, is the

coefficient of performance and is the wind speed. The coefficient performance of the wind

turbine is influenced by the ratio of turbine rotational speed to the wind speed or TSR as

= (2)

where is the turbine rotation speed and is turbine radius.

To illustrate the captured energy problem in constant speed turbine, figure 2 shows the

relationship between the power transmitted to hub and the rotor speed for different wind

speeds (1 < 2 < 3 < 4). It is apparent that as the wind speed increased the captured

energy increased. However, due to high mechanical load at high wind speed, the wind turbine

is shut down, as a consequence, the energy captured will fall down [8]. Furthermore, the

energy capturing at different speeds does not reach the optimal power value [1, 9].

Fig.2. Power transmitted to the hub shaft at different wind speeds [9].

Another raised issue in constant speed turbine is the mechanical stress. The mechanical stress

appeared in fixed speed of the wind turbine, because the variations in the wind power are

converted to torque pulsations. Most fixed turbine speeds system require the drive train and



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gear-box ,in necessity, be able to endure the absolute peak loading conditions, however this

suggestion need further safety factors to be taken in consideration [9].

2.3 Variable Speed Turbine

Although it possible for the wind turbine produces the rated power at a specific speed, at high

wind speeds the generated energy is small. Accordingly, the trends in modern wind energy

conversion are certainly towards variable speed constant frequency (VSCF) generating

systems.

Adapting the rotational speed of wind turbine will continuously allow the possible maximum

power to be achieved. However, the electrical system must be controlled to manage power

overload, in addition to that, in designing variable speed turbine, suitable inverter-generator

topology should be selected [8].

2.4 Variable Speed Turbine Generators

The converter in wind turbine has three main components. They are the generator, the

rectifier and the inverter. Mainly, the generator can be either synchronous or induction

generator. Examples on synchronous generator are permanent magnet and filed winding. As

claimed by [8], the common way is to use a filed winding, due to its advantageous of

controlling the three-phase voltage level. However, the cost of high performance permanent

magnet has dropped recently, making it an alternative solution for such kind of generator.

In the literature, three main topologies for Permanent Magnet Synchronous Generator (PMSG)

have been considered: thyristor supply-side inverter, Hard-switching supply-side inverter and

DC-DC Voltage Source Inverter (VSC), as shown in figure 3 a, b and c respectively.

If the thyristor converter can control the speed and power by adjusting the firing angle, that

means the whole system can be controlled. “An AC/DC/AC system consisting of the diode

rectifier (in generator side) and thyristor converter (in supply side) can provide optimal real

power conversion and speed control” [10].

In order to achieve optimal power, the converter should control each of the maximum energy

capturing and the shaft speed, if so, as the wind speed increases, the tip speed ratio which is

the blade tip speed/wind speed, reach it is optimum value. Subsequently, as the wind speed

below the cut-out speed, the turbine operates at the rated power and rotational speed [10].

On another hand, the system speed can be controlled by the firing angle obtained by the

thyristor. This parameter is determined by the torque reaction in the generator. Figure 3b



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plots the controlling scheme corresponding to the simple thyristor inverter shown in figure 3c

[10].

As mentioned in [10], for the thyristor converter, it is preferable to use the digital controller

as shown in figure 3b. The inputs to this controller are machine speed, DC-link voltage,

current and AC network voltage, while the output is only the firing angle (α). The controller

compares the ideal DC-link voltage and current with the measured ones, stores the results and

then adjusts the firing angle as discussed before.

Although thyristor-based scheme include lower device cost and higher available power rating

than other inverters, it suffers from the need for an active compensator for the reactive power

demand and harmonic distortion [2]. Another PMSG topology is the hard-switching inverter,

shown in figure 3b, for which some mapping techniques is used in order to maximise the

system’s power output.

Alternatively, using voltage source inverter (VSI) with DC/DC converter offers set of

advantages over the previous mentioned topologies; first, it helps to manipulate the

generator-side through diversity of the switching ratio, and preserves a good DC-voltage on

the inverter-side. Second, it permits selective harmonic elimination (SHE) switching which in

turn gives minimal losses. Third,. It is not important for the inverter to control DC-voltage,

and it has pliable control [2].

This project will not investigate the control techniques in thyrsitor or hard switching inverters,

whereas the Voltage Source Converter (VSC) controlling schemes will be given in detail.

b



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c

Fig.3. PMSG Converters topologies [2], a) Thyristor inverter system [10], b) controlling

scheme [10], c) simple thyristor inverter, d)Hard-switching inverter and e). Voltage source

inverter

e

d



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2.5 Back-To-Back Voltage Source Converter

As mentioned before, most of the converter configurations, like thyristor and hard-switching

converters, are limited in use due to the harmonic distortion, weak power factor, as well as

the system control complexity. Hence, for variable speed generator, back-to-back PWM

converter with a DC-link is an suitable solution, by which we can recognize advanced control,

and therefore achieving overall active and reactive power control [2]. However, new control

issues for both sides arise and the most important addition to control is the coordination

between the two PWM converters. For convenience, in this study, the two converters are

termed machine-side converter and line side-converter, respectively.

The VSC is not sued as a rectifier connected to generator solely, moreover, it can be used for

the inverter itself as well. However, in such scenario, VSC requires a minimum DC-link

voltage and sometimes need to DC/DC converter in order to increase the voltage level [11].

Likewise, to carry-out the optimum use of the VSC, it is important to select the proper

controlling and modulation schemes. In term of Pulse-Width Modulation (PWM), either the

current control or voltage control are commonly used [12].

2.5.1 Machine-Side Converter Control

In Variable Speed Constant Frequency (VSCF) generating system, the control schemes in the

machine-side are expected to perform the following objectives [13]: for maximum power

capturing, it is required to track a prescribed torque-speed curve, the voltage frequency of the

stator output must be constant, and then achieve flexible reactive power control.

It is emphasised by [11] that, in the machine-side converter, “it is essential to keep the DC-

link voltage constant regardless of the magnitude and direction of the rotor power”. To

achieve this objective, Current-Vector control approach has been developed.

2.5.2 Line-Side Converter Control

In the same way as in the machine-side converter, for which the optimal torque-speed profilecan be tracked, in line-side converter, the stator output reactive power control is the main

line-side converter objective. In addition, the DC link capacitor provides DC voltage to the

machine side converter, and store the active power in the capacitor, as a result the capacitor’s

voltage level will increases. One to ensure the consistent DC level of the DC-link, the power

flow of the converters should attempt to convene the following control objective [13]:

− = − (3)



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where and are the power and power loss of the line-side inverter, and and are

the power and power loss of the rotor-side inverter. The power flow through machine-side

and line-side converter is shown in Figure 4.

The derivative equation of the DC-link can be written as

= 1 − 2 (4)

Where 1and 2 are DC-link current, is the DC-link voltage and is capacitance value. The

DC-link current 1and 2 can be derived as

1 =− , 2 =

− (5)

Equation (3) through (5) emphasise the stability of the DC-link voltage with possible small

variation due to the instant inequality of 1and 2.

Fig.4. Power flow through line side and machine side converter [13].

2.6 Control Schemes

In general, the performance of the converter is largely depends on the quality of the used

current control technique, as a consequence, it becomes one of the most important subjects of

modern renewable energy. In literature, different control strategies for the PWM converters

have been proposed. A well-known suggestion of indirect active and reactive power control is

based on current vector orientation with respect to the line voltage vector.



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2.6.1 Current Control (CC)

In contrast to conventional open-loop voltage PWM converters, the current-controlled PWM

(CC-PWM) have the following advantages [14]: “Control of instantaneous current wave form,

high accuracy, peak current projection, overload rejection, compensation of semiconductor

voltage drop of the inverter and compensation of the DC-link and AC-side voltage changes”.

The main task of the control scheme for CC-PWM converter is shown in figure 4. Three-

phase AC load can be supplied by the CC-PWM. Based on the switching states

(SA , SB , SC) for the converter power devices, and by comparing the three loads iA , iB , iC,current control can determine the current errors (εA , εB , εC), and obviously, can decrease

these errors.

Fig.5. Basic Block Diagram of CC-PWM Converter [14].

Recently, numerous methods have been developed for the CC. Paper in [15] have discussed

the basic CC techniques for the voltage source inverter. Examples for this are Hysteresis

Controller for three dependant and independent controllers. For independent one, threecontrollers each for one phase are constructed [14]. While in the dependant hysteresis, three

controllers are incorporated together to reduce the switching frequency when, at certain time,

zero-voltage vector is applied, and to limit the maximum current error [16].

2.6.2 Space-Vector (VS) Control

According to [17], Space-Vector modulation techniques based on PWM (SV-PWM) is

considered to be the most extended modulation strategies for three-phase converters. In this



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strategy, maximum output voltage, better load controlling and low switching frequency can

be achieved.

In Space-Vector (VS) 8-different switching states can be found. Each state is composed of

= , , . These switches corresponding to 8-voltage

vector 0 = 000,… ,7 = 111. Table 1 shows the corresponding switching states, figure

6a Illustrates the basic block diagram of the three-phase SV control, and figure 6b sketches

the space vector sections.

Table1. VSC switching States [18]

(a)



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(b)

Fig.6. Three-phase SV control [18]. a. Basic block diagram, b. Space vector sections.

2.6.3 Direct Power Control (DPC)

DPC is based on the instantaneous active and reactive power control loops. The key point of

the DPC implementation is a correct and fast estimation of the active and reactive line power

[12]. In DPC there are no internal current control loops and no PWM modulator block,

however, the converter switching states are selected by a switching table based on the

instantaneous errors between the commanded and estimated values of active and reactive

power.

In DPC configuration, tow main features appeared. First the dc-bus voltage will be regulated

by controlling active power operation, and the second the unity power factor is achieved by

controlling the reactive power to be zero [19]. Figure 7a shows the basic configuration of the

DPC. The errors between active and reactive power commands and the estimated feedback

power are used as input to the hysteresis comparators and then digitized to the signals and

. The estimated three-phase signals ( , ,) of the power-source voltage vector is

converted to the digitized signal Ө . Figure 7b illustrates the twelve-sector on stationary

coordinates and the corresponding switching states are listed in table 2. The previous

mentioned controls schemes employ the use of sensors in their operations. These sensors are



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used for: AC current, DC-link voltage and AC voltage. However, as claimed by [20], it is

possible to apply DPC technique without using the AC-voltage sensor, this will improve the

total power factor and efficiency of the PWM converter.

Table 2. Switching Table for direct Power Control

(a)

(b)

Fig.7. Direct Power control [19] a. Controller Configuration, b. Twelve sectors on stationary

coordinates



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Chapter 3 Simulation of the system

As it was stated in the Literature Review, the project mainly focuses on different control

schemes for the Back-To-Back Voltage Source Converter (B-B VSC). To make it more

precisely, the control schemes for Voltage Source Inverter (VSI) are studied mainly. Among

all the control schemes that are applied to the VSI, sine-wave PWM control, space vector

modulation (SVM) control and the direct power control will be studied and simulated. The

simulation work would be done using Matlab/Simulink.

3.1 Simulation of sine-wave PWM control

The first step towards the project is to simulate a three-phase voltage source inverter. As it

can be seen in Figure 1, the power stage part is a three-phase voltage source inverter, and the

controller part is a sine-wave PWM control generator.

Figure 8. A three phase voltage source inverter and the controller unit

This model can be easily realised in Matlab/Simulink. But the first step, an appropriate

parameter setting should be chosen. According to reality, a 800V DC link is chosen and the

line side resistance and inductance are chosen to be 0.1Ω and 0.01H respectively. A quite

high value dummy resistance (100000 Ω) is also chosen to connect the neutral point to theground. So the whole simulation model is shown in Figure 2.



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Figure 9. Simulation model of sine-wave PWM control scheme

The right part of Figure 2 shows that the control scheme of the inverter. A repeating sequence

block is chosen to generate the PWM signal. In this case the PWM frequency is chosen to be

10K Hz. Of course, higher value of the PWM frequency means better performance of the

inverter. But considering the switching losses of the power stage could be higher as well, the

10k Hz seems to be reasonable. The reference signals given to the controller are three-phase

sine-waveforms with frequency of 50 Hz and are displaced 120° with each other. The

modulation index is chosen to be 1 to give the maximum dc link utilization in this case. The

result waveforms of the voltage between to common, the actual voltage over the coil, the

neutral voltage and the phase currents are shown in Figure 3.

As it can be seen in Figure 3, the peak to peak voltage of the voltage between to common

is 800V, which is equal to the DC link voltage. The phase voltage is shown as 400V, the

reason for this is because the neutral voltage of the inverter is 400V, so the maxim voltage foreach phase is 400V, which is half of the DC link voltage. The current waveform is not

balanced as it is shown in Figure 3. This happens because the inductance of the inverter is

fairly big, this results in a very long transient time. When the simulation is run for a longer

time, the balanced waveform can be seen in the scope. The peak current value can be

validated using the equation below:

=

2+

2 (1)



15

Where = 50

Figure 10. Output waveforms of the sine-wave PWM scheme



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It is noted that in the controller part of the simulation, the zero order hold block is used as a

sampling device. This is because in reality, the controller units are normally digital devices

such as DSP, A/D transformer and so on. Zero order hold samples the signal discretely

according to the sampling period given. In this case, the sampling period is the same as the

PWM period.

It is also noted that the bipolar PWM scheme is chosen in this case, because in

Matlab/Simulink the power electronic device is thought of as perfect, which means no dead

time delay is applied, so the bipolar scheme actually makes sure that at any given time, when

the upper switch of one phase is switched on/off, the lower switch of the same phase is

switched off/on at the same time, so no over-shoot happens in the simulation.

As it can be seen from the result, the maximum peak voltage of one phase only reaches 400V,

which means the line to line voltage is = 3 × = 3 × 400 = 692.82 . As it is

known, the maximum line to line voltage available should be the same as the DC link voltage,

in this case is 800V. The DC link utilization is only 692.8/800=86.6%.

In spite of the relatively low DC link utilization compared with other control scheme, it is the

easiest method to realize in both simulation and practical work. Besides, other control

schemes could be realized by some modification on this initial model.

3.2 Simulation of third harmonic injection PWM

In order to obtain more utilization of the DC link voltage, some alternative schemes are

introduced. Amongst them the third harmonic injection method could be obtained by

modifying the existing sine-wave PWM scheme. The power stage of the inverter stays the

same as it is shown in Figure 1, it is only the controller unit part changes. Or put it more

precisely, the reference signals that are put into the controller unit changes.

The basic idea about the third order harmonic injection PWM is to put the reference signal as

=2

3 sin+1

3 3 sin3 , as it can be seen from the reference equation, the

fundamental part is higher compared with the sine-wave PWM, and because the frequency of

the third harmonic part is tripled, so there’s effective cancellation of the third harmonic

component when it comes to the line to line voltage. The modulation index inputs are shown

in Figure 4 below:



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Figure 11. Simulation of third harmonic PWM scheme — the controller unit

And the result waveforms of the voltage between to common, the actual voltage over the

coil, the neutral voltage and the phase currents are shown in Figure 5



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Figure 12. Output waveforms of third harmonic PWM scheme

It can be noted that the voltage between

and common is not sinusoidal in this case, but

the actual phase voltage over the coil is sinusoidal with the peak amplitude of 463.5V, this

leads to the line to line voltage to be near 300V, which realizes the full utilization of the DC

link voltage. Compared to sine-wave PWM, this third harmonic injection method gives 15%

more DC link voltage utilization.

One of the interesting features about this scheme, as it can be seen in Figure 5, the neutral

point voltage does not stay with 400V; the neutral point voltage actually follows the third

harmonic component.



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3.3 Simulation of Space Vector Modulation (SVM)

As it was concluded in the Literature Review, the SVM scheme is the most suitable strategy

for the project. However, simulation of SVM from scratch is quite difficult. Firstly, there’ssix parts of the hexagon, each part counts 1/6 of 1 power cycle; secondly, not like the control

schemes mentioned before, SVM looks at the invert as a whole; thirdly, how to pick up the 3

vectors each time, how to choose the zero space vector and make the right combination.

These three main issues become the obstacles of building SVM model, especially when the

time is limited. But substantial literature survey is been done in this area and hopefully the

obstacles will be conquered.

All these control schemes mentioned above are simple open loop control. But in reality,

there’s no such system without control loop. A good control loop not only copes with error

correction between the given value and the output value, but it gives the fast response as well.

Either current control or direct power control, a block called PLL is needed.

Phase Locked Loop (PLL)

PLL is widely used in three-phase closed loop system. The basic idea behind it is to make 3

to 2, 2S to 2r transformation, so that the ABC reference frame could be transformed into d-q-

o rotation reference frame. Because in natural reference frame, all the quantities we’ve got

are AC quantities. Both the voltage and current quantities vary all the time, not to mention the

power. Actually the real power is pulsating forward and reactive power is pulsating backward

and forward all the time. So it is quite useful to use controller like PI controller to track these

error signals. That’s why the phase locked loop plays an important role in reference frame

transformation. By changing the natural reference frame to rotational reference frame, all the

AC quantities become DC quantities. If it’s current control, then , , are changed into , in the d-q-0 co-ordinate. If it’s direct power control, then , , and

, , are changed into , . These signals will be compared with the given signals, and

then the error signals will be fed into the PI controller so that the PI controller could do a

good job.

3.4 Simulation of Phase Locked loop (PLL)

As mentioned above, the core of PLL is reference frame transformation. While 3s to 2s could

be easily realized using equation below:



20

=

2

3− 1

3− 1

3

01

3 − 1

3 (2)

In Matlab/Simulink, this 3s to 2s can be easily built using simple mathematical model as it is

shown below

Figure 13. Simulation of 3s/2s

From 2s to 2r, an angle between the two reference frames is needed. This angle theta, is the

intergral of the supply frequency of the system. In this project, the supply frequency is 50 Hz.

The supply frequency is known, the rotating electrical velocity is obtained as = 2 × π ×

50; and the theta is easily obtained. Once theta is obtained, the 2s to 2r can be concluded by

the equation below:

= cos θ sin θ

−sin θ cos θ

(3)

Again in Matlab/Simulink, 2s to 2r is shown below:

Figure 14. Simulation of 2s/2r



21

Connecting 3s/2s and 2s/2r together gives us the natural reference frame to rotating reference

frame transformation. Figure 8 shows the whole 3/2 system.

Figure 15. Simulation of natural reference frame into rotation reference frame

The result shows that the 3 phase AC input are transferred into 2 DC quantities as it is shown

below:

Figure 16. The output waveform of the rotation reference frame



22

As it can be seen the currents and tend to be DC quantities after transient. When it

comes to the controller, in current controller normally ∗ is set to zero while in direct power

control it is the ∗ that is set to zero so as to obtain the maximum power factor.

So far, a lot of simulation work has been done. Different control schemes are simulated and

compared and the PLL has been simulated using simple 3/2 transformation.

.



23

Chapter 4 control of the system

4.1 Introduction

A model of the back to back converter, which is used between the DC link capacitor and the

grid, is implemented and controlled in this section. Using Matlab/Simulink the simulation

model is designed. The main purpose of the project is the controlling of the grid current via

the use of an appropriate scheme, afterwards the simulation of the voltage source converter

between DC link voltage and the grid is given more consideration. Because, as stated above,

the central function in this project is the control the grid current, the constancy of the DC link

capacitor voltage must to be considered. Also, the simulation should be only of the voltage

source converter that is connected to the grid. The circuit that will be both implemented and

simulated via Matlab/Simulink is shown in Figure (17).

Figure 17: Voltage source converter which is connected to the grid

The first step, according to the project description, in the modelling process of the voltage

source converter that is connected to the grid, is the implementation, using Matlab/Simulink,

of a model of the PWM voltage source converter. In this project a phase two level voltage

source converter is used as the PWM voltage source converter, this is a widespread topology.

Figure (18) shows the design of the circuit, a three phase converter consisting of six switches.

It is apparent that by controlling the switches, for example by controlling the sine wave PWM,

and filtering the output, a quasi-sinusoidal waveform is attained. It is noteworthy however,

that without the use of the filter the voltage at the output would be a square wave.



24

For the sake of simulating the three phase voltage source converter operation, a carrier

waveform and three reference waveforms are chosen. The voltage source converter operation

is switched in Matlab/Simulink using sine wave PWM. A 120 degree phase angle is between

the three reference waveforms in order to achieve symmetry between the waveforms. This

model is shown implemented in figure (18). The PWM carrier frequency in this project is set

to 10KHZ.

Figure18: The simulation block of the three phase two level of voltage source converter

The converter output voltage has two levels, these are 2 modulation index and holding it

constant over the entire following PWM cycle is done by the zero order hold blocks. The zero

order hold block should have the time setting as the PWM cycle. In figure (19) the output

voltage of the simulated voltage source converter is shown. The output voltage changes

between 360 and -360, this is clearly because of the voltage of the DC link capacitor is set to

720 volts.

s1

s2

s3v3

3

v2

2

v1

1

Zero -Order

Hold 2

Zero -Order

Hold 1

Zero -Order

Hold

Switch2

Switch1

Switch

Repeating

Sequence

Relational

Operator 2

<=

Relational

Operator 1

<=

RelationalOperator

<=

vdc 2

5

vdc 1

4

m3

3

m2

2

m1

1



25

Figure (19): The output voltage of the simulated voltage source converter

Figure (20) shows a single equivalent circuit of the back to back voltage source converter that

is connected to the grid.

Figure 20: single phase equivalent circuit

As a result, an equivalent circuit can be written according to Kirchhoff’s voltage law.

= + +

Or

=1 − −

Hence, developing a suitable transfer function model in Matlab/Simulink for the back to back

voltage source converter which is connected to the grid can now be done. A transfer function

model of the circuit is shown in Figure (21).

resistance and inductanceof distribution line

gridvoltage

Back to BackVoltage Source

converter





27

Table (3) shows a summary of the values which are used in the project.

variable value

Three phase Power 60000 (W)

Frequency 50 (Hz)

The phase to phase voltage of grid 415 (V)Carrier frequency 10000 (Hz)

Inductance of the line 0.45 (mH)

Resistance of the line 0.03 (ohm)

DC link voltage 720 (V)

Table (3): value of parameters when voltage source converter supply the load

The modulation signal is an important parameter in attaining the needed value of current.

This is made clear in the model above, where changing the modulation index, results in a

change in the amount of current. The figure below (figure (22)) shows the current when the

modulation index is 1.

Figure 22: The current of inductor when modulation index is unity

When changing the amplitude of modulation signal to 0.5 the amount of the rms voltage of

the inverter becomes equal to0.5∗360

2 or 127.27 V. Figure (23) demonstrates the phase current

of the system and it is clear that the amplitude of current increases.



28

Figure 23: The current of inductor when the modulation index is 0.5

All the above analysis clearly shows that controlling the modulation index enables reaching

the desired power for transfer. This is based on the fact that the modulation index is needed to

control the transfer power between back to back voltage source converter and the grid.

A fundamental issue in the performance of the connected back to back voltage source

converter is the control system. Maximizing the extracted power from the back to back

voltage source converter can be achieved with a great controller; confirmation that the power

that is transferred to the grid is satisfactory according the grid requirement can also be

achieved with a great controller. The full controllability of the system is allowed, due to the

fact that a voltage source converter is used to connect the DC link voltage to the grid.

The control of grid connected voltage source converter is performed by different control

schemes; these schemes are subject-concentrated. Examples of subject-concentrated schemes:

controlling the active and reactive power that is delivered to the grid, the DC link voltage and

the reduction in the harmonics that are injected to the network. Most control schemes have of

two cascaded control loops; these are named inner loop and outer loop. The handling of error

corrections between given value and the output value is an important characteristic of control

loops, this and the ability to give fast response. The determination and transmission of the

signal that is desired to be controlled is required in each loop. This is done by different

methods; these include the Proportional-Integral (PI) controller and Proportional-Rotational

(PR) controller.



29

4.2 The PI controller

The wanted signal is determined and transmitted in the PI controller. The PI controllers

determined output signal is dependent upon on the proportional gain , the integral gain and error

. One of the above factors, which is the proportional gain

, changes the error

value proportional output and can make the system unstable if it’s value too high. In addition,

the controller is made less sensitive when a small value with a small output response has a

large input error. A signal cannot be driven at the demanded value if the proportional

controller is not suitable. A steady state error, named the offset, stays with the proportional

controller, thus the integral term is added to the controller, for the cancellation of the offset

effect [21].

The error signal’s magnitude and the length are both affected by the integral term. Theintegral gain is used to calculate the magnitude of the effect to the integral term of the

whole control action. In actual fact, the speed of the response of the controller is increased

and the residual steady state error is eliminated by the integral gain. The residual steady state

error occurs because of a pure proportional controller. Nonetheless, an overshoot can happen

in the output due to the integral control term. This happens because the response in the

integral term to the accumulated errors of the past [21].

The PI controller is good in the control of DC values; this is an important feature and needs to

be considered. And because of the above and because all the current and voltage variables

are AC, the transformation of the grid voltages and currents from the abc to the dq reference

frame, is needed for the use of the PI controller in this project. Thus, the variables are

converted to DC values, and can be more easily controlled by the PI controller [21].

4.3 The reference frame transform

As was previously mentioned for the use of the PI controller, the stationery frame (abc) needs

to be transformed to the synchronous frame (dq). An important concept of reference frame

theory has to be introduced for the sake of achieving this aim. First of all, the three phase

quantity needs to be transformed, as an example , , , into two vector, positive and

negative phase sequence vector. This, in a complex ref erence frame, is called the αβ frame.

The Clarke transform which is used, uses three time varying variables, which can be

demonstrated by a space vector, in the process of determining their two components in the

orthogonal axis. The space vector is defined as:

=2

3( + + 2)



30

Where = 23 =

−1

2+ 3

2.

The three time varying variables van be established in a stationary reference frame αβ,

via the use of Clark transformation, where the real axis is α and the imaginary axis is β. The

expressions for the αβ axis variables in the terms of the three phase variables can be found by

the substitution of the rectangular form of the α operator in the equation above and following

this it is separated into real and imaginary parts. A transform matrix is defined as:

=

2

3

−1

3

−1

3

01

3−1

3

The implementation of a block that transforms from the abc frame to the αβ frame can be

easily be done with the Simulink component in Matlab/Simulink. The following figure

(figure (24)) shows the block, this block is built using a simple mathematical model.

Figure 24: transform block from abc reference frame to αβ reference frame

So that the implemented block performance is investigated a three phase sinusoidal signal

with 120 degree phase shift between each phase, with a frequency of 50Hz and an amplitude

of 100 applied to the block. The 90 degree phase shift is apparent between the signals in

Figure (25). The two output signals from the block are shown in the figure below:



31

Figure 25: The output signal from abc to αβ transform

An angle, generally called Theta, between the two reference frames, αβ reference frame and

the dq reference frame, is needed for the transformation between the two. This angle can be

concluded with the integration of the frequency supply of the grid. The calculation process

for Theta is easy, this being due to the fact that the grid frequency is known (50 Hz). The

clark transform is the transform which is used for the transformation of the variable the αβ

reference frame to the dq reference frame shown in figure (26). This transform can be

written by

= cos θ sin θ

−sin θ cos θ

Figure 26: Block diagram for transforming the αβ reference frame to the dq reference frame

Figure (27) show an illustration of the output of the dq reference block when the previous

blocks output is applied to this new block.



32

Figure (27): The output of the dq reference frame block

Additionally, the transforms’ output variable is clearly a DC value, the variable in the q axis

is 100 and the d axis variable is zero. Thus, when these two transforms are in a cascaded

format, the variable can be changed from an AC to DC signal, and this will enable the use of

the PI controller. However, the output of PI controller, which is a DC value, has to be

transformed to an AC value. And to do so, opposite measures to the one above are applied.

The inverse transform is presented by:

αβ = cos θ sin θ− sin θ cos θ de

And

=

1 0−1

2

32−1

2

− 32

[ ]

A Matlab/Simulink implemented block diagram for the dq to αβ to abc reference frametransformation is shown in figure (28). And it is noteworthy, that the Theta angle has not

changed.

Figure (28): Block in matlab/simulink for transforming from the dq to abc reference frame





34

In determining the filter capacitors’ value, a cut off frequency has to be chosen and

henceforth after using the inductor previously calculated the filter capacitors value can then

be calculated.

= 142 2

Figure (30): The transfer function model of the voltage source converter with the load

Thus, the value of filter capacitor is calculated to be 56.290 µF.

Table (4) shows a summary of the used values in the project.

Variable value

Three phase Power 60000 (W)

Frequency 50 (Hz)

The phase to phase voltage of grid 415 (V)

Carrier frequency 10000 (Hz)

Inductance of the filter 0.45 (mH)

Resistance of the filter 0.03 (ohm)Capacitance of the filter 56.290 (µF)

DC link voltage 720 (V)

Resistance of the load 3.239 (Ω) Table (4): Value of parameters when voltage source converter connected to the grid and load

After the application of unity modulation index to the voltage source converter mazimum

current flows in the load. Of course, the above means that 254.55V is the amount of rms

voltage applied. Figure(31) shows the converter current with unity modulation index. Thecurrent peak to peak amplitude is the same as previously calculated which is 111.11.



35

Figure (31): The converter current with unity modulation index

The load current and convert decrease when the modulation index is changed to 0.5. this

effectively halves the rms value of the applied voltage by the voltage source converter, and is

now equal to 127.27 V. Consequently, 39.05 is now the value of the rms, while 55.23 is the

value for the peak to peak to peak current for the modulation index. The current wave when

the modulation index is equal to 0.5 is shown in figure (32).

Figure (32): The current of the inverter when modulation index is 0.5

To summarize, the modulation index has clearly a considerable effect on the output voltage

and current of the voltage source converter. And that a demanded value of the current can be

achieved with changing the modulation index.

4.5 Voltage source converter connected to the resistive load with control loop

The controllers’ most frequent arrangement is the current control. It is used in many

industrial drives, small and large. The main reason is its simplicity and low cost, it consists of

a feedback loop for controlling the current.

What is done in the manual controlling, needs to be considered in order to appreciate the

overall operation of the control scheme. In the investigation it was made apparent that for the



36

sake of producing more current to supply the load, the input voltage needs to be raised. This

can be done by increasing the modulation index.

In order to understand the systems operation, consider the voltage source converter which

supplies the load and the current of the load to reach the steady state value. After this, if the

output current is needed to increase, a current error signal is created which is a difference

between the actual output current and desired output current. The required current error signal

is specified by the error signal. Therefore, to compensate the error between the actual current

and the desired current, the quantity of the output voltage of converter needs to be increased.

The main aim is to achieve a zero error signal in the steady state mode by creating a relation

between the error signal and the modulation index of the voltage source converter.

A good current loop should be the first thing aimed for when designing the controller. This

means that the steady state current has to closely correspond with the current reference and

there should be fast and well damped transient response to step changes in the current

reference. The PI controller is needed to attain these objectives, the integral term in the PI

controller satisfies the first requirement, and the second is satisfied by an appropriate choice

of the proportional gain.

Because a three phase voltage source converter is connected to three phase load and becausethe voltage and current signals are sinusoidal, it is appropriate to use of abc to dq transform to

obtain a DC value for the current in dq reference frame. In addition, it is more suitable to use

the PI controller to compare the actual and desired values of the current. In another part of the

system the PI’s controller output as a voltage signal is abc reference frame transformed, in

order to be applied to the voltage source converter. In the figure (33) the voltage source

converter connected to load with current controller block diagram is shown.



37

Figure (33): The voltage source converter connected to the load with the controller

Because there are only two components, d and q, in the dq reference frame, two PI controllers

are needed by the system. After this Kp and Ki need to be adjusted. The trial and error method

is used for regulating the digital PI controller and the value of controller parameters is listed

in table (5).

Controller Parameter Value

Kp of the PI controller in the d axis 0.0205

Ki of the PI controller in the d axis 0.003

Kp of the PI controller in the q axis 5*10-6

Ki of the PI controller in the q axis 6.12*10-5

Table 5: The value of controller parameters for load

To regulate the digital PI controller the trial and error method is used. In Table(2) the value

of controller parameters are found.

For the sake of investigating the controllers’ performance, the demanded current is set is put

to 110A as shown in figure (34). This is the maximum current that can be applied by the

voltage source to the load. This means in actual fact that Iq=110 and Id=0. The following



38

figure shows the current waveform converter for one phase, it is apparent that the demanded

value is reached after two cycles.

Figure (34): The voltage source converter current waveform.

The demanded and actual value of the voltage source converter current in the q axis and d

axis of the dq reference frame is shown in figures (35) and (36) respectively. Furthermore, it

is apparent that the demanded value is being followed as quickly as possible by the currents’

actual value in the q axis, however a minute fluctuation appears in the current signal’s actual

value around the demanded value in the d axis.

Figure (35): The actual value and the demanded value in the q axis

Figure (36): The actual value and the demanded value in the d axis



39

Voltage source converter that is connected to a grid is analysed and modelled in this part. As

in the previous section, a transfer function of the system is implemented in Matlab/Simulink

first. A model of the transfer function without the control scheme is shown in figure (37).

Additionally, to investigate the transfer function model the modulation has to be set to unity

and the simulation has to run for a long time. The converter current is shown in figure (37)

when the modulation index is equal to 1, and the waveform of the current can be seen as a

perfect sinusoid after a transient time.

4.6 Voltage source converter connected to the grid with controller

The PWM previously described performs as an open loop or feed forward control of the

voltage source converters’ output voltages. The systems aim is the control of the output

currents demanded value, for this current sensor feedback must be present. A control system

compares between the actual currents with the reference currents and then produces the

appropriate modulation index for each phase. This results in the waveforms output current

following the reference waveforms.

The control scheme consists of a current loop and a feedback from the grid voltage. This

control scheme is used for the grid connected voltage source converter. This control scheme

is proposed in order to follow the three phase voltage of the grid, thus adding the grid

voltage’s feedback with a proportional gain to the current loop. Figure ( 37) shows the

proposed control scheme, which is used in this project.

Figure (37): transfer function model of the grid connected voltage source converter

It is obvious that the entire variable is first transformed to the dq reference frame, and afterthis the output waveform of the PI controllers is used as a reference value for the voltage loop.



40

It is noteworthy to mention that one digital PI controller is used for each axis. The table 6

below shows values of the PI controller.

Controller Parameter Value

Kp of the PI controller in the d axis 0.0207

Ki of the PI controller in the d axis 0

Kp of the PI controller in the q axis 5*10-4

Ki of the PI controller in the q axis 0

Table 6: The value of controller parameters for grid

The simulations result, when the demand current is set 110, is shown in figure (38). The

steady state mode, after a transient, it is clear that the actual current (iq) is very near to the

demand value.

Figure (38): The currents (iq & i∗q) waveform of voltage source converter with the grid

However, the steady state mode, after a transient , as figure 39 shows that it is clear, there is

some deference between actual current and demand current (id).

Figure (39): The currents (id& i∗d) waveform of voltage source converter with the grid



41

Chapter 5 Conclusion

This project deals with an investigation on the back to back voltage source converter which is

so much popular in the wind power industry these days. Firstly, various topologies of theback to back voltage source converter have been presented and their advantages and

limitations are described. Moreover, different control strategies for the generator side and the

grid side of converter are explained.

It is obvious that the performance of the converter is largely depends on the quality of the

control scheme which is employed. The space vector control scheme is the most suitable

strategy among other schemes, due to converter can achieve maximum output voltage, better

load controlling and low switching frequency.

Furthermore, due to the computational complexity of space vector control scheme, numerous

improvements have been done to achieve an excellent performance. This project attempts to

develop and model a control scheme to improve the performance and efficiency of the

converter based on the space vector control scheme.

In the simulation and modelling part, different control schemes have been simulated and

compared for the converter. A simple and excellent kind of direct power control scheme is

chosen as the main control scheme and the transient and steady state performance of a

voltage source converter have been investigated in different conditions. In every case, the

proposed control schemes have been shown to provide fast and satisfactory responses for the

voltage source converter. From the simulation we can deduce that the voltage source

converter can accomplish fast power transfers.



42

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