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Preliminary model comparison for Dynamic Thermal Rating estimation

Preliminary model comparison for Dynamic
Thermal Rating estimation
Emanuele Ogliari, Alfredo Nespoli, Roberto Faranda
Department of Energy
Politecnico di Milano
Milan, Italy
Davide Poli
University of Pisa
Pisa, Italy
Fabio Bassi
Terna Rete Italia S.p.A.
National Dispatcing
Abstract—The large-scale diffusion of renewable power gener-
ators contributes to trigger a crisis in power system components
that started to operate closest to their thermal limits, thus
increasing the risk of network congestions. To manage with these
contingencies induced by Renewable Energy Sources generators,
the Transmission System Operators have to implement proper
corrective actions. Transmission System Operators usually adopts
well-known physical methods, based on weather forecasts, to
estimate the temperature of the lines in order to avoid an
expensive installation of monitoring devices on their network.
However, this estimation often results in inaccurate forecasts
of the conductors’ temperature, due to many complexities and
parameters which should be considered in the physical model of
the line or to not precise weather forecasts. This paper proposes
an innovative method based on Artificial Neural Network to eval-
uate the conductor’s temperature and consequently the Dynamic
Thermal Rating in a given overhead line. The results based on
real case studies and measures, clearly show the effectiveness and
the potential of the proposed method.
Index Terms—DTR, Thermal estimation, CIGRE thermal
model, ANN, Overhead line
The large-scale diffusion of renewable power generators all
over the transmission and distribution networks is leading a
global transition from a centralized to a distributed generation.
In particular, the inherent unpredictability of the generation
of wind and photovoltaic power systems has required the
system operators to schedule more reserve resources for the
instantaneous balancing between the power produced by the
generators and the one requested by the loads, including
system losses.
The increasing penetration of renewable energy sources
(RES) in power systems, together with the decentralization
of the energy production, is requiring increasing capacity
of the electrical grid in order to integrate such a variable
power generation. Therefore, in order to avoid exceeding the
degradation of the mechanical properties of the conductors
and to respect phase-to-ground clearances, maximum current
in the lines must be limited [1] [2] [3] [4].
It is well known that reliable OverHead Line (OHL) op-
eration requires, amongst other things, the rigorous satisfac-
tion of proper thermal constraints, which limit the conductor
temperature in order to keep the line sag in fixed allowable
ranges, avoiding the risk of ground faults. The transmission
capacity of an OHL is the current (ampacity) that corresponds
to the maximum acceptable temperature of conductors. Hence
the maximum acceptable temperature is limited by the thermal
performance of the material. Therefore it is extremely useful
to give an accurate evaluation of the temperature of any line in
the grid, namely Dynamic Thermal Rating (DTR) of the line.
DTR, also referred to as Dynamic Line Rating (DLR), can be
done by directly monitoring the temperatures of conductors,
or uses weather and load forecasting to estimate their future
trend, in order to calculate the actual capacity of a transmission
line [5] [6]. Therefore, this can be achieved either by means
of direct measurements or by an effective estimation method.
The former implies a very expensive solution which is not
adopted, while the latter is cheaper but often can be not very
accurate. Indeed, the adopted method has to consider several
parameters affecting the temperature of the line and, at the
same time, should be not too complicated to be used. The
temperature of the conductors depends on the current in the
line and on the local weather conditions [7] [8] [9] [10].
The benefits deriving by the application of DTR techniques
in existing power systems have been assessed in several papers,
which proposed different solution methodologies, including
those based on first-order components thermal models, or
using distributed sensors for the direct measurement of the
conductor temperature [11].
These techniques, if integrated in advanced optimization
frameworks, known as Weather Condition-based Optimal
Power Flow (W-OPF) or Electro-Thermal OPF (ET-OPF),
could reliably improve the components loadability, enhancing
the congestion management flexibility, and maximizing the
RES generators exploitation [12] [13] [14] [15].
The goal of this work is to compare the performances
of different methods for the forecast of the temperature of
OHL. The comparison is made between a physical model
(CIGRE) [1] [16], and a statistical method, based on Artificial
Neural Networks (ANN) [17]. Such comparison is of particular
interest, especially when the forecasted wind speed is lower
than 2 m/s, which is proven to be the range where physical
models provide a worse result [18].
978-1-7281-0653-3/19/$31.00 © 2019 IEEE
In the scientific literature it is possible to find several DTR
estimation models, in the following the physical CIGRE model
and a novel technique based on ANN, are presented.
A. Physical CIGRE model
In deterministic weather-based DTR procedures, the temper-
ature of conductors is estimated using a proper thermal model
of the transmission line, usually the one developed by CIGRE
[7] or by IEEE [8].
Conductor’s temperature depends on various factors such as
conductor material, diameter, superficial characteristics, load
current, and weather conditions insisting on it. Once these
latter are known, the above mentioned standard allows to cal-
culate the conductor’s temperature given the line current or the
capability, given the maximum feasible operating temperature.
In physical models like CIGRE or IEEE, the thermal behavior
of the conductor is assessed based on the following first order
dynamic equation:
dt =1
Fig. 1. Thermal behavior of OHL Conductor [7]
mcpis the conductor heat capacity per unit length, defined
as the product of its specific heat capacity, cp, and the mass
per unit of length, m. If the conductor consists of different
materials, its heat capacity is the sum of heat capacities of all
the ith strands, as mcp=Pimi·cp,i.
qcis the convected heat loss rate per unit of length. Its
calculation requires a different expression depending on the
wind speed.
When the wind speed is different from zero, forced convection
occurs and the convective heat losses can be computed through
equation 2 and 3.
qc1=Kangle·1.01 + 1.35·Re0.52·kf·(TcTa)(2)
where Re is the Reynolds number, Tathe air temperature
and Tcthe conductor core temperature. While qc1applies for
low wind speed, qc2is for high wind speed. To properly choose
the correct one, for any wind speed both of them have to be
computed and the largest one has to be used [8].
The term Kangle accounts for the dependance of the con-
vective heat loss rate on the wind direction and it is calculated
Kangle = 1.194 cos(φ)+0.194·cos(2φ)+0.368·sin(2φ)(4)
where φrepresents the angle between the wind direction and
the conductor axis.
When the wind speed is zero, natural convection occurs and
the rate of heat loss can be computed as following:
qcn = 3.645·ρ0.5
0·(TcTa)1.25 (5)
In order to compute the air density, air viscosity and air
thermal conductivity are estimated at the temperature Tfilm =
0.5·(Tc+Ta)through the polynomial expressions:
µf=1.458 ·106·(Tfilm + 273)1.5
Tfilm + 383.4(6)
ρf=1.293 1.525 ·104·He+ 6.379 ·109·H2
kf= 2.424 ·102+ 7.477 ·105·Tfilm 4.407 ·109·T2
qris the radiated heat loss rate per unit length, calculated
qr= 17.8·D0·ε·"Tc+ 273
100 4
Ta+ 273
100 4#(9)
where εis the conductor emissivity, which depends on the
age of the conductor, and ranges between 0.27 to 0.95, with
a value of 0.5 proposed for example by IEEE, and D0is the
external conductor diameter.
qsis the solar heat gain rate per unit length and is given by
the expression:
θ=arcos[cos(Hc)·cos(ZcZl)] (11)
and Hcis the solar altitude, Zcthe solar azimuth, and Zlthe
azimuth of line. Corrected rate of solar heat gain as a function
of the altitude, Qse, equals Ksolar ·Qs, where Ksolar =A+
e, and:
A= 1
B= 1.148 ·104
C=1.108 ·108
Qsis given, for a clear or industrial atmosphere, by a
polynomial expression in Hc:
where the constants A,B,C,D,E,F,G,Hare shown
in Table I
Clear atmosphere Industrial atmosphere
A42.2391 A53.1821
B63.8044 B14.2110
C1.9220 C6.6138 ·101
D3.46921 ·102D3.1658 ·102
E3.61118 ·104E5.4654 ·104
F1.94318 ·106F4.3446 ·106
G4.07608 ·109G1.3236 ·108
Finally, qjare joule heat losses, i.e. the contribution of
thermal energy loss for Joule effect. This term depends on the
electric resistance of the conductor at the temperature Tavg
and on the square of line current I:
The conductor resistance R(Tc)depends on the system
frequency, the line current and the temperature. In the CIGRE
and in the IEEE standards, the electric resistance is assumed
to change only with respect to temperature Tc. Given a value
of electric resistance for high temperatures, Th, and one for
low temperatures, Tl, it is possible to derive a linear model
for electric resistance as a function of conductor temperature:
R(Tc) = R(Th)R(Tl)
ThTl·(TcTl) + R(Tl)(15)
Fig. 2. Resistance-Temperature of the conductor trend
Actually, the resistance of the conductor increases with
temperature somewhat faster than the linear model as shown
in figure 2. This means that, if one calculates the resistance
for a value of Tavg between Tland Th, the value of resistance
calculated with the linear model will be greater than the real
one, and so it is conservative for the conductor temperature
calculation. Instead, if we calculate the resistance for Tavg
larger than Th, the calculated value of resistance will be lower
than the real one, whence an estimation of a non-conservative
conductor temperature value. For this reason equation 15 is
commonly adopted for a conductor temperature lower than
175 oC. Resistance value has to include variations due to Skin
Effect, Magnetic Core Effect and Radial Temperature Gradient
in the conductor.
B. Statistical ANN based model
Artificial Intelligence (AI) has been long used by the
scientific community in several branches. Among the different
forecasting techniques, Artificial Neural Network (ANN) is
one of the most used [19] [20]. The basic structural and
functional unit of ANN is the “neuron”. The inputs of each kth
neuron xiare multiplied by some properly tuned parameters
called weights wk,i then summed with the neuron bias bk, as
shown in Figure 3. Finally, the output ykis produced through
an activation function fby means of the following equation:
yk=f X
(xi·wk,i +bk)!(16)
Fig. 3. Neuron model
Given its ability to generalize an arbitrary complex function,
a two-layer Feed Forward Neural Network (FFNN) is adopted
in this work. For this type of architecture, neurons are orga-
nized in layers and each layer receives in input the output of
the previous layer and provides its output to the following one
as in figure 4. To properly choose its size in terms of number
of neurons, a sensitivity analysis must be performed [21].
The weights among the layers are initially randomly chosen,
then they have to be optimized using a procedure called
training; as explained and proven in [21], to reduce the error,
it is best to adopt an ensemble forecast. Hence, the algorithm
is run independently several times (trials). Each trial requires
then a newly initialized FFNN, trained randomly allocating the
available samples between training and validation set, keeping
only their numerosity constant. Finally, the obtained results
are averaged. The number of trials is then a parameter to be
optimized. A trade off between the increase of the performance
and the computational burden is necessary.
The two previously described methods were implemented
and tested to estimate the conductor’s temperature of an Italian
Fig. 4. Example of a generic Feed Forward Neural Network architecture
Transmission OHL. Further details on the line such as voltage
and current are intentionally not provided on TSO request,
without loosing the generality and the validity of the proposed
The CIGRE model is able to forecast the conductor tempera-
ture providing the weather parameters and the OHL variables
together. The coefficients of the thermal model are available
in literature and do not require to be furtherly tuned. The
main drawback of this physicalmodel is that with wind speed
lower than 2 m/s, the accuracy of the model is highly
jeopardized. On the other hand, ANNs learn main trends and
correlations among the different parameters, therefore they are
able to adapt to varying conditions and to capture correlations
not explicated in the physical model, provided that they are
properly trained with historical data.
The experimental data employed in this analysis refer to the
time period of one month in which the following weather
forecast were available:
Day of the Year
Hour of the Day
Ambient Temperature (K)
Wind Speed (m/s)
Wind Direction ()
Global Solar Radiation (W/m2)
Atmospheric Pressure (bar)
Relative Humidity (%)
In the same time frame, the temperature of the OHL was
measured every 5 minutes.
For a coherent sampling of all the considered parameters, the
hourly mean values were calculated. In the following section,
the comparison has been performed only for the 64 samples
with wind speed below 2 m/s. These parameters represent
the input of both methods compared in this paper for the
temperature of the conductor estimation.
As CIGRE method is a physical model, the temperature esti-
mation for each sample can be obtained directly by following
the procedure described in II-A, while for the ANN method a
tuning of the statistical model parameters must be performed
in advance, as previously described in II-B. In particular,
a sensitivity analysis has been carried out to set the ANN
parameters such as, number of neurons in the hidden layers,
number of trials in the ensemble forecast and samples amount
in the training and validation set respectively. In this work
90% of the available samples are assigned to the training set,
while the remaining 10% were devoted to validate the model
similarly to what is performed in [22]; 40 trials were adopted
in the ensemble forecast of an ANN with 8 neurons in each
of the two hidden layers.
In this section, 64 hourly samples with a wind speed lower
than 2 m/s are used for the comparison of the two estimation
The absolute errors made by the two forecasting methods,
expressed by equation 17, are compared in Figure 5:
|Th|=|Tm,h Tf,h |(17)
where Tm,h is the measured temperature of the conductor
at time hand Tf,h is the forecast temperature, obtained either
with the physical or the statistical method, at the same time
10 20 30 40 50 60
Selected hourly samples
| Th|
Fig. 5. Comparison of the absolute errors committed by the analysed methods
In Figure 5 it is possible to see that the ANN method
provides a very good estimation performance with respect to
the CIGRE method, giving a maximum absolute error equal
to 4.55 oC. Generally speaking, this is largely below the one
made by the physical model. In Figure 6 the outcomes of
the simulations are shown. To better highlight the comparison
between the two methods, results are here presented in terms
of the ratio between the statistical and the physical method.
On the x-axis the number of samples are reported, while
the y-axis shows on a logarithmic scale the corresponding
ratio (Rh) between the errors made by ANN (TANN,h) and
(TCI GRE,h ), as in equation 18
Rh=TANN ,h
The blu line in Figure 6 is drawn as a reference, being the
case in which the two methods make the same forecasting
As it is possible to notice observing the orange line in the
graph, the ANN outperforms the physical model, returning a
more accurate result in 60 cases out of 64.
Furthermore, as far as the four remaining cases are concerned,
10 20 30 40 50 60
Selected hourly samples
Fig. 6. Absolute errors of the Statistical method compared to the Physical as
the reference
which correspond to the two positive spikes in Figure 6 the
absolute error made by ANN is lower than 2oC: in those
specific cases, the error made by the physical method is very
low, so the ratio is increased. In these cases, it must be pointed
out that both estimations are very close to the measured values.
Indicator |TANN (oC)| |TCI GRE (oC)|Rh
Min 0.01 0.08 0.14
Max 4.55 9.63 0.47
Mean 1.06 4.50 0.24
Std dev 0.93 1.90 0.49
In Table II, some aggregate statistical values are provided to
better compare the two methods. As it is possible to see, the
temperature forecast performed with the ANN is more reliable
within the described wind range, being both the average error
committed and its standard deviation lower, as well as the
maximum and minimum values.
In this work two methods for the estimation of the tem-
perature of the conductor of a given OHL are compared.
In literature the CIGRE physical model is well known and
adopted, however it shows limited accuracy for peculiar wind
speed conditions. For this reason an ANN has been trained
and the preliminary results of the two forecasting method have
been compared with wind speed less than 2 m/s.
In this condition ANN has shown a better forecasting accuracy
outperforming the physical method on 60 over the 64 hourly
samples that which have been considered, with an absolute
mean error of 1.06 oCinstead of 4.5oC. These preliminary
results encourage future works and a deeper analysis will be
extended to different transmission line typologies increasing
the number of cases under investigation.
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The continuous increase in electrical power demand entails the need for larger ratings of overhead lines. For spatial, economic and ecological reasons, contemporary solutions are focused on incrementing the ratings of existing lines. One of these solutions is the real-time determination of line ampacity according to the measured or predicted weather and/or line parameters. The paper is focused on a novel calculation procedure and analysis of the steady-state line ampacity (SSLA) weather sensitivity coefficients (WSCs). The calculation of WSCs is based on the sensitivity analysis of the methodology for the SSLA given in Cigre N° 601 Technical Brochure. On the one hand these WSCs allow a fast estimate of the potential in the introduction of real-time ampacity calculation concept. On the other hand they give a good basis on the requirements for the measurement equipment installed in contemporary dynamical line rating systems (DLRSs). The interrelations between the WSCs and the SSLA are investigated using correlation and regression analysis. Finally, according to the typical design parameters of overhead lines the WSCs and their interrelations with the SSLA are calculated and analysed for typical aluminium steel-reinforced conductors (ACSRs) present in the Croatian transmission system.
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It is extremely difficult to realize real-time active-reactive optimal power flow (RT-AR-OPF) in distribution networks (DNs) with wind stations (WSs) due to the conflict between the fast changes in wind power and the slow response from the optimization computation. To address this problem, a new lookup-table-based RT-AR-OPF framework is developed in this paper. According to the forecasted wind power for a prediction horizon, scenarios are generated based on its stochastic distribution. The corresponding mixed-integer nonlinear programming (MINLP) problems are solved online which simultaneously optimize the active and reactive power dispatch of WSs, active-reactive reverse power flow, and discrete slack bus voltage, resulting in a lookup table. Based on the actual wind power available in a sampling time, one of the solutions will be selected and realized to the DN. A new reconciliation algorithm is proposed to ensure both the feasibility and optimality of the realized operation strategy. The applicability of the proposed framework is shown using a medium-voltage DN.
In the last years, dynamic thermal rating assessment of overhead lines has gained a critical importance in power system operation, since it allows transmission system operators to reliably increase the exploitation of existing infrastructures, avoiding the construction of new transmission assets, and increasing the hosting capacity of renewable power generators. Amongst the possible approaches that can be adopted to solve the thermal estimation problem, the one based on synchrophasor data processing is considered as one of the most promising enabling technologies, since it does not require the need for deploying dedicated sensing technologies distributed along the line route, but only the availability of synchronized measurements already available in the control centers for supporting wide area power system applications. Anyway, the deployment of this technology in real operation conditions is still at its infancy, and several open problems need to be addressed, such as the accuracy drop in low loading conditions, and the need for properly representing and managing the data uncertainties in the thermal estimation process. In trying to address these issues, this paper presents a comprehensive analysis of the most promising solution methods proposed in the literature, evaluating their performances on a real case-study based on a thermally constrained power transmission line located in the north of Italy.
Developing a suitable framework for real-time optimal power flow (RT-OPF) is of utmost importance for ensuring both optimality and feasibility in the operation of energy distribution networks (DNs) under intermittent wind energy penetration. The most challenging issue thereby is that a large-scale complex optimization problem has to be solved in real-time. Online simultaneous optimization of the wind power curtailments of wind stations and the discrete reference values of the slack bus voltage which leads to a mixed-integer nonlinear programming (MINLP) problem, in addition to considering variable reverse power flow, make the optimization problem even much more complicated. To address these difficulties, a two-phase solution approach to RT-OPF is proposed in this paper. In the prediction phase, a number of MINLP OPF problems corresponding to the most probable scenarios of the wind energy penetration in the prediction horizon, by taking its forecasted value and stochastic distribution into account, are solved in parallel. The solution provides a lookup table for optional control strategies for the current prediction horizon which is further divided into a certain number of short time intervals. In the realization phase, one of the control strategies is selected from the lookup table based on the actual wind power and realized to the grid in the current time interval, which will proceed from one interval to the next, till the end of the current prediction horizon. Then, the prediction phase for the next prediction horizon will be activated. A 41-bus medium-voltage DN is taken as a case study to demonstrate the proposed RT-OPF approach.