U.S. patent application number 13/709474 was filed with the patent office on 2014-06-12 for method and system for the determination of wind speeds and incident radiation parameters of overhead power lines.
This patent application is currently assigned to UNIVERSITE DE LIEGE. The applicant listed for this patent is UNIVERSITE DE LIEGE. Invention is credited to Bertrand Godard, Jean-Louis Lilien, Huu-Minh Nguyen.
Application Number | 20140163884 13/709474 |
Document ID | / |
Family ID | 47997402 |
Filed Date | 2014-06-12 |
United States Patent
Application |
20140163884 |
Kind Code |
A1 |
Lilien; Jean-Louis ; et
al. |
June 12, 2014 |
METHOD AND SYSTEM FOR THE DETERMINATION OF WIND SPEEDS AND INCIDENT
RADIATION PARAMETERS OF OVERHEAD POWER LINES
Abstract
The present invention relates to a method and system for the
determination of parameters related to the speed of wind that blows
near an overhead electrical power line (single or bundle
conductors). The parameters include an "effective wind speed" as
well as an "effective incident radiation" acting on a power line
span. The measurement is made by using the combination of
mechanical vibrations and movements/positions in two or three
dimensions through sensors in direct link with the power line
conductor.
Inventors: |
Lilien; Jean-Louis;
(Angleur, BE) ; Nguyen; Huu-Minh; (Liege, BE)
; Godard; Bertrand; (Liege, BE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
UNIVERSITE DE LIEGE |
ANGLEUR |
|
BE |
|
|
Assignee: |
UNIVERSITE DE LIEGE
ANGLEUR
BE
|
Family ID: |
47997402 |
Appl. No.: |
13/709474 |
Filed: |
December 10, 2012 |
Current U.S.
Class: |
702/3 |
Current CPC
Class: |
G01P 5/02 20130101; H02G
1/02 20130101; G01P 5/12 20130101; G06F 17/00 20130101; H02G 7/00
20130101; Y04S 10/00 20130101; G01W 1/00 20130101; Y04S 10/30
20130101 |
Class at
Publication: |
702/3 |
International
Class: |
G01W 1/00 20060101
G01W001/00; G06F 17/00 20060101 G06F017/00 |
Claims
1. A method for the determination of wind speed to be used for
evaluation of the ampacity in using real-time monitoring of at
least one span of overhead power lines, comprising the steps of:
measuring Aeolian vibration frequency by using outputs of at least
one oscillation sensor; and determining wind speed component
perpendicular to the conductor axis according to the following
equation: V=fd/S wherein f is the Aeolian vibration frequency (Hz),
S is the Strouhal number, V is perpendicular wind speed (m/s), and
d is conductor diameter (m).
2. The method according to claim 1, comprising the steps of:
acquiring monitoring information from at least one monitoring
device of the power line by using at least one oscillation sensor;
performing a frequency or time-frequency analysis from at least one
monitoring device of said oscillation measurement signals ranging
from 0 to about 100 Hz with a sensitivity of about or more than 100
micro-G for accelerations; determining a fundamental frequency from
said frequency or time-frequency analysis; and determining sag of
the span, on which at least one monitoring device is clamped.
3. The method according to claim 2 further comprising the step of
determining signature of Aeolian vibrations.
4. The method according to claim 2 further comprising the step of
determining the frequency spectrum partly or totally, including DC
component, of a transversal inclination of the overhead line in
service in the range of about 0 to mechanical fundamental frequency
of the span, the DC component being proportional to the square of
the mean wind speed component perpendicular to the power line
measured for about 5 minutes, wherein self-calibration of the
conversion from inclination to the effective wind speed is obtained
owing the recovery range with the same wind speed deduced by
Aeolian vibration.
5. The method according to claim 2, further comprising the
determination of effective incident radiation by using the sag of
the span, the relationship between sag and conductor temperature,
the measured ambient temperature, the electrical current flowing in
the line and the effective wind speed.
6. A device for the determination of wind speed for evaluation of
the ampacity in using real-time monitoring of at least one span of
overhead power lines, comprising: a sensor for attaching to a
conductor of the power line, said sensor comprising an
accelerometer; and a processor in connection with the sensor for
calculating the wind speed; wherein the processor determining wind
speed component perpendicular to the conductor axis according to
the following equation: V=fd/S wherein f is the Aeolian vibration
frequency (Hz), S is the Strouhal number, V is perpendicular wind
speed (m/s), and d is conductor diameter (m).
7. The device according to claim 6, wherein the sensor is an
oscillation sensor measuring Aeolian vibration frequency.
8. The device according to claim 6, wherein the accelerometer is
able to detect accelerations about maximum 100 micro-G in a
vertical direction and a transversal direction.
9. The device according to claim 6, wherein the accelerometer is
able to measure acceleration in three-dimensional directions.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to a method and system for the
determination of parameters related to the speed of wind that blows
near an overhead electrical power line (single or bundle
conductors). In particular, such parameters include an effective
perpendicular wind speed (hereinafter referred to as the "effective
wind speed"), which is the speed that would have a wind blowing
perpendicularly to the conductor axis and having the same cooling
effect on the conductor as the actual wind. In addition, the
combination of solar radiation and albedo on power line conductor
is hereinafter referred to as the "effective incident
radiation".
BACKGROUND OF THE INVENTION
[0002] As explained in U.S. Pat. No. 8,184,015, continuous
monitoring of electrical power lines, in particular high-voltage
overhead lines, is essential to timely detect anomalous conditions
which could lead to a power outage. Measurement of the sag of power
lines to determine whether the sag is lower than a maximum value is
becoming a mandatory requirement in some countries.
[0003] The device and method described in U.S. Pat. No. 8,184,015
can monitor the sag continuously on a power line span, without the
need for external data, such as topological data, conductor or span
data, weather data, or sagging conditions, which makes the
invention unique. The basic principle of that invention is the
detection of mechanical dynamic properties of the power lines only
based on mechanical frequencies detection from 0 to some tens of
Hertz (Hz). Indeed, power lines in the field are always subject to
movements and vibrations, which may be very small but detectable by
their accelerations in both time and frequency domains.
[0004] Such remarkable properties may be used to determine many
other features. The new method of the present invention can also be
used by other devices equipped with accelerometers.
[0005] The ampacity of a conductor is that maximal constant
electrical current which will meet the design, security and safety
criteria (e.g. electrical clearance) of a particular line on which
the conductor is used (see reference 5). The method to evaluate
ampacity from data are explained in many books (such as reference
1) and technical brochures from international organizations, such
as The International Council on Large Electric Systems (CIGRE)
publications (see references 2, 4 and 5), which use weather data as
locally measured or simulated following international
recommendations as explained, for example, in CIGRE (see reference
3) or The Institute of Electrical and Electronics Engineers (IEEE)
publication of 2006 (see reference 10).
[0006] A drawback of all these methods about weather conditions is
that none of them is able to generate appropriate weather data
which are actually to be used to calculate ampacity, which is a
value linked to all critical spans of a power lines. A critical
span is a span for which there is a significant risk of potential
clearance violation in any kind of weather situations. The critical
spans of a section may depend on span orientation, local screening
effects, local obstacles (vegetation, buildings, roads, . . . ),
etc. They have been defined at the design stage but may be reviewed
by more modern techniques like Light Detection And Ranging (LIDAR)
survey.
[0007] The wind speed has a dramatic impact on power line ampacity
as it is the main variable responsible for cooling down the
conductor, and hence for the sag value.
[0008] But wind speed measurement is tricky for various reasons.
First, it is not stationary as wind speed can vary significantly
within minutes, and there may be wind gusts. Second, it also varies
along the span (spatial coherence): wind vortices have a typical
average size of several tens of meters (Simiu & Scanlan, 1996).
Therefore, a typical span length of several hundreds of meters is
subject to a variable wind speed along its length. Third, the wind
speed also varies greatly vertically, as the conductor is fastened
within the boundary layer, and as the span's lowest point is
generally about 10 meters over the ground. The wind speed may also
vary due to local effects, such as screening from trees or
buildings, altitude of the conductor which may change in a single
span of more than 15 meters if only the sag is considered, but
which may also be subject to difference of levels between end
points of a span. Such a difference in altitude near the ground may
have huge effects as the conductor lies in an air layer located in
the boundary conditions of wind speed variation due to the ground
proximity.
[0009] Therefore, a single-spot measurement does not allow
computing the global effect of the wind over the whole span.
[0010] All of these factors are particularly important for low wind
speeds (typically for wind speeds component perpendicular to the
conductor axis lower than 3 m/s) which are dramatic for ampacity
determination. Similarly, a single-spot measurement of "effective
incident radiation" does not allow computing the global effect of
the combined effect of sun and albedo over the whole span.
[0011] Given the importance of power line monitoring, several
devices have been proposed to measure at least some of the relevant
parameters. For example, it is known that displacement measurement
systems placed at a given short distance (e.g. 89 mm) from a cable
suspension point (EPRI, 2009) can measure high-frequency
vibrations. However, this is only a partial solution to the
monitoring problem and such systems are solely oriented to evaluate
the life time of power line conductor due to the bending fatigue
induced by Aeolian vibrations cycles on conductor strands near
clamps.
[0012] A number of different methods which perform sag measurement
are also known. An example of tentative sag measurement consists in
the optical detection of a target clamped on the monitored
conductor by a camera fixed to a pylon (U.S. Pat. No. 6,205,867).
Other examples of such methods include measurement of the conductor
temperature or tension or inclination of the span. A conductor
replica is sometimes attached to the tower to catch an assimilated
conductor temperature without Joule effect. Beside the fact that
they only allow a partial monitoring of the power line, all of
these methods suffer from drawbacks: optical techniques are
sensitive to reductions of the visibility induced by meteorological
conditions while the other measurement methods are inaccurate,
since sag has to be deduced by algorithms which depend on
unavailable and/or uncertain data (e.g. wind speeds, topological
data, actual conductor characteristics, . . . ) and/or uncertain
models.
[0013] U.S. Pat. Nos. 5,140,257 and 5,341,088 disclose a monitoring
device whose housing is attached to the conductor. Some features
are related to the measurement of wind speed and direction based on
hot wire anemometers. The drawback of this device is that hot wires
anemometer is extremely difficult to manage on a sensor attached to
a conductor. Moreover, wind speed is deformed by the sensor itself
as hot wire needs to be protected against corona.
[0014] U.S. Pat. Nos. 6,441,603 and 5,559,430 disclose a monitoring
device for overhead power line rating but not attached to the
conductor. It is a kind of conductor replica. The combined effect
of wind, solar radiation, albedo, ambient temperature evaluation is
based on the behavior of dedicated rods installed apart from the
line. Drawback of such method is that the effect along the span was
not taken into account and that such local measurement is not a
good indication of what is actually the mean wind speed and global
incident radiation along spans of several hundreds of meters with
possible variable altitudes and different kind of wind action along
the span. Moreover, there are obvious errors for replica compared
to conductor emissivity and absorptivity and global incident
radiation mean value along the span.
[0015] U.S. Pat. No. 4,728,887 discloses a monitoring device whose
housing is adjacent to the overhead line. There is no information
about how wind speed and its direction are taken into account to
evaluate ampacity.
[0016] U.S. Pat. No. 5,933,355 discloses software to evaluate
ampacity of power line. This has no relationship with wind speed
measurement.
[0017] U.S. Pat. No. 6,205,867 discloses a power line sag monitor
based on inclination measurement. There is no information about how
wind speed and direction are taken into account to calculate
ampacity.
[0018] PCT Application WO 2010/054072 is related to real time power
line rating. It alleged the existence of a sensor about wind speed
direction and amplitude but offered no explanation how these
sensors are constituted.
[0019] PCT Application WO 2004/038891 and Norway Application
N020024833 disclose a monitoring device whose housing is attached
to the conductor. The wind is measured by "a traditional wind
gauge" and that such wind gauge "operates with an opening in the
outer casing". Such traditional gauge has no relationship with the
proposal of the inventors. The drawback of such traditional gauge
is that the sensor itself constitutes a perturbation in the local
measurement and that low wind speed cannot be measured properly by
such gauge.
[0020] European Patent Application EP 1.574.822 discloses a
monitoring device whose housing is attached to the conductor. There
is no information about how wind speed and direction are taken into
account to evaluate ampacity.
[0021] Korean Patent Application KR20090050671 discloses a
monitoring device whose housing is attached to the conductor. A
drawback of this device is that there is no way to properly
determine the "effective wind speed" perpendicular to the conductor
if they are less than 3 m/s, which are the basic cases for ampacity
determination under critical conditions.
[0022] U.S. Patent Application Publication No. US 20120029871 A1
discloses a monitoring device whose housing is attached to the
conductor. A drawback of this device is that there is no
explanation on how to evaluate the wind speed to consider for
ampacity determination. There is neither description nor any patent
on use about wind speed evaluation for ampacity determination. On a
website of that system, it is stated that "We also tasked the
sensors to detect Aeolian vibration, which is an indication of wind
blowing across the conductor, and `galloping.` "(extracted from
http://www.lindsey-usa.com/newProduct.php). But there is no
explanation on how such link is done. It is well known from the
literature that Aeolian vibration frequencies are linked to wind
speed (see references 6, 8 and 9). However, there is no mention in
the literature to exploit such link in evaluating precisely the
acting wind speed on a power line span to compute the ampacity of
that line. To do so, it needs the precise determination by an
appropriate system of the Aeolian vibration periods with their
acting main frequency, which is detailed in this invention by the
inventors.
SUMMARY OF THE INVENTION
[0023] The present invention meets a need for a power line device
and method overcoming at least some of the problems left open by
prior art solutions. The present invention is based on a power line
sensor directly fixed on the power line conductor (or one of it in
case of bundle conductors) and equipped with accelerometers outputs
in several directions. The present invention will use redundant
information made available in all or part by these
accelerometers.
[0024] An object of the present invention is to provide a method to
measure "effective wind speed" acting on a power line span by using
the combination of mechanical vibrations and movements/positions in
two or three dimensions outputs through sensors in direct link with
the power line conductor.
[0025] Another object of the present invention is also to provide a
method to determine indirectly an "effective incident radiation"
acting on a power line span by using the combination of mechanical
vibrations and movements/positions in two or three dimensions
outputs through sensors in direct link with the power line
conductor.
[0026] The sensor must be located at any in-span position. The
device used to detect vibration may be based (but not necessarily)
on U.S. Pat. No. 8,184,015, in which the device was used in the
harsh environment constituted by the vicinity of a high voltage
(tens to hundreds of kV) overhead power line.
[0027] The sensor must be equipped with accelerometers of
significant sensitivity, typically able to detect accelerations
near about maximum 100 micro-G in vertical, (longitudinal) and
transversal directions (means minimum 2D, possibly 3D
accelerometers).
BRIEF DESCRIPTION OF THE DRAWINGS
[0028] FIG. 1 is a schematic diagram showing how the wind is acting
on conductor including wind effect and mean swing angle .theta. of
power line span, wherein "transversal swing angle" is defined as
tan(.theta.).
[0029] FIGS. 2a and 2b show the sag as deduced by oscillation
sensor outputs (with its maximum value) (FIG. 2a) and deduced
conductor temperature (FIG. 2b) together with ambient temperature
(here measured in the vicinity of the power line span) during a one
day time evolution. In FIG. 2a, sag is deduced by an oscillation
sensor from U.S. Pat. No. 8,184,015 (with its maximum allowable
value in dotted line). In FIG. 2b, the thin line represents deduced
conductor temperature, and the dotted line represents ambient
temperature (here measured in the vicinity of the power line
span).
[0030] FIGS. 3a and 3b show , on the same day, the deduced
"effective incident radiation" power as detailed in the invention
(FIG. 3a) and the load current (bottom curve), the static rating
(horizontal dotted line at 850 A) and the dynamic rating (thick
line) as deduced from effective three weather data, two of them
being determined by the invention (FIG. 3b).
[0031] FIGS. 4a and 4b show, on the same day, the frequency
detection as obtained by using the accelerometers detailed in the
invention and tracking of Aeolian periods. FIG. 4a is a
simultaneous view of typical time evolution of detected vibration
frequencies and corresponding reinforced Aeolian period vibration
frequency tracking according to the invention. FIG. 4b shows
extracted Aeolian vibration tracking as detailed in the invention.
Missing data around 12:00 during about 4 hours are due to the
absence of detected Aeolian vibration during the corresponding
period.
[0032] FIGS. 5a and 5b show, on the same day at time 12:00, the
frequency-amplitude content of the measured signal by the
accelerometers detailed in the invention. The typical frequency of
"Type I" (buffeting) content as can be extracted from FIGS. 4a and
4b (reproduced in FIG. 5a) at measurement time of about 12:00
(vertical dotted line on the frequency-time figure).
[0033] FIGS. 6a and 6b show, on the same day at time 04:30, the
frequency-amplitude content of the measured signal by the
accelerometers detailed in the invention. Typical frequency of
"Type II" (Aeolian vibrations) as can be extracted from FIGS. 4a
and 4b (reproduced in FIG. 6a) at measurement time of about 04:30
(vertical dotted line on the frequency-time figure).
[0034] FIG. 7 shows the values of power line conductor "transversal
swing angle" as obtained using the accelerometer-based method
detailed in the invention. Swing angle (radians) of the power line
span (in this case a conductor of about 0.257 kg/m and a diameter
of 12.5 mm) during the same day of observation as for FIGS. 2 to 6.
The value is extracted from transversal acceleration of the
embedded corresponding accelerometer into the in-span power line
sensor. For about 3 m/s wind speed, the mean swing angle is about
0.025 rd or 1.4.degree.. Values below about 0.0025 radian are below
the expected precision of the system and cannot be considered for
use.
[0035] FIG. 8 shows the "effective wind speed" during the same day,
as calculated according to the present invention. In this case, the
thick black part of the curve has been fully deduced from actually
observed Aeolian vibrations in a range limited to wind speed lower
than about 1.6 m/s (larger range are also possible). The curve has
been completed for larger wind speed, by the thick grey part of the
curve deduced from transversal acceleration analysis as detailed in
the invention. The typical continuous wind speed value obtained as
detailed in the invention. Wind speed deduced by combining Aeolian
vibration tracking and transversal acceleration analysis. The thick
black line represents wind speed deduced from Aeolian vibrations
during such periods, as deduced from FIG. 4 using the invention.
The thin cross line represents wind speed deduced from mean
transversal acceleration, as deduced from FIG. 7 using the
invention.
[0036] FIGS. 9a-9d show a typical time evolution on 10 minutes of
vertical and horizontal accelerations (Type I) during a buffeting
period. FIGS. 9a and 9c show transversal accelerations. FIGS. 9b
and 9d show vertical accelerations. The range of relative changes
are similar in both directions.
[0037] FIGS. 10a and 10b show a typical growing up and decay of
Aeolian vibrations (Type II) of about 10 minutes inside a global
observation period of 50 minutes. FIG. 10a shows transversal
accelerations and FIG. 10b shows vertical accelerations. Range of
relative changes are very different with a clear dominance in
vertical amplitudes.
DETAILED DESCRIPTION OF THE INVENTION
[0038] The new method according to the present invention adds, in
parallel with the thermal equilibrium equation (as described in
detail, for example, in IEEE 2006 and reproduced in pages 15 to
17), a second independent equation to determine the most changeable
(both in time and space) and most important weather variable for
ampacity determination: the wind speed perpendicular component to
the conductor axis averaged over the whole span, so called
"effective wind speed".
[0039] The required wind speed for ampacity determination is
evaluated independently from the thermal equation by means of two
independent methods (the results of which are being superimposed or
complemented in some range of detected wind speeds). Those two
methods determine the wind speed perpendicular component averaged
over the span: [0040] (1) The measurement of the frequency of the
Aeolian vibration that is linked to the wind speed perpendicular
component via the well documented Strouhal equation. Aeolian
vibrations may be active on all the range of wind speeds of
interest for ampacity calculation and are particularly useful in
the very low wind speed range, from near 0 m/s to a few m/s, most
preferably between 0.1 and 3 m/s. [0041] (2) The span "transversal
swing angle" that, according to the measurement of the present
invention (owing to transversal acceleration sensor), has shown to
be a good indicator of wind speed perpendicular components
exceeding about 1 m/s. For a one-span section, the cooling effect
of the wind speed perpendicular component is always very close to
the one resulting from the "effective wind speed", for actual winds
blowing with angles to the conductor axis ranging between
45.degree. and 90.degree.. Considering wind speed perpendicular
component in calculations thus yield a very good estimate of the
ampacity in that case. For angles ranging from 0.degree. to
45.degree., the cooling effect of the wind speed perpendicular
component is always inferior to the one resulting from the
"effective wind speed", thus leading to a conservative ampacity
calculation.
[0042] For a multiple-span section, a sensor has to be repeated on
all critical spans along the section and the worst case is
considered for ampacity evaluation.
[0043] A three-axis accelerometer assembly with a range of
frequency comprised between 0 and about 100 Hz and a minimum
sensitivity of 100 micro-G may detect ambient Aeolian vibrations,
often existing at very low wind speed, preferably, comprised
between 0.05 and about 7 m/s and, most preferably, between 0.2 and
3 m/s. The accelerometers are able to detect basic oscillation
modes of the power line. It is noted here that only the detection
of Aeolian vibration frequency is needed. The vibration could be of
very low amplitude. An observed Aeolian vibration is obviously
linked to a lock-in (as detailed in EPRI 2009) of the vortex
shedding with one mode (sometimes a few modes in a very narrow band
of frequencies) of vibration of the cable. That detectable
frequency(ies) by the line monitoring device is the driving mode or
the converted energy from the wind to the vibration in its dominant
mode all over the span. Thus, it is representative of the dominant
mean wind speed to consider all along the span for thermal
convection heat exchange.
[0044] The "effective wind speed" for power line span may be
deduced from vibrations analysis. This method is particularly
valuable for very low wind speed, lower than about 7 m/s, most
preferably lower than 3 m/s, which are the dramatic cases for
ampacity determination.
[0045] It is known from fluid mechanics (Blevins1990, Simiu et al,
1996) that the peaks of power spectral density of oscillations
(preferably comprised between 3 and 100 Hz and most preferably
between 2 and 40 Hz) is observed at frequencies related to the wind
speed and the conductor diameter by the Strouhal relationship, so
that a given wind speed will generate vibrations in a close range
of frequencies and vice-versa. The observed frequencies are an
image of the actual wind speed component perpendicular to the
conductor axis as observed in Godard, 2011. Detailed literature
exists on that subject as Aeolian vibration is a key phenomenon in
connection with the fatigue of the conductors (EPRI 2009). But the
phenomenon is used in a another way in the present invention, using
observed vibration frequencies to evaluate the speed of wind acting
on the span and in turn use such wind speed to compute ampacity of
the line.
[0046] Appropriate algorithm has been developed by the inventors to
extract period of Aeolian vibrations inside the global frequency
spectrum. This method is based on the following two steps: [0047]
(1) Step 1: Detection of conductor accelerations ranging from near
0 Hz to a few tens of Hertz, most preferably between 0 and about 15
Hz. This last upper value of observation is linked to conductor
diameter and range of wind speed to be detected following the
Strouhal relationship (with S=0.185 or close to that value). For
example to detect wind speed from near 0 m/s to 2 m/s on a
conductor diameter of 30 mm (=0.03 m), range of frequencies to be
observed should be near 0 to 12.3 Hz (12.3=2.times.0.185/0.03).
Sensitivity of accelerometer(s) must be most preferably close to or
better than 100 micro-G. The quasi-vertical movement (based on
normalized amplitudes of the accelerations sample in each
direction) is detected. Observations period sample needed to
perform the frequency analysis is near a few minutes, most
preferably between 2 and 5 minutes. A typical output of such
detection is shown on FIG. 4. [0048] (2) Step 2: Detection of
Aeolian vibration pattern and its major frequency component, into
the general frequency spectrum deduced from step 1. The
acceleration spectrum, as shown on FIG. 4, can be divided into
three main classes of frequency spectrum shapes and corresponding
periods of movements. [0049] (2.1) Type I: buffeting [0050]
Buffeting pattern, as shown on FIG. 5 for the period of observation
near 12:00, mainly relates to random and irregular effects due to
variation of wind speed both in module and direction along the
span. Such power line span excitation does not allow the formation
of "quasi-stationary" vibrations. This causes random excitation of
the conductor over a broad range of frequencies and corresponding
vibrations modes simultaneously. A large number of modes are
present due to the spatial/temporal non uniformity of wind. A
typical time evolution during 10 minutes is given on FIG. 9
(accelerations). [0051] (2.2) Type II: Aeolian vibrations [0052] As
shown on FIG. 6 (extracted from FIG. 4 at near 04:30 time, but also
valid for the whole period of observation between 00:00 and about
11:00) a very limited number of (medium to high, in this case
between 3 and 15 Hz) frequencies are excited. [0053] On the other
hand, lower range of vibrations modes with frequency lower than
Strouhal frequency corresponding to very low or low wind speeds
(typically near 0.2 m/s), are not excited. This frequency threshold
is given by Strouhal equation and depends on conductor diameter.
For a conductor with diameter of 30 mm this "lower range" limit is
typically near 1.2 Hz.(=0.2.times.0.185/0.03 following the Strouhal
relationship). [0054] For a given cylinder diameter and given fluid
velocity, the shedding frequency of the flow is given by the
Strouhal equation. For a real conductor, the problem is complicated
both by the fact that the conductor does not behave as a rigid
cylinder and the wind speed is a function of time and space (wind
speed is changing not only in time but also along the span with its
spatial coherence). So some close frequencies are excited and thus
beat with each other. The frequency component with highest
normalized displacement amplitude is considered here. [0055] An
Aeolian vibration is characterized to be a more or less stationary
process in frequency domain, but not necessarily in amplitude.
Correlation between the frequency content of a few successive
periods of analysis is checked. The positive correlation
coefficient must be over about 0.9. In others words, an Aeolian
vibrations period corresponds to a series of successive correlated
periods of analysis with very limited number, typically about 3
close values, of medium or high frequencies. [0056] Additional
information used to detect Aeolian vibration is the ratio of
vertical to transversal amplitudes of vibrations analysis. During
buffeting, gusts put the conductor in motion, in both vertical and
transversal directions. During Aeolian vibration, conductor motion
is mainly perpendicular to the flow, i.e vibrations mainly occurs
in the vertical plane for power Lines as the flows mainly blows
horizontally on a flat terrain. The mainly vertical resultant
oscillation in case of Aeolian vibrations is resonant (a very
narrow band of frequencies are excited). A ratio near 10 is
observed between vertical and transversal movement. [0057] A
typical time evolution of Aeolian vibrations is shown on FIG. 10.
[0058] (2.3) Type III: transition period [0059] It is a period of
transition from type I to type II (or vice versa) class as defined
hereinabove. During the transition from Type I to Type II,
low-frequency amplitudes (For a 30 mm diameter conductor, this
"lower range" limit is typically near 0.2.times.0.185/0.03=1.2 Hz,
following the Strouhal relationship) decrease and the medium to
high frequency amplitudes increase. Aeolian vibration is building
up. When the Aeolian vibration is built up the conductor is
vibrating with a frequency corresponding to the wind velocity given
by Strouhal equation. The frequency of vibration will not change
when the velocity is changing slightly owing to the well-known
(EPRI 2009; Blevins 1990) lock-in phenomenon: only the vibration
amplitude will decrease but if the wind speed changes too much, the
Aeolian vibration will die (transition to buffeting period) or a
new Aeolian vibration at a new main frequency will build up. Such a
transition period can last a few minutes, typically between about 2
and about 5 minutes. [0060] Observing amplitudes trends of excited
frequencies on a given period allows characterizing transition
period.
[0061] Determination of the "Effective Wind Speed"
[0062] The observed established Aeolian vibration is directly
linked to the wind speed and conductor diameter as given by the
Strouhal relationship:
f=SV/d (1)
where f is the frequency of vibration (Hz) as extracted from step
2, S is the Strouhal number (dimensionless), V is the perpendicular
wind speed (m/s), d is the conductor diameter (m). The Strouhal
number, for typical power line conductor is close to 0.185 and is
dimensionless. (See Blevins 1990, Simiu et al., 1996, EPRI
2009).
[0063] FIG. 8 shows a typical output of "effective wind speed"
using Aeolian vibration detection algorithm. In this case (one full
day), the values have been completed by some transversal
inclination (also obtained by accelerometers) during high wind
speed periods.
[0064] The power line span swing angle (shown in FIG. 1) can be
evaluated by considering the equilibrium per unit length between
the weight of the conductor and the drag force F.sub.D of wind.
Hereinbelow, "transversal swing angle" is referred to as
tan(.THETA.) where (.THETA.) is the mean swing angle of the power
line span, see FIG. 1.
[0065] The following equation is obtained.
tan ( ) = F D .rho. g ( 2 ) ##EQU00001##
[0066] where .rho. is the linear density of conductor [kg/m] and g
is the gravity constant [9.81 m/s.sup.2 on earth].
[0067] Resulting drag force F.sub.D generated by wind is related to
wind speed U [m/s] by the well-known equation (see references 7, 8
or 9):
F D = 1 2 .rho. air C D d U 2 ( 3 ) ##EQU00002##
[0068] Where d [m] is the diameter of the conductor, .rho..sub.air
the air density [kg/m.sup.3] and C.sub.D the drag coefficient
[dimensionless].
[0069] The two previous equations show that the "transversal swing
angle" of conductor is linearly related to the square of wind
speed, depending on some constants.
[0070] As can be seen on FIG. 1, "transversal swing angle" is also
given by inclination of transversal axis t with gravity g, that
value may be extracted from embedded accelerometers into the sensor
installed on the power line conductor:
tan ( ) = transversal static acceleration gravity constant = g t g
( 4 ) ##EQU00003##
[0071] By combining previous equations, wind speed can be
determined, using transversal acceleration g.sub.t [m/s.sup.2].
U 2 = .rho. 0.5 .rho. air C D d g t = k i g t ( 5 )
##EQU00004##
[0072] As an example, the following values could be used: (i) the
air density r.sub.air=1.2 kg/m.sup.3 at 20.degree. C. (ii), the
drag coefficient C.sub.D=1. This means that, for a conductor with
diameter of 0.03 m and a linear density of 1 [kg/m], equation (5)
gives an approximated relationship between wind speed and static
transversal acceleration given by U.sup.2=55 g.sub.t (means in this
case k.sub.i=55 m).
[0073] In real cases, dynamic motion in transversal direction is
induced by wind gusts and transversal acceleration can change
rapidly. Mean value of transversal acceleration is measured to
evaluate mean wind speed acting on the conductor. That mean value
is obtained on sample size range from about 5 to 20 minutes, most
preferably around 10 minutes mean value is used.
[0074] Choosing accelerometers of sensitivity better than 100
micro-G, it is possible to get transversal inclination values once
the wind speed is still in the range of Aeolian vibration, which
gives a self-calibration (=find the "k.sub.i" value) of the linear
relationship between transversal inclination and the square of the
wind speed, as shown on FIG. 7. Obviously, when there is no wind,
inclination must be zero, which gives an obvious starting point of
the linear fit. Initial offset of inclination, if any, may be
determined by that method.
[0075] Determination of the Worst Weather Conditions Acting on the
Power Line, in Particular the "Effective Incident Radiation"
[0076] Based on the new method, one can determine the effective
worst weather conditions needed to compute the real-time thermal
rating (also called dynamic line rating--DLR--or real time thermal
rating--RTTR--) (shown on FIG. 3, right upper curve) of the
overhead line in three steps:
[0077] 1. Effective perpendicular wind speed ("effective wind
speed"), the variable with the most influence on the RTTR/DLR is
determined as described above: at low wind speeds using the Aeolian
vibration and at higher wind speeds, if needed, using the
"transversal swing angle" (FIG. 1).
[0078] 2. Ambient temperature (shown on FIG. 2, right bottom curve)
is determined based on an external or internal measurement in the
monitoring sensor or located in general vicinity of the line. As
ambient temperature varies little (compared to the other variables)
over time, distance or altitude, a measurement performed even
several kilometers away from the overhead line may be adequate.
[0079] 3. The "effective incident radiation" (comprising direct
solar radiation and environment's albedo along the span) (FIG. 3a)
is determined by using the sag measurement (FIG. 2b, upper
curve)(which may be also obtained by accelerometers as explained in
U.S. Pat. No. 8,184,015 which allows for calculating the sag
without any external data) as follows:
[0080] This is done by using thermal equilibrium equation (as
detailed in IEEE 2006 and reproduced in appendix) and will need the
load current in the line (FIG. 3 right bottom)(deduced from load
flow in the line which is either transmitted by the TSO or directly
measured into a sensor installed on the power line) to quantify the
Joule effect, the "effective wind speed" (determined in step 1),
ambient temperature (determined in step 2), and the conductor
average temperature over the span (which is a direct image of the
measured sag in a single-span section, as they are bound to each
other by a one-to-one relationship as detailed in reference 4); the
"effective incident radiation" can then be calculated by solving
the thermal equilibrium equation:
q.sub.s=q.sub.c+q.sub.r-R(T.sub.c) I.sup.2 (6)
wherein [0081] q.sub.s: heat gain rate per unit length by
"effective incident radiation" (W/m); [0082] q.sub.s: convected
heat loss rate per unit length by "effective wind speed" (W/m);
[0083] q.sub.r: radiated heat loss rate per unit length (W/m); and
[0084] R(T) I.sup.2: heat gain rate per unit length by Joule effect
(W/m).
[0085] The last term being the Joule effect, considering the
resistance as a function of the conductor's mean temperature.
[0086] The other terms are described below (written here only for
forced convection, other formulas to be extracted from ref 2 or
10):
q c 1 = [ 1.01 + 0.0372 ( 10 3 d .rho. f V .mu. f ) 0.52 ] k f ( T
c - T a ) ( i ) q c 2 = [ 0.0119 ( 10 3 d .rho. f V .mu. f ) 0.6 ]
k f ( T c - T a ) ( ii ) ##EQU00005##
[0087] Equation (i) applies at low winds but is incorrect at high
wind speeds. Equation (ii) applies at high wind speeds, being
incorrect at low wind speeds. At any wind speed, the larger of the
two calculated convection heat loss rates is used.
[0088] There is a natural convection formula defined in both
references 2 and 10, but it is seldom applied, as a minimum wind
speed threshold (typically of 0.5 m/s, perpendicular or not) is
usually defined by the TSO.
[0089] Here the equations are simplified by taking into account
that the patent determine the "effective wind speed" which is the
perpendicular equivalent wind speed needed.
[0090] Thus, there is no more angular coefficient to take into
account for the present method.
[0091] Radiated heat loss rate
q r = 0.0178 .10 3 d [ ( T c + 273 100 ) 4 - ( T a + 273 100 ) 4 ]
##EQU00006##
[0092] This radiation term follows the well-know Stefan-Boltzmann
law.
[0093] The rate of "effective incident radiation" is then simply
deduced by the formula:
q.sub.s=q.sub.c+q.sub.r-R(T.sub.c) I.sup.2
[0094] This radiation term includes solar heat, if any, and
albedo.
[0095] The variables used in this appendix are described in the
following list:
[0096] R(T.sub.c): AC resistance of conductor at temperature
T.sub.c(.OMEGA.m)
[0097] I: conductor current (A)
[0098] d: conductor diameter (m) (typically around 0.03 m)
[0099] .rho..sub.f: density of air (kg/m.sup.3) (1.184 kg/m.sup.3
at T.sub.a=25.degree. C. and altitude=0 m)
[0100] V: "effective wind speed" (m/s)
[0101] .mu..sub.f: dynamic viscosity of air (Pas) (1.8410.sup.-5
Pas at T.sub.a=25.degree. C.)
[0102] k.sub.f: thermal conductivity of air (W/(m..degree. C.))
(0.0261 W/(m..degree. C.) at T.sub.a=25.degree. C.)
[0103] T.sub.c: conductor temperature (.degree. C.)
[0104] T.sub.a: ambient air temperature (.degree. C.)
[0105] .epsilon.: emissivity (0.23 to 0.91) (dimensionless)
[0106] In FIG. 3a, the "theoretical" sun power deduced from
latitude and date (following equations detailed in IEEE, 2006) are
given for comparison with actual output from the invention.
[0107] This approach, comprising redundant information (two
measurements of the "effective wind speed", plus the sag
measurement), allows one to determine RTTR (real time thermal
rating) with a precision not yet attained by any of the current
methods and tools, as point measurement methods are corrected using
the behavior of the overhead line itself and even approximations of
the thermal model and its variables (emissivity, humidity for
example) are compensated by the correction applied to the
"effective incident radiation" using the sag measurement.
[0108] Such weather data can be evaluated on all critical spans of
the line and help to compute ampacity for each case and select the
worst case for the line. "Effective wind speed" can be used for an
even broader range of applications, like the determination of the
wind dynamic pressure coefficient, or the conductor maximum swing
angle, used for line design.
[0109] A side outputs of these measurement is the availability of
past behavior (in both sag, lateral movement, "effective wind
speed", ampacity, . . . ) including long term behavior.
REFERENCES
[0110] [1] A. Deb. "Power line ampacity system." 2000. CRC Press
(251 pages). [0111] [2] "Thermal behaviour of overhead conductors".
2002. Cigre Technical brochure No. 207. Study Committee B2. [0112]
[3] "Guide for selection of weather parameters for bare overhead
conductor ratings". 2006. Cigre technical Brochure No. 299.Study
Committee B2. [0113] [4] "Sag-tension calculation methods for
overhead lines". 2007. Cigre Technical Brochure No. 324. Study
Committee B2. [0114] [5] "Guide for application of direct real-time
monitoring systems". 2012. Cigre Technical brochure No. 498. Study
Committee B2. [0115] [6] Godard, B, Guerard, S, & Lilien, J.-L.
Original real-time observations of aeolian vibrations on power-line
conductors. 2011. IEEE Transactions on Power Delivery, 26(4),
2111-2117. http:/lhdl.handle.net/2268/102095 [0116] [7] Blevins R.
D. Flow Induced Vibration. 1990. Van Nostrand Reinhold, New York,
Second Edition. [0117] [8] EPRI Transmission line reference book:
Wind induced conductor motion. Second Edition. 2009. EPRI, Palo
Alto, Calif.: 2009. 1018554. [0118] [9] Simiu E., Scanlan R. Wind
effects on structures. 1996. John Wiley & Sons, Inc. (688
pages). [0119] [10] IEEE Std 738-2006--IEEE Standard for
Calculating the Current-Temperature of Bare Overhead Conductors.
IEEE Power Engineering Society. 2006.
* * * * *
References