Contactless Power Supply System for
Transmission Line Inspection Robots
João Pedro Trindade Caxias Ferreira
Dissertação para obtenção do Grau de Mestre em
Engenharia Electrotécnica e de Computadores
Júri
Presidente: Prof. Paulo José da Costa Branco
Orientador: Prof. José Fernando Alves da Silva
Co-orientador: Prof. João Silva Sequeira
Vogal: Prof. João Carlos Pires da Palma
Outubro de 2010
5 Abstract
The power lines have today an important role in the electric power grid. Transporting
energy in the best conditions is a goal of all electricity companies in the world.
The premise of this work is to develop an innovative power system for use in a robot, with a
nominal power of 800 W. The main purpose of this robot is inspect the high voltage power lines.
The purpose of the power supply system is to provide a stable DC voltage to the robot so that it
is energetically self-sustaining. This is obtained from the magnetic energy surrounding a power
line, using a current transformer, a system for monitoring the output voltage in conjunction with
an internal control system of chain, and an AC / DC converter in full-wave bridge.
When simulated, this method achieves the objectives of the project. The results prove a
good regulation of output voltage and small disturbances in the power line. The yield of the
circuit is highly dependent on the amplitude of the current line being above 90% for most of the
amplitudes considered.
i
5 Resumo
As linhas de alta tensão têm nos dias de hoje um papel importante na rede de energia
eléctrica. Fazer chegar a energia a todos nas melhores condições é uma das metas de todas
as companhias de electricidade em todo o mundo.
A premissa do presente trabalho visa desenvolver um sistema de alimentação inovador
para ser usado num robô, com uma potência nominal de 800 W. A principal finalidade deste
robô é vir a inspecionar as linhas eléctricas de média e alta tensão. O objectivo do sistema de
alimentação é de proporcionar uma tensão DC estável ao robô para que este seja
energicamente auto-sustentável. Esta é obtida a partir da energia magnética envolvente a uma
linha de alta tensão, com recurso a um transformador de corrente, a um sistema de controlo da
tensão de saída conjugado com um sistema de controlo interno de corrente, e a um conversor
AC/DC em ponte de onda completa.
Quando simulado, este método atinge os objectivos do projeto. Os resultados provam uma
boa regulação da tensão de saída e pequenas perturbações na linha de alta tensão. O
rendimento do circuito é altamente dependente da amplitude da linha actual sendo acima dos
90% para a maioria das amplitudes consideradas.
ii
5 Acknowledgments
I would like to express my heartfelt gratitude to my project coordinator, José Fernando.
Silva, for his constant guidance and support through all this work. His insightful academic
advice is very much appreciated. I was very fortunate to have worked with him over all these
months.
I would like to thanks my project co-ordinator, João Sequeira, for his implication to create a
so attractive topic as a final thesis, and to do all the research that becomes it possible.
My thanks are also extended to my fellow friends who along my studies I could exchange
so long gratitude and good moments. With their support was not possible to get so far.
I am deeply grateful to my parents and my brother, as all the other family members for their
endless love, support, and encouragement in all my endeavours. Without their sacrifice and
love, I could not reach so interesting and motivating course.
iii
Table of Contents
1
INTRODUCTION .............................................................................................................. 1
1.1
MOTIVATION ................................................................................................................... 3
1.2
OBJECTIVE ..................................................................................................................... 3
1.3
W ALKTHROUGH .............................................................................................................. 4
2
POWER SUPPLY CONFIGURATION ............................................................................. 5
2.1
CLAMP-ON TRANSFORMER (COT) ................................................................................... 6
2.2
CIRCUIT COMPONENTS SIZING ....................................................................................... 11
2.2.1
Full-Bridge inverter semiconductors characteristics ........................................... 11
2.2.2
DC output capacitor ............................................................................................ 12
2.2.3
AC input low pass 3 order filter ........................................................................ 14
2.2.4
Resonant second harmonic band-stop filter ....................................................... 16
2.3
RECTIFIER CONTROLLER ............................................................................................... 17
2.3.1
Full-Bridge inverter PWM generator ................................................................... 17
2.3.2
Control of the DC Output Voltage ....................................................................... 19
3
4
rd
SIMULATIONS ............................................................................................................... 22
3.1
OUTPUT VOLTAGE IN STEADY STATE FOR DIFFERENT LINE CURRENTS .............................. 23
3.2
START UP TRANSIENT .................................................................................................... 24
3.2.1
Study of a
initial current on the high voltage power line .......................... 24
3.2.2
Study of a
initial current on the high voltage power line ........................ 25
3.3
CURRENT STEP RESPONSE ............................................................................................ 26
3.4
SECONDARY TRANSFORMER VOLTAGE IN STEADY STATE FOR DIFFERENT LINE CURRENTS . 27
3.5
PWM VOLTAGE AND 3 ORDER FILTER SIMULATION ....................................................... 27
3.6
TRANSFORMER PARAMETERS SIMULATION ...................................................................... 28
RD
3.6.1
Open-circuit test ................................................................................................. 28
3.6.2
Short-circuit test .................................................................................................. 29
3.7
PRIMARY TRANSFORMER VOLTAGE AND CURRENT WHEN HAPPENS A STEP ....................... 31
3.8
RESULTS DISCUSSION ................................................................................................... 31
3.9
MODEL EFFICIENCY ....................................................................................................... 32
CONCLUSIONS ............................................................................................................. 33
iv
Table of Figures
Figure 1 - RIOL virtual prototype model [2] ................................................................................... 2
Figure 2 - Power supply system model ......................................................................................... 6
Figure 3 - COT lateral cut to describe core magnetization ........................................................... 6
Figure 4 – COT upper view to describe secondary coil induction ................................................. 7
Figure 5 - Hysteresis loop curve .................................................................................................... 8
Figure 6 - Clamp-on current transformer equivalent circuit ........................................................... 8
rd
Figure 7 – Low pass 3 order filter circuit ................................................................................... 14
rd
Figure 8 - Bode diagram of AC input low pass 3 order filter ..................................................... 15
Figure 9 – Output filters solution ................................................................................................. 16
Figure 10 – Full-bridge inverter PWM generator ......................................................................... 19
Figure 11 - Ouput voltage control block diagram ........................................................................ 20
Figure 12 - Linear output voltage control block diagram ............................................................. 20
Figure 13 - Output voltage
(upper graph) and current
(lower graph) in stready state for
100 A ................................................................................................................................... 23
Figure 14 - Output voltage
(upper graph) and current
(lower graph) in stready state for
500 A ................................................................................................................................... 23
Figure 15 - Output voltage
(upper graph) and current
(lower graph) in stready state for
1000 A ................................................................................................................................. 24
Figure 16 - Start up transient load voltage
(upper graph) and load current
(lower
graph) for 100 A................................................................................................................... 24
Figure 17 - Start up transient secondary transformer voltage
(upper graph), PWM voltage
(center graph) and secondary transformer current
(lower graph) for 100 A ...... 25
Figure 18 - - Start up transient load voltage
(upper graph) and load current
(lower
graph) for 1000 A................................................................................................................. 25
Figure 19 - Start up transient secondary transformer voltage
(upper graph), PWM voltage
(center graph) and secondary transformer current
(lower graph) for 1000 A .... 26
Figure 20 - Load voltage (upper graph) and current start-up transient (lower graph) and
response to AC line current from 100 A to 1000 A .............................................................. 26
Figure 21 - Secondary transformer voltage
in steady state for 100 A ................................... 27
v
Figure 22 - Secondary transformer voltage
in steady state for 500 A ................................... 27
Figure 23 - PWM voltage ............................................................................................................. 28
Figure 24 - Secondary transformer voltage
(upper graph) and current
(lower graph) ...... 28
Figure 25 - Simulink/SimPowerSystems implementation of the open-circuit test ....................... 28
Figure 26 - Simulink/SimPowerSystems implementation of the open-circuit test ....................... 30
Figure 27 - Primary transformer voltage
(upper graph) and current
vi
(lower graph) ........... 31
List of Tables
Table 1 – Transformer characteristics ................................................................................................... 11
Table 2 – Input current amplitude simulation steps ............................................................................... 22
vii
List of Acronyms
IST
Instituto Superior Técnico
RIOL
Robot Inspection Over Power Lines
COT
Clamp-on Transformer
PVC
Polyvinyl chloride
dof
Degrees of freedom
MOSFET
Metal Oxide Semiconductor Field Effect Transistor
PWM
Pulse Width Modulated
PI
Proportional integral controller
DC
Direct current
AC
Alternating current
RMS
Root mean square
LiPo
Lithium ion polymer
viii
List of Symbols
Time variant Thévenin equivalent
Transformer nominal power
Current on the primary transformer side
RMS value of
Voltage on the primary transformer side
RMS value of
Current on the secondary transformer side
RMS value of
Voltage on the secondary transformer side
RMS value of
Transformer turns ratio
Primary, secondary transformer winding losses
Primary, secondary transformer inductances
Transformer magnetizing inductance
Transformer magnetizing resistance
Primary transformer impedance
Secondary transformer impedance
Transformer power losses
Instantaneous rectifier input power
Instantaneous rectifier output power
Arms transistors state functions
MOSFET semiconductors of full-bridge
Output filter capacitance
Rectifier input voltage
Rectifier input voltage average
PWM wave period
Output voltage (applied on the load)
DC component of
Peak voltage ripple
Rectifier ouput current component (applied on the load)
DC component of
ix
Current at robot input
3rd order filter components
Thévenin equivalent resistor (seen from the transformer)
Voltage difference between output voltage and reference
one
Product between efficiency and the power factor
Rectifier DC gain
Feedback gain
Efficiency
Ouput voltage error margin
Damping factor
Controller delay
PI controller pole
PI controller zero
Model nominal frequency
RMS voltage when secondary transformer has no load
RMS current when secondary transformer has no load
Power on the primary transformer under no load conditions
RMS voltage when secondary transformer is short circuited
RMS current when secondary transformer is short circuited
Power on the secondary transformer when short circuited
x
Chapter 1
1 Introduction
The electric power transportation system uses very high voltage overhead lines. For reliability,
these lines must be structurally and electrically inspected to detect ageing and prevent short-circuits
and other malfunctions. To ensure continuity of service, inspections must be carried out while the
lines are energized using helicopters and expert workers and methods, besides the high costs and
precision required. Costs can be lowered using dedicated autonomous robots. These robots need to
gather power from the overhead high voltage lines to ensure high autonomy, not possible to achieve
using the robot onboard batteries.
This work aims at developing an energy harvesting system to use with a RIOL [1], for inspection
of high voltage overhead power lines. The power supply operating principle is based on harvesting
the magnetic energy around the power supply lines [3], by clamping a transformer around the line [6]
to produce power enough for the robot.
The robot described is a 5 degrees-of-freedom articulated multi-body with three claws used for
cable grasping. The body structure is made mainly of PVC and link couplings of light metal alloys. The
robot is able to overcome support towers and most of the obstacles arising in power lines, e.g. the
spherical aviation markers. The energy harvesting transformers are to be mounted at the claws.
1
Figure 1 - RIOL virtual prototype model [2]
Two types of locomotion gaits are used. In absence of obstacles the motion is generated by
traction wheels located in the grasping claws. Under this gait the robot essentially becomes a
suspended cart when moving along obstacle free catenaries between support towers. In this case the
clamp on transformer surrounds the line and the system operates normally.
The second gait is suitable to overcome obstacles. It is inspired by the concertina (contractanchor-extend) motion of some invertebrates. Each of the three claws can (i) grabs the cable tightly;
(ii) grabs the cable loosely, allowing the claw to slide along; (iii) disengage from the line. To overcome
an obstacle the robot disengages each of the claws in sequence such that there are always two claws
grabbing the cable, thus ensuring static stability. Under this gait, the clamp transformer opens so that
the claws can disengage from the line. [1][2]
The robot is equipped with a lithium ion polymer (LiPo) battery pack that provides energy while
overcoming an obstacle and crossing a support tower. When moving along catenaries, and in the
absence of obstacles, the supply system feeds the robot and can also recharge the battery pack.
It is considered that robot operates on power cables carrying currents from nearly
roughly
to
. When transmission current drops below a certain limit the robot hibernates and a
signal is sent to the operation centre, and when the current exceeds the maximum the clamp-on
transformer is opened to prevent damage to the robot.
2
1.1 Motivation
Nowadays the procedure to detect imperfections on the power lines is subject of the experience
of one technician who inspects those using helicopters. Since the beginnings of 90's researchers are
studying solutions for new approaches to this problem. In Sawada at 1991, the first model is reported.
On the following years some others projects were published later e.g. Peungsungwal in 2000. All
these projects had limitations connected with power autonomy.
Full autonomy is the key factor when assessing the economical advantages in use robots with
such functions. Monitoring the power lines network during long periods and long distances will permit
to detect failures easily and this way increase the power network quality, by reporting on real time the
line problems. A 100 % autonomous robot, 80 % of operation time powered by a robot external
source, will permit it to operate without any interruptions for recharging or refuelling operation breaks.
The only times without be in operation will happen for check up the robot components.
Following the work already developed by Luis Tavares and João Sequeira, their suggestion for a
future work the development of a power source based on the magnetic power surrounding the
transmission line that supports the robot. The present work main goal is to obtain the robot
autonomous power supply. Full autonomy doesn’t mean full power dependence from the power
source developed here. Batteries should still be used to pass line obstacles, or for any other
emergency situation. [1]
1.2 Objective
The objective of this research work is to study a power supply solution consisting on a COT and a
full MOSFET bridge rectifier. In this work is studied the clamp-on transformer (COT), together with the
MOSFET bridge rectifier, and implemented a control system for the rectifier. The control system
applies an output voltage controller with an inner loop input current controller.
Well known unity power factor rectifiers cannot be used in this case, because if the clamp-on
transformer was ideal, it would operate as a current transformer and not as a voltage source (as
usually required by these rectifiers). Furthermore, a current mode controlled unity power factor
rectifier is not suited for this application due to possible iron saturation arising from the DC bias of the
AC current introduced by the fast dynamic action of the DC voltage controller, as revealed in
preliminary approaches.
The control is done by using a pulse width modulation (PWM) signal and devised to obtain a
voltage proportional to the secondary current so the power converter and the load are seen as a
resistance at COT secondary terminals. Since the primary current depends on the high voltage line
transmitted powers, this resistance must vary in order to provide the robot needed power, despite the
tenfold line current variation.
3
Using this control approach is expected a higher efficiency, comparing with other topologies, a
model with line current variation control and a power factor close to unit.
1.3 Walkthrough
This thesis is organized as follows. On Chapter 2 is explained the converter, transformer and
controller modules. This knowledge leads us to develop the new power converter model to use on the
robot. It starts with the clamp on transformer study. This study regards core magnetization, and
parameters dimension. Inside the same chapter is dimensioned the full-bridge inverter
semiconductors, and the filters components used. To end up with this chapter is studied in detail the
rectifier controller, considering just rectifier dynamics.
In Chapter 3, is applied to show you the results obtained by model simulation, and in the end of
this chapter the simulation results are discussed and new philosophies for the job model are
presented. To conclude this work, Chapter 4 has of work made summary and directions for future
researches.
4
Chapter 2
2 Power Supply Configuration
A power supply must provide power with the characteristics required by the load from a primary
power source. When the load requires DC, and the primary power source is AC, the power supply to
use is an AC/DC converter, also called a rectifier.
Figure 2 shows the design of the proposed power supply system. The maximum power absorbed
by the robot (800 W) is much lower than the high voltage line transmitted power. With this in mind, the
current in the high voltage line is almost not disturbed by the robot power supply and can be assumed
to be a sinusoidal current source
rd
with a frequency of 50 Hz. Through a low pass 3 order filter to
reduce high frequency switching harmonics, the clamp-on transformer feeds a power MOSFET fullbridge converter, the DC filter
and the load, robot, ant the battery charger.
The MOSFET bridge is operated as a PWM converter and controlled to convert to DC the AC
current of the transformer secondary winding. The PWM is devised to obtain a
proportional to the secondary current
voltage
so the power converter and the load are seen as a resistance.
Since the primary current depends on the high voltage lines transmitted power, this resistance
must vary (slowly) in order to provide the robot needed power, despite the tenfold line current
variation.
5
Figure 2 - Power supply system model
2.1 Clamp-On Transformer (COT)
To permit the transformer clamping around a power line, a COT is used. This device has two
jaws that open when obstacles appear on the power line, e.g. aviation markers. This option permits to
use the magnetic energy around the line without a physical contact.
A wire coil is wound round both jaws, forming the secondary winding, and the conductor clamped
by the transformer forms the one turn primary. An energised power line induces on the secondary coil
a sinusoidal voltage which can originate a current through the full bridge converter. The connected
filters and the AC/DC converter, work as non-linear load at the transformer terminals.
The clamp-on transformer can be seen, on a first approach, as a linear current transformer. On
the primary is imposed a sinusoidal current,
.
Figure 3 - COT lateral cut to describe core magnetization
6
The power line current density
is obtained by
(1)
where L is the power line section. The magnetic field surrounding the line can be obtained by
applying the Ampere Law
(2)
where surface S enclosed by the curve C means the transformer core. The magnetic flux on the
core is obtained by
(3)
where R is the side surface.
Figure 4 – COT upper view to describe secondary coil induction
The voltage induced across the secondary coil,
may be calculated from Faraday's Law
(4)
When the COT has a load connected on the secondary terminals, a linear ratio sinusoidal current
is obtained on the secondary output,
.
(5)
where
is the ratio between the number of turns in the primary and the secondary coils.
When the load attached to the transformer is not linear, it will not work on linear region. This
situation can saturate the transformer.
7
Saturatio
n
Linear
Saturatio
Region
Figure 5 - Hysteresis loop curve
n
When transformer is surrounding by an energised high voltage AC power line, the COT primary
current
is
(6)
where
is the primary current amplitude, and
is
rad/s.
In steady state the transformer losses are easily explained with the help of equivalent circuit,
show in Figure 6, where
and
are primary and secondary winding resistances;
primary and secondary leakage inductances;
resistance
and
are
is the magnetizing inductance in parallel with the
. The transformer will operate for a low frequency of
. For such frequency the stray
capacitance of windings is negligible.
Figure 6 - Clamp-on current transformer equivalent circuit
When the leakage flux increases, the linkage flux and, consequently, the secondary winding
inducted voltage decreases. Moreover, the leakage inductances increase, causing the secondary
current to decrease and the algebraic value of the ratio error to decrease [6]. Between jaws an air gap
exists when it closes around the line and it must be taken in consideration on the flux leakage
prediction.
8
Power losses in the windings, represented on the schematic as
and
, are the main factors
causing the transformer heating. The power losses vary with the square of the RMS current on its
terminals
(7)
The COT nominal power needs to be adjusted depending on the load attached. Considering that
the maximum load power is around 800 W [1] and a safety margin of 25 % over-dimensioned, a 1 kW
nominal power transformer is used and sized for this project.
Regarding the fact that the primary current
power
is imposed by the power line, and the nominal
is established by design, the RMS value of the primary side voltage
, considering near
unitary power factor and efficiency, can be defined as
(8)
In this case it is relevant to know the maximum value that
can be measured up. It happens
when the power transmitted is the smallest possible for robot operation (
current line
is
. When this situation occurs a
), or it means when
primary COT voltage or higher is expected.
Considering this voltage applied on the line, it is predicted that the robot will almost not affect the line
power losses on the line stretch of its localization.
To deliver the predicted power to the load, is necessary to define the COT turns ratio
Considering a voltage drop on the full-bridge rectifier semiconductors of
.
, the RMS secondary
voltage is given for
(9)
Using the values obtained for
and
the ratio between turns is
(10)
The equivalent circuit present at Figure 6 is used to facilitate the computation of various operating
quantities such as losses, voltage regulation, and efficiency. The parameters of the equivalent circuit
can be obtained from the open-circuit and short-circuit tests of a real transformer.
The open-circuit test is performed in order to determine exciting branch parameters of the
equivalent circuit, the no-load loss, the no-load exciting current, and the no-load power factor. While
secondary winding is open circuited, a rated voltage is applied to the primary winding, and the input
voltage,
; input current,
; and input real power,
, to the transformer should be measured.
9
The short-circuit test is conducted by short-circuiting the secondary terminal of the transformer,
and applying a reduced voltage to the primary side, such that the rated current flows through the
windings. The input voltage,
; input current,
; and input real power,
, to the transformer should
be measured.
For this project these tests are simulated and results are compared with theoretical values at
Chapter 3.6.
Theoretical values are idealized for a common current transformer. Regarding that on this
transformers the biggest voltage drop happens on the magnetization branch, the primary losses are
consider to be a small part of the total voltage drop. For this circuit it is considered a 0.5 % of the total
voltage drop.
Using the following expression to obtain the impedance of the primary side
(11)
the values for primary winding losses
and primary leakage inductance
can be quantified as
(12)
(13)
Core magnetization current and magnetic reluctance caused by the air gap of the core material
should be minimized. Consider the maximum value for voltage drop when the secondary circuit is
interrupted (10 V), a factor of 1.5 permit to define the value for magnetizing inductance
(14)
Considering that 1% of efficiency losses due to core losses, the equivalent resistance
can be
calculated as
With a similar approach to the transformer secondary, the theoretical values are idealized for
secondary losses of
of the total voltage drop. Using the following expression to obtain the
impedance of the secondary side
(15)
where a transformer efficiency of
was considered.
10
The values for secondary winding losses
and secondary leakage inductance
can be
quantified as
(16)
(17)
The values obtained are resumed at Table 1. Regardless the voltage level, the transformer
characteristics are present on per-unit system at Table 2.
Table 1 – Transformer characteristics
In per-unit
system
0.160 pu
0.082 pu
100.0 pu
0.869 pu
0.097 pu
1.500 pu
2.2 Circuit components sizing
2.2.1
Full-Bridge inverter semiconductors characteristics
The power semiconductors used should support drain-source voltages
amplitude as load voltage
with the same
. The semiconductors used has to have
(18)
Regarding the circuit configuration present at Figure 2, the current in each transistor is given by
(19)
Using the average values of each expression component,
(20)
where
is the average drain current in each semiconductor .
11
Using the same expression, the maximum and RMS drain current are given by
(21)
(22)
The protection diodes should support
(23)
2.2.2
DC output capacitor
The RIOL robot needs
DC, and consumes
to
(including power needed to recharge
the batteries). In steady state, the voltage applied on the robot should have an error less than
smaller error corresponds to a bigger capacitor
with such size that will not fit on the robot. The
error measured in the voltage is due to the voltage ripple in the DC capacitor
The full bridge rectifier input current
.A
.
has a fundamental component at
and high
frequency components that arise from the semiconductors switching action. The instantaneous power
injected in the rectifier
can be obtained from
(24)
where F is the product between efficiency and the power factor. Focusing our study on the
fundamental frequency,
and
are
(25)
(26)
Neglecting the switching components, since they must be small compared to the fundamental
component [6], it equals the instantaneous output power
:
(27)
12
Applying the trigonometry relation
(28)
it is obtained
(29)
Then when resolved for
, it permits to conclude
(30)
The capacitor voltage ripple
can be obtained integrating the AC component of current
obtained at Equation 30
(31)
The peak voltage ripple must be less than VDC < 0.025 VDC as said in the beginning on this sub
chapter. The variation around the average value
can be so written as
(32)
Using Equation 30 the capacitance is obtained
(33)
When robot is operating at its maximum power, it needs a load average current
around 15 A.
The output capacitor should be dimensioned for this worst case. Applying the values to Equation 33 a
capacitance of 35 mF should be used for
.
13
2.2.3
AC input low pass 3rd order filter
To reduce the amount of voltage harmonics on the line injected by the
voltage, a filter
rd
between the transformer and the rectifier is used. A low pass 3 order filter is consider to fulfil the
premises to reduce mainly the high frequency harmonics present at
Assuming a Thévenin equivalent network resistor
.
seen from the transformer, and, as before a
close to unitary , the resistor can be dimensioned as
(34)
From Equation 43, and applying for the smallest possible current on power line, it is obtained a
Thévenin equivalent network resistor
of
.
The filter output should be a current, so an inductor (
) should be the filter component
rd
connected to the converter. Assuming it, the low pass 3 order filter represented at Figure 7 is used.
Figure 7 – Low pass 3rd order filter circuit
To design the filter components, let’s consider the
voltage transfer function
(35)
Assuming a Chebyshev approach with a pass-band ripple equal to
of at least
and cut-off frequency
times upper than the fundamental frequency, the approach equates the denominator
coefficients with the Chebyshev polynomial
(36)
14
From last equations is possible to write the following three equations
(37)
Solving it, for a
close to
the following components values are obtained
®
Using MATLAB application the Bode diagram for this filter can be obtained. Studying the result it
is observed that filter has an attenuation of
fundamental frequency
per decade. The rectifier input voltage
, or it means in the maximum around
frequency the attenuation is
.
Figure 8 - Bode diagram of AC input low pass 3rd order filter
15
has a
. For this
2.2.4
Resonant second harmonic band-stop filter
Regarding the size of the DC output capacitor obtained at Section 2.2.2, an extra filter in parallel
is dimensioned. The combination of both filters will permit to decrease
decrease the load voltage oscillation
size, or will permit to
.
For this case it is used a resonant
band-stop filter. With this filter, the load part of circuit
looks as described at Figure 11.
Resonant second harmonic
band-stop filter
if
Figure 9 – Output filters solution
These filter is resonant, and them natural frequency can be defined as
(
38)
At resonant frequency the inductive reactance magnitude equals the capacitive reactance
(39)
As the components used are not ideal, is consider an internal inductance resistance
. The
existence of this resistance is the reason why all second harmonic is not attenuated, and still a
voltage drop happens on this branch. Regarding this
(40)
For this model is consider a voltage drop
, or it means the components will be
16
2.3 Rectifier controller
The rectifier controller approach at this work considers all components ideal, as well as all the
circuit filters. This simplification is important to don’t create a higher order system more difficult to be
analysed and warranty its stability.
2.3.1
Full-Bridge inverter PWM generator
The rectifier controller emulates a slow time varying resistor
at the secondary transformer
terminals. If a simple resistive load was connected at the COT terminals, it would be working on the
linear zone. Considering the secondary winding current
as a ratio of
(Equation 5), and applying
the Ohm’s Law, the transformer should see a secondary winding voltage
(41)
in phase with the input sinusoidal current,
(42)
Considering the input low pass 3
voltage
rd
order filter (Chapter 2.2.3) as nearly ideal, the secondary
is the low frequency contents of the PWM voltage output of the full-bridge inverter.
Therefore, the PWM is devised to obtain a
average voltage,
, within a switching period
, proportional to the secondary current
(43)
A three level PWM (+1, 0, -1) to minimize voltage and current ripple will be used. When the
modulating waveform is higher that the carrier (level +1), it means system should increase output.
When it is lower than the carrier (level -1), it acts by decreasing output. When modulation waveform
equals the input signal, the system is inside the expected values, so no power should be transferred
(level 0).
(44)
17
Regarding the full bridge rectifier design, the previous expression results on
(45)
Recording that the circuit in study is a MOSFET full-bridge converter, with two arms, and each
one containing two transistors, the two switching variables
and
can be defined
(46)
Using the switching variables on Equation 42 the instantaneous value of the voltage
of the
bridge can also be written as
(47)
As said,
must in each switching period
constant at each switching period since
equals the desired
voltage, considered
is much smaller than the line period (
). Therefore,
it can be written:
(48)
Considering the voltage error as
(49)
Regarding the stability of the controller, an error
and its variation should be always negative
(50)
Considering the last equations and a sufficiently small quantity , then
Equation 51
–
18
This switching law gives the full-bridge PWM modulator (Figure 10), where the gain before the
integrator is
and helps to define the switching frequency in addition to the
value. The
switching law (Equation 47) is implemented using two hysteretic comparators with different hysteresis
widths
and
, that directly give the switching variables
and
. The switching signals for the
lower semiconductors are obtained using two inverter gates.
Figure 10 – Full-bridge inverter PWM generator
2.3.2
Control of the DC Output Voltage
The dynamics of the DC output voltage
represented by an equivalent resistor
(
can be written, assuming all the DC loads
):
(52)
This equation means that, in steady-state (
is the DC gain
, the average value of the term
of the full bridge rectifier, given by:
(53)
Considering that the full-bridge rectifier is almost conservative and the rectifier input power factor
is almost unitary, the input power
(54)
nearly equals the output power
(55)
19
Then, the DC current conversion gain can be defined as
(56)
The DC output voltage dynamics (Equation 48) can be rewritten for average values:
(57)
Considering Equation 54, the term
is
(58)
Then, the
control block diagram can be represented in Figure 11, where the action of the
controller (Equation 49) is assumed to have a delay
approximated by a first order polynomial (since
(pole in the origin and a zero at
, whose transfer function has been
is very small). A simple PI controller was chosen
), to increase speed and guarantee zero steady state error.
Figure 11 - Ouput voltage control block diagram
Linearizing around the DC operating point, the
control linear block diagram is represented in
Figure 12.
Figure 12 - Linear output voltage control block diagram
20
nd
Cancelling the load pole (
dynamics whose damping factor
) with the PI zero, the obtained system has a 2
can be used to determine the
order
value.
Therefore, the PI parameters are:
(59)
(60)
To ensure stability it is useful to consider
.
Making:


;
,
The PI gains are respectively
and
21
.
Chapter 3
3 Simulations
®
The power supply system has been modelled and simulated with MATLAB/Simulink .
The simulation values were obtained for a power transmission line with currents ranging from
to
. They include circuit analysis for steady state and for circuit answer to current steps,
and the circuit start-up is shown in detail. The increasing steps temporization is described at Table 2.
Table 2 – Input current amplitude simulation steps
Simulation time (s)
0 – 0.6
0.6 – 0.8
0.8 – 1.0
Power transmission
line current in study
100 A
200 A
400 A
22
1.0 – 1.2 1.2 – 1.4
500 A
700 A
1.4 – 1.6
1.6 – 2.0
900 A
1000 A
3.1 Output voltage in steady state for different line currents
In steady state, simulation results shown that for load currents near
oscillation of
. It means
of the predict
ripple will be 0.4 % for DC currents near
, can be measured an
voltage. This way the peak to peak voltage
, and are obtained in steady-state at primary currents of
.
Figure 13 - Output voltage
(upper graph) and current
(lower graph) in stready state for 100 A
This error decreases for other line AC currents in study, except for
be measured an oscillation of
Figure 14 - Output voltage
,
of
line. In this case can
, or it means a peak to peak voltage ripple of
(upper graph) and current
23
(lower graph) in stready state for 500 A
.
Figure 15 - Output voltage
(upper graph) and current
(lower graph) in stready state for 1000 A
3.2 Start up transient
3.2.1
Study of a
initial current on the high voltage power line
The start up transient for a current line of
stable with the predict output voltage after
amplitude of
is present at Figure 16. It shows that circuit get
. An over voltage is present on
with a maximum
.
Figure 16 - Start up transient load voltage
(upper graph) and load current
24
(lower graph) for 100 A
It is interesting to look for waveforms of secondary transformer voltage and current, as well as the
PWM voltage (Figure 17). During the first
the transformer is not working on linear zone due to
strong initial magnetization.
Figure 17 - Start up transient secondary transformer voltage
(upper graph), PWM voltage
graph) and secondary transformer current (lower graph) for 100 A
3.2.2
Study of a
(center
initial current on the high voltage power line
The start up transient for a current line of
is present at Figure 18. It shows that circuit get
stable with the predict output voltage after
. An over voltage is present with a maximum
amplitude of
.
Figure 18 - - Start up transient load voltage
(upper graph) and load current
25
(lower graph) for 1000 A
It is interesting to look for waveforms of secondary transformer voltage and current, as well as the
PWM voltage (Figure 19).
Figure 19 - Start up transient secondary transformer voltage
(upper graph), PWM voltage
graph) and secondary transformer current (lower graph) for 1000 A
(center
3.3 Current step response
When is applied the current steps present at Table 2, the following output is obtained. It shows
that the DC voltage stays close to its set-point (
) even when occur strong AC current variations.
The results suggest a good line regulation with step changes, and a satisfactory sensitivity to
disturbances. The worst case happens on the step from
the load voltage, or it means an increase of
to
that perturbation increases in
.
Figure 20 - Load voltage (upper graph) and current start-up transient (lower graph) and response to AC line
current from 100 A to 1000 A
26
3.4 Secondary transformer voltage in steady state for different line
currents
Looking back for Section 2.4.2, the Thévenin equivalent network resistor
is obtained for the
smallest possible current on power line. When circuit is simulated for this line current is obtained the
Figure 21 simulations.
Figure 21 - Secondary transformer voltage
in steady state for 100 A
rd
When current on power line changes, the 3 order filter is not so accurate dimensioned anymore.
Regarding it, when circuit is simulated for
(Figure 22) is possible to see the effect of other signal
frequencies that not only the fundamental.
Figure 22 - Secondary transformer voltage
in steady state for 500 A
3.5 PWM voltage and 3rd order filter simulation
At Figure 23 is present the PWM voltage at the converter input. The pulse waveform obtained is
the reason why a 3
rd
filter is used to reduce the high frequency content and to obtain a primary
voltage close to a sine-wave.
27
Figure 23 - PWM voltage
The secondary transformer voltage and the current are shown at Figure 24. The current still has
some high frequency harmonics due to the fact that filter added between transformer and bridge was
not designed for the current but for the voltage. However, the current ripple is small enough and will
have detrimental effect on the power supply behaviour.
Figure 24 - Secondary transformer voltage
(upper graph) and current
(lower graph)
3.6 Transformer parameters simulation
3.6.1
Open-circuit test
To do the following test was used in Simulink/SimPowersystems the Figure 25 implementation.
Figure 25 - Simulink/SimPowerSystems implementation of the open-circuit test
28
A
AC voltage source is applied to the primary side to obtain a current of
. Since in
Simulink environment, all elements must be electrically connected, the secondary side of the
transformer cannot be left open and a load has to be connected. In order to simulate no-load
condition, a high impedance model to
reflect loading is used, and the resistance and inductance
values are set to very large numbers while the value of the capacitor is set to a very small number
On the primary side, current, and voltage measurement blocks are used to measure the
instantaneous current and voltage. The output of each meter is connected to a RMS block, to
determine the RMS values of primary current and voltage.
The magnitude of the excitation admittance
from the open-circuit voltage and current is
(61)
The phase angle of the admittance can be found from the knowledge of the power factor. The
open-circuit power factor,
, is given by
(62)
For this circuit were obtained
Regarding this values
These values are not so close to the ones explain at Chapter 2.1. The reason why this situation
happens is because primary leakage inductance
3.6.2
is not so small, and affects this test results.
Short-circuit test
To do the following test was used in Simulink/SimPowersystems the Figure 26 implementation.
A
AC voltage source is applied to the primary side. The rest of the model is similar with short-
circuit one. The only difference is that secondary side is short circuited.
29
Figure 26 - Simulink/SimPowerSystems implementation of the open-circuit test
Since a reduced voltage is applied to the primary windings, a negligible current flows through the
excitation branch. Ignoring this current, the magnitude of the series impedance referred to the primary
side of the transformer can easily be computed as
(63)
Neglecting the core loss at the low value of
, the series resistance and leakage reactance
equivalent can be found by
(64)
(65)
For this circuit were obtained
Regarding this values
30
3.7 Primary transformer voltage and current when happens a step
Figure 27 shows the voltage at the transformer primary at primary currents of
to
. The
voltage amplitude is small, meaning that the power supply system will not disturb the normal
operation of the AC transmission power line.
Figure 27 - Primary transformer voltage
(upper graph) and current
(lower graph)
3.8 Results discussion
The simulation results obtained are a prove that the theory concepts used at this work could be
used for a future prototype of a power supply for an autonomous robot moving on active high voltage
power lines.
Simulation results show that the DC voltage is well regulated (disturbances are lower than the
predicted
) in all the AC line current range from
to
components were tuning, in steady-state, ripples are smaller than
lower than
. In fact, when all the
and disturbances sensitivity
.
The RIOL robot power needs of
is reached using this model, and the use of a clamp on
transformer to obtain such amount of power is proved that can work for such applications.
The AC voltages injected in the transformer primary are low enough for the AC line (
smaller of the line voltage for the worst case (
rd
line)). Even, by using a 3 order low pass filter,
the harmonic distortion is decreased, and the robot by itself doesn’t increase line THD.
31
When the circuit is tested with different transformer characteristics from the specified ones at this
work, the results obtained are similar with the ones presented. This way is expected that circuit will be
able to accept some characteristics variations when a prototype will be implemented.
3.9 Model efficiency
Predicted efficiency is lower than desired at high AC currents (
the normal operating AC currents (
at
at
), but it is good at
), and very good for low AC currents (
at
).
For high AC currents the model efficiency is related with transformer saturation. To increase the
efficiency for such high AC current lines it is needed to consider another power supply topology, or
study thoroughly the clamp on transformer.
32
Chapter 4
4 Conclusions
The current thesis intended to demonstrate that a power supply for the RIOL can be done
to permit its autonomy. The circuit solution described at this work was designed and tested on
®
MATLAB software, and the results obtained let a door open for creating a future model to be
implemented on the robot.
The power supply harvests magnetic energy from active overhead power lines, using a
clamp-on transformer around the line. The transformer supplies a full bridge MOSFET based
rd
rectifier with a DC output filters through a 3
order Chebyshev low-pass filter. The control
systems uses sliding mode in the inner AC voltage control loop to emulate a resistor, and a
linear PI controller in the outer DC voltage loop. The value of the time dependent virtual resistor
is obtained using a PI to deliver the desired output voltage (55V ± 2.5%) and power (maximum
800 W). The controller laws and parameters, together with transformer and filter design were
addressed.
The energy absorbed by the robot comes from the line, producing an increment in the line
impedance and, therefore, a slight voltage drop in the point of the line where the robot is located
during the inspection. This voltage drop is very small compared with the voltage level of the high
voltage transmission line. It affects, for the worst case,
transmission line.
33
(
) the voltage
On this project was not discussing some aspects that can be important for future
development. RIOL deal with some constrains that should be consider about on future
researches. Nowadays high voltage overhead power lines are full of line obstacles, e.g. aviation
balloons. The robot in develop is already prepared for this situation, but its dimension and/or
weight distribution should be prepared for the case this will happen often on a line.
The extraction of energy from a transmission line in a quantity important enough to feed an
inspection robot can be achieved by means of the proposed system.
The continuous circulation of current along the phase conductors ensures the feeding of the
robot in such a way that the batteries can be size optimized and hence its weight.
The next steps for developing this work pass through analyse in depth the transformer
characteristics, and to build a prototype to give consistency to all the theoretical approach used
on this work.
34
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35