METHODOLOGY FOR TRANSMISSION LINE
CAPACITY ASSESSEMENT BASED ON PMU
DATA
Anna Mutule [1], Ervin Grebesh [2], Irina Oleinikova [3], Artjoms Obushevs [4]
[1]–[4]
Smart Grid Research Centre
Institute of Physical Energetics
Riga, Latvia
amutule@edi.lv [1], ervins.grebess@gmail.com [2], irina.oleinikova@edi.lv [3], a.obusev@gmail.com [4]
Abstract— This paper reflects the authors’ experience in
conductor thermal part (temperature) and mechanical part (sag
and clearance) estimation in real Latvian PS conditions using
IEEE, CIGRE, Girshin and classical mechanics methods. Both
theoretical and practical results of the research are discussed.
Theoretical calculations based on real Phasor Measurement
Unit (PMU) measurements of 330 kV line and environmental
data collected from meteo-websites have shown that deviation is
low in conductor thermal calculation methods. The Dynamic
Line Rating (DLR) measurements are improved with the PMU
data, which permit accurate line current data with GPS
timestamps. The authors have calculated the conditions of
conductor thermal dynamics at a step of one second; such
accuracy together with environmental data can provide an
excess of maximum line capacity without harming the conductor
life cycle.
Index Terms-- Conductor temperature, dynamic line rating
(DLR), line sag, phasor measurement unit (PMU).
I.
INTRODUCTION
The electric power industry worldwide is experiencing the
need to push more power through existing assets. This is a
result of the ever-growing demand for electric power, and it
requires continuous investment in new assets. This is all
particularly true for overhead transmission lines, which are
the limiting circuit components in most cases, and the most
expensive and difficult ones to replace or upgrade. However,
the industry is recognising that for almost all cases, existing
transmission lines have significant extra power capacity, and
there is a growing need to take advantage of that extra
capacity. To solve the problem of maximum transmission
capacity, it is necessary to obtain sag estimation that could be
achieved using a PMU. At the same time, PMU application
can help in a situation when the line is being operated near its
maximum allowable power. This can be considered true in
the case when transmission line operator uses permanent
throughput and makes necessary corrections depending on the
season.
This research was supported by Nordic Energy Research Council
funding programme for Sustainable Energy Systems 2050 through the Smart
Transmission Grids Operation and Control (STRONg2rid) project (No.79).
Phasor measurement unit is a device that uses the global
positioning system (GPS) to synchronise wide-area
measurements in power systems and to stamp the time of
measurements of high precision, i.e., less than 1 microsecond.
These measurements are then transmitted over a high-speed
broadband network to control centres [2]. The result is a
highly detailed and synchronised feed of power system data
that provides operators with real-time intelligence allowing
them to react more quickly to system disturbances and take
actions to avoid a blackout or prevent a disturbance from
cascading. Apart from the early detection of equipment
failures, system monitoring and operation, the PMU
application can provide a much clearer view of the entire
transmission system parameters in dynamics, such as
technical losses, corona losses, line parameters and
transmission capacity.
II.
BACKGROUND
Sag and clearance calculations are a topical issue for
Latvian and Estonian PS interconnection. In 1960 these lines
were put into operation for 220 kV. In 1962 the lines were
reconstructed for 330 kV leaving old pylons. Nowadays this
transmission line poses difficulties to the power system
operation. There is a problem in sag value especially in warm
summer time, when temperature increases to 30 °C. This
problem leads to a decrease in maximum power throughput
capability to avoid a short circuit possibility. This situation
creates unnecessary and unacceptable uncertainties about the
safe carrying capacity of individual lines on the transmission
networks [1], [11]. Instead, utilising online voltage and
current phasor measurements by PMU, transmission line
parameters and temperature can be estimated.
The approach to resolving the issues of sag and maximum
conducted power consists of determining the thermal
condition of the conductor measured by means of the
methods described below.
A solution to the problem of high-voltage lines may be
DLR, which considers the line under constantly changing
conditions: weather, mechanical and electrical load. This
issue has been discussed quite extensively in many countries,
from both the theoretical and practical perspectives –
monitoring of parameters and the behavior of the line for up
to several years [8]-[10]. Results of examining the issue of
DLR by other countries demonstrate positive ratings. The
ratio of static and dynamic evaluation of the line is depicted
in Figure 1.
equilibrium. For solving DLR questions dynamic thermal
condition is used, which means - at some time t0 line
conductor stores some heat value, and can be described in the
following equation:
Pst =
dT
= PJ + P S − PC − PR .
dt
(1)
where T is the line conductor temperature, Pst is heat
stored in the conductor; PJ is Joule heating; PS is solar
heating; PC is convective cooling and PR is radiative
cooling. The relationship of energy input, output and the
following conductor of line No. 301 are shown in Figure 2.
Figure 1. General form of capacity increase by DLR
Obtaining spare area by DLR and the output of the
maximum allowable capacity of the line will depend on these
factors: weather conditions, mechanical characteristics of the
conductor as well as pylon height and span length.
Further, the appropriate use of dynamic line ratings needs
to be included in this review because adjusting a line rating
according to changes in ambient conditions may enable the
line to carry a larger load while still meeting safety
requirements.
III.
METHODOLOGY FORMULATION
The algorithm can be divided into two parts: the first part
being thermal, which describes the determination of
temperature, and the second one being mechanical, which
involves the calculation of sag and ground clearance, as
shown in Figure 3.
Figure 2. Relationship between coming and going energy in conductor
It should be noted that IEEE method for conductor
thermal calculation is not exclusive; there are also such
methods as CIGRE and Girshin. All of them give pretty
similar results. Methods comparison was done by authors in
their previous work [1], [4], [5].
To find conductor temperature T, at moment of time t the
following values should be known (Figure 3) : current value
from PMU data, environmental parameters such as wind
speed, wind direction, solar radiated heat flux, ambient
temperature as well as constant values, such as solar
absorptivity, degrees of latitude etc.
A.
Transmission Line Temperature Estimation
Parameter that mainly characterises sag and clearance
variation is line temperature. In this case, if temperature
estimation is correct, line sag and clearance estimation will
have fewer differences from real line sag and clearance,
respectively.
For line temperature calculation IEEE std. 738-2006 has
been chosen, that describes the standard for calculation of the
current-temperature relationship of bare overhead conductors
[3]. This method is presented in such a way to solve a current
value, based on the known conductor temperature and other
parameters. To use this equation oppositely Newton`s method
was used to express a conductor temperature value if a
current value is known.
The IEEE standard describes two possible conditions of
thermal rate: steady state and dynamic conditions. Steady
state is described by equation in thermal balance, where heat
value of conductor at any time period is zero. Dynamic
conditions describe the same equation without thermal
Figure 3. Transmission line sag estimation graph.
B.
Transmission Line Sag Estimation
For calculation of mechanical part equations from
classical mechanics are used, which are applied at the design
stage [6]. To find sag value fcal after temperature calculation
several steps should be performed (Figure 4.).
Figure 5. Sag value at pylons with different height.
IV.
Figure 4. Mechanical part calculation algorithm.
First of all, based on conductor data linear and specific
mechanical loads should be defined for different conditions.
Based on the load value and considered span length, critical
span values should be clarified. Their relation will give initial
conditions for tension component σ0, specific load γ0 and
temperature t0. Using obtained temperature tcal and initial
conditions cubic equation of conductor state can be solved.
Finally horizontal tension component for temperature tcal and
sag value fcal can be estimated.
σ cal
γ 2 l2E
γ 2l 2 E
− max
= σ 0 − 0 2 − αE (t cal − t 0 )
24σ cal
24σ 0
f cal
γ ⋅l2
= 1
8 ⋅ σ cal
To test the theoretical methods, an experiment has been
done in collaboration with the Latvian TSO. For experiment
line No.301 Valmiera (LV)-Tartu (EE) was chosen, in span
No.1143-1142 on 11 August 2015 between 11.00 am and
12.00 am. The measured parameters and their values are
given in Table I. Figure 6 shows thermovisor camera
measurement. Several values that were not measured by
equipment were taken from the Latvian Meteorological
Centre (LMC) station, which is located at the distance above
50 km from experiment location.
TABLE I.
Parameter
(2)
(3)
Conductor
temperature
Line span
clearance
Wind speed
where, γmax is maximal specific mechanical load, E is
conductor flexibility coefficient, α is linear thermal
elongation coefficient and γ1 is weight of conductor.
Line sag value fcal describes the middle point of pylon
span lowest point when the pylon height is the same. In real
line topology scenario it is hard to find two pylons with equal
conductor suspension height.
CASE STUDY
Wind
direction
Ambient
temperature
MEASUREMENT VALUES
Method/
Equipment
Description
Value
FLIR T640
Thermovision camera
30-34 °C
Clearance to
ground gear
KESTREL
4000
LMC
Bases on infrared
sensor signal
7.23-7.24 m
Pocket weather station
1.5-2.0 m/s
Historical data
2.0-2.2 m/s
LMC
FLIR MR77
Line topology
Longitudinal
line profile
Historical data
~90°
Thermovision camera
option
Provided by TSO and
digitized in MATLab
model
26.4-26.6
°C
In such a case the lowest point of conductor is described
by point O (Figure 5.). Here, it should be noted that
maximum sag value and sag positioning do not change for
such a situation [7]. To find y, the length to point O, it is
necessary to know: pylon height A and B difference - ∆h, the
distance between line sag fcal and the lowest point at y-axis O
- yc, correction by x-axis for the clearance lowest point xc.
The mentioned parts can be found as follows:
σ cal  ∆h 
2

 ,
2 ⋅ y1  l 
σ ⋅ ∆h
xc = cal
.
γ1 ⋅l
yc =
(4)
(5)
Figure 6. Thermovision camera measurement.
-
A.
Thermal part
PMU current flow for experiment period is shown in
Figure 7. Also there are presented conductor temperature
results, based on IEEE std. 738-2006 calculated based on
dynamic conditions. Due to frequent PMU measurements and
relatively smooth changes in thermodynamic conditions PMU
data were sieved per 1/60/600 seconds timestamps
respectively. Based on the results shown in Figure 7, the most
optimal timestamp size is 1 second, where PMU data are
reduced 50 times and thermodynamic accuracy does not lost
in relatively fast current change.
Conductor temperature value calculated with IEEE
standard varies from thermovision camera measurements
from 0 to 3 °C for all experiment time. Theoretical results are
lower than practical measurements. The reason for such
difference could be a systematic error when IEEE calculation
will give lesser temperature, several coefficients which value
could be predetermined wrong - absorptivity and emissivity
coefficients, such parameter as wind was not provided in
dynamics change for experiment location but was set as
constant value for this hour.
ground is graphically illustrated in Figure 8. The difference
between the theoretical and practical calculations is
approximately 20-30 cm, which can be considered a
permissible error taking into account the possible error of the
device and possible changes in the ground topology [6], [7].
TABLE II.
Symol
Unit
MECHANICAL PARAMETERS DESCRIPTION
Description
Value
Pylon
PVS-330A
Pylon
PVS-330A
70.9
72.4
HA,B
m
Conductor suspension
height on sea level
l
m
m
Span length
Pylon height difference
326.9
1.5
Weight of conductor
0.0034
Linear thermal
elongation
19.85 ⋅ 10 −6
∆h
γ1
α
tcal
σcal
daN
mm 2
1
°C
°C
daN
mm 2
fcal
m
ccal_real
m
Conductor temperature
by IEEE
Horizontal tension
component
Sag value
Clearance to ground
value
33
5.66
8.01
7.46
Despite theoretical and practical part difference in few
degrees such results for the first DLR experience in Latvia
give the possibility of considering IEEE std. 738-2006 as
reliable for further experiments, with all parameter dynamical
monitoring and for long-term DLR monitoring creation [3].
Figure 7. Conductor temperature by IEEE and current value from PMU.
B.
Mechanical part
To calculate the mechanical part of line No. 301, the
longitudinal line topology provided by Latvian TSO has been
digitised. The need to digitise the line is determined by
several reasons: graphical observability of the results,
including the ground profile in the mechanical calculation,
which in turn is tied to the sea level, as well as the ability to
integrate data into other calculations or into the real-time
mode.
Data on mechanical parameters and pylons used in the
experiment are aggregated in Table II. Due to the fact that
changes in the conductor temperature are not big, a constant
value has been chosen. The situation occurring during the
experiment between the pylons and the minimum clearance to
Figure 8. a) Whole line topology, b) Experiment pylons and situation model
for calculated temperature
V.
A.
DISCUSSION
Thermal part
Although IEEE Standard 738-2006 can be considered a
fairly accurate method for calculating the conductor
temperature proved also by other studies, to monitor the line
in the continuous mode it is necessary to consider the
formation of a neural network, as already performed in.
Annual monitoring of DLR provides results on a particular
terrain and weather conditions that can be more precise than
using common methods [10].
Mechanical part
Based on the result shown in Figure 8, it is possible to
distinguish a few common features associated with
calculations of a particular line and mechanics in general:
line clearance to ground value. Based on this restriction
optimal conductor temperatures are in the range of 35 – 40°C.
B.
1) Provided that the ground topology is taken into
account in the calculation of clearance to the ground, it can be
stated that the real minimum clearance to the ground will be
less than the one in which the ground topology is a straight
line. In some cases, a strong deviation from the axis Ox is
possible.
VI.
CONCLUSIONS
Taking into account clearance results for line No.301 it
can be concluded that line conductor thermal restriction
should be set at 35-40°C value to avoid a short circuit
possibility, while such type of conductor theoretically can
withstand 70°C.
Despite these limitations, the use of DLR is possible for
such conditions and becomes even more topical, namely: the
reduction in the line conductivity in the summer and
maximum increase in the line conductivity demonstrated by
thermodynamic calculations based on the DLR data.
As the next step, in order to refuse the use of thermal
standards, it is also necessary to decrease mistake probability
based on the predetermined coefficients and in order to
clarify results for local conditions the machine learning
model should be used.
Power companies can use these methodologies to
maximise power throughput of existing assets, defer capital
expenditures, and simultaneously increase safe and reliable
operation of their assets.
ACKNOWLEDGEMENT
Figure 9. Clearance to ground deviation.
As can been seen from Figure 9, clearance to ground
value with correction by including ground topology can reach
difference about 0.5 m or more that is significant and should
be taken into account.
2) Due to the feature of line No. 301, whose pylons were
originally supposed to be used for 220kV, a situation occurs
when clearance to ground is lower than it is permitted by the
Latvian standards on power line transmission operation [11].
Figure 10. Clearance values for different temperature values.
As can been seen from Figure 10, clearance to ground
values for 70°C exceeds Latvian standards for transmission
Authors would like to thank the Latvian Transmission
System Operator “Augstsprieguma Tīkls” for the
organization and great assistance in conducting experimental
part of this research, although they may not agree with all of
the interpretations provided in this paper.
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