U.S. patent application number 11/503164 was filed with the patent office on 2007-02-15 for parameter estimation for and use of a thermal model of a power line.
This patent application is currently assigned to ABB Schweiz AG. Invention is credited to Petr Korba, Mats Larsson, Albert Leirbukt, Marek Zima.
Application Number | 20070038396 11/503164 |
Document ID | / |
Family ID | 8184332 |
Filed Date | 2007-02-15 |
United States Patent
Application |
20070038396 |
Kind Code |
A1 |
Zima; Marek ; et
al. |
February 15, 2007 |
Parameter estimation for and use of a thermal model of a power
line
Abstract
A relationship between a temperature T.sub.l of a power line or
power transmission conductor 10, an electrical quantity of the
power line such as a current l or power flow P through the power
line, as well as meteorological quantities or ambient conditions of
the power line such as wind speed W, wind direction, humidity,
solar radiation S and ambient temperature T.sub.a, is established
in the form of a thermal model of the power line. Values of the
aforementioned quantities or variables are continuously measured,
and the collected values of the quantities are evaluated in order
to update model parameters of the thermal model during operation of
the power line. In an exemplary embodiment, an average temperature
representative of the entire line is determined via two phasor
measurement units (PMU) 11, 11' providing synchronized phasor
values from two ends of the power line. An ohmic resistance of the
power line can be computed from the phasor values, from which in
turn the average line temperature can be derived.
Inventors: |
Zima; Marek; (Zurich,
CH) ; Korba; Petr; (Turgi, CH) ; Leirbukt;
Albert; (Oslo, NO) ; Larsson; Mats; (Baden,
CH) |
Correspondence
Address: |
BUCHANAN, INGERSOLL & ROONEY PC
POST OFFICE BOX 1404
ALEXANDRIA
VA
22313-1404
US
|
Assignee: |
ABB Schweiz AG
Baden
CH
|
Family ID: |
8184332 |
Appl. No.: |
11/503164 |
Filed: |
August 14, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
10499701 |
May 3, 2005 |
7107162 |
|
|
PCT/CH02/00682 |
Dec 11, 2002 |
|
|
|
11503164 |
Aug 14, 2006 |
|
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Current U.S.
Class: |
702/65 |
Current CPC
Class: |
H02H 6/005 20130101;
H02H 3/40 20130101; H02H 7/226 20130101 |
Class at
Publication: |
702/065 |
International
Class: |
G06F 19/00 20060101
G06F019/00 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 21, 2001 |
EP |
01811254.0 |
Claims
1. A method of estimating model parameters (A, B, . . . ; C.sub.l,
. . . ) of a thermal model of a power line, comprising: measuring
values of an electrical quantity (l, P) of the power line and of
meteorological quantities (T.sub.a, S, W) representing ambient
conditions of the power line; calculating values of the model
parameters from said measured values; measuring, repeatedly during
operation of the power line, momentary values (l.sup.i,
T.sub.a.sup.i, S.sup.i, W.sup.i) of the electrical and
meteorological quantities; measuring concurrently a momentary value
(T.sub.l.sup.i) of a temperature (T.sub.l) of the power line; and
calculating, repeatedly during operation of the power line, the
values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, . . . ) of the
model parameters from said measured values.
2. The method according to claim 1, wherein measuring a momentary
value (T.sub.l.sup.i) of the temperature of the power line
comprises: measuring, by means of two Phasor Measurement Units,
synchronized phasor data (v.sub.1.sup.i, i.sub.1.sup.i;
v.sub.2.sup.i, i.sub.2.sup.i) at two ends of the power line;
computing a value (R.sub.l.sup.i) of an electrical resistance
(R.sub.l) of the power line from the phasor data; and computing,
from the value (R.sub.l.sup.i) of the electrical resistance of the
power line, an average line temperature as the momentary value
(T.sub.l.sup.i) of the temperature of the power line.
3. The method according to claim 2, wherein computing the average
line temperature involves an analytical expression with parameters
(R.sub.0, .alpha..sub.0) suitably calibrated by means of an
independent line temperature measuring device.
4. The method according to claim 1, wherein measuring momentary
values (T.sub.a.sup.i, S.sup.i, W.sup.i) of the meteorological
quantities involves measuring the values by a provider of
meteorological data other than an operator of the power line.
5. The method according to claim 1, comprising: generating a series
of measured values (T.sub.l.sup.1, T.sub.l.sup.2, . . . ; u.sup.1,
u.sup.2, . . . ) of the temperature of the power line and the
electrical and meteorological quantities; and adaptively
calculating updated values (A.sup.k, B.sup.k; . . . ;
C.sub.l.sup.k, . . . ) of said model parameters every time a new
value (T.sub.l.sup.k, u.sup.k) of the temperature of the power line
or the electrical and meteorological quantities is measured.
6. The method according to claim 1, wherein the thermal model is a
nonlinear parametric model based on a heat balance equation.
7. A method for predicting a value (T.sub.l.sup.f) of the line
temperature of the power line, using a thermal model with momentary
model parameter values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, .
. . ) estimated according to claim 1, comprising: providing
forecasted values (u.sup.f) of the electrical and meteorological
quantities; and calculating a power line temperature forecast
(T.sub.l.sup.f) based on the momentary model parameters and the
forecasted values of the electrical and meteorological
quantities.
8. The method according to claim 7, comprising: comparing the power
line temperature forecast (T.sub.l.sup.f) with a power line
temperature limit; and calculating a maximum allowable value of the
electrical quantity (l, P) there from.
9. The use according to claim 8, comprising: using a linear thermal
model for the power line; and providing the maximum allowable value
of the electrical quantity (l, P) to a balance market clearing
process.
10. The method according to claim 2, comprising generating a series
of measured values (T.sub.l.sup.1, T.sub.l.sup.2, . . . ; u.sup.1,
u.sup.2, . . . ) of the temperature of the power line and the
electrical and meteorological quantities; and adaptively
calculating updated values (A.sup.k, B.sup.k; . . . ;
C.sub.l.sup.k, . . . ) of said model parameters every time a new
value (T.sub.l.sup.k, u.sup.k) of the temperature of the power line
or the electrical and meteorological quantities is measured.
11. A method for predicting a value (T.sub.l.sup.f) of the line
temperature of the power line, using a thermal model with momentary
model parameter values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, .
. . ) estimated according to claim 2, comprising: providing
forecasted values (u.sup.f) of the electrical and meteorological
quantities; and calculating a power line temperature forecast
(T.sub.l.sup.f) based on the momentary model parameters and the
forecasted values of the electrical and meteorological
quantities.
12. A method for predicting a value (T.sub.l.sup.f) of the line
temperature of the power line, using a thermal model with momentary
model parameter values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, .
. . ) estimated according to claim 3, comprising: providing
forecasted values (u.sup.f) of the electrical and meteorological
quantities; and calculating a power line temperature forecast
(T.sub.l.sup.f) based on the momentary model parameters and the
forecasted values of the electrical and meteorological
quantities.
13. A method for predicting a value (T.sub.l.sup.f) of the line
temperature of the power line, using a thermal model with momentary
model parameter values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, .
. . ) estimated according to claim 4, comprising: providing
forecasted values (u.sup.f) of the electrical and meteorological
quantities; and calculating a power line temperature forecast
(T.sub.l.sup.f) based on the momentary model parameters and the
forecasted values of the electrical and meteorological
quantities.
14. A method for predicting a value (T.sub.l.sup.f) of the line
temperature of the power line, using a thermal model with momentary
model parameter values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, .
. . ) estimated according to claim 5, comprising: providing
forecasted values (u.sup.f) of the electrical and meteorological
quantities; calculating a power line temperature forecast
(T.sub.l.sup.f) based on the momentary model parameters and the
forecasted values of the electrical and meteorological
quantities.
15. A method for predicting a value (T.sub.l.sup.f) of the line
temperature of the power line, using a thermal model with momentary
model parameter values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, .
. . ) estimated according to claim 6, comprising: providing
forecasted values (u.sup.f) of the electrical and meteorological
quantities; calculating a power line temperature forecast
(T.sub.l.sup.f) based on the momentary model parameters and the
forecasted values of the electrical and meteorological
quantities.
16. A method for predicting a value (T.sub.l.sup.f) of the line
temperature of the power line, using a thermal model with momentary
model parameter values (A.sup.i, B.sup.i; . . . ; C.sub.l.sup.i, .
. . ) estimated according to claim 10, comprising: providing
forecasted values (u.sup.f) of the electrical and meteorological
quantities; and calculating a power line temperature forecast
(T.sub.l.sup.f) based on the momentary model parameters and the
forecasted values of the electrical and meteorological
quantities.
17. A method of estimating a parameter of a thermal model of a
power line, comprising: measuring a value of an electrical quantity
of the power line and at least one meteorological quantity
representing an ambient condition of the power line; calculating a
value of the parameter of the thermal model from said electrical
quantity and said meteorological quantity; measuring, during
operation of the power line, a momentary value of each the
electrical quantity an the meteorological quantity; measuring a
momentary value of a temperature of the power line; and
calculating, during operation of the power line, a value of the
parameter from said measured values of the electrical quantity, the
meteorological quantity and the temperature.
Description
CROSS-REFERENCE TO RELATED PATENT APPLICATIONS
[0001] This application is a continuation-in-part application under
35 U.S.C. .sctn.120 which claims the benefit of the filing date of
allowed U.S. patent application Ser. No. 10/499,701, fled May 3,
2005 as a 35 U.S.C. .sctn.371 application of PCT/CH02/00682 filed
Dec. 11, 2002, and which in return claims priority under 35 U.S.C.
.sctn.119 to European Patent Application No. 1811254.0, filed on
Dec. 21, 2001 in the European Patent Office, the disclosures of
which are all incorporated herein in their entireties by
reference.
BACKGROUND
[0002] An operation of electric power transmission lines is
disclosed.
[0003] As a consequence of the electric utility industry
deregulation and liberalization of electricity markets, the amount
of electric power exchanged between remote regions and trading
activities between different countries are steadily increasing. In
addition, due to the emerging desire to optimize assets,
substantially increased amounts of power are transmitted through
the existing networks, occasionally causing congestion,
transmission bottlenecks and/or oscillations of parts of the power
transmission systems. In particular, thermal constraints can impose
limitations on power flow in critical power flow paths or power
transmission corridors interconnecting distinct areas. Exemplary
reasons for these thermal constraints are an annealing of and/or a
permanent damage to the conductors caused by severe overloads as
well as an increase in conductor length with the temperature of the
power line conductor. The latter may lead to unsatisfactory ground
clearance due to line sag and possible flash-over to nearby trees
or other line conductors, with subsequent trip by the protection
system as a result.
[0004] A number of symptoms or effects relate to an elevated line
temperature and therefore can influence the maximum allowable
temperature of a specific electric power transmission line. Among
the former are a degradation of mechanical properties of the
conductors and connectors (loss of mechanical strength and
integrity as well as accelerated component aging), an increase in
conductor sag, an increase in resistive losses, and a potential
damage to devices or equipment attached to the conductors (e.g. for
power line communication).
[0005] Both the maximum allowable conductor temperature and the
worst-case weather conditions used in calculating line ratings are
selected by the individual network owners or independent
Transmission System Operators (TSO). The operational temperature
for a specific overhead power lines generally varies between, for
example, 50 and 100.degree. C.
[0006] Since the line temperature is not measurable in a straight
forward way, an alternative limit in terms of maximum allowable
power transfer or maximum allowable current can be derived based on
worst-case scenario assumptions. This limit is usually referred to
as the "ampacity" of the line. The additional assumptions made can
be subjective, and/or the resulting thermal limits in terms of
power transfer or current can be made on a somewhat ad-hoc basis.
Also, since they are based on a worst-case scenario, they can be
unnecessarily conservative. Consequentially, direct monitoring of
the thermal limits in terms of temperature instead of power
transfer or current can be provided using an on-line measurement of
the line temperature in order to evaluate, during operation,
whether a line is loaded close to its operational temperature limit
or not.
[0007] A number of techniques have been proposed and several
products are available to measure or infer the temperature of power
line conductors during operation. These comprise the use of
infrared cameras, mechanical tension measurements, direct sag
measurements, predictive meteorological methods, or the use of
phasor measurement data.
[0008] Infrared cameras may be used to take a digital picture of a
power line, the color information of which is subsequently analyzed
in a signal processing step in order to derive the temperature of
the conductors. This technique can perform monitoring of the
temperature of particular hotspots that are known a-priori.
[0009] Mechanical tension measurements between the tower and the
isolator in combination with solar radiation and ambient
temperature measurements can be based on the fact that the tension
of the line conductor is approximately inversely proportional to
its length. From the relationship between tension and length of the
conductor, the line sag of a single span and the conductor
temperature can be inferred. Likewise, line sag monitors directly
measure the line sag of a single span through for example GPS
(global positioning system) or laser measurement techniques.
[0010] Predictive meteorological methods and products based on the
IEEE 738-1993 "Standard for Calculating the Current-Temperature of
Bare Overhead Conductors", the disclosure of which is incorporated
herein by reference in its entirety, have been proposed to model
the dependency between the line ampacity and various operational
and ambient properties. These methods involve a number of
meteorological measurements such as air temperature, wind speed,
angle between wind and conductor and the elevation above sea level.
The IEEE 738-1993 standard then specifies a computational procedure
that can be used to estimate a steady-state conductor temperature
from the meteorological measurements alone, i.e. without reverting
to an independent measurement of the line temperature. The standard
is based on a purely static model which does not account for the
time-dependent behaviour of the line temperature and which is
difficult to tune since various input parameter data may be assumed
and detailed meteorological data is required.
[0011] The patent application EP 1324454, the contents of which are
hereby incorporated herein by reference, describes a way of
determining an actual average conductor temperature, via a
calculated series resistance, from on-line phasor measurements. The
average line temperature is largely independent of assumptions
regarding any line parameters, such as the inductance, reactance or
susceptance of the power line conductor. The method includes
determining time-stamped current phasor information and voltage
phasor information for a first end and a second end of the line,
computing an ohmic resistance of the line from the phasor
information, and computing an average line temperature from the
ohmic resistance.
[0012] A state or condition of an electric power system at one
specific point in time can be obtained from a plurality of
synchronized phasor measurements or snapshots collected across the
electric power system or power transmission network. Phasors are
time-stamped, complex values such as amplitude and phase, of local
electric quantities such as currents, voltages and load flows, and
can be provided by means of Phasor Measurement Units (PMU). These
units involve a very accurate global time reference, obtained e.g.
by using the Global Positioning Satellite (GPS) system or any other
comparable means, and allowing synchronization of the time-stamped
values from different locations. The phasors are sampled at, for
example, a rate of 20 to 60 Hz with a temporal resolution of less
than 1 millisecond, and thus can provide a rather dynamic view on
transient states that goes beyond the rather static view as
provided by scalar values such as RMS values of voltages or
currents and relied upon by SCADA/EMS systems.
[0013] Accordingly, parameters of an electric power network may be
estimated by repeatedly measuring, at a plurality of network
locations, synchronized values of electrical network variables; and
identifying there from, during network operation, currently valid
parameters of a mathematical model of the power network. In
particular and by way of example, the Patent Application EP-A 1 489
714, the contents of which are incorporated herein by reference,
discloses an adaptive detection of electromechanical oscillations
in electric power systems based on a linear time-varying model. A
system quantity or signal such as e.g. the amplitude or angle of
the voltage or current at a selected node of the network is
sampled, and the parameters of the linear model representing the
behaviour of the power system are estimated by means of Kalman
filtering techniques. This process can be carried out in a
recursive manner, i.e. every time a new value of the system
quantity is measured the parameters of the model are updated.
Finally, from the estimated parameters of the model, the parameters
of the oscillatory modes, such as frequency and damping, are
deduced and presented to an operator. This adaptive identification
process can provide a real-time analysis of the present state of
the power system.
SUMMARY
[0014] A method and system are disclosed that can, at any time
during operation, provide a reliable forecast of a power line
conductor temperature. An exemplary method of estimating model
parameters of a thermal model of a power line as well as a use of
the thermal model are disclosed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] The subject matter of the invention will be explained in
more detail in the following text with reference to preferred
exemplary embodiments which are illustrated in the attached
drawings, of which:
[0016] FIG. 1 schematically shows a power line with a number of
measurement devices,
[0017] FIG. 2 depicts a process of model parameter estimation,
and
[0018] FIG. 3 depicts measured values of a number of quantities
recorded for a period of 6 h.
[0019] The reference symbols used in the drawings, and their
meanings, are listed in summary form in the list of reference
symbols. In principle, identical parts are provided with the same
reference symbols in the figures.
DETAILED DESCRIPTION
[0020] In accordance with exemplary embodiments, a relationship
between a temperature of a power line or power transmission
conductor, an electrical quantity of the power line such as a
current or power flow through the power line, as well as
meteorological quantities or ambient conditions of the power line
such as wind speed, wind direction, humidity, solar radiation and
ambient temperature, can be established in the form of a thermal
model of the power line and repeatedly calculated or updated during
operation of the power line. To this end, values of the
aforementioned quantities or variables can be continuously or
periodically measured or sampled, and the collected values of the
quantities evaluated in order to update or tune model parameters of
the thermal model. Including the temperature of the power line as a
variable of the thermal model allows using, without diminishing its
validity, a simple model or even a black box model with a limited
number of model parameters. The latter may be updated without
excessive computational efforts as frequently as desired, which
ultimately increases the reliability, at any time during operation,
of a forthcoming line temperature prediction.
[0021] In an exemplary embodiment disclosed herein, an average
temperature representative of the entire line is determined via two
Phasor Measurement Units (PMU) providing synchronized phasor values
from two ends of the power line. An ohmic resistance of the power
line is computed from the phasor values, from which in turn the
average line temperature can be derived. As the PMUs are primarily
provided for other purposes, e.g. for determining electrical
quantities, such a double use avoids the need for any dedicated
line temperature sensing device. In addition, as the PMUs are
generally mounted indoors in a protected environment, they are less
exposed to environmental stress than any other line temperature
sensing device.
[0022] On the other hand, it can be advantageous to calibrate the
conversion from the resistance to the temperature of the power line
by means of such a dedicated line temperature sensor. As the latter
may only be temporarily needed for the specific purpose of
calibration, it may be expensive or otherwise cumbersome without
impairing the subsequent operation of the power line.
[0023] In an exemplary variant, the meteorological data is obtained
by subscription and imported from an external source such as a
meteorological institute which is distinct from the Transmission
System Operator (TSO). Relying on the data from a specialist can,
if desired, avoid dedicated measurement units located on or close
to the line conductor and operated by the TSO. Due to a relatively
slow change in ambient conditions and their small geographical
gradients, any potential temporal or geographical offset between
the meteorological data and electrical data is of a lesser concern
and can be ignored.
[0024] In an advantageous variant, an adaptive method or algorithm
is based on a recursive calculation of the model parameters for
each time-step, based on new values of the measured quantities and
the old values of the model parameters. As opposed to the
collection of data over a time window and then performing the
parameter identification at once, any change in the power system
can thus be detected much faster. In this context, the thermal
model can be a linear autoregressive model of finite order, and an
adaptive Kalman Filter can be used to estimate its model
parameters.
[0025] The thermal model may be a nonlinear parametric model based
on a heat balance equation. Such a physically inspired model can
offer higher confidence when used for simulation, prediction or
extrapolation and can be used in place of, e.g. a linear parametric
model with no physical meaning, such as an Auto-Regressive Moving
Average model (ARMA). The ARMA model on the other hand has the
advantage that, except for the model order, no a-priori assumptions
on model structure and parameters have to be made.
[0026] In a further aspect of an exemplary embodiment, the thermal
model can be used to calculate a power line temperature given
actual or forecasted values of electrical and meteorological
quantities as e.g. provided by load predictions or weather
forecasts. By comparing this predicted temperature with a
temperature limit for the power line, a maximum amount of current
or electrical power flow that can be transported on the line
without violating the line temperature or sag limits may be
derived, for example, by means of a simulation or inversion of the
thermal model. Determination of a maximum flow that will result in
a certain conductor temperature is particularly useful in order to
determine the actual power flow limits to be used in a balance
market clearing process. Since these limits are less conservative
than a-priori known limits, less expensive balance power can be
scheduled resulting in an economical gain for the TSO.
[0027] A computer program product is disclosed which includes
computer program code means for controlling one or more processors
of a model parameter estimator, a line temperature predictor or a
Power Flow Control device connected to the power line. Such a
computer program product can include a computer readable medium
containing therein the computer program code means.
[0028] FIG. 1 shows a power line 10 that is part of a power system
comprising a plurality of power generating means and power
consumers interconnected by a transmission network. At two ends of
the power line, two synchronized Phasor Measurement Units (PMU) 11,
11' are provided and can be mounted in respective substation
control buildings or any desired, suitable location. Sensing
devices for measuring meteorological quantities at one or more
locations in the vicinity of the power line 10 are collectively
referred to as weather station 12. Means 13 for measuring
electrical quantities of the power line are depicted schematically,
some of their components such as instrument transformers or process
busses may also be used by the PMUs. An independent line
temperature measurement device 14 is likewise shown. The weather
station 12, the means 13 and the device 14 collect and provide a
number of equidistantly sampled measurements of ambient conditions
(wind speed W, wind direction, solar radiation S, ambient
temperature T.sub.a, humidity), electrical quantities (line current
l, power flow P) and line temperature (T.sub.l) to a processor 15
of a model parameter estimator, a line temperature predictor or a
Power Flow Control device.
[0029] FIG. 2 depicts an exemplary process of model parameter
estimation according to an exemplary embodiment. The measured
values of the meteorological and electrical quantities,
collectively denoted as input variables u, are fed to the processor
15 for estimating or tuning, based on parameter identification or
fitting techniques such as Kalman filters, Maximum Likelihood or
Least-Squares, values of model parameters A, B, . . . ; C.sub.l, .
. . of a thermal model of the power line. Based on the momentary
values of the electrical and meteorological quantities as well as
of the model parameters, a line temperature prediction
T.sub.l.sup.f is produced as an output variable, and any difference
between the latter and a corresponding independent measurement of
the line temperature T.sub.l, is fed back for further
evaluation.
[0030] The thermal model can be a standard linear black box model
in transfer function or state-space form. For dealing with several
input variables u the discrete-time state-space form:
x(kT+T)=Ax(kT)+Bu(kT)+Ke(kT) (a) y(kT)=Cx(kT)+Du(kT)+e(kT) (b)
x(0)=x0 (c) is the most convenient one. Here, x denotes the dynamic
state of the model, u the driving input variables, y the output of
the system that model should reproduce and e Gaussian white noise,
whereas A, B, . . . are model parameters. Linear models are
attractive because of the simple parameter estimation techniques
that are available and because of the fact that virtually no
a-priori knowledge needs to be given, except for which measurements
to use. On the other hand, such linear models can only be used to
predict the line behaviour with rather small variations in the
input variables, since non-linear contributions between the
conductor temperature and the measured quantities could be quite
substantial when the variations in the conductor temperature and/or
measurement quantities are large. Accordingly, a linear model is
suitable for short-term predictions on the order of minutes.
Particularly a prediction interval of some 5-30 minutes (or lesser
or greater) can be used to compute dynamic ratings of power lines
based on a 5-30 minute forecast (or lesser or greater) and based on
the identified dependencies between the conductor temperature and
the electrical and meteorological measurements. This rating can be
most beneficially used in the market clearing for the balance
market which usually takes place on a similar time scale.
[0031] Alternatively, a physically inspired thermal model based on
a heat-balance equation can have the advantage that model
parameters which are known with enough certainty can be fixed
a-priori, wherein such a thermal model could be valid also with
quite large variations in the operating points. However, such a
model would be non-linear and can involve more complicated
parameter estimation techniques than the linear black box models.
The extended Kalman filter has been shown to perform well in the
estimation of parameters in non-linear models, although also other
options are available. An exemplary heat balance equation has the
form C l .times. d T l i d t = q i .times. .times. n ( I i i , T a
i , Solar i , .times. ) - q out ( T a i , Wind i , .times. ) ,
##EQU1## where C.sub.l is a model parameter reflecting a
characteristic thermal time or thermal capacity of the line, and
where q.sub.in represents the incoming heat flow to the conductor
with main contributions from the sun's radiation and the heat
produced by resistive losses in the conductor, and where q.sub.out
is the total heat loss of the conductor. The heat loss depends on
many factors, for example the radiation and conduction to the
surrounding air which in turn depends on factors like the wind
speed and direction and the air humidity. The two heat transfer
terms can involve a number of further model parameters.
[0032] For prediction in the longer term a higher model order and
long data sets can be used so that the daily and even weekly or
monthly variations can be modelled. Predictions based on such
models could be used for example in the computation dynamic ratings
of lines in the day ahead market, which typically are executed 24
hours ahead with update intervals of one hour.
[0033] FIG. 3 shows some measurement data from a field test, in
which the weather and electrical phasor measurements were recorded
during an observation window of six hours following the connection
of a 380 kV transmission line at midday. The measured quantities
are (top left plot) the conductor temperature (continuous line) and
the ambient temperature (dashed line), the line current (top right
plot) the humidity (middle left plot), the wind speed (middle right
plot) and the solar radiation (bottom plot) at a specific location
along the line. The recorded measurement samples were evaluated for
the identification of the parameters A, B, . . . of a first order
discrete time state-space model as indicated above, with the aim of
accurately reproducing the line temperature. On the basis of the
identified model parameters, the effect of a 100 A increase in line
current and of a one degree change in ambient temperature have been
simulated, yielding an increase in the line temperature of about
2.5.degree. C. and 1.degree. C. respectively.
[0034] The phasor data v.sub.1, i.sub.1; v.sub.2, i.sub.2 can be
collected from phasor measurement units that are distributed over a
large geographical area, i.e. over tens to hundreds of kilometres.
Since the phasor data from these disparate sources are analysed in
conjunction, they refer to a common phase reference. Therefore, the
different phasor measurement units have local clocks that are
synchronised with each other to within a given precision. Such a
synchronisation of the phasor measurement units can be achieved
with a known time distribution system, for example the global
positioning (GPS) system. In a typical implementation, the phasor
data is determined, for example, at least every 200, or every 100,
or preferably every 20 milliseconds, with a temporal resolution,
for example, less than 1 millisecond. In an exemplary embodiment,
the temporal resolution is less than 10 microseconds, which
corresponds to a phase error of 0.2 degrees. Each measurement is
associated with a time stamp derived from the synchronised local
clock. The phasor data therefore comprises time stamp data.
[0035] According to an exemplary variant, the temperature of the
line is determined in the following way: The electric line
parameters, or at least the ohmic resistance R.sub.l of the line,
i.e. the real part R.sub.l of the line impedance Z=R.sub.l+jX.sub.l
are determined from measured or computed phasor information
representing some or all of the voltage and current phasors at the
two ends of line.
[0036] In a first variant, it is assumed that the shunt capacitance
jX.sub.c remains essentially constant (e.g., .+-.10 percent or
lesser or greater) during power line operation and is known from
other measurements, design parameters or calculations. Then the two
voltage phasors v.sub.1 and v.sub.2 are determined at either end of
the line and one of the current phasors i.sub.1 or i.sub.2. Let
i.sub.1 be measured. Then the impedance Z is Z = v 1 - v 2 i 1 - v
1 jX C . ##EQU2##
[0037] In a second variant, no assumption on shunt impedances is
made, and the two voltage phasors v.sub.1 and v.sub.2 and the two
current phasors i.sub.1 or i.sub.2 are measured or determined from
measurements. Determining the actual electrical line parameters
R.sub.l, X.sub.l, X.sub.c from these measurements is common
knowledge. Since resulting equations for the electrical line
parameters are non-linear, numerical methods such as Newton-Raphson
approximation are used for determining actual parameter values. The
resulting line parameters are actual values wherein they are
determined online and represent the actual state of the power line.
The average line temperature T.sub.1 is computed from the ohmic
resistance R.sub.l by modelling a relationship between temperature
and resistance as linear, i.e.
R.sub.l=R.sub.0(1+.alpha..sub.0(T.sub.l-T.sub.0)), where R.sub.0 is
a known material property specified by the power line conductor
manufacturer, i.e. a reference resistance dependent on the
construction of the line, and where .alpha..sub.0 is a material
constant for the line cable and wherein T.sub.0 is, for example, a
reference (e.g., ambient) temperature of the line. The linear
relationship is typical for common conductor materials such as
copper or aluminium. As an example, the parameter values are such
that for a line temperature change of .DELTA.T=30.degree. C. the
resistance changes by about .DELTA.R.sub.l=12%. The equation for
the chosen relationship is solved for T.sub.1, which gives the
desired average line temperature.
[0038] It will be appreciated by those skilled in the art that the
present invention can be embodied in other specific forms without
departing from the spirit or essential characteristics thereof. The
presently disclosed embodiments are therefore considered in all
respects to be illustrative and not restricted. The scope of the
invention is indicated by the appended claims rather than the
foregoing description and all changes that come within the meaning
and range and equivalence thereof are intended to be embraced
therein.
List of Designations
[0039] 10 power line [0040] 11, 11' Phasor Measurement Units [0041]
12 weather station [0042] 13 electrical quantity measurement means
[0043] 14 line temperature measurement device [0044] 15
processor
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