2.2 Sub circuit
In this section, the theory of the sub circuit is presented. The first parts describe the role
of protection, faults, fault calculations and theory about parts that can be used in a safety
circuit.
In the second part, some different ways in measuring currents and voltages are described.
In the last section, the theory behind pulse width modulation is introduced.
2.2.1 Role of protection and Faults
A power system fault can be defined as:
”any condition or abnormality of the system which involves the electrical failure of
primary equipment, the reference to primary (as opposed to ancillary) equipment
implying equipment such as generators, transformers, busbars, overhead lines and cables
and all other items of plants which operate at power system voltage” [12].
There is a risk for a power system with a connected fault, that one or more of the three
following effects will occur:



The individual generators, or a group of generators, lose synchronism. This leads
to a splitting of the system.
Large risk of damage to affected plant.
Risk of damage to healthy plant.
Much of the electronic components in a substation are sensitive to high voltage and
currents. Because of the mentioned effects, a protection system that can remove a part on
which a fault has occurred is necessary.
The faults in a power system can be divided into four different groups [12]:




Short-circuited phases
Open-circuited phases
Simultaneous faults
Winding faults
Short-circuited phases are caused by insulation failure. The failure can either be between
phase conductors or between a phase conductor and earth (or both) see Figure 2.33.
Three-phase clear of earth
Three-phase-to-earth
Phase-to-phase
Single-phase-to-earth
Two-phase-to-earth
Phase-to-phase and single-phase-to-earth
Figure 2.33. Different types of short-circuit faults.
A three-phase fault of earth or clear of earth is the only balanced fault (symmetrical
short-circuit condition). A three-phase short-circuit is often used as a standard fault
condition. For example, to decide a systems fault-level, a quote of the three-phase shortcircuit value is often used [12].
An open-circuited phase occurs when one or more phases have problem to conduct, see
Figure 2.34. This condition cause unbalance for the systems voltage and currents.
Single-phase open-circuit
Two-phase open-circuit
Three-phase open-circuit
Figure 2.34. Open-circuit faults that can occur in a three phase system.
Simultaneous faults are when two or more faults of the same or of different types occur
at the same time.
Winding faults occurs in transformer and machine windings and consist mainly of shortcircuits from one phase winding to earth.
2.2.1.2 Fault calculations
Fault calculations are based on a normal behaviour of a system, when the system is in a
steady state. To calculate the relations between currents, voltages and impedances, three
basic laws are used;



Ohm’s law
First law of Kirchhoff
Second law of Kirchhoff.
When these three laws are not fulfilled, there is something wrong with the circuit.
Ohm’s law states that the vector voltage drop, V, produced by a vector current, I, flowing
through complex impedance, Z, is given by Equation 2.47 and illustrated in Figure 2.35
V  I Z
(2.47)
I
Z
V
Figure 2.35. Illustration of Ohm’s law.
Kirchoff´s first law states that the vector-sum of all currents in a circuit should be zero;

I
 i 0
(2.48)
i
The vector currents that flows into a node are treated as positive inflowing currents and
the vector currents that flow out from a node are treated as negative.
I2
I1
I3
I4
I1 + I2 - I3 - I4 = 0
Figure 2.36. Kirchhoff´s first law.
Kirchhoff´s second law states that in any closed electric circuit the vector sum of all the
driving voltage is equal to the vector sum of the products of impedance and current in
each part of the network;


V   I Z
i
i
i
(2.49)
i
i
V1
Z1
I1
Z4
V2
I2
I4
Z2
V4
I3
Z3
V3
V1 + V2 + V3 + V4 = I1 Z1 + I2 Z2 + I3 Z3 + I4 Z4
Figure 2.37. Kirchhoff’s second law.
In a three-phase system, each phase has the same self-impedance and the voltage is
divided equally between the phases. The three-phase currents and the three-phase neutral
voltage will be equal in magnitude at a given point in the system and displaced 1200 from
each other in time-phase. This condition is called for positive-sequence phase-order and
the currents and voltages are often termed positive-sequence currents and voltages (see
Figure 2.38).
Ic
Vc
Va
Ib
0
0
Vb
Ia
Figure 2.38. Phase-diagram for the positive-sequence voltages and currents.
The mathematical relations for the voltages and currents in figure 2.38 are:
Ib  x2Ia 
I c  xI a 


2
Vb  x Va 

Vc  xVa 
(2.50)
The 1200 operator x is given by:
1
3
x  j
 1120 0
2
2
(2.51)
An unbalanced condition in a three-phase system can be represented by the sum of three
sets of balanced (symmetrical) vectors [12]; positive-sequence set, negative-sequence set
and zero-sequence set. The positive-sequence set has already been discussed. The
negative sequence set is similar to the positive-sequence but the phase-order is the
reverse, it rotates in the phase order a, c, b. The zero-sequence set consists of three
vectors that are equal in magnitude and phase.
c
c
a
a
0
0
0
a
b
C
b
b
Positive-sequence
Zero-sequence
Negative-sequence
Figure 2.39. Phase-diagram for the different sequences.
An unbalanced three-phase vector system with the currents, Ia, Ib and Ic, the subscripts a,
b and c denotes the three phases. The positive-, negative- and zero phase-sequence are
denoted by a second subscript 1, 2 and 0, respectively and
I a  I a1  I a 2  I a 0

I b  I b1  I b 2  I b 0
I  I  I  I
c1
c2
c0
 c
(2.52)
Equation 2.52 can with help of the 1200 operator and the reference phase be written as:




1

2
 I 1  3 I a  xIb  x I c

1

2
 I 2  I a  x I b  xI c
3

1

 I 3  3 I a  I b  I c 

(2.53)
With help of Equation 2.47 – 2.53, the voltages and currents can be calculated at a fault
in a three-phase system [12].
2.2.2 Safety circuit
The safety circuit consists of two parts; one protects the main circuit (and generator) from
over currents and the other part protects the main circuit (and generator) from over
voltages.
Relay protection systems are used to protect the circuit from over currents. A relay
protection system consists of a relay or relay-group with accessories. The relay protection
system gives an impulse to switch off a certain construction part (or switch off a signal)
at a fault or an abnormal condition in the construction.
To protect the circuit from over voltages, variable resistors are used.
2.2.2.1 Relays
The concept relay is often used to describe a component that can control a contactfunction with help of a voltage (or current). This type of relay is for example used in
telephone-stations or in cars. In power system, the concept relay has a more extensive
meaning. According to IEEE, the definition of a relay is [11]:
“An electric device that is designed to interpret input conditions in a prescribed manner
and after specified conditions is met to respond to cause contact operation or similar
abrupt change in associated electric control circuits.”
Figure 2.40. Circuit symbol for a relay.
Figure 2.40 shows the circuit symbol for a relay, COM (common contact) is the moving
part of the switch, NO stands for normally open and COM is connected to this when the
relay is on and COM is connected to NC (normally closed) when the relay is off.
There are several types of relays and many of them have the same basic construction with
just a few distinctions. In this assignment, the relays will be divided into two main
groups, comparators and auxiliary relays with subgroups. Comparators, or measuring
relays, should detect and measure abnormal conditions and then send a “signal” to close
contacts (breakers). Auxiliary relays repeat a controlling signal. This second group is also
called “all or nothing” relays or “non measuring relays” [12]. These two groups can in
turn be divided in to sub groups.
If the relay must not be time delayed, the relays for over current protection are
comparators. The most common comparators for over current protection are
electromagnetic relays, moving coil relays and static relays [11].
The electromagnetic relay or attracted-armature relay consists of an iron core with an
armature, a multi turn coil wound around a core and an air gap see Figure 2.41.
Figure 2.41 Mechanical operation of an electromagnetic relay.
When an AC current flow thought the coil contacts, the coil will be energised and the
core becomes temporally magnetised. The magnetised core attracts the armature (see the
metal arm in Figure 2.41) with a force. The armature is then pivoted so it moves in line
with the magnetic field and operates one or more contacts. In Figure 2.41, COM is moved
to the NO contact when the coli are energised and the relay is on. When the coil is deenergised, the armature and contacts are released and the relay is off again.
The electromagnetic relay has a simple construction, a long lifetime and is one of the
most common relay [12].
A moving coil relay consists of a permanent magnet, a coil and a circular iron core. The
moving coil relay utilises a DC as the incoming signal and the AC is therefore often
rectified in a Graetz’s semiconductor bridge that consists of four diodes [11] (the diodes
are discussed in section 2.1). The moving coil relay and the bridge are illustrated in
Figure 2.42.
Permanent
magnet
Ir
Coil
Iron core
COM
Figure 2.42. To the left, the moving coil relay and to the right, the relay and diode
bridge.
When a current, ir, flows through the movable coil, the coil is exposed to a torque, m,
which is proportional to ir and COM is moved to the NO contact.
A static relay consists of a static measure circuit and a fast electromagnetic relay. The
incoming current is often rectified in a Graetz semiconductor bridge before the relay, just
as the moving coil relay. With a static measuring circuit, the relay power consumption
can be neglected [11]. The working principle for the static relay is illustrated in Figure
2.43.
(A)
V
Va
A
Vc
Vb
C
B
D
Vr
V
Open
Va
Vb=0
(B)
V
Va
Vr
Vc=0
Vb
Vc
(C)
Closed
Vz
Figure 2.43.(A) A block scheme for the measure circuit where A is an amplifier, B a
duster (vippa), C an integrating unit and D the electromagnetic relay.
(B) The incoming signal V is too small and Vb=0 because Va<Vr, the relay will not have a
function.
(C) Va>Vb and Vc>Vz the relay functions.
The function value for the relay is decided from the relation between the reinforcement in
the amplifier A and the value of the reference quantities Vr and Vz. Tow conditions must
be fulfilled before the relay will function and these are (see Figure 2.43 (B) and (C) for an
example):
Va  Vr and Vc  V z
(2.54)
2.2.2.2 Electric-connector, circuit breaker
The instruments that let through or stop currents are called electric-connectors. The
breakers used in a high voltage power system should break and close normal load
currents and should be able to break any short-circuit who can occur at a fault. Power
breakers and disconnectors are often used in high voltage power systems. They can
break, close and under a certain time lead the short circuit current.
In low voltage power systems, breakers with a break-capacity that can handle couplings
at normal load-currents are used. The most common types are switch-disconnectors and
contactors. Fuses are often used as a complement to break short-circuits in low voltage
systems [17].
Figure 2.44. Circuit symbol for a circuit breaker.
A switch-disconnector can break the load current but not short-circuit currents. The
switch-disconnector is manoeuvrable by hand and they can therefore not be used in this
substation.
A contactor makes it possible to have one circuit to switch a second circuit. A low
voltage battery circuit can for example switch a high voltage circuit. The circuits have no
electrical connection to each other; they are connected mechanical and magnetic. A
contactor is similar to an electromagnetic relay, both uses a magnetic coli to close a
contact, but the contactor is designed to break a high current load.
Figure 2.45. Different parts in a contactor.
1: Part fixes magnetic circuit.
2: Moving part of the magnetic circuit.
3: Winding.
4: Screw of connection of the reel, part orders.
5: Mechanical connection.
6: Insulating part.
7: Mobile contacts 1 for this example.
Contactors have a long lifetime because the movable contact operates with a coil and not
with a spring, this leads to a small piece of movable details and this leads to a less
damage on the contactor. In electrical circuits, fuses are often used as a complement to
the contactors because they have a shorter switching time.
Fuses are the most common devices to use for turning off an incorrect construction part
[17]. The fuse can carry load currents and will break the circuit when the current become
higher than a settled value.
Melt-fuses are often used in low voltage systems. The main part of a melt fuse is the fuse
element. Usually, the element is made of silver or silver covered with cupper. The
element is enclosed in a porcelain cartridge filled with sand. When the current rice over a
certain value (called fuse voltage rating) the element melts and the current will break.
The sand makes it easier to put out the light bow that occurs in the break moment and
helps to lead away the generated heat [17]. The problem with this type of fuse is when
they once has cleared a current it has to be replaced.
Another type of fuse used in low voltage system is the automatic fuse. This fuse can
sometimes be called a self-resetting fuse.
Figure 2.46. An automatic fuse.
This type of fuse observes the current in two different ways. The fuse turns off the circuit
after a certain time depending on the current, at moderate over currents, this is done by a
terminal protection and the circuit will be restored when it is cold. At higher over
currents, an electromagnetically controlled breaker in the fuse instantaneously offconnect the circuit.
2.2.2.3 Instrument transformer
An instrument transformer is an electrical device that transfers energy from one circuit to
another. Instrument transformers are often used in substations to measure currents and
voltages or to operate a safety circuit, relay. A measure transformer and a transformer for
protection are constructed similar to each other, but they have different requirements. A
measure transformer should have a good accuracy in the given measure interval and a
low secondary current is preferable at over currents to protect the measure instrument. A
transformer for protection does not have the same demand in measure-accuracy but the
transformer should have a reasonable measure-accuracy at high over currents.
The different types of instrument transformers are often termed CT for current
transformers, VT for voltage transformers. The CT is the same as a short circuit
transformer, the voltage is almost zero, and can be described with Equation 2.55. The VT
is described with Equation 2.56 and can be seen as an idling transformer:
IP NP  IS NS
VP N P

VS N S
(2.55)
(2.56)
A CT produces an alternating current or an alternating voltage that is proportional to the
primary current. The CT:s can be divided into two basic types, wound and toroidal. A
wound CT consists of primary windings in series with the conductor. The toroidal CT
does not have a primary winding. Usually, these CT:s have a circular core with the
secondary windings around the core (current out) and the primary winding will be the
“sensed conductor”, see Figure 2.47.
Figure 2.47. A toroidal CT.
Wound CTs are often used when the primary current is low, the primary winding must
then be strengthening whit more wounding around the core to produce a better secondary
current [23], see Equation 2.55.
ZH
1:n
ZL
Rm
Burden
(ZB)
Xm
a)
Ip
1:n
Ip /n
RL
Ie
IL
Xm
Burden
(ZB)
b)
Figure 2.48. a) Equivalent circuit for a CT.
b) Reduced equivalent circuit for a CT.
Figure 2.48 a) illustrates an approximate equivalent circuit for a current transformer. ZH
is the primary leakage impedance and ZL is the secondary impedance. Rm and Xm are the
exiting components and represent the core loss. This circuit can be reduced to the circuit
in Figure 2.48 b). The primary impedance is neglected since it does not influence the
transformed current Ip/n or the voltage over Xm. The Rm branch has a negligible influence
on the circuit and can be neglected. The current through the other branch Xm, the
magnetizing branch, is the exiting current Ie.
The biggest problem with a current transformer is when the core saturates. The
performance of a CT is its ability to reproduce the primary current in the secondary
winding. A CTs performance can be determined in three different ways (with the
assumption that the primary current is symmetrical i.e. it does not include a DC
component) [27]:



By formula
By the current transformer excitation curves
By transformer relaying accuracy classes
For all these three methods, the generated secondary voltage, VS, must be known;
VS  I S Z L  Z lead  Z B 
(2.57)
where
VS = rms secondary induced voltage
IS = maximum secondary current
ZB = connected impedance
ZL = secondary winding impedance
Zlead = connecting lead impedance
In the formula method, the maximal flux before saturation is calculated.
Bmax 
VS
4.44  N S  A  f
(2.58)
where
f = frequency.
VS = secondary e.m.f in volts
NS = the number of turns in the secondary winding
A = the net core section in sqare meters
If Bmax is larger than the CTs given saturation level, the secondary current has errors.
In the excitation curve method, the primary current is plotted versus the secondary
current. This curve is done in five steps. First, assume the secondary current, IL, the
secondary voltage, VS, is then (second) calculated from Equation 2.57. Third, find the
exiting current, Ie. For a given secondary voltage, VS, Ie approximately can be estimated
from the excitation curve for the CT, Figure 2.49.
Figure 2.49. Excitation curves for a CT [29].
The excitation curve has a linear region and a non linear region. In the linear legion, the
exciting current increases with an increasing secondary voltage. Exciting current will not
exceed the curve value by more than 25%. In the non linear region, the exciting current
increases more with an increasing secondary voltage. The exciting current will not be less
than 95% of the curve value.
When Ie is known, the primary current can be calculated;
I P  I S  I e 
NS
NP
(2.59)
The last step is to repeat the four first steps and plot the values of the primary current
versus the values of the secondary current. For any given value of the primary current,
the secondary can be estimated with help of the plotted curve, an example of a curve is
shown in Figure 2.50.
IS
IP
Figure 2.50. Example of a curve plotted with help of the excitation curve method.
This method incurs an error when IP is calculated by adding Ie and IS together
arithmetically, in a correct way, they should be seen as vectors and be added as vectors.
Transformer relaying accuracy classes are according to IEC standards described in
terms of protection and measurement classes in Europe [27]. The protection limit
classes have the designation P and the standards factors are 5, 10, 15, 20 and 30. A CT
label 5P has a maximum error of 5% at the maximum rated current. The maximum
current is specified in terms of an accuracy limit current [30]. The accuracy limit factor is
a ratio of the accuracy limit current and the rated current. A current transformer for
protection is specified in terms of the burden VA at rated current. If the VA burden is
known, the coil impedance, or the impedance of burden, can be calculated;
Zb 
VA(burden )
I S2
(2.60)
where
IS = rated secondary current
The total relay impedance can now be calculated and a new calculated value of the
burden can be compared with the label burden of a CT.
These three methods requires that the CT is in a steady state and do not take into account
the DC transient component of the fault current. There are two factors that produce a DC
component [27]:
1) The current in an inductance cannot change instantaneously.
2) The steady state current before and after a change must lag (or lead) the voltage by
the proper power factor angle.
Equation 2.61 gives a condition for the saturation of a CT [27].
Vk  6.28I  R  T
where
(2.61)
Vk = voltage at the knee of the saturation curve
I = symmetrical secondary current
R = total secondary resistance
T = DC time constant of the primary circuit
T can be calculated from
T
LP
f
RP
(2.62)
LP = primary circuit inductance
RP = primary circuit resistance
f = frequency
If Equation 2.61 is fulfilled, the DC component of a fault will not produce saturation in
the CT.
2.2.2.4 Variable resistor
A variable resistor can in short be called a varistor [20]. Varistors are voltage dependent
resistors with a symmetrical V/I characteristic curve whose resistance decreases whit
increasing voltage.
Figure 2.51. a) Varistor symbol.
b) The V/I ideal characteristic curve of a varistor.
The resistance in a varistor can be changed in two different ways. In the first way, the
resistance in the varistor can be adjusted by hand, like the volume adjustment of a CDplayer. The second way is to use a non linear two-electrode semiconductor voltagedependent resistor. These types of varistors are used to fine-tune a circuit and to
compensate for the inaccuracies of the resistor. To stop a surge voltage in a circuit, the
varistor absorb pulse energy in the bulk of the material so only a relatively small increase
in voltage appears and thereby protecting the circuit.
Every real voltage source has, and therefore also every surge voltage, a voltageindependent impendence, Zsource, greater than zero. Zsource can for example be the
resistance in a cable or the inductive reactance of a coil. When a surge voltage occurs, a
current, i, will flow across Zsource and Ohm’s law states that the relation between the
voltage and current is
v source  Z source  i
(2.63)
where vsource is the voltage over Zsource.
Zsource
V
ZVAR
VVAR
Figure 2.52. An equivalent scheme with the voltage-independent source impedance,
Zsource, and a voltage-dependent varistor, ZVAR. V is the voltage source and VVAR is the
voltage after the varistor.
The varistor, ZVAR, in Figure 2.52 will cause a proportional voltage drop across Zsource and
voltage division gives:


ZVAR
v
vVAR  
Z

Z
source 
 VAR
(2.64)
The voltage drop that ZVAR causes is almost independent of the current and this result in a
voltage drop over Zsource, the circuit parallel to ZVAR will be protected.
Curve a
Curve b
Figure 2.53. The principle of over voltage protection by varistors. On top, an equivalent
scheme with a fault is illustrated and at the bottom, the protection by the varistor is
illustrated in two curves [22].
The operating voltage, VB, and the surge voltage VS are illustrated in Figure 2.53, Curve
a. The surge voltage amplitude 1 will be reduced to 2 by the varistor. The
intersection of “the load line” with the V/I characteristic curve in Curve b gives the surge
current amplitude and the protection level, i.e. the protection level can be decided from
the characteristic curve of the varistor.
2.2.3 Measure part
The currents and the voltages in the circuit should be measured with good accuracy in the
measuring part. Currents and voltages can be measured by using instrument transformers,
but the easiest way is to use resistors.
2.2.3.1 Current measuring
At current measuring, a device with a low resistance should be coupled in series with the
circuit, so all current flows thorough it. A current measuring device should have a small
inner resistance because this result in a small affect on the system. An ideal instrument
therefore has the inner resistance equal to zero.
One way to measure the current is to use a shunt. A shunt is defined as [25]:
“a device which allows electrical current to pass around another point in the circuit”.
Shunts have high temperature accuracy and have a certain mark current, the highest
current the shunt can measure.
Figure 2.54. A shunt.
Shunts have an accurately known resistance and by measuring a voltage drop over the
shunt, a current can be calculated according to Ohm’s law. Current measuring with a
shunt results in a small signal level requiring amplification. One other disadvantage with
the shunt is that the cable must be split up. The advantages with a shunt is the prize (it is
cheaper than other measure devises) do not need any isolation or any extern voltage
source.
One other way to measure current is to use a LEM Hall Effect current sensor.
The Hall Effect can be defined as [32]:
“If an electric current flows through a conductor in a magnetic field, the magnetic field
exerts a transverse force on the moving charge carriers which tends to push them to one
side of the conductor. This is most evident in a thin flat conductor. A build up of charge
at the sides of the conductors will balance this magnetic influence, producing a
measurable voltage between the two sides of the conductor. The presence of this
measurable transverse voltage is called the Hall Effect after E. H. Hall who discovered it
in 1879.”
The disadvantages with a LEM current sensor is the prize, they are relative expensive, it
is a more complex device than a shunt. The LEM current sensor also needs an extern
voltage source and the accuracy is not quite as good as in the current shunt. With a LEM
current sensor, the cable must not be split up and the signal does not need any
amplification.
2.2.3.2 Voltage measuring
The main principle in voltage measuring is to have an instrument that measures a
potential difference between two measuring points. In a low voltage system, the voltage
can be measured directly without any transformations before measuring [24]. A voltmeter
is often used to measure the voltage directly. The voltmeter is always coupled in parallel
with the circuit. The inner resistance, RV, should in contrast to the shunt be as large as
possible; an ideal voltmeter has an infinite resistance.
Rv
V
V
Figure 2.55. In-coupling of a voltmeter.
2.2.4 Control circuit
To get a desired out-put signal from a DC to AC-inverter, each transistor in the inverter is
fed with a gate signal. The signal can be seen as a sample of pulses with the value 1 or 0,
the transistor is totally conducting at 1 and it is not conducting at 0. These pulses
resemble a pattern and can be created with help of PWM (Pulse Width Modulation).
Angle (degrees)
Figure 2.56. Pulses from the PWM to the different gates.
Figure 2.56 shows an example of the pulses to the gates in a three phase inverter. There is
a phase difference 600 between the pulses and the transistors on the same “phase-line”
will have a phase different at 1800 because the line will be short-circuited if both of the
transistors are leading at the same time.
2.2.4.1 PWM-Pulse Width Modulation
There are several different PWM techniques used to modulate the inverter switches to
form the output AC to be as close to a sinusoidal shaped wave as possible. In this section,
the sinusoidal PWM is discussed in detail and some other PWM techniques are presented
briefly.
To create a pulse pattern in sinusoidal PWM, a triangle shaped wave, Vtri, is compared
with a control signal, Vcont (a sinusoidal wave), see Figure 2.57. Vcont should have the
same frequency, fm, as the desired frequency of the wave out from the IGBT, fout [10].
Vcont  Vˆcont sin t 
(2.65)
Figure 2.57. Control signal and triangle wave.
The switching frequency of the output signal from the PWM is dependent up on the
triangular wave frequency, fs, (fs can sometimes be called carrier frequency). The
triangular wave frequency is often kept constant and the switch frequency will get the
same value as fs. fs is often created with help of a resistor and a capacitor connected to an
oscillator.
f m  f out and f s  f switch
(2.66)
Figure 2.58. Pulse out from the PWM and the control signal (dashed curve).
The control signal decides the width of the pulses, under how long time the transistor is
in a conducting condition. By varying the control signal, the out coming voltage and
current can be changed. The time when the pulses are equal to zero is called the deadtime.
The amplitude-modulation ratio, ma, and the frequency-modulation ratio are two
important parameters in PWM. The modulation ratio for the amplitude is:
ma 
Vˆcont
Vˆ
(2.67)
tri
Vˆcont is the peak amplitude of the control signal and the peak amplitude of the triangle
wave is Vˆ ( Vˆ is generally kept constant).
tri
tri
Different values of ma give different conditions on the modulation;

For ma  1, the amplitude on the voltages keynote varies linear with ma, this makes
the modulation simple to control. The harmonics is in a high frequency range
around the switching frequency. When the control signal increases, the time when
the voltage of the triangular waveform is greater than the control signal voltage
decreases, the output pulse duration will therefore decrease.

ma >1 results in over-modulation. The amplitude of control signal is not linear
against ma and the out voltage will contain more harmonics than the case ma  1 and
the harmonics with dominant amplitudes in the linear range may not be dominant
during over-modulation [10].

For ma >>1, the wanted pulse signal is a square-wave with the same frequency as
the control signal.
Figure 2.59. Voltage-regulation by varying ma [28].
The relation for the frequency-modulation ratio is
mf 
fs
fm
(2.68)
There are several factors that decide the choice of fs and mf. The switch frequency is
often chosen as high as possible [10]. A high switch frequency results in a better shape of
the out coming wave from the IGBT, but the switch-losses in the transistor increases in
proportional with fs.
The relation between the switch frequency and the control signal frequency is dependent
on the value of mf, see Equation 2.68. According to [10] is mf = 21 the limit between a
small and a large value of mf.

When mf is small, the triangle wave and the control signal should be synchronized
to each other and mf should be an integer, otherwise sub-harmonics will occur.

When mf is large, the triangle wave and the control signal do not have to be
synchronized with each other because the amplitude of the sub–harmonics is small.
The harmonics numbers for bipolar voltage switching in a sinusoidal PWM is
n  j mf  k
(2.69)
Equation 2.69 is satisfied when ma≤1. j and k are integers and for odd values of j, only
even values of k are possible and vice versa. The fundamental frequency is denoted by
n=1. In the case of over modulation, the harmonic content will be higher, the harmonics
for the two cases are shown in Figure 2.60.
a
b
Figure 2.60. a, Harmonics for a sinusoidal PWM when ma≤1.
b, Harmonics for a sinusoidal PWM when ma>1.
For a unipolar (the switches are not switching simultaneous) voltage switching the
harmonics contents will be less than for bipolar voltage switching [28].
In a three phase inverter system, the triangular voltage waveform is compared with three
sinusoidal control voltages which have a 1200 phase different to each other, see Figure
2.61.
Figure 2.61. Three-phase PWM waveforms and harmonic spectrum [10].
For a linear modulation (ma≤1), the fundamental-frequency component in the output
voltage from the PWM varies linear with ma.
In the square wave scheme, the switching frequency of the semiconductors is equal to
the output frequency and the output AC voltage has a waveform similar to a square-wave.
In this method, only the frequency is controlled. The harmonics in the output is high and
therefore, this method is often used in applications with a high frequency output [28]. The
square wave modulation has only odd harmonic numbers and for a three-phase inverter,
the harmonic numbers are
n  6c  1
where c = 1,2,3…
(2.70)
A programmed harmonic elimination switching is a combination of the sinusoidal PWM
and the square wave technique. This technique reduces the harmonics and only some
specific odd harmonics will be present [10].
A current-regulated (current-mode) modulation is for example used in DC and AC
motor servo drivers and in other applications where the current must be controllable. The
measured current (real current) is compared with a reference current and the difference
between them is used to control the switches of the inverter.
3. Simulations
In this chapter, the filter is simulated with a different number of generators connected to
it. The AC from the generators is rectified in six-pulse diode bridges and then, the DC is
filtrated.
The aim of the filter simulations is to see how the performance of the filter varies with
the number of connected generators and to decide what values of the filter components
that
are necessary to get a smooth DC output. After the filter simulations, a simple model of a
PWM is simulated.
Last, the complete system with ten generators, rectification, filtration and DC to AC
inversion is simulated.
The simulations are done in MATLAB and in PSpice. The voltage equations for the
linear generators are implemented in MATLAB and the data is stored in files and then
used as an input for the generators in PSpice. An example of a three phase MATLAB
simulated linear generator output voltage is shown in Figure 1.3. The simulations of the
bridge and filter, PWM and IGBT are done in PSpice.
3.1 Voltage from the linear generator
A modeled voltage from the linear generator can be described with equation 3.1 [33]
e(t ) 
2Bt  t dpqch
p
 2h

 cost   sin 
sin t    


 p

(3.1)
The values for the parameters in Equation 3.1 are listed in Table 3.1.
Parameter
Name
Value
Unit
Magnetic field in tooth
Bt
1.55
T
Tooth width
ωt
8
mm
Width of stator side d
400
mm
Total number of poles p
100
Winding ratio q
6/5
slots/ (pole, phase)
Number of cables in slot
c
6
Translator motion height
h
1
m
Wave angular frequency
Ω
1.2566
rad/s
Pole pair width
ωp
100
mm
Phase displacement δ
rad
Table 3.1. Values of the parameters in equation 3.1.
The phase displacement, δ, will vary so the voltage out from one generator has a phase
difference 2π/3.
The wave height will be constant in the simulations, but in reality, the waves vary in
amplitude.
3.2 AC to DC
Figure 3.1 shows the first circuit setup that is simulated in PSpice.
e(t)
R
L
G
RLOAD
e(t)
R
E
L
G
Figure 3.1. Simulation of the rectification in the six pulse diode bridge.
Two generators are coupled in parallel in this figure, but the number of generators
connected in parallel will vary in the simulations.
The generator resistance and inductance are constant in all simulations and are listed in
Table 3.2. In these simulations, the generators are designed to generate a mean power of
10kW each. The burden, RLOAD, will vary dependent on how many generators that are
connected to the substation because the total generated power will vary. The max power,
Pmax, can be calculated over the load resistor as:
2
Pmax  I DC
max  R Load
(3.2)
and the max power over E is:
Pmax  I DC max  E
(3.3)
Parameter
Name
Value Unit
Generator resistance and cable resistance
R
0.5
Ω
Generator inductance
L
11.5 mH
DC voltage
E
200
V
Table 3.2. Constant parameters in the simulations [33].
The simulations are divided into different cases depending on how many generators that
are simulated and how the time shift between the generators are. The simulations are
listed in Table 3.3.
Case 1
Case 2
Case 3
Case 4
Number of generators Displacement (A) [rad]
1
—
2
π
5
2π/5
10
π/5
Displacement (B) [rad]
—
3π/5
4π/25, 3π/5, π , 9π/5
4π/25, π/5, 3π/5, 18π/25, 4π/5,
28π/25, 7π/5, 8π/5, 42π/25
Table 3.3. Different simulation cases.
Displacement A: the displacement is ideal the generators have the same displacement
between each other.
Displacement B: The displacement is chosen at random.
3.3 Filter
The DC after the rectifier bridge includes a lot of ripples and is far from an ideal DC, a
filter is therefore necessary. The filter after the rectifier is illustrated in Figure 3.2.
L
C1
DC IN
DC OUT
C1
L
Figure 3.2. Simulation setup for the filter.
The values of the components will be calculated with equations from the theory in
Chapter 2 and the simulations of the rectifier for the different cases. The capacitor, C, in
the filter is calculated by Equation 2.26 to get a ripple voltage below 4%. The DC choke,
will be used in those cases where the current ripples are big to help the capacitor to filter
the DC.
3.4 PWM
The ground principle for a PWM is a control wave, a triangular wave and a comparator.
The comparator compares the control wave with a triangular wave and creates a pulse
pattern.
Three different simulations are done on the PWM.
Vcont [V]
Vtri [V]
Modulation index ma
Simulation 1: 0.7
1.0
0.7, linear modulation
Simulation 2: 1.05 1.0
1.05, over modulation
Simulation 3: 1.4
1
1.4, over modulation
Table 3.4. Different PWM simulations.
Figure 3.3. Coupling scheme for the PWM circuit in PSpice.
3.5 AC to AC
One simulation is done on the whole substation (the simulation do not includes the safety
system), with ten generators with a purely resistive load at 10 Ohm. The coupling scheme
used in PSpice is shown and described in appendix A. In the simulations, the IGBT
bridge consists of four IGBT:s and this results in one phase out. A PWM is controlling
the IGBT:s and supplying the gate with a Voltage to control the on and off state of the
IGBT:s. The switching frequency is set to 2 kHz, and the modulation index ma is 0.9. The
control wave to the comparator has a frequency of 50Hz.
The purpose with the substation is to connect ten generators and transform their voltage
to a 50Hz sinusoidal wave.
4. Experiment: DC to AC inverter
In the experiment, a DC to AC inverter is built and the main goal is to get a deeper
understanding of PWM and IGBT bridge technique. The inverter built here consists of an
IGBT bridge, a PWM and a drive circuit. The different tests on the parts will be presented
in this chapter.
4.1 Experimental test setup
The IGBT Bridge consists of two IGBT:s connected in one arm, the connections of the
bridge is shown in Figure 4.1.
DC input
+
Vdc
-
Upper IGBT
IGBT
Lower IGBT
IGBT
G C E
G C E
AC output
Vac
Figure 4.1. IGBT Bridge.
The wirings in Figure 4.1 are colored to see the connections clearly; different colors will
be used in the real test setup. The red wire goes from the positive DC side to the collector
in the upper IGBT. The black wire is connected to the emitter on the lower IGBT.
Connection between the upper and lower IGBT is done by the blue wire, this wire goes
from the emitter on the upper IGBT to the collector on the lower IGBT. The AC output is
showed with the yellow wire that comes from the collector on the lower IGBT. The gate
to the IGBT:s are not connected to the drive circuit in this figure, the connection will be
shown in Figure 4.3.
The IGBT:s will be clamped to a heat sink to keep them cold, a fan or other devices can
be used together with the heat sink to lower the temperature even more. The DC input
will be provided with a DC voltage unit and the output will be examined by an analog
oscilloscope.
To create the pulses to the gate on the IGBT, a gate driver and a PWM are used.
The coupling scheme of the drive circuit and the PWM is shown in Figure 4.2 and 4.3.
R3
R8
R2
R1
R4
CL
RL
R5
C1
1
2
3
4
5
6
7
16
15
14
13
PWM
12
11
10
8
9
R7
R6
Output sinals to the gate driver
Figure 4.2. Coupling scheme for the PWM.
12V
To get the right signal with the right amplitude to the gates, the outputs from the PWM
are connected to a gate driver.
D1
12V
1
2
3
4
5
6
7
8
IN
IN
R9
12
13
28
27
26
25
24
23
22
21
20
19
18
17
16
14
15
9
10
11
C2
RG
RG
R10
Figure 4.3. Gate driver circuit with input to the IGBT arm.
The gate driver has a capacity to drive six gates, a three-phase bridge. The experiment
setup consists of two IGBTs which results in two gates that must be controlled.
The type of IGBT, PWM and driver used in the experiment are presented in Table 4.1. To
get a further description of the devices, the datasheets are presented in appendix.
Component
IGBT
Gate driver
PWM
Name
Datasheet
Appendix B
IR2130 International IOR Rectifier Appendix C
TL494 Texas Instruments
Appendix D
Table 4.1. Names of the main components used in experiment.
The equipment for the experiment is shown in Figure 4.4.
Figure 4.4. a) Two DC power supplies.
b) A function generator.
c) Digital oscilloscope.
The DC power supplies are used to generate a DC signal into the IGBT arm and to drive
the PWM and gate driver. A function generator is used to generate a voltage with a
sinusoidal wave form, which creates the desired pulses in the PWM. The measurements
and curves are done with the help of a digital oscilloscope.
The constructions of the PWM and gate driver on the circuit board can be seen in Figure
4.5 a) and b).
Figure 4.5. a) PWM circuit board.
b) Gate driver circuit board.
Pictures of the IGBT arm is shown in Figure 4.6 and the significant parts are marked in
Figure 4.6 a.
a)
b)
Figure 4.6. a) IGBT arm. The marked parts are:
1. DC + voltage from DC power supply
2. AC voltage out to the load
3. DC- voltage
4. IGBT on a heat sink
5. Emitter
6. Gate
7. Source
8. High side input from the gate driver
9. Supply return to driver
10. Low side input from the gate driver
b) The IGBT arm from the side.
4.2 Experiments
Five different tests will be done on the PWM, driver and IGBT. The first four testes are
done on the PWM and the last test is on the whole system.
Test 1: The switching frequency of the triangle wave. RL is 50kΩ and the pulse width is
constant. The calculated value of the switching frequency of the triangle wave is (see
appendix C):
ftricalc= 1/(RL·CL) = 20kHz
(4.1)
Test 2: Linear modulation (ma ≤ 1) with a sinusoidal wave.
Test 3: Over modulation (ma > 1) with a sinusoidal wave. At over modulation is the
control signal sometimes greater than the triangle wave which results in an enabled out
signal, the output gradually merge.
Test 4: Square modulation (ma >> 1) with a sinusoidal wave. In the square region, all of
the on-time pulses are merged.
Test 5: The IGBT arm is tested with a linear modulation of the incoming pulses from the
driver (as in test 3) to the gate.
5. Results
The results from Chapter 3 and 4 are presented in this chapter.
5.1 Diode rectifier
The result for the different cases is shown in Figure 5.1-5.7.
In Case 1, one generator is rectified, E is holding the potential between positive voltage
and the negative voltage, otherwise the voltage would reach zero in this case. In Case 2a,
the DC current never reaches zero, the smaller current peak between the larger on is
formed when the to currents is imposed on each other. This peaks will grove in size when
more currents are involved and gives a raise in the current, this can be seen in Case 3a4b. In Case 2b and 3b, the current has big ripples because they are imposed on each other
at one time and far away from each other at another time. The small ripples seen in
voltage are done by the diode rectifier and are about 30-50Hz. This noise makes it harder
to se the low frequency ripples. This is clearer in Case 3a-4b but the rippled current is
easier to see. In Case 3a and 3b, the importance to keep the generators in perfect phase
between each other is shown. In Case 3a, the low frequency ripples is almost gone and in
3b the low frequency ripples is very clear. In Case 4a, the DC is almost constant accept
for the higher frequency ripples, and Case 4b shows some of the lower frequencies. The
simulation of the diode rectification agrees well with the theory.
Figure 5.1. The voltage and current over the load in case 1, one generator.
Figure 5.2. Case 2a, the voltage and current from two generators with an ideal time
displacement.
Figure 5.3. Case 2b, the voltage and current over the load from two generators.
Figure 5.4. Case 3a, the voltage and current over the load from five generators with an
ideal time displaced.
Figure 5.5 Case 3b, the voltage and current over the load from five generators with a
time displacement that is chosen randomly.
Figure 5.6. Case 4a, the voltage and current over the load from ten generators with an
ideal time displacement.
Figure 5.7. Case 4b, the voltage and current over the load from ten generators with a
time displacement that is chosen randomly.
5.2 Filter simulations
The values for the capacitance, C and the voltage ripple DC is shown in Table 5.1. The
output DC for each case is shown in Figure 5.9-5.17. For case 1, 2b and 3b, the current
has big ripples as can be seen in simulation from the rectification to help the capacitor
with the filtration an inductor is placed in series this improves the current ripples and
lower the value of the capacitor. Table 5.2 shows the value of the inductor, capacitor and
the ripple voltage. Figure 5.8 compare capacitance to the number of generators connected
in parallel here, the time displacement is ideal between each generator.
The ripple period for the voltage and current in the different cases arises from the phases
of the different generators, the ripple frequency gets higher when the number of
generators is increasing and out of phase. In Figure 5.9, 5.11, 5.14 and 5.17, the DC is
clearly getting better with increasing numbers of generators. In Case 3a, 4a and 4b the
use of a large capacitor is gone, the ripples consist mostly of higher frequency done by
the rectifier. This higher frequency is about 30-50Hz and in the simulations, this
frequency was reduced much below 1V.
C [F]
Case 1
6
V (ripple %)
4.1
Case 2a
1.6
3.3
Case 2b
7
3.6
Case 3a
0.26
2.8
Case 3b
8
3.8
Case 4a
0.08
--Case 4b
0.12
--Table 5.1. Calculated values for the capacitor.
C[F]
L[H]
V (ripple %)
Case 1
5.5
0.5
3.9
Case 2b
4
0.5
3.3
Case 3b
2
0.5
3.9
Table 5.2. Simulated values for the capacitor together with an inductor.
7
6
5
C [F]
4
Series1
3
2
1
0
0
2
4
6
8
10
12
Number of Generators
Figure 5.8. Capacitance VS number of generators, the generator has perfect phase
between each other.
Figure 5.9. Case 1, the filtrated voltage and current from one generator, measured over
the load, filtered with a capacitor.
Figure 5.10. Case 1, the filtrated voltage and current from one generator, measured over
the load, filtered with an inductor and a capacitor.
Figure 5.11. Case 2a, the filtrated voltage and current from two generators, with an ideal
time displacement, measured over the load, filtered with a capacitor.
Figure 5.12. Case 2b, the filtrated voltage and current from two generators, with a time
displacement chosen randomly, measured over the load, filtered with a capacitor.
Figure 5.13. Case 2b, the filtrated voltage and current from two generators, with a time
displacement chosen randomly, measured over the load, filtered with an inductor and a capacitor.
Figure 5.14. Case 3a, the filtrated voltage and current from five generators, with an ideal
time displacement, measured over the load, filtered with a capacitor.
Figure 5.15. Case 3b, the filtrated voltage and current from five generators, with a time
displacement chosen randomly, measured over the load, filtered with a capacitor.
Figure 5.16. Case 3b, the filtrated voltage and current from five generators, with a time
displacement chosen randomly, measured over the load, filtered with an inductor and a
capacitor.
Figure 5.17.Case 4a, the filtrated voltage and current from ten generators, filtered with a
capacitor.
Figure 5.18.Case 4b the filtrated voltage and current from ten generators, with a time
displacement chosen randomly, measured over the load, filtered with a capacitor.
5.3 Results of PWM
The three results from the simulations are presented and then, the results from the
experiment are presented in the following sections.
5.3.1 Simulation 1
In Simulation 1, the PWM is tested in the linear region, see Figure 5.19.
Figure 5.19. The pulses out from the comparator (blue curve) and the control wave and
triangular wave.
The result from this simulation agrees very well with theory. The pulse width varies with
the amplitude of the control wave.
5.3.2 Simulation 2 and 3
The simulations in the over modulation region are presented in Figure 5.20 a) and b). The
results are as expected, the pulses is merged in the over modulation region.
Figure5.20. a) The modulation index is just into the over modulation region.
b) The pulses are clearly merged.
5.3.3 Test 1
Figure 5.21 shows the simulation of the triangle wave and the pulses out from the PWM
with a constant pulse width.
a)
b)
Figure 5.21. a) Test 1, the pulse train out from the PWM.
b) The two pulses out in a push-pull operation.
The switching frequency of the measured triangle wave is:
ftri= 20.05kHz
and
ftri ~ ftricalc
The simulated value agrees well with the calculated value. The pulse out, as expected
from theory is constant when the control voltage is constant.
In Figure 5.21 b), one of the pulses can be seen as an inverse of the other pulse, i.e. one
of the curves is an inversion of what is expected.
5.3.4 Test 2
The result from Test 2, linear modulation, is shown in Figure 5.22. The orange curve is
the pulses out from the PWM and the blue curve is the control wave.
Figure 5.22. Test 2, linear modulation, the upper curve is the pulses out from the PWM
and the lower cure is the signal from the function generator.
The dead time of the pulses decreases when the control signal amplitude increases, as
expected from the theory. Due to the high switching frequency the pulses are hard to see
and a sequence is therefore enlarged.
5.3.5 Test 3
In Figure 5.23 a), ma is just into the over modulation region (ma is almost one) and a split
can be seen in the pulses when the control wave reaches its peak value.
In Figure 5.23 b), the pulse is clearly merged when the control signal is in the region for
over modulation.
a)
b)
Figure 5.23. Test 3 over modulation.
a) The control wave is a little bit over 3V.
b) ma is in the over modulation region.
5.3.6 Test 4
The results from the test on square modulation agrees quite well with the theory, see
Figure 5.24. Here, the output signal is almost merged all the time. The pulses out from
the PWM can be seen as a square wave and have almost the same frequency as the
control wave.
Figure 5.24. Test 4, square modulation.
5.3.7 Test 5
The voltage out from the IGBT-arm is shown in Figure 5.25. The voltage is a half wave
and has a sinusoidal form if the ripples are ignored. The DC voltage into the IGBT is only
23V. The ripples will be constant for different voltages and at a voltage of for example
200V, the ratio between the ripples and the voltage will be smaller, but a filter is still
necessary to get a desired wave out from the IGBT-arm.
Figure 5.25. Wave out from the IGBT arm at linear modulation.
5.4 AC to AC
The AC voltage and current is shown in Figure 5.26. The Voltage is almost a sinus wave
with small ripples and it has like the control wave a frequency of 50 Hz. The current is
also formed as a sinus wave with a frequency of 50 Hz. The amplitude of the voltage is
about 420V and the amplitude of the current is about 40A. The relation between the
modulation index, DC voltage and the output amplitude of the AC agrees well with the
simulation.
Figure 5.26. The blue curve is the sinusoidal wave out from the IGBT bridge and filter
and the black curve is the current out.
6. Design of safety circuit
In this master thesis, a model of a linear generator is used in the simulations. This model
differs from reality; the waves for example, have a varying height which results in a
wider spectrum of voltages and currents. The peak power for one linear generator in the
simulations is approximately 30kW and in real, the peak power can be much higher. The
consequence of this is also; a higher peak voltage and current (only a higher peak current
if the generator is voltage regulated) can be expected. In this case, with a linear generator,
it is important to decide what currents and voltages that can be expected from the
generator.
There are two main problems that must be solved before a safety circuit can be designed:
1) What should the voltage and current settings be?
2) The low frequency. The frequency out from the generator is 0-15 Hz and a CT has
problem to reproduce a primary current with a low frequency.
The problematic to set a limit for a fault is the varying voltage and current. Assume that a
fault occurs when the wave climate results in a low voltage and current. The resulting
fault current can still be in the “normal” current interval for the generator and can be seen
as normal but it is generated by a fault.
In this case, with a durable generator, a fault can be seen as a normal condition for the
generator and the substation and the fault will not damage any components in the
generator. A fault that occurs at a lower voltage can therefore remain in the circuit until
the voltage rise and the current rises over the highest current that is accepted in the
system.
The voltage and current settings for the safety system must therefore be decided on the
basis of the highest expected voltage and currents from the generator. The electronics in
the substation must be able to manage these voltage and currents.
Now, only one problem is left to solve, the low frequency. A CT needs approximately
5Hz to be able to generate a secondary current (the core of the CT must be over
dimensioned to be able to reproduce the primary currents at this frequency). This problem
is not really a problem any more because faults at lover voltages are accepted. The
frequency of the voltage and current is proportional to the velocity of the waves. The high
currents and voltages occur when the wave velocity is high and at high voltages the
frequency is expected to be about 10-15Hz.
The over voltage protection here consist of varistors that leads away the over voltages to
logic ground, see figure 6.1
Generator
Substation
G
Figure 6.1. Over voltage protection with varistors.
A varistor lifetime is dependent on the value of the currents the varistor is exposed for. A
diagram for this is shown in figure 6.2.
Figure 6.2. The logarithmic curve with the current on the y-axis and expose-time on the
x-axis. The value on the curves tells how many exposes the varistor can handle before it
breaks [34].
An over current protection system can be build in many different ways, some of them are
more complex than other systems. The substation is placed at the bottom of the ocean and
a broken component is not easy to replace. A design example of an over current system is
shown in figure 6.3.
NO
NC
COM
NO
NC
COM
NO
NC
COM
NO
NC
COM
+
-
Figure 6.3. An over current protection system. The parts in this over current protection
system are CT:s, relays, contactors and a battery.
This system includes few components; CT:s, relays, contactors and a battery. When a
fault occurs, the CT or CT:s produces a secondary current and the relays (or relays)
switch on the battery and the contactor breaks off-connects the linear generator.
a)
b)
c)
Figure 6.5 a) Contactor [35]
b) Current transformer [36]
c) Relay [37]
As mentioned in the theory, fuses are often used as a complement in low voltage system,
because they have a faster function time than the breakers. The linear generators do not
require a fast safety system and fuses are therefore not necessary. In this construction, no
fuses will be used, this reduce the number of components and the fuses must either be
replaced or recovered after a releasing which is a problem in this case.
This protection system does not protect the circuit from high DC currents, which is a
draw back with the system.
7. Discussion
In this project, a design of a substation for two or more wave generators was examined. A
substation consists of a number of devices such as safety circuits, converter, inverters,
transformers, filter and voltage-regulators to mention some of the parts. These parts are
presented in the theory. Simulations and experiments are done on some of the parts, but
not at all of them. The aim of this work is more to present a design for the substation.
Further work is needed in detail on the different parts to get a more accurate design.
The analytic model of the linear generator was done in MATLAB and the rectification of
the AC from the generator was done in Pspice, the results of these simulations were
successful. Pspice was used to simulate the filtration of the ripples in the DC after the
rectifier. The results were as expected less filtering was needed with an increasing
number of generators, if the phase difference was the same for each generator. When the
phases between the generators where random, the filtering action increase, this is very
important in the design of the filter. Also the AC amplitude from the generators will have
impact on the filter size. The ocean wave high in this project was set to 1m, this height
might vary between each wave power plant and may also increase the filter size. Further
studies of these cases are need to size the filter, also a more accurate model or real data
from one or more generators needs to be used to get the correct size of the filter.
The DC after the diode bridge is unregulated and this DC needs to be regulated. In this
work, two models are presented. In the first case, a DC to DC converter is placed after the
rectifier and will have a regulated DC as its output. This alternative will make the sub
station more complex with more parts and may give more losses such as switching losses.
In this case, a transformer is still necessary after the inverter.
The second case is a transformer at the output of the inverter that can change its windings
depending on the AC output from the inverter to get a desirable level of the AC. This
transformer is driven by a motor and a feedback loop to get a regulated AC. If the losses
is the same in this kind of transformer as in a step-up or step-down transformer, then this
alternative is to prefer compared with the DC to DC converter. In this project it is hard to
draw any conclusion about these to cases, because no simulations or experiments have
been done. The choice between them has to be grounded on simulations and experiments
that might be done in another project.
The IGBT bridge with control system for the substation will be similar to the IGBT,
PWM and driver circuits described in Chapter 4. The circuits in Chapter 4 were
constructed for one IGBT arm and for the substation a circuit with three IGBT arms is
needed. The pulse pattern used in the experiment was created with help of a function
generator. In reality, the pulses must be controlled with respect to the voltage at the grid.
This can be done with a DSP, the frequencies of the three control phase voltages are
regulated to the wanted value.
In the simulation of the AC to AC, the IGBT:s was controlled by pulses created with a
triangular wave, control wave and a comparator. The aim in this simulation was to create
one phase AC out from the inverter. According to the results, the simulated circuit has the
potential to work in the planned substation in the project Islandsberg.
The current measuring in the substation are easiest done with current shunts or LEM Hall
Effect current sensors. Instrument transformers are not to prefer because of the low
frequency. The two devices have different advantages and disadvantages. A current shunt
is cheaper and easier to understand, but the measured signal must be amplified. The LEM
shunt is mounted around the cable and the measured voltage do not need any
amplification, but the voltage out from a LEM shunt is often noise and a LEM shunt is
expensive. The LEM current sensor needs also an external DC source. The current shunt
used for measuring high currents, has a higher accuracy than a LEM shunt. Because of
the price and accuracy, a current shunt is to prefer for current measuring.
The proposal protection system in the substation includes a simple over voltage
protection and over current protection system. The linear generator is durable against
over currents and over voltages and a more complex system is not needed here. The
special with the linear generator protection, is to decide which currents and voltages that
are caused by a fault. The wide voltage and current range makes it possible that a current
caused by a fault can be in the “normal” current range.
In figure 1.4, an over current protection system is placed at the end of the substation, if
this protection is necessary or not is hard to decide. The purpose with a safety circuit here
is to break the circuit if there are a fault with the voltage and currents out from the
substation. Most of the parts in the substation have built-in safety systems, as snubber
circuits and a safety circuit at the end of the substation will not protect the parts. The AC
is not connected to the grid just after the substation and to have a safety system here is
not necessary. But it could be desirable to be able to break the circuit at the end of the
substation. Contactors can be placed here and if there is any problem to adjust the three
phase voltage after the three phase voltage at the grid, the substation can be offconnected.
8. Conclusion
The simulated and the experimental results compared with the calculated values were
satisfactory. Simulations of the rectification of the AC with Pspice agreed well with the
theory. The filter simulations in Pspice have drawbacks when it comes to the component
library but overall the simulations were as expected. The conclusion of the rectification
and the filter is the importance of the phase difference of the generator together with the
number of generators. The filter has to be oversized but how much is to some degree
probability theory of ocean waves. In the ideal cases, when the phase difference between
each generator is the same, the filter size will decrease with increasing number of
generators. When the generators phase difference between each other where random, the
capacitor size increased, in some cases with over 3000% compared with the ideal phase
difference. The need of an inductor together with the capacitor in these cases, with high
current ripples, increases. The inductor decrease the current ripples and lower the
capacitance needed to filter the DC. The inductor also helps reducing harmonics created
by the non linear loads. In the simulations, the need of additional filter capacitors for the
higher frequency might be needed but where not a big impact on the result in this work.
The simulations of the AC to AC circuit with ten generators connected to it works in a
proper way. The system was able to connect and transform the incoming AC from the ten
generators to a sinusoidal 50 Hz AC which is the main goal with the substation.
The simulations and experiments on the PWM agree well with the theory and calculated
switching frequencies. The IGBT arm works in a proper way but the AC out from the
IGBT must be filtrated. A printed circuit card is to prefer, this reduces the risk for leading
faults and coupling faults.
The linear generator is dimensioned to manage a wide range of currents and voltages, the
demands of the safety system are therefore less than for other generators.
9. Acknowledgement
10. References
[1] www.el.agnstrom.uu.se, Karl Åstrand
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generator”
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Appendix A – Circuit scheme for the AC to AC simulations
Appendix B – Datasheet IGBT
Appendix C – Datasheet gate driver
Appendix D – PWM