Substation for wave power
Erik Lejerskog
Cecilia Boström
Abstract
This master thesis is a part of the bigger project Islandsberg that has been going on since
2002 at the division of Electricity and Lightning research at Uppsala University. In the
project, a farm of wave power plants will be constructed. The idea is to extract energy
from waves by a linear generator, a rope and a buoy. To connect generators to a farm, a
substation is needed.
The aim of this master thesis is to develop a model for a substation. The substation will
connect the wave generators to the grid. The substation consists of a main circuit and a
sub circuit. In the main circuit, the AC from the generators will be rectified and then
connected together. The DC after the rectifier needs to be filtered and inverted to AC and
then connected to the grid. The sub circuit can be divided into three parts, a safety circuit,
measuring circuit and a control part.
The rectifier, filter, IGBT bridge and PWM were simulated in MATLAB and in PSpice.
A test setup was built to test the performance of a PWM, driver circuit and IGBT bridge.
All of the parts in the substation are not tested in this master thesis. One large part of this
thesis is to find out a design of the substation.
The results from the simulations agrees well with theory, but to achieve more realistic
results, tests on a real wave generator is needed. The tests on the IGBT bridge, PWM and
driver circuit works in a proper way.
Abbreviations
AC Alternating Current
CT Current Transformer
DC Direct Current
DSP Digital Signal Processor
IGBT Insulated Gate Bipolar Transistor
LEM Linear emission module
LL Line to Line
PWM Pulse Width Modutation
THD Total harmonic Distortion
VT Voltage Transformer
Contents
1. Introduction .............................................................................................................................7
1.1 The wave power project – Islandsberg .............................................................................7
1.2 Problem formulation .........................................................................................................7
1.3 Limitation ..........................................................................................................................8
1.4 Purpose..............................................................................................................................8
1.5 Disposition ........................................................................................................................8
1.6 Ocean waves .....................................................................................................................8
1.7 Wave power plant .............................................................................................................9
1.8 Substation..........................................................................................................................9
2. Theory ...................................................................................................................................13
2.1 Main circuit .....................................................................................................................13
2.1.1 Rectifier....................................................................................................................13
2.1.1.1 Diode .................................................................................................................13
2.1.1.2 Six pulse diode rectifier ....................................................................................14
2.1.2 Passive Filter ............................................................................................................16
2.1.2.1 Capacitor ...........................................................................................................16
2.1.2.2 Supercapacitor...................................................................................................18
2.1.2.3 Ceramic capacitor .............................................................................................18
2.1.2.4 Inductor .............................................................................................................18
2.1.2.5 Harmonics .........................................................................................................20
2.1.2.6 Filter ..................................................................................................................22
2.1.3 The DC to AC inverter .............................................................................................25
2.1.3.3 Snubber circuits ................................................................................................28
2.1.4 Transformer..............................................................................................................29
2.1.4.1 Basic transformer ..............................................................................................29
2.1.4.2 Different types of transformers .........................................................................32
2.1.4.3 Power losses in transformer ..............................................................................32
2.1.5 DC to DC converter .................................................................................................33
2.1.5.1 Step-down (buck) converter ..............................................................................34
2.1.5.2 Step-up (boost) converter ..................................................................................35
2.1.5.3 Other types of DC to DC converters .................................................................35
2.2 Sub circuit ....................................................................... Error! Bookmark not defined.
2.2.1 Role of protection and Faults ................................... Error! Bookmark not defined.
2.2.1.2 Fault calculations .............................................. Error! Bookmark not defined.
2.2.2 Safety circuit ............................................................ Error! Bookmark not defined.
2.2.2.1 Relays ................................................................ Error! Bookmark not defined.
2.2.2.2 Electric-connector, circuit breaker .................... Error! Bookmark not defined.
2.2.2.3 Instrument transformer...................................... Error! Bookmark not defined.
2.2.2.4 Variable resistor ................................................ Error! Bookmark not defined.
2.2.3 Measure part............................................................. Error! Bookmark not defined.
2.2.3.1 Current measuring ............................................. Error! Bookmark not defined.
2.2.3.2 Voltage measuring ............................................ Error! Bookmark not defined.
2.2.4 Control circuit .......................................................... Error! Bookmark not defined.
2.2.4.1 PWM-Pulse Width Modulation ........................ Error! Bookmark not defined.
3. Simulations ........................................................................... Error! Bookmark not defined.
3.1 Voltage from the linear generator ................................... Error! Bookmark not defined.
3.2 AC to DC ........................................................................ Error! Bookmark not defined.
3.3 Filter ................................................................................ Error! Bookmark not defined.
3.4 PWM ............................................................................... Error! Bookmark not defined.
3.5 AC to AC ........................................................................ Error! Bookmark not defined.
4. Experiment: DC to AC inverter ............................................ Error! Bookmark not defined.
4.1 Experimental test setup ................................................... Error! Bookmark not defined.
4.2 Experiments .................................................................... Error! Bookmark not defined.
5. Results ................................................................................... Error! Bookmark not defined.
5.1 Diode rectifier ................................................................. Error! Bookmark not defined.
5.2 Filter simulations ............................................................ Error! Bookmark not defined.
5.3 Results of PWM .............................................................. Error! Bookmark not defined.
5.3.1 Simulation 1 ............................................................. Error! Bookmark not defined.
5.3.2 Simulation 2 and 3 ................................................... Error! Bookmark not defined.
5.3.3 Test 1 ........................................................................ Error! Bookmark not defined.
5.3.4 Test 2 ........................................................................ Error! Bookmark not defined.
5.3.5 Test 3 ........................................................................ Error! Bookmark not defined.
5.3.6 Test 4 ........................................................................ Error! Bookmark not defined.
5.3.7 Test 5 ........................................................................ Error! Bookmark not defined.
5.4 AC to AC ........................................................................ Error! Bookmark not defined.
6. Design of safety circuit ......................................................... Error! Bookmark not defined.
7. Discussion ............................................................................. Error! Bookmark not defined.
8. Conclusion ............................................................................ Error! Bookmark not defined.
9. Acknowledgement ................................................................ Error! Bookmark not defined.
10. References ........................................................................... Error! Bookmark not defined.
Appendix A – Circuit scheme for the AC to AC simulations... Error! Bookmark not defined.
Appendix B – Datasheet IGBT ................................................. Error! Bookmark not defined.
Appendix C – Datasheet gate driver ......................................... Error! Bookmark not defined.
Appendix D – PWM ................................................................. Error! Bookmark not defined.
1. Introduction
1.1 The wave power project – Islandsberg
This master thesis is a part of the bigger project Islandsberg that has been going on since
2002 at the division of Electricity and Lightning research at Uppsala University.
Islandsberg is based on the idea of transforming wave energy to electricity. This will be
done through linear generators placed at the bottom of the ocean. The linear generator is
connected to a buoy via a rope, see Figure 1.1. The waves will get the buoy to move
vertically which generates a motion in the linear generator and a current is produced.
In the project, one wave power plant is planned to produce a mean power for about 10
kW. To get a higher output, more power plants can be connected. In this project 10 power
plants will be connected, this results in a common mean power for about 100 kW. The
wave park is planned to be finished and in use around 2008.
Figure 1.1. A farm of wave power plants [1].
1.2 Problem formulation
When one or more wave power plant is connected, a substation is needed. In this case,
the AC from the power plant is varying in frequency and in amplitude. The AC must
therefore be transformed and filtered in the substation before the wave power plants can
be connected to the grid. A safety circuit is necessary to have in a substation; this safety
circuit can disconnect or break a power plant from the grid if there are any faults with the
power plants.
The main task in this assignment is to design a model of an underwater substation that
safely can connect ten wave power plants to the grid.
1.3 Limitation
This assignment is only going to consider the main circuit and the safety circuit in the
substation. It starts with the signal from the power plant and ends where the cable to the
grid begins. The assignment is not going to involve any construction of the outer casing
and no theory about the cable from the substation to the shore.
1.4 Purpose
This assignment will be the foundation for the underwater substation constructed in the
project Islandsberg.
The purpose with the assignment is to design and examine some parts in the substation. A
model for an underwater substation that can connect and transform the currents and
voltages form the power plants in a proper way should be examined.
1.5 Disposition
The assignment begins with a literature study and research. Then, simulations are done of
the rectifier, filter and DC to AC inverter. A model of the PWM and IGBT bridge is
constructed and a design of a safety system is presented.
We are two persons writing this assignment. Erik has done the parts about the main
circuit and Cecilia has done the parts about the sub circuit. The introduction, conclusion
and discussion are chapters written in common by us both.
1.6 Ocean waves
Waves are created by the wind and the wind in turn is created by the sun, so the extracted
energy comes from the sun energy. The power produced by the generator is dependent of
the wave height, HS, and the period T. The generator (translator) motion is dependent of
the wave angular frequency, Ω, and the wavelength, λ. These two parameters can be
described with the equations:
  2f 

2
T
2
k
(1.1)
(1.2)
where
f = wave frequency [Hz]
T = wave period [s]
k = wave number
λ = wave length [m]
The wave angular frequency is also related to the wave number by the dispersion relation.
The deep-water dispersion relation is
  gk
(1.3)
where
g = acceleration of gravity [m/s2]
ω = angular frequency [rad/s]
1.7 Wave power plant
The wave power plant consists of a buoy, a rope, a linear generator and a steel shell that
surrounds the generator. The generator is fixed at the bottom of the ocean with a concrete
block and the buoy is connected to the generator with a rope.
The linear generator is build up with two main parts, the translator and the stator, where
the translator is a moving part and the stator is fixed. Permanent magnets with opposite
polarity are mounted on the translator. The stator consists of coil windings of copper or
aluminium and stator steel. When the translator moves up and down between the coil
windings, a flux change is created around the coils which results in a current in the coils.
The produced current and voltage will be the input in the substation.
a)
b)
c)
Figure 1.2. a) The linear generator. The rotor is also called translator.
b) Coil winding of the stator.
c) Permanent magnets mounted on the rotor [3].
When permanent magnets are used, sensitive electrical connections to the stator can be
avoided [2]. The generator must also be able to manage different wave climates, which
results in a generator with a wide voltage and current region. This makes the generator
less sensitive against over current and over voltages.
1.8 Substation
The main purpose with a substation is to connect different transmission lines to each
other. There are more complex substations including many different part and simpler
constructions where the transmission lines just are coupled together to a common
transmission line. Also, to connect more then one generator to the grid, a substation is
used.
The linear generator output AC is varying both in amplitude and frequency, see Figure
1.3. This kind of output can not be connected to the grid directly; it needs to be
transformed to a sinus wave with a constant frequency and amplitude. This kind of
transformation can be done in an AC to AC converter.
300
200
Voltage [V]
100
0
-100
-200
-300
0
0.5
1
1.5
2
Time [s]
2.5
3
3.5
4
Figure 1.3. The three phase voltage out from the linear generator simulated in matlab.
The sinus modulated AC in Figure 1.3 is simulated for a wave height of 1 meter and a
period of 5 seconds. The design parameters for the linear generator is can be seen in
Chapter 3.
The substations in this project are divided into a main and sub circuit, see Figure 1.4. The
different parts in the circuits are briefly presented here, a more detailed presentation of
the parts are done in the Chapter 2.
MAIN CIRCUIT 2
5
1
G
4
RECTIFIER
FILTER
DC to DC
DC to AC
TRANSFORMER
CASE1
G
CIRCUIT 3
SUB
DC to
DC
OVER
VOLTAGE
CURRENT CURRENT
RELAYS
MEASURE
PWM
CONTROL
PART
CASE2
+
+
+
-
B
A
T
T
E
R
Y
OVER
CURRENT
RELAYS
+
+
+
-
Figure 1.4. An example of a substation. This substation has two generators (1) connected
to it, but the substation is dimensioned for ten generators. The substation is divided into
two parts; the main circuit (2) and the sub circuit (3). (4) illustrates the over voltage
protection.
The input AC from the linear generator needs to be transformed to a desired sinusoidal
waveform. To do so the AC from the linear generator needs to take some steps in the
main circuit.
The first step in the main circuit (AC/AC converter) is a rectifier; this stage will convert
the input AC to DC. In the above circuit, a diode bridge is used. It consists of six diodes
connected as in Figure 1.4. The diode conducts when it is subject to a voltage drop in the
forward direction and in the ideal case; the diode blocks the current when the voltage is
reversed. This diode bridge can also be made with thyristors instead of diodes, then it
would be called a controlled rectifier, when diodes are used it is called uncontrolled
rectifier. This means that the DC voltage after the rectifier is determent by the input AC
from the linear generator. A consequence of this is that the DC will vary with changing
wave climate.
When the input AC has been converted to DC in the rectifier it needs to be filtrated, this
is because the DC consists of both an AC and a DC part. The AC part is called ripples
and should be reduced to a minimum. This is done through a filter. The filter can be built
in many different ways depending on what the filter is supposed to remove. One way to
reduce the ripples is to use passive components like capacitors and inductors. These
filters are called passive filters. The filter can also be used to remove or reduce harmonic
disturbance that usually appears after a rectifier.
When the AC from the linear generator has been rectified and filtered to a smooth DC
voltage it will be inverted back to an AC with a constant amplitude and frequency, this is
done by an inverter. The inverter is build up of six IGBT:s, they are connected much like
the rectifier bridge but here IGBT:s is used instead of diodes. The IGBT is controlled
between the on and of state by a gate signal, this can be done by PWM (Pulse width
modulation).
The AC output from the inverter will also vary in amplitude because of the varying DC.
This AC needs to be regulated before it is connected to the grid. Two cases are presented;
how to regulate the amplitude. Case 1 is a DC to DC converter this converter can take an
unregulated DC as input and regulate the DC to a specific value at the output. A DC to
DC usually consists of a switch together with a capacitor or an inductor or both. Case 2
involve a transformer; the transformer in this project needs to be able to change the
number windings around its core to regulate the AC. This can be done with a motor that
can change the winding depending on the voltage level on the dc side, and in turn keep
the AC to the grid constant. A transformer that can change the winding around the core
will be referred as a variable transformer in this project.
The different parts in the sub circuit can be divided into three groups according to their
purpose; one safety part, one control part and one measure part, see Figure 1.4. These
three groups will perform different tasks on or to the main circuit.
The main goal with the safety part is that the system should fulfil the following points in
such a good way as possible:





Have a fast enough function time, some systems demand a shorter function time
than others. The function time is defined as the time it takes for the safety circuit
to switch off a generator at a fault.
Switch off a generator at an over current fault and lead away over voltages.
Be stable for external faults.
Easy to understand.
Every component in a circuit has a fault factor. With more components added to
the circuit, there is a larger risk for a fault to occur. The number of components
in the safety circuit (and in the rest of the substation) should therefore be
considered.
With these points in mind, a model for a safety circuit that protects the main circuit from
faults should be designed.
The linear generators are protected from over voltages by using a variable resistor. A
variable resistor is often placed in the generator but the linear generator is designed to
manage over voltages, therefore the variable resistor can be placed in the substation.
The over current protection is built up of a relay system. The relay system is connected to
breakers and when a fault that causes over current occurs, the generator(s) will be
switched off. The over current protection that is placed after the transformer in Figure 1.4
may not be necessary.
In the circuit, the voltages and currents can be measured by using instrument
transformers, resistors, shunts or LEM shunts.
The IGBTs in the main part are fed with a control signal. This control signal can
concisely be described as a pulse pattern that creates an out signal from the IGBT with
the desired frequency and with a sinusoidal shape. The control signal adjusts the voltage
from the IGBT:s to the voltage on the grid.
2. Theory
2.1 Main circuit
The aim in the main circuit is to transform the output AC from the wave power plant in
different stages to an AC that is acceptable to connect to the grid. These different stages
will be described in this part.
2.1.1 Rectifier
This part in the main circuit will transform the incoming AC from the generator to a
pulsating DC at the output of the rectifier. The pulsating DC can be divided in to two
parts; an AC part and a DC part where the AC part calls ripples in the DC. The rectifier
used in this design consists of diodes, these diodes only let throw current at forward
direction and block the current in reverse direction. In this chapter a six pulse diode
bridge will be described.
2.1.1.1 Diode
The diode is an important component among the semiconductors. It is build up of a pnjunction of p-doped and n-doped silicon. The diode works like a vent; it only let through
current in the forward direction, (that will say that) it has a low resistance in the forward
direction but a very high resistance in the backward direction. This is for the ideal diode,
but for a real silicon diode there will be a forward voltage drop and a leakage current in
the backward direction. The forward voltage drop for silicon diode is about 0.7V, but will
get higher when it works with higher currents. When the diode gets a voltage over the
backward direction it lets throw a leakage current. This current is very small, about a
million part of the current in the forward direction. If the maximum voltage in the
backward direction is override the leakage current will grow large very drastically.
Because of these points, the choice of diode needs to be considered carefully.
Figure 2.1. The figure to the left shows V-I characteristics of an ideal diode and to the
left V-I characteristics of a silicon diode [4].
In Figure 2.1, the difference between an ideal diode and a silicon diode is shown. The
symbol used for diodes in circuits diagram can be seen in Figure 2.2
Figure 2.2. Diode symbol.
2.1.1.2 Six pulse diode rectifier
The six pulse diode rectifier consists of six diodes connected as in Figure 2.3
where V an , Vbn and Vcn is the phase voltage. V 0 is the DC voltage over the load and R is a
resistive load.
+
Van
D1
D2
D3
Vbn
V0
Vcn
D4
D5
R
D6
Figure 2.3. Six pulse diode rectifier with resistive load
This diode bridge conducts six times in one period. Diodes D1, D2 and D3 provide the
forward path and D4, D5 and D6 establish the return path. It works as follows the current
will flow through one diode that provide the forward path and one that provide the return
path. The diode in the forward path with its anode at the highest potential will start to
conduct and the other two will be revered bias. The diode in return path with its cathode
at the lowest potential will start to conduct. The conduction sequence per time period is
as follows [5]:
(1): from 0  to 60  :
Vcb supplies power to R via D3 and D5


(2): from 60 to 120 :
Vab supplies power to R via D1 and D5


(3): from 120 to 180 : Vac supplies power to R via D1 and D6
(4): from 180  to 240  : Vbc supplies power to R via D2 and D6
(5): from 240  to 300  : Vba supplies power to R via D2 and D4
(6): from 300  to 360  : Vca supplies power to R via D3 and D4
Figure 2.4 Plot of six line voltage [6].
The diodes will only let through current when its anode has the highest potential or the
other way around for the diodes in the return path. In Figure 2.4, the diode will stop the
current for a diode when the diode does not have the highest or lowest potential.
Figure 2.5. The output voltage from a six pulse rectifier.
The waveforms that will come out of the three phase rectifier with a resistive load can be
seen in Figure 2.5. The DC voltage is the difference between the higher and the lower
envelop and this DC consists of six pulses per period. The average DC voltage, Vd, will
be:

Vd 
3

6


2VLL cos td (t )  1.35VLL
(2.1)
6
VLL is the rms value of line-to-line voltage.
The effective output voltage is:

Vdrms 
3

6
 (
2VLL sin( t )) 2 d (t )
(2.2)

6
The form factor can be calculated from Equation 2.1 and 2.2:
FF 
Vdrms
Vd
(2.3)
and by using Equation 2.3, the ripple factor can be calculated:
RF  FF 2  1
(2.4)
Usually for a six pulse rectifier, the ripple factor will be around 4% [41].
2.1.2 Passive Filter
The filter after the rectifier is used to remove or smooth out the DC ripples that are
formed after the rectifier se Figure 2.5. The filter is also used to remove harmonics. There
are many types of filter that can be used for this purpose but the aim in this chapter is to
explain passive filter and its main parts.
2.1.2.1 Capacitor
The capacitor is an energy storage device, it consists of two conductive electrodes with
an intermediate layer of an insulator or dielectric .The capacitance C is proportional
against the intermediate layer and inverted proportional to the distance of the two
conductive plates. The capacitors capacitance can be calculated from the amount of
charge Q stored in each plate for a given voltage V that appears between them. The
relations between them are
C
Q
V
(2.5)
The stored energy in a capacitor is calculated as:
V2
E C
2
(2.6)
V in this equation stands for the voltage across the capacitor.
In a DC circuit, when a current is flowing through the capacitor electrons accumulates on
one of the plate and is removed from the other. This process is called charging the
capacitor. The separation of charge gives a rise to an electric field between the two plates
witch gives a rise in voltage over the capacitor. This voltage is direct proportional to the
amount of charge separations.
dQ
dV
C*
(2.7)
dt
dt
When a capacitor is used in an AC circuit, the current alternately charge the plates, but
when the current change direction the current is non zero at all time during the period.
For an AC sinus wave there will be a phase difference of 90o between the current and
voltage. The amplitude of the voltage depends on the amplitude of the current divided by
the product of the frequency of the current with the capacitance C. The ratio between the
voltage amplitude to the current amplitude is called the reactance of the capacitor. The
capacitive reactance is given by:
I
XC  
1
2fC
(2.8)
where f is the AC frequency in Hertz. The ratio between the phasor voltage and current is
called the impedance (ZC) of the capacitor and is given by:
Z C   jX C
(2.9)
The reactance is inversely proportional to the frequency, see Equation 2.8. At a very high
frequency, the reactance approaches zero and the capacitor is therefore nearly a short
circuit for a very high frequency. And when the frequency is low the reactance goes to
infinity, the capacitor is almost an open circuit. The symbol used for capacitors in circuits
can be seen in Figure 2.6
Figure 2.6. Capacitor symbol.
When capacitor is connected in parallel, see Figure 2.7, the equation for the total
capacitance will be:
CTot  C1  C 2  ....  C n
(2.10)
Figure 2.7. Capacitor connected in parallel.
Capacitors connected in series see Figure 2.8, have the total capacitance
1
1
1
1


 .... 
CTot C1 C2
Cn
(2.11)
Figure 2.8. Capacitor connected in series.
2.1.2.2 Supercapacitor
The supercapacitor is an electrochemical capacitor with a very high energy storage
capability. One of the most common models is the carbon double layer capacitor. This
capacitor is buildup of small particles of activated carbon in contact with diluted sulfuric
acid. Carbon in contact with the acid gives the electric double layer where carbon is the
positive pole and acid connected with metal is the negative pole.
2.1.2.3 Ceramic capacitor
These capacitors are constructed with material such as titanium acid barium for dielectric.
Internally, these capacitors are not constructed as a coil, so they are well suited for high
frequency applications. These capacitors are often used in filters to bypass high
frequency signals to ground.
2.1.2.4 Inductor
An inductor consist of a coil, usually copper wired around a core, the core consists of air
or ferromagnetic material. When the core in an inductor has a higher permeability then
air, it confines the magnetic field closely to the inductor and thereby increasing the
inductance. The inductance L can be written as:
L
0 r N 2 A
(2.12)
l
where
 0 = permeability of free space
 r = relative permeability of the core
N = number of turns
A = Area of the cross-section of the coil
l = length of the coil
The energy that the magnetic field can store is
E stored 
1 2
LI
2
(2.13)
Where I is the current running through the inductor.
The inductive reactance X L is given by
X L  2fL 
VL
I
(2.14)
Where f is the current frequency
the impedance can be written as
Z L  jX L
(2.15)
In contrast to a capacitor that opposes changes in voltage, an inductor opposes changes in
current. If a current from a diode bridge flows through the coil connected in series, a
magnetic field start to build up around the inductor. This magnetic field gives the emf
that opposes changes in the current. Because of the ripples in the DC, the current goes up
and down with a fixed frequency. When the current goes down the magnetic field starts
to break down, the windings cuts and a current is induced in the coil. And when the
current goes up the magnetic field is starting to build up again. This procedure will help
to keep the current constant. The symbol used to denote an inductor and an inductor with
an iron core is seen in Figure 2.9.
a)
b)
Figure 2.9. a) Inductor b) Inductor with iron core
The total equivalent inductance for a parallel configuration Figure 2.10 is
1
1
1
1


 .... 
LTot L1 L2
Ln
(2.16)
Figure 2.10. Inductors connected in parallel.
The total inductance for inductors in series Figure 2.11 is:
LTot  L1  L2  ....  Ln
(2.17)
Figure 2.11. Inductors coupled in series.
2.1.2.5 Harmonics
Harmonic current and voltage in a power distribution system are commonly produced by
non linear loads. Typical devices that can create or increase harmonic disturbance on a
system are rectifiers, DC motor drives, AC motor drives [5]. Harmonics are defined as: a
sinusoidal component of a periodic wave having a frequency that is an integral multiple
of the fundamental frequency [5]. For example, the 7th harmonic on a system with a 50Hz
fundamental frequency waveform would have a frequency 7 times 50Hz that will say
350Hz. The collective sum of the fundamental and each harmonics is called Fourier
series. This series can be viewed as a spectrum analysis. Figure 2.12 shows the harmonic
content in a theoretical rectangular current of a six pulse rectifier.
Figure 2.12. Harmonic current vs. order of harmonic component of a six pulse diode
rectifier [9].
In Figure 2.13, an example of how the harmonic components are added to the
fundamental current is shown. In this figure only the 5th harmonic is shown with the
fundamental current.
Figure 2.13. The total current as the sum of the fundamental and 5thharmonic [9].
When higher order harmonic currents are added to the fundamental current waveform, as
in Figure 2.13 the waveform will look more square shaped, but less harmonics currents
will give a more sinusoidal looking waveform. A balanced three phase rectifier type load
will not create any harmonics with 3 as a multiple. The harmonic component for a typical
six pulse rectifier can be calculated from Equation 2.18.
Harmonicco mponents  6k  1
where k=1, 2, 3,…
(2.18)
The harmonic components magnitude will decrease to a very low level when it reaches
the 11th harmonic or higher. The 5th and 7th harmonic is the most important harmonics to
reduce to a minimum because of there high magnitude. One way to reduce these
harmonics is to use an inductor or a low pass filter. The inductor will not let the current
change too fast. The addition of an inductor can reduce typical distortion levels from
more than 80% to less than 20% THD depending on source impedance [10]. Here THD
stands for total harmonic distortion and it defines the harmonic distortion in terms of the
fundamental current drawn by the load:
h 
THD % 
 (M
h2
h
)2
M fundamental
*100%
(2.19)
where Mh is the magnitude of either the voltage or current harmonic component and
Mfundamental is the magnitude of either the fundamental voltage or current.
2.1.2.6 Filter
The passive filter consists of passive components like capacitors, resistors and inductors
arranged in different ways depending on what is going to be filtered. A filter capacitor
will smooth the output voltage from the rectifier because the capacitor opposes any
changes in the voltage. The capacitor charges through the low internal resistance of the
conducting rectifier. Because of the higher resistance in the load the RC time constant is
long, and this in turn makes the discharge time of the capacitor much slower then the
charge time. As a result of this the output voltage will be relatively constant [8]. This can
be seen in Figure 2.14 as shown in the figure the charging time at the peak is much faster
then the discharge time between the peaks.
Figure 2.14. The charge and discharge of a capacitor. The dot line describes the rippled
DC after the rectifier and the solid line is the charging and discharging of the capacitor.
The filter inductor or filter choke smoothes the output current because the inductance
opposes any variations in the current. The inductor is connected in series so that the DC
output current must flow trough it.
There are many types of passive filters, the four basic circuit types is listed below [38].
 Simple capacitor filter
 LC shock-input filter
 LC capacitor-input filter (  -type)
 RC capacitor-input filter (  -type)
In Figure 2.15, an LC capacitor-input filter is shown, this filter is called  -type.
Figure 2.15. LC capacitor-input filters [8].
The LC capacitor-input filter has as the name describes a capacitor at the output of the
rectifier in parallel with the load resistance RL. The value of the input-capacitor is usually
quite large, and has a relatively low reactance X C to the pulsating current. A capacitor
offers low impedance to AC. Because of this most of the AC will flow through the
capacitor and leave a relatively small amount of AC over the load. One can say that the
AC components are shunted around the load resistance leaves the entire DC component
flow through the load. The inductor L1 in Figure 2.15 is in series with the load resistance
and has an iron core (as indicated in Figure 2.15 with two lines) with a high inductance.
Because of the high value of the inductance and Equation 2.14, the inductor also has a
high value of the reactance X L . Since the action of the inductor is to oppose any changes
in the current flow, it tends to keep the current constant over the load. And with a high
value on the reactance the inductor tends to stop the AC components and let through the
DC components. C2 in Figure 2.15 together with L1 forms a voltage divider (low pass
filter) for the AC components of the applied output voltage. Because of the high value of
reactance for L1 and the low reactance for C2 most of the ripple voltage is dropped
across L1 leaves only a slight trace of the ripples over C2 and the load [38]. To get a
balanced filter circuit, it is necessary to put inductance on the negative branch as well, see
Figure 2.16.
C2
C1
LOAD
L1
L1
Figure 2.16. Balanced pi filter.
The cut off frequency f0 of the low pass filter should be much less then the first harmonic
where the cut off frequency is:
f0 
1
2 L1C2
(2.20)
To calculate a value for the inductor in the filter Equation 2.14 can be used [41]:
L
Vl
2f I
(2.21)
where f is the ripple frequency:
The ripple frequency for a six pulse rectifier is:
f  6 f fundamental
(2.22)
The capacitance can be calculated using Equation 2.9 and assuming all the energy is
taken from the capacitor:
E 
P
1
1
2
2
CVmax
 CVmin
2
2
(2.23)
E
t
(2.24)
where t can be described with the frequency of the rippled voltage as:
f ripple 
1
t
(2.25)
Using Equation 2.23 and 2.24 gives the capacitance:
C
2 Pt
2
V  Vmin
(2.26)
2
max
2
2
P is the load power in watts, Vmax
is the peak rippled voltage and Vmin
is determent by the
maximum acceptable rippled voltage [39].
The current frequency characteristic for a low frequency filter can be seen in Figure 2.17.
Current
Frequency
Figure 2.17. Current-frequency characteristics for a low frequency filter.
The LC-filter filter provides a good filtering action over a wide rang of currents. This is
because of the complimentary nature of the two components. Capacitor filters best when
the load is drawing little current, this because the capacitor discharge very slow and
almost keep the DC over the load constant. Inductor filtering action is best when the
current is highest [38].
2.1.3 The DC to AC inverter
This part of the main circuit will transform the DC after the rectifier and the filter to a
three phase AC. To invert the DC to AC a six pulse IGBT inverter will be used.
2.1.3.1 Insulated Gate Bipolar Transistor (IGBT)
The IGBT is a switching device and design to have a high speed switching performance
and gate voltage control of a power MOSFET as well as the high voltage and large
current handling capacity of a bipolar transistor. The IGBT consists of a gate, collector
and an emitter as seen in Figure 2.18. When a positive voltage is applied to the gate
typically 15Vdc the IGBT will turn on, and a current will flow between the collector and
the emitter. To turn off the IGBT the positive voltage at the gate is removed. During the
time when the IGBT is turned off a small negative voltage normally -15Vdc is held over
the gate to prevent the device to turn on.
Figure 2.18 IGBT circuit.
An IGBT is capable to switch from the on state to the off state several thousand times per
second. The time it takes for the IGBT to turn on is below 400 nanoseconds and the time
it takes for it to turn off is approximately 500 nanoseconds. These fast switching times
are necessary for the PWM to work properly [40]. The switching waveform of an IGBT
is presented in Figure 2.19.
Figure 2.19. IGBT switching waveform.
2.1.3.2 Six pulse IGBT inverter
The inverter consists of six switching devices, two at each leg. Various devices can be
used, such as thyristors, bipolar-transistor, MOSFET and IGBT. In this section the IGBT
will be explained. Figure 2.20 shows the circuit of a six pulse IGBT inverter.
+
3-Phase
Vdc
Figure 2.20. IGBT-bridge
The switches (transistors) are controlled by pulse width modulation (PWM). This
modulation will be explained in more detail later in this chapter. But in short, this means
that the switches open and closes irregular so that a half period of the output voltage
consists of a number of pulses with varying width. Independent of the output voltage
frequency the amplitude of the pulses is constant; the size of the voltage will be varied
with varying pulse width. The anti parallel diode in Figure 2.20 connected to each IGBT
allows current flow in the opposite direction when the switch is open. These freewheeling
diodes prevent inductive current interruption and this provides protection against
transient over voltage, which may cause reverse breakdown of the IGBT switches.
The advantage when using IGBT is the fact that they can switch with very high
frequency up to some 100 kHz. This gives advantage when it comes to the shape of the
outgoing AC, when the switching frequency get higher the AC output shape gets more
and more sinus-like. The disadvantage when turning up the switching frequency is that
IGBT open and closes faster and this adds up in switching losses which gives lower
efficiency of the IGBT Bridge. The AC output from the IGBT Bridge can be regulated
with the PWM as seen in Figure 2.21.
Vdc
Vdc
Figure 2.21. Control of the output AC.
By varying the on and off time on the IGBT, the magnitude of the output AC can be
controlled. This control of the magnitude is done by the linear modulation index ma and it
will be discussed in further later in this chapter. The peak value of the fundamentalfrequency voltage in one of the inverter legs can be calculated as [10]:
(VˆAN )1  ma
Vdc
2
(2.27)
The line to line rms voltage at the fundamental frequency, due to 1200 phase
displacement between phase voltages can be written as:
VLL1 
3 ˆ
(V AN )1
2
(2.28)
and with Equation 2.27 and 2.28 we get:
VLL1 
3
maVdc
2 2
(2.29)
Equation (2.27), (2.28) and (2.29) can be used when modulation index ma  1
The power losses in the bridge are determined by the IGBT and the anti parallel diode.
The losses in the semiconductors can be divided into two groups:


Conduction losses
Switching losses
Conduction losses depend upon the on-stage voltage drop across the IGBT or the forward
voltage drop across the diode. These two are ideally independent of switching frequency
and switching voltage and both increase with conducted current.
Switching losses increase with increasing current, voltage frequency and switching
frequency. In the IGBT the switching losses mainly occur during turn on and turn off
transient. In the diode the major component of switching losses are due to its reverse
recovery. The total power losses for an IGBT can be calculated:
PIGBTTotal  PConductionlosses  PSwitchinglosses
(2.30)
and for the diode, the power losses can be calculated as:
PDiodeTotal  PConductionlosses  PSwitchinglosses
(2.31)
When designing an IGBT bridge the cooling of the semiconductors has to be considered,
this factor has a big influence of the power losses in the bridge. Usually, the
semiconductors are mounted on a heat sink for cooling.
2.1.3.3 Snubber circuits
One way to reduce power losses is to use snubber circuits. These are usually used to
protect power electronic components, but will also help to reduce switching losses. When
used with IGBT they help to reduce current and voltage peaks and also current and
voltage derivative. Snubber circuits can be classified into two groups; individual and
lump circuit [42]. The individual circuit is connected over each IGBT, while the lump
circuit is connected over the DC bus and the ground. One of the simplest lump circuits
can be seen in Figure 2.22a, this is just a capacitor put over one arm of the IGBT Bridge.
+
+
C
C
-
-
a)
b)
Figure 2.22. a) C-snubber circuit
b) A RCD-snubber
The C-snubber circuit in Figure 2.22a will suppress over current and this in a quite sheep
and simple way with only a capacitor. The C snubber is only effective in low or middle
current handling and low power applications. Another lump circuit is the RCD-snubber
circuit (see figure 2.22b) this circuit is used for medium current applications. It contains a
diode, resistor and a capacitor. Turn off voltage transient in a RCD-snubber is reduced
directly; the switching waveform of the IGBT see Figure 2.19 will be much smoother.
The losses in the RCD-snubber are low. The turn on transients is good, and because the
snubber diode blocks oscillations we get a stable wave. [43] The two snubber circuits
mentioned here are just two of many types of snubber circuits that can be used, but the
main goal for these circuits is to [10]:





Limiting voltage applied to devices during turn-off transients
Limiting devices current during turn-on transients
Limiting the rate of rise (di/dt) of currents trough devices at device turn-on
Limiting the rate of rise (dv/dt) of voltage across devices during device turn-off
or during reapplied forward blocking voltage
Shaping of the switching trajectory of the device as it turns on and off
2.1.4 Transformer
This step in the main circuit is to transform the three phase AC from the IGBT bridge to a
desired value of current and voltage. The current and voltage will then feed the grid.
2.1.4.1 Basic transformer
The transformers are an important links in electric power transport. There are some
different types of transformer like step up; step down and some of them will be
mentioned in this section. The basic is the same for all transformers and the relations can
be used for one phase as well as for three phases. The transformer consists in principle of
two windings wound around an iron core, one primary and one secondary. When a
current flows in the primary winding a magnetic field is created in the iron core. This
result in a flux from the core, the flux induces then a voltage in all the windings wounded
on or linked to the core see Figure 2.23.
Figure 2.23. a) Working principle for an ideal transformer.
b) Equivalent circuit for an ideal transformer.
For an ideal transformer, the resistance in the primary and secondary windings are equal
to zero and the leakage flux from the windings are equal to zero. Assume a sinusoidal
time variation of flux:
   m sin( t )
(2.32)
The induced voltage will then be:
d
 N 1     m  cost 
dt
d
e2  N 2
 N 2     m  cost 
dt
e1  N1
(2.33)
(2.34)
The ratio of the induced voltage is
e1 E1 N1


a
e2 E 2 N 2
(2.35)
where a is called winding ratio.
For an ideal transformer is
V1  E1 and V2  E2
(2.36)
V1 N1

V2 N 2
(2.37)
There are no power losses:
P1  P2  V1 I1  V2 I 2
(2.38)
Equation 2.37 and 2.38 gives:
I1 N1  I 2 N 2
(2.39)
There exists no ideal transformers because it will always occur a core exiting current, Ie,
caused by the induced voltage in the transformer.
Figure2.24. A real transformer.
Figure 2.25. Equivalent circuit for a real transformer.
For the magnetic field in a complex notation:
Bme  Bm1  Bm 2
(2.40)
Bme is the magnetic field that generates the flux Ф. Equation (2.37) can also be written as:
N1 I e  N1 I 1  N 2 I 2
(2.41)
the core exiting current is thus
I e  I1  I 2
N2
N1
(2.42)
The efficiency of a transformer is:

P2
P1
(2.43)
2.1.4.2 Different types of transformers
If the inductance on the primary or secondary side is changed, the voltage and current
will change. This can either be a step-up or a step-down transformer. The step-up
transformer will raise the voltage and lower the current on the secondary side, this is done
by reducing the windings on the primary side, see Equation 2.12. If the winding N is
reduced the inductance L will be reduced. If Equation 2.34 and 2.36 for an ideal
transformer is used one can see that when reducing the windings on the primary side the
voltage on the secondary side will raise and the current will get lower. The step-down
transformer is the step-up transformer reversed as seen in Figure 2.26.
AC
Many turns
high voltage
low current
Few turns
low voltage
high current
Step-down
AC
Load
Few turns
low voltage
high current
Many turns
high voltage
low current
Load
Step-up
Figure 2.26. A step-down and a step-up transformer.
Aside from the ability to step-up and down voltage and current, the transformer also
provides isolation which is: “the ability to couple one circuit to another without the use of
direct wire connections” [8]. When the function of the transformer is just to provide
isolation they are usually called isolation transformer.
2.1.4.3 Power losses in transformer
A modern transformer usually has efficiency over 95% [8]. But, when designing power
supply it is good to know where these 5% losses in the transformer come from and what
cause it. The resistance in the wire, that are wired around the core will lead to power
losses, because of the heat that will be produced in the wire when current runs through it.
One solution to this is to increase the width of the winding wires, but when doing so there
will be an increase in cost, size and weight of the transformer. The bigger part of the
power losses depend upon magnetic effects in the core, where one of the most significant
core losses are the exiting current, I e from Equation 2.42. Iron is a fairly good conductor
of electricity as well as magnetic flux, a current can be induced in the iron just as the
current is induced in the secondary windings from the alternating magnetic field. The
current induced in the iron core tends to circulate through the cross-section of the core
perpendicularly to the primary winding turns. One way to minimizing I e is to divide the
core in thin slices, where each slice is covered with varnish. A second core loss comes
from magnetic hysteresis. All ferromagnetic materials tend to retain some degree of
magnetization after exposure to an external magnetic field; this tendency to stay
magnetized is called hysteresis [8]. Hysteresis causes saturation in the core. The
saturation phenomenon can be seen as a limitation occurring when a ferromagnetic
material is used in the core. When the current increases, the flux increases in proportion
to it. At some point further increases in current do not lead to a proportional increase in
flux, see Figure 2.27.
Figure 2.27. The magnetisation curve shows the saturation characteristic for the core
materials [5].
2.1.5 DC to DC converter
A DC to DC converter is a device that accepts a DC input and produces a desired DC
output. The DC to DC converter may work as a voltage regulator at the input to the IGBT
inverter, instead of a variable transformer to regulate the voltage after the inverter.
There are two basic types of DC to DC converters, the step-down (buck) converter and
the step-up (boost) converter. These two types are described in this part; other converters
are often combinations of these two and will be mentioned briefly.
The average value of the output voltage from the DC to DC converter needs to be
controlled, even when the input DC or output load is varying. This control is done by
controlling the on and off durations of the switch, this is often done with PWM
switching. PWM has been mentioned earlier in this chapter, but in contrast to the DC to
AC inverter, the pulse width will here be constant to form a DC. This means that the
switching time period Ts=ton + toff is constant, to control the average output voltage from
the DC to DC the on duration is adjusted see Figure 2.28.
v0
Vd
V0
t
t off
ton
Ts
Figure 2.28. Voltage regulation pulses of a DC to DC inverter.
2.1.5.1 Step-down (buck) converter
This converter step-down the average input voltage to a lower output voltage. It consists
of a switch, a diode and a low pass filter. The diode is used to overcome the problem of
stored inductive current and the low pass filter will eliminate the switching frequency
ripple in the output voltage. The switch in the converter will control the DC output
voltage V0:
T
t
1 s
V0   v0 (t )dt  onVd  DVd
Ts 0
Ts
(2.44)
D is called the duty cycle. Equation 2.44 is assumes an ideal switch, a constant
instantaneous input voltage and a purely resistive load [10].
+
Vd
L
C
-
+
Vo
-
R(Load)
Figure 2.29. Step-down (buck) converter with filter.
When the switch is on, the diode will become reversed bias and energy will be provided
over the load and the inductor. When the switch is in the off state, the current from the
inductor will flow through the diode; and providing energy to the load.
2.1.5.2 Step-up (boost) converter
The step-up converter step-up the average input voltage to a higher output voltage. This
converter consists of an inductor at the input to the switch, a diode and a capacitor filter.
When the switch is on, the output stage is isolated because the diode is reversed biased.
Under this condition the supply will energize the inductor. During off state, the inductor
and the input will provide the output stage with energy.
L
+
+
Vd
C
Vo
R
-
Figure 2.30. Step-up (boost) converter
Under steady state condition the DC output voltage is:
V0 
Ts
1
Vd 
Vd
Toff
1 D
(2.45)
2.1.5.3 Other types of DC to DC converters
The buck-boost converter is used when the output voltage needs to be regulated both to a
higher and a lower value of the input voltage. It is a combination of the step-up and stepdown converters, the output voltage can be described as:
V0  D
1
Vd
1 D
(2.46)
+
Vd
L
-
C
Vo
+
Figure 2.31. Buck-boost converter
R
The CÚK-converter is similar to the buck-boost converter in that it can be used to step-up
and step-down the voltage.
C1
+
Vd
-
L1
L2
C2
R Vo
+
Figure 2.32 CÚK converter
In this converter, the capacitor C1 store and transfer the energy from the input to the
output.