Low-Voltage DC Power Transmission Line Model Utilizing 3Phase Wind Power Generation
Fredric W. Fyvie
Trevor D. Jackson
May 10th, 2013
Department of Electrical Engineering
University of Minnesota Duluth
Duluth, MN 55812
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Table of Contents
I.
II.
III.
IV.
V.
VI.
VII.
Abstract
Introduction
Overview
a. AC vs. DC
b. Thyristor Theory in Rectification Control
c. Inversion
Specifications and Methods
a. Turbine
b. AC-DC Rectifier
c. DC-AC Inverter
Considerations
a. Economic Concerns
b. Environmental
c. Sustainability
d. Manufacturability
e. Health and Safety
f. Political
Results and Discussion
Conclusions
References
Page
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4
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5
7
8
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10
11
14
14
15
16
16
17
17
17
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List of Tables
Table 1:
Table 2:
Table 3:
Table 4:
Table 5:
Table 6:
Table 7:
Turbine Generation Values
Rectified Voltages
Arduino Input Signal Voltages
Duty Ratios
Point Generation Data
Duty Cycle Equation
Transmission Circuitry Values
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List of Equations
Equation 1:
Equation 2:
Corner Frequency
Phase to Rectified Voltage
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List of Figures
Figure 1:
Figure 2:
Figure 3:
Figure 4:
Figure 5:
Figure 6:
Figure 7:
Figure 8:
Figure 9:
Figure 10:
Figure 11:
Figure 12:
Figure 13:
Figure 14:
Figure 15:
Figure 16:
Figure 17:
Thyristor Schematic
Firing Angle
AC-DC Pseudo-Sinusoidal Inverter
Wire Coil Placement
3-Phase AC to DC Rectification and Control
3-Phase Bridge Rectifier Output Waveform
Inverter Circuit
Phasing of PWMs
Pseudo-Sinusoidal Signal
Smoothed Output Waveform with Harmonics
AC vs. DC ROW Comparison
Break-Even Distance (Point)
Magnetic Field in a DC Line
Low Wind Speed Rectification and Transmission
Medium Wind Speed Rectification, PWM, and Transmission
High Wind Speed Rectification, PWM, and Transmission
Inversion Output
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7
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Abstract
Power is essential to our every-day lives, and challenges arise in how to distribute such power to
consumers. Three-phase AC transmission lines have primarily taken over our grid in the United States as
the standard form of power transmission from power generators to substations and
household/commercial loads. However, for long distance transmission, AC transmission suffers from
multiple sources of power loss and non-idealities, and thus is not as ideal for long transmission runs.
However, DC transmission doesn't suffer from these same issues, and is often times more ideal for
longer distances. Such a system is already present locally, running from a 75MW wind farm in North
Dakota to Arrowhead Substation in Hermantown, Minnesota [1]. This project takes a DC transmission
line and scales it down to a low-voltage model. Incorporating a 3-phase AC wind turbine, 3-phase AC to
DC conversion utilizing thyristor modeling, as well as DC to 3-phase AC oscillation, this physical model
demonstrates the principles of what must occur in order to make such a transmission line possible while
educating about the benefits and pitfalls of using such technology.
4
I. Introduction
Power will always be a commodity that we greatly value due to its high necessity in our everyday lives, and how to produce it is, without a doubt, a hot-topic in today's culture. However, how to
transmit this power to residential and commercial buildings is another issue not many think about.
There exist two ways of transmitting this power, one being through the use of alternating current (AC),
and the other being through direct current (DC). While both have their benefits and pitfalls, each is
beneficial for certain scenarios. This report outlines the research, development, and testing of a lowvoltage DC transmission line model to educate about the mechanics and engineering that must occur in
order to make the less-common DC transmission line properly function. While AC is the predominate
system, it suffers from issues that the DC system doesn't, more notably in long distance transmission.
The benefits and faults of both these systems will be analyzed in this report, along with outlining the
work done to build a working low-voltage direct current (LVDC) transmission line, complete with a 3phase AC wind generation source, 3-phase AC to DC conversion, and DC-3-phase AC inversion or
oscillation.
II. Overview
AC vs. DC
Power transmission has long been a prevalent issue in the United States, and the world in
general. While so many devices today depend on electricity, the transmission of this power from a
generation source to a standard pluggable AC wall terminal has become a necessity. Alternating current
(AC) has long taken over as the primary way of distributing this power across the electrical grid, due in
large part to the use of transformers. These devices allow the line voltages to be stepped up or down
depending on the required load voltage. The cost of DC stations to convert AC to DC and invert DC to AC
are very costly, and often times rid the need for considering if a DC transmission line should even be an
option.
While the cost of the substations for an AC line is relatively cheap when compared to that of a
DC station, the power losses experienced due to a long AC transmission distance are vastly greater. It is
important to mention the difference in the number of conductors required for each transmission
scheme. Typically, 3-phase AC lines use a total number of six conductors for the duration of the run:
one conductor is used for each phase (three) typically being transmitted as a double AC circuit to cancel
interference [2]. Sometimes, even a seventh conductor is added for a neutral return [3]. DC lines,
however, only use two: one for the positive DC transmission and one for ground [2]. These added
conductors in the AC system contribute more
power losses. With one third the number of
conductors, HVDC starts to become more economically feasible both in power loss and conductor cost.
The right of way (ROW) is also an important factor to consider when building AC transmission lines. The
ROW is the safe distance around the power lines that must be kept clear of any natural growth. With DC
lines, this ROW is much narrower [2].
5
DC lines have much lower EMI (Electromagnetic Interference) due to the absence of an
alternating current flow, and thus have much less of an environmental impact. DC lines also do not have
inherent series reactance and shunt reactance that introduce regulation issues, stability problems, and
power loss [4]. The skin effect, or the fact that nearly all the AC current is carried in the outermost
"skin" of the conductor, accounts for a high power loss in AC transmission systems. Also, the distance
from line to ground or line to line conductors in an AC system is much greater than that of the distance
required between the positive to ground conductors in a DC system. This means more space is required
to install AC transmission towers versus DC transmission towers, which leads to a larger ROW. The
effect of standing waves in AC systems also leads to attenuation distortion of the system, due to
impedance mismatch, which is far from ideal. Therefore, the transmission distance needs to be
matched to the AC frequency to ensure no standing waves can be present.
While the current AC infrastructure dominates DC in short transmission distances due to the
high cost of conversion technology in HVDC systems, there comes a transmission distance where the
two technologies become economically equal to each other. This is typically coined the "break-even
distance" [2]. At this distance, the AC cost of running more conductors and loss of power due to AC nonidealities begins to catch up to the initial high cost of building conversion technology for a DC system.
For distances equal or great to this break-even distance, DC transmission makes more sense, both
economically and environmentally.
With these thoughts in mind, it seems as though DC, despite its high cost in rectification and
inversion stations, has the upper hand in long transmission distances. With the advent of the thyristor,
the power conversion efficiency of DC stations has become even more prominent, thus reducing some
of the high cost of energy conversion in the DC stations. With thyristors, the efficiency of a converter
station can be expected to be in the 99% range [5]. This efficiency is vastly higher than in previous
history and thus DC transmission begins to make more sense despite its initial downfall of high cost
conversion technology.
While this project is not meant to disprove the benefits of AC transmission, it does have aim to
give credit to DC transmission and the environmental and economic reasons it exists. But if the benefits
of DC can primarily be seen in the transmission phase, how then is the conversion from AC to DC done
effectively, and namely at the 99% efficiency as noted before? This is through the use of thyristors.
Thyristor Technology in Rectification Control
In order to keep a constant voltage over the DC line, thyristors are used to cut off the generated
waveform using an external control signal. Thyristors act very much like diodes in the fact that they only
allow current to flow in one direction (anode to cathode). However, unlike normal diodes, an external
gate is used to turn on the thyristor to allow current to flow [6]. In this regard, thyristors behave much
like a MOSFET or BJT. However, thyristors continue to conduct through the device even after the gate
voltage is removed. This is due to a gated structure of alternating P-type and N-type semiconductor
material. In a sense, a thyristor can be modeled by using two BJT's, with the collector of one BJT
controlling the base of the other. The schematic, P-N-P-N structure, and BJT transistor model can all be
seen in Figure 1 [6].
6
Figure 1: Thyristor Schematic [6]
Thyristors are relatively easy to turn on. By simply applying a gate voltage above the threshold
level at the gate of the thyristor, the current is able to flow from the anode to the cathode with little
leakage current from the gate. However, turning the thyristor off is not as simple. Due to the gating
characteristic of the thyristor, one the gate voltage is applied, the current that flows through the device
continues to bias the gate so the device continues to conduct. Therefore, it can be stated that the
device only turns off when the input waveform to the anode returns to zero [6].
This type of behavior is ideal for AC to DC conversion as the rectified AC waveform naturally
returns to zero after every rectified cycle. Therefore, the thyristor will naturally turn off after the
waveform returns to zero. This natural turn-off ability is a convenience as it eliminates a signal required
to turn off the device. Only one signal is required to be supplied to the thyristor: a firing signal.
A firing signal is simply a control voltage applied to the gate of the thyristor in order to turn the
device on and allow it to conduct. The crucial part of this signal comes in its timing, or a "firing angle".
Due to the need of constant voltage over the DC transmission line, the thyristor plays a crucial role in
making sure this happens. If too much power is being generated, the thyristor is responsible for cutting
the waveform to ensure that the line voltage doesn't spike. By watching the frequency of the incoming
waveform (and therefore voltage), a control scheme can be made to send a firing signal to turn on the
thyristor after a certain portion of the rectified waveform has passed. This allows only a section of the
waveform to pass, so that the input voltage can continuously be monitored to ensure constant output
voltage. Of course smoothing of the chopped waveform is then needed to transform it into a clean DC
signal. Figure 2 depicts the delay angle or phase angle and the times of conduction and turn-off in the
device. It must be noted that turning off the thyristor is not always simple. If the input waveform
doesn't settle to zero for a long enough period, the thyristor may never turn off and the device would be
allowed to conduct for another rectified period [7].
7
Figure 2: Firing Angle [6]
Inversion
The process of converting the generated AC waveform into a constant DC waveform is one
crucial step in the transmission of a DC signal. However, in order for this waveform to be useful to
residential and commercial loads, it must be transformed back into a 3-phase AC waveform. This allows
for use of transformers to step down the voltage (and sometimes step up) to a level that is required by a
load center. Transformers cannot be used with a DC signal, and thus the transformation into AC is
required.
While there are many schemes available for phase-offsetting and oscillating a DC waveform, one
way is through the use of pulse width modulation. By using a set of insulated gate bipolar transistors, it
is possible to transform the signal into a pseudo-sinusoidal signal. Such a scheme can be seen in Figure
3. By phase shifting the control signals to the gates, it is possible to offset the sinusoids from each
other. Then, by referencing each phase to each other, a sinusoidal waveform can be made from a series
of square waves. This pseudo-sinusoidal signal can then be smoothed using a low pass filter attached
between each phase. It is important to note that each phase can be found between each upper and
lower IGBT. The low pass system would be connected between each set of two phases, yielded an
overall 3-phase system output [7].
Figure 3: AC-DC Pseudo-Sinusoidal Inverter [7]
8
While inverter systems in the field may be different than this technique, this form of system
offers a cheap and simple solution to the problem. For larger systems, more insulation is required to
ensure equipment is not damaged and that safety is ensured.
III. Specifications and Methods
In order to implement a small signal, low-voltage model, three sections were required. The first
was the creation of a 3-phase turbine to generate the power that would be converted to DC,
transmitted, and inverted back to 3-phase AC. The second involved the 3-phase AC to DC rectification.
This section includes the controlling of the firing angle in order to properly keep a steady voltage over
the line. The third and final stage included designing a DC to 3-phase AC inverter.
For each section of the project, certain materials were required in order to properly build the
small-signal model. For each section, the materials can be seen below. Note that these were the final
material required for the project. Not listed below are intermediate materials that were not used in the
final design (mostly due to non-idealities).
Turbine:
1. PicoTurbine Kit
2. Lomanco BIB-12 MILL Whirlybird Turbine Ventilator
3. Epoxy Glue
4. Tape
5. Wire (22AWG or up)
AC-DC Rectifier
1. Breadboard
2. Wire (22AWG or up)
3. 39uH Inductor
4. 100uF Capacitors
5. N-Channel Power MOSFET
6. Power Diodes
7. 1MΩ Load Resistor
8. Push Button (for discharging capacitors)
9. Toggle Switch (for ground switching)
10. Arduino Uno and Cable
11. 5V Power Supply
DC-AC Inverter
1. Breadboard
2. Wire (22AWG or up)
3. 39uH Inductors
4. 10uF Capacitors
9
5.
6.
7.
8.
9.
Power Diodes
Perfboard/Plastic Board (for mounting capacitor banks)
100Ω Load Resistors
Arduino Uno and Cable
Variable Power Supply
Additional Materials
1. Cat-5 Cables (for communications)
2. Cat-5 Receptacles
3. Oscilloscopes
4. Arduino Development Software
Using the materials and software listed above, it was possible to construct a working smallsignal DC transmission line model. The small-signal model was made to represent the larger real-world
DC transmission systems in place in our infrastructure. The first step was creating a turbine to properly
generate 3-phase power.
Turbine
In order to create a turbine to properly generate three phase power, it was important to
understand Faraday's Law. Through this law, it is proven that a moving magnetic field over a wire coil
induces a magnetic field in the wire coil. By exploiting this concept, a stronger current can be draw by
using multiple coils and multiple magnets. To generate a single phase of power, four wire coils could be
connected in series to one another and places on the base of the Lomanco WhirlyBird. Each wire coil
could be placed 90° apart from each other. Then, 16 bar magnets could be secured to the rotating
section of the WhirlyBird, with every-other magnet facing in an alternate direction and therefore
creating an alternating north-south pole structure. After connecting the rotor to the stator and spinning
the rotor (simulating wind), the magnets would continually rotate over the wire coils allowing magnetic
flux to flow between them. This, in turn, generates an electric current through the coils and can be used
to power external devices. By adding four more wire coils (each in series with each other) 120° apart
from the first phase, a second phase could be created. Finally, by adding four more wire coils 120° apart
from the second phase, a third phase could be created. The overall layout of the wire coils can be seen
in Figure 4 (where P1,1 denotes phase 1, coil 1, etc).
Figure 4: Wire Coil Placement
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The leads of each phase could be extracted from the turbine and used to connect to the AC-DC
rectifier unit.
AC-DC Rectifier
In order to properly rectify and control the 3-phase power generated by the Whirlybird, a couple
concepts needed to be put together. The first involved created a 3-phase bridge rectifier. This type of
rectifier takes in three phase voltages, and outputs a nearly constant DC voltage. Then, this waveform
was smoothed using a smoothing capacitor. The second was a Buck converter utilizing an N-channel
MOSFET. This part of the circuit would chop the waveform using a PWM generated by an Arduino if the
turbine was generating too much power. Otherwise it would pass the signal straight through with a
duty ratio of 1. If the turbine wasn't generating enough power (DC line voltage would be too low), then
the rectified signal would not be allowed to pass with a duty ratio of 0. If the waveform was anywhere
above the wanted transmittance voltage, the Arduino would change the duty ratio accordingly to only
pass a percentage of the rectified waveform. As noted, the rectified and smoothed waveform also
needed to be sent to an Arduino in order for it to calculate the Duty ratio needed to be applied to the
buck converter. Finally, the chopped waveform was smoothed using one final smoothing capacitor that
would hold the voltage at a constant DC level.
Figure 5 shows the circuitry used to simulate the conversion from 3-phase AC to DC through the
use of rectification control. The diode section constitutes the 3-phase bridge rectifier. The first
capacitor is a smoothing capacitor to give the input of the Arduino a clean DC signal. This signal also
goes into the drain of the MOSFET. Finally, the MOSFET, lone diode, and second capacitor constitute
the buck converter. Using the duty ratio supplied by the Arduino, the input to the MOSFET with either
be passed through or attenuated depending on the magnitude of the voltage after rectification.
Figure 5: 3-Phase AC to DC Rectification and Control
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Figure 6 demonstrate the expected output waveform of the 3-phase bridge rectifier before any
smoothing is done. After smoothing, the slight ripple in the bottom waveform will be removed and will
be used as an input to the Arduino to send the level of power generation currently being attained.
Figure 6: 3-Phase Bridge Rectifier Output Waveform [9]
An important note needs to be addressed regarding the use of the buck converter. A buck
converter works on the concept that it will either pass through the voltage it is given, or attenuate it.
Therefore, this is an ideal circuit to simulate the behavior of a thyristor. Thyristors were originally
chosen to be used, but unfortunately would not turn off properly. With thyristors connect, the 3-phase
bridge rectifier was not used, and instead, each phase was rectified separately. With the thyristors not
properly turning off and some small gate current trickling through to the output, thyristors were
abandoned and a buck converter was used to simulate the effect the thyristors would have on the
conversion.
DC-AC Inverter
After transmission, the DC waveform needs to be inverted back into a 3-phase AC signal so that
it can be used within the local infrastructure. This voltage will usually be stepped down using
transformers. The DC waveform needs to be oscillated as well as phase shifted in order to yield three
sinusoidal signals, each 120° apart from each other.
Our approach to this problem involved using six MOSFETs (three N-channel and three PChannel). Initially, insulated-gate bipolar transistors (IGBTs) were going to be used. However, it was
discovered that, due to non-idealities, the gates of these transistors were not truly "insulated".
Therefore, the six MOSFETs were used instead. The design of the inverter can be seen in Figure 7.
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Figure 7: Inverter Circuit
All MOSFETs received a duty ratio of 33% (to prevent shorting) at 60Hz. The MOSFETs, however,
were all pulse width modulated at different phases. The top three MOSFETs (P-channel) were all set
120° apart from each other. The three bottom MOSFETs (N-channel) were each set 180° apart from its
corresponding-phase P-channel MOSFET. This phasing sequence can be seen in Figure 8.
Figure 8: Phasing of PWMs
Each phase constitutes one vertical column of MOSFETs. However, in order to get the proper
phasing, one phase must be referenced to that of another phase. Therefore, by taking the mid-point of
one phase in reference to the midpoint of another phase, a phase voltage could be measured. This
waveform was not expected to be sinusoidal, but instead pseudo-sinusoidal. Each would appear to be a
sinusoid in the form of a stepping waveform as shown in Figure9. Therefore, the lower section of the
circuit containing the inductor and capacitor constitutes a LC low-pass filter. In North America, the
standard AC frequency used is 60Hz. Therefore, the DC signal needed to be oscillated back into a 60Hz
waveform so that it could be utilized in the modern infrastructure.
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Figure 9: Pseudo-Sinusoidal Signal
In order to properly oscillate into 60Hz, two things needed to occur. First, the PWM signals
needed to be created properly at 60Hz. To do so, a timer was created so that every 60°, one MOSFET
would turn on and another one would turn off. This 60° translates to 2.77ms for a 60Hz waveform as
the period for a 60Hz oscillation is 1/60Hz or 16.66ms. For 60° (or 1/6 of this period), it would
calculated out to be 2.77ms per 60° switch.
The second important trait in properly oscillating at 60Hz is to properly filter the pseudosinusoidal waveform. Simply measuring the phase to phase voltages without filtering yields a sinusoid in
the form of continuous stepping. In order to filter it properly, a low-pass LC circuit was created to filter
out harmonics higher than those required. For this system, anything above 60Hz are unnecessary
harmonics. This corner frequency (60Hz) could be used to set the inductance values capacitance values
to those necessary to filter out any frequency greater that 60Hz. Due to component limitations, an
inductance of 39mH was used and with a capacitance of 60uF. Using Equation 1, this comes to a corner
frequency of 104Hz. Therefore, it should be expected that slight harmonics above 60Hz are seen in the
output waveform as shown in Figure 10.
Equation 1: Corner Frequency
Figure 10: Smoothed Output Waveform with Harmonics
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IV. Considerations
Economic Concerns
Unfortunately, if DC transmission lines were cheaper than AC systems, they'd be flooding our
infrastructure in an attempt to save money. However, this is not necessarily the case. The real issue
with DC transmission is in the conversion between both AC and DC through rectification and inversion.
This is due to the large cost of installation and operation of the conversion stations [2]. AC stations are
much cheaper to implement and are therefore often times more suitable. However, AC systems are
much more expensive to line due to numerous factors when compared to DC systems.
Additional costs in AC systems include the fact that AC systems require three times as many
conductors as compared to a DC system. When running a three phase system, the lines will typically be
placed in a double AC configuration. Therefore, three conductors are needed per 3-phase system, and
with two AC systems, this brings the number of conductors up to six. Typically, a shielding wire will also
be used and occasionally a neutral return. This brings the total conductor count for an AC system up to
seven or eight conductors which is vastly greater than the two required for a DC system [2]. Therefore,
as the length of transmission rises, AC transmission becomes less of an economic feasibility.
In addition, more power losses can be found in AC systems due to the skin effect. This
phenomenon only affects AC systems and relates to the waveform of alternating current. Therefore,
most of the current that flows through an AC line will flow in the outer 10% of the line. This leads to a
much greater power loss due to a loss in usable conductor area. In DC lines, the current density is
distributed evenly throughout the conductor, and thus less power loss is seen [2].
AC systems also require a larger right-of-way (ROW). This is the space around the utility pole
that must be kept free of natural growth and buildings. Due to the larger number of conductors and the
larger distance these lines must be separated from each other, the ROW of an AC system becomes much
larger than that of a DC system. This leads to added costs of clearing way for AC utility lines to be
installed, as well as the higher cost of installing larger utility poles due to the necessary separation gap
between conductors [2]. This smaller ROW in a DC system can be seen in Figure XXX below.
Figure 11: AC (left) vs. DC (right) ROW Comparison [2]
With these considerations in mind, there comes a transmission distances where DC becomes
more economically advantageous and should be installed over an AC system which is typically called a
break-even point of break-even distance [10]. Despite the high initial cost of DC conversion stations, the
low cost of actual transmittance brings DC to an economic level where it could be installed given a long
15
enough transmission distance. This break-even distance is typically for distances greater than 500 miles
or 800 kilometers [10]. The general trend for the installation of a DC line versus an AC line can be seen
in Figure XXX.
Figure 12: Break-Even Distance (Point) [10]
Environmental Concerns
As previously mentioned, DC lines have a much smaller ROW. This leads to less destruction of
natural growth that could change an ecosystem. It is also important to look at the electromagnetic
interference (EMI) that AC lines emit. This EMI can be very dangerous to life living around these lines,
and must always be considered a factor when deciding where to build AC transmission lines. The
magnetic field of AC lines is much higher than that of DC lines, and thus must become a factor in
determining which type of line should be installed [11]. Figure XXX gives a graphical representation of
the lower level of magnetic field generated in a DC transmission line.
Figure 13: Magnetic Field in a DC Line [11]
16
It is also important to note the smaller amount of aluminum needed for building the DC utility
poles as compared to AC utility poles as well as the larger amount of conductor metal required for a
double AC transmission system as compared to DC. Both of these factors become important when
analyzing the small amount of natural resources we have here on Earth.
DC transmission lines are also typically used with renewable energy sources. This is true due to
the fact that the sources of renewable energy are often times very distant from the locations that
require large amounts of power. Therefore, DC transmission will always be associated with renewable
energy.
Sustainability Concerns
Unfortunately, DC transmission lines are subject to more maintenance to ensure it is working
properly [2]. Therefore, DC systems must continuously be monitored to ensure safety and reliability in
order to continuously operate.
DC lines, however, can be used in under-water locations without the worry of harming the sea
life already living there. Due to the lower amount of EMI and the lack of having to charge to line
capacitance up every cycle, DC transmission makes this under-water transmission much more feasible
[10].
Again, it is important to note that DC lines will always be associated with renewable energy, as
this type of energy is often harvested at locations that are very distant from heavy load centers. This
means, with a large distance, a DC would most likely be built to transfer this energy, since AC
transmission is much more expensive for longer transmissions.
Manufacturability Concerns
As noted before, DC transmission requires a much lower number of conductors. Also, the utility
pole size is greatly reduced in a DC system, thus less manufactured metal is needed. This means a
lighter weight for transportation is required as well as a smaller utility line to install in a similar location.
Therefore, it is much cheaper and quicker to manufacture materials for DC transmission than it is for AC
transmission.
Due to the smaller ROW, the reduced height and width of the utility poles, as well as the lighter
weight, DC transmission utility poles are much easier to install and can often times be set up much more
quickly. Less work is needed to clear the area of natural growth, or any obstruction blocking the path of
the line. All of this leads to a much easier manufacturability, as well as ease of installation.
However, added manufacturing comes in the construction of conversion stations. These
locations are often very large and require a lot of specific mechanics that need to be custom built. The
time to install these conversion stations can sometimes trump the added ease of installing the utility
poles and lines.
17
Health and Safety Concerns
It is needless to say that DC transmission requires much more care and attention in terms of
conversion. This means that utility workers must remain close to the conversion stations at all times in
order to ensure all systems are working properly. Due to the switching in the thyristors and during
oscillation, large electromagnetic noise can be found in the converter stations [11]. This is not healthy
when exposed for prolonged periods of time. This leads to a more hazardous work environment.
However, once outside the conversion stations, the EMI emitted along the DC lines is much
smaller when compared to AC lines. This was previously discussed in the environmental concerns
sections. The lower EMI outside the conversion stations means a smaller environmental footprint for
the DC line. As long as the conversion stations are properly shielded and workers are not exposed for
prolonged periods of time, DC transmission is a healthier and safer technology to use.
Political Concerns
While political concerns are not very prevalent in DC transmission, the main political issue
centers around the sharing of power between countries. Due to the ease of using DC transmission in
under-water applications, it makes the transfer of power between countries much more plausible. The
primary reason such power transfer is ideal in DC as compared to AC is due to countries having different
operating frequencies of power transmission. In America, we operate with a frequency of 60Hz.
However, not all countries operate at this 60Hz standard. With DC transmission, this incompatibility of
frequencies does not have to be a concern. Power can be generated at whatever frequency is necessary
in one country, then converted to DC and transmitted to another country, and finally converted back to
AC at whatever frequency is necessary. This allows countries to share power without having to change
their frequency standards. This allows countries to form alliances with other countries for power, so
they may equally share each other's resources when needed. DC transmission opens up a political
boundary that allows countries to communicate and work together to find ways around energy crises
around the world. This can help stabilize power in areas of poor integrity and allow countries to come
together for a joint energy effort.
V. Results and Discussion
The first step of the circuit was to create baseline information for generation from the turbine,
seen in Table 1. These readings were taken from the turbine directly, and with no additional circuitry
attached. The measured voltages are a single phase and are reported as the peak-to-peak voltage.
18
Wind Speed
Phase Voltage(p-p)
Frequency
LOW
3.1 V
20 Hz
MEDIUM
3.9 V
27.5 Hz
HIGH
5.0 V
36 Hz
Table 1: Turbine Generation Values
The voltage generated was also not always consistent for a given wind speed. This was
attributed to the relative positioning of the turbine to the fan that was creating the wind. This created
slight fluctuations in our input which proved to be helpful and harmful. The fluctuations were helpful in
that it further simulated real-world conditions. However it was harmful in that this caused difficulties in
generating a stable baseline of operation. The values in Table 1 are the most consistently obtained data.
Immediately after generation, the signals were brought into a 3-phase rectifier. This merged the
three phases together into a single signal with an amplitude according to Equation 2. As is seen, the
voltages from each of the three phases are not simply added together, but instead are multiplied and
the square root is taken.
Vo = √3 * Vphase
Equation 2: Phase to Rectified Voltage
The change brought by the rectification can be seen in Table 2.
Wind Speed
Rectified Voltage
LOW
6.4 V
MEDIUM
8.0 V
HIGH
11.4 V
Table 2: Rectified Voltages
With the addition of a smoothing capacitor directly after the rectification, the rectified voltages
were very stable, and easily read. This allowed the Arduino to take a very clean reading of that rectified
voltage. As was stated in the “AC-DC Rectifier” section, the Arduino was used first to generate a PWM
signal that would drive a buck converter circuit. This PWM signal would determine the amount of the
input voltage that was passed through to the buck converter, and thus transmitted. With a low duty
ratio, the buck converter would pass a lower voltage, and with a high duty ratio, the buck converter
would pass almost the entire input voltage. By measuring this input voltage, the Arduino was able to
generate the proper duty ratio needed to keep the output voltage constant. Since the Arduino had a
built in Analog-to-Digital converter, the input signal would be turned into a integer value between 0 and
1023 corresponding to 0 and 5 volts respectively. This also meant that the input voltage read from the
rectification had to be lowered down to a maximum of 5 volts. This was achieved by using a voltage
divider to lower the input signal by dividing by a factor of 2.5. This yielded the input to the Arduino as is
shown in Table 3.
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Wind Speed
Rectified Voltage
Arduino Signal Voltage
LOW
6.4 V
2.56 V
MEDIUM
8.0 V
3.2 V
HIGH
11.4 V
4.56 V
Table 3: Arduino Input Signal Voltages
In order to generate the correct duty cycle, this had to then be transformed to fit on a scale
from 0 to 255 representing 0% and 100% respectively. The ideal duty ratios were calculated using the
medium wind speed as a baseline. This means that at a higher speed, more voltage will be generated,
and the duty ratio will go down. At a lower speed, less voltage will be generated, and was determined
to simulate a lack of sufficient power, thus no voltage is transferred to protect the system and the duty
ratio is brought down to zero. These are shown in Table 4.
Wind Speed
Duty Ratio
LOW
0
MEDIUM
1
HIGH
0.701
Table 4: Duty Ratios
To achieve this duty ratio a linear fit line was generated based on the input reading (0 to 1023)
and the required duty cycle level (0 to 255). These points and the equation generated from them are
shown in Table 5 and Table 6.
Input Values
Output Values
Wind Speed
Arduino Input
Voltage
Arduino Read
Value
PWM Value
LOW
2.56
523
0
MWDIUM
3.2
655
255
HIGH
4.56
933
179
Table 5: Point Generation Data
X
655
255
Y
933
179
Equation
f(x) = -0.273x + 433
Table 6: Duty Cycle Equation
The equation generated was not perfect, but would approximate the duty cycle needed to
within less than 1%, and thus was deemed to be an accurate enough approximation to be used.
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Given the mostly stable rectified voltage as the input, the Arduino was able to generate a PWM
signal to drive the Buck converter. Within the Buck converter though were voltage losses over
components, thus lowering the available transmission voltage. These had been evaluated to be
approximately 3 volts between the rectification and Buck converter output. These losses are shown as
part of Table 7, which details a reading of the entire transmission circuitry.
Wind Speed
Rectified Voltage
Possible
Transmittable
Voltage
Ideal Transmission
Voltage
Experimental
Transmission
Voltage
LOW
6.0
0
0
0
MEDIUM
8.4
5.3
5.3
4.9
HIGH
10.7
7.6
5.3
5.5
Table 7: Transmission Circuitry Values
As is shown in Table 7, the experimentally transmitted voltage did follow the expected trend of
passing through almost the entire voltage generated from a medium speed, and also passed through
only a percentage of the voltage generated at a high speed. These numbers were not exact as
compared to the ideal transmission voltages, but were within a 10% fluctuation at all times. The
experimental readings can be seen in Figure 14, Figure 15, and Figure 16 below.
Figure 14: Low Wind Speed Rectification (1) and Transmission (4)
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Figure 15: Medium Wind Speed Rectification (1), PWM (2), and Transmission (4)
Figure 16: High Wind Speed Rectification (1), PWM (2), and Transmission (4)
The transmitted voltage as read from Figures 14, 15, and 16 shows that the duty cycle generated
was indeed working as expected as the voltage level altered by only 0.06 volts between the medium and
high wind speeds while the rectified voltage increased greatly. The transmitted voltage was slightly less
than the calculated ideal of 5.3 volts, but was accepted given slight variations in generation as well as
from losses in components.
After transmission, the transmitted voltage is then inverted back into an AC waveform. As was
explained previously in “AC – DC Rectifier”, the Arduino would generate six separate PWM signals being
generated at 60 Hz. These were done using a simple timer and counter to generate when the MOSFETs
would be switched on and off by using the counter to simulate a finite state machine. Depending on
where the counter is at, a specific set of two of the MOSFETs would toggle which is on and which is off
every 2.77ms. This would ensure there would be a controlled frequency of oscillation being created at
approximately 60 Hz. As stated previously, the generated oscillation needed to be smoothed to be a
useable waveform. The output of this smoothing can be seen in Figure 17.
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Figure 17: Inversion Output
As is shown in Figure 14, the resulting waveforms are oscillating at 58.94 Hz, which is just under
the desired 60 Hz. Likewise, the phase shifting yields an almost perfect 120º separation between each
generated waveform. It can also be seen that the waveforms are not perfectly sinusoidal. This is
attributed to the LC low pass filter's corner frequency. Due to component availability, the corner
frequency was experimentally set at 104 Hz. This means that there are some higher harmonics that are
still present after filtration. These higher harmonics distorted the waveform to have a distinct triangular
aspect still present. This distortion is still minimal, and would not affect the function of a load
connected to it.
VI. Conclusions
Power is essential to our everyday lives. Understanding how that power is generated and
transferred throughout the world can help us understand how to improve it. Though this was a low
level model of a DC power transmission system, the concepts used are still relevant regardless of the
size of the system. The system designed in this project was created in a way that every part would
mimic that of a high power system. Under testing, this was shown to be true for each section of our
design. The turbine was generating three pure sinusoidal waveforms at 120° phase separation from
each other. The three-phase rectification yielded a single almost DC waveform at the expected voltage
given a wind speed. The Arduino generated an easily controlled and stable PWM signal that controlled
the level of attenuation of the Buck converter accordingly, thus providing a stable transmission voltage.
The inversion circuitry would then take the transmitted voltage level, and would generate three
sinusoidal waveforms at the expected frequency and with the expected phase shifting as well.
Limitations in the individual components, however, altered the functionality of model as a
whole. As was just stated, it can be shown that every component worked properly, but would not work
properly together. The greatest limitation that could be found was within the turbine. The way the
turbine was constructed created a large internal impedance, which in turn would limit the amount of
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current that could be generated from it. The voltage levels that were generated were easily usable,
however the high internal impedance would overpower the external impedance of the rest of the
circuitry, and thus the current provided to it would not be enough to overcome the non-idealities of that
external circuitry.
The non-idealities of the external circuitry also led to many losses not accounted for through
theory or simulation. Most notably in this were the inductors that were used. In order to properly
ensure the Buck converter worked as it should, as well as create a corner frequency in the LC low pass of
the inverting circuit, the inductors that were used needed to be a large value. Due to limitations of
availability, the inductors also had a large DC resistance. The large DC resistance of the inductors, as
well as losses to properly bias the diodes in order for them to conduct added to unexpected losses, and
created an even larger strain on the turbine. For this reason, we were not able to transmit the
generated voltage across to the inverter circuitry. The large number of inductors created too much of a
loss in order to operate. The turbine could not generate enough power to overcome this, and thus the
model was unusable as one complete system. Instead a separate voltage source was used to supply the
inversion circuit with an input, matching what the turbine would be transmitting but able to provide a
larger current to overcome any biasing and losses encountered.
Finally, since the turbine was generating an AC waveform, there was not a well defined ground
potential within the system. This made it difficult to accurately measure various voltage levels
throughout any of the circuitry. This was most notably prevalent for the input signal to the Arduino.
The formula used to calculate the proper duty ratio relied on the input voltage level to be within 0 to 5
volts of the Arduino's own ground potential. This meant that the Arduino had to be bound in some way
to the same ground potential as the generated voltage was. To do this, a DC power supply was used to
take the Buck converter ground, and generate a voltage higher than that to power the Arduino. In this
way, the Arduino was then grounded to the same voltage as the rectified voltage, and a more proper
reading could be made. Creating a common ground potential was a problem throughout the circuitry
though, and was even created by trying to use the same ground reference across two different
oscilloscopes. When both oscilloscopes were measuring with the ground wire attached, the readings
from each one would be altered, thus creating great difficulty to ensure proper function across even
short distances.
Given the chance to create this project over again, there are a few key points that would be
changed. Firstly, the turbine used proved to be the greatest source of non-ideal function. The internal
impedance of it was too large, and as such it was not able to provide the power needed to properly
operate the circuitry as expected. A more efficient turbine would be needed to effectively create a
working model. Second, the components that were found to have high losses would also be replaced to
improve efficiency. The inductors were easily the source of greatest loss, and could be replaced with
ones that did not have as high of an internal DC resistance. Replacing the inductors alone would greatly
reduce the losses seen. Likewise, the diodes used were of average quality due to high availability.
Replacing the diodes with higher efficiency ones would reduce the voltage level requirements of the
system, and thus reduce the overall losses seen. Third, the capacitor banks used for the inversion could
also be improved. Due to the function of the capacitors, electrolytic capacitors could not be used. This
required a large number of capacitors to achieve a capacitance level large enough to create the correct
corner frequency of the LC low passing. More specialized capacitors would be able to give us the value
that would create a proper corner frequency. Lastly, better electrical isolation throughout the circuit
would aid in creating precise measurements. The Arduino in particular relies on a precise voltage
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measurement, and by having irregular ground potentials throughout the circuitry, those readings could
be thrown off.
Power is all around us, and the systems that generate, control, transmit, and distribute that
power will continuously be changing as the world's power use continues to grow power all the time.
Understanding the systems used to create this infrastructure now can help to continue the
improvement needed to provide to that power use. The small signal model designed in this project has
provided a deeper understanding of all the challenges needed to overcome as well as provided insight as
how to improve upon the design.
25
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