Dynamic thermal rating of power
transmission lines related to
renewable resources
Jiri Hosek
Institute of Atmospheric Physics, Prague, Czech Rep.
Background and motivation
• modern renewable energy sources (e.g. wind turbines) are booming
and cause significant decentralization of electricity production
• an alternative to building a new power line may be a dynamic thermal
rating (DTR) system
• there are two methods of thermal rating of transmission lines:
1) static rating based on information about conductor type and
the overall climatology of the site
2) dynamic rating calculation using an online monitoring system
of conductor temperature, sag, or weather conditions
• thermal model is driven by met. measurements or post-processed
outputs from a numerical weather prediction (NWP) model
• dynamic rating generally increase line capacity (ampacity)
• the energy production from renewable resources is no more
independent on the ambient atmospheric conditions, as it is for
traditional sources
Dynamic thermal rating of power lines
The DTR calculations are based
on a heat balance equation:
DTR may be calculated as:
dTc
qc  qr  mC p
 qs  I 2 RTc 
dt
- total heat losses and gains
are in equilibrium
- dTc/dt=0
qc .. convective heat loss
qr .. heat loss due to long wave radiation
qs .. heat gain due to solar radiation
I2R(Tc) .. heat gain due to Joule heating
mCp .. heat capacity of the conductor
1. steady state
or
2. transient
- necessary for conductor
temperature calculations
under varying current
and/or ambient conditions
Thermal model
• based on the IEEE standard 738-2006
• the model allows:
1) steady-state calculations of conductor temperature and ampacity
2) transient calculation of conductor temperature with changing
ambient parameters and/or transmitted current
• the most important factor is convective cooling based on wind velocity
and ambient air temperature
• solar radiation is either calculated, using the time of day, or obtained
from measuring instruments or from a NWP model
• electrical resistance for Joule heating is calculated as a function of
conductor temperature with linear interpolation between specified
points
Thermal model – convective heat transfer
Convective heat transfer consists of either:
1. Natural convection heat loss:
2. Forced convective heat loss:
qc  0.0205 0f .5 D0.75 (Tc  Ta )1.25
qc  Ck f K  (Tc  Ta )
Tc .. temperatures of the conductor
Ta .. temperature of the airstream
ρf .. air density

D .. conductor diameter
kf .. thermal conductivity of air
Kβ .. wind direction factor
• the constant C in forced
convection is evaluated using
expressions of McAdams (1959)
• the higher of the natural or
forced convection is used
in the model
The wind direction factor is calculated as follows:
K   1.194 sin( )  0.194cos(2 )  0.38sin(2 )
β .. angle between wind direction and normal to the line
Thermal model – radiative heat transfer
Solar radiation is calculated as follows:
qs  Qse sin( ) A'
α .. Solar absorptivity
Qse .. Total solar and sky radiation
(elevation corrected)
θ .. Angle of incidence of sun rays
A’ .. Projected area of conductor
(per unit length)
• α mainly depends on age of
the conductor
• θ is calculated using current
position of the sun (altitude and
azimuth) and heading of the power
line
• Qse is calculated using an empirically
fitted polynomial of the altitude and
azimuth of the sun
Long wave radiation loss is based on the Stefan-Boltzman law:
 Tc  273.15  4  Ta  273.15  4 
qr  0.0178D 
 
 
100
100



 

ε .. emissivity
D .. conductor diameter
Tc .. conductor temperature
Ta .. ambient air temperature
Thermal model – sensitivity
Instantaneous vs. average inputs
• wind speed is typically averaged over
a specified interval
instantaneous
• use of instantaneous values of the
meteorological inputs causes
significantly higher variability and
phase shifts of the results
• recommended averaging intervals for
DTR calculations is 10-15 mins,
details in:
J. Hosek, P. Musilek, E. Lozowski, P. Pytlak: Effect of
time resolution of meteorological inputs on dynamic
thermal rating calculations, accepted to IET
Generation, Transmission & Distribution
averaged
Dlouha Louka, Ore Mountains
• elevation: 880 m a.s.l.
• wind mast measurements
• height above ground: 50 m
Teplice
• elevation: 230 m a.s.l.
• standard met. station
• height above ground: 10 m
Meteorological mast at Dlouha Louka
Site and meteorological data specification
Wind speed measurements
• period Apr 2003 – Apr 2005
• logarithmic profile used for height adjustment:
- for DTR calculations 30 m a.g.l.
- for WT production calculations 98 m a.g.l.
Benefits of DTR for WE production - setup
Conductor parameters
• AlFe6 120mm2
• voltage: 110 kV
• diameter: 31.3 mm
• resistance at 75 degC: 0.234 ohm/km
• static ampacity: 420A
- calculated for 0.6 m/s wind speed,
wind direction parallel to the line,
30 degC ambient temperature,
300 W/m2 solar radiation
WT parameters
• Enercon E82
• nominal power: 2300 kW
• hub height: 98 m
• rotor diameter: 82 m
Benefits of DTR for WE production
1600
2500
DTR ampacity [A]
WT production [kW]
2000
1200
1500
1000
1000
800
600
400
Case study
• the line capacity considered blocked with 240A, leaving 180A available
• three cases studied:
1) 13 WTs, max current delivered 272 A
2) 17 WTs, max current delivered 356 A
3) 26 WTs, max current delivered 544 A
500
0
WT production [kW]
DTR ampacity [A]
1400
Required and available ampacity – 13 WTs
Required and available ampacity – 17 WTs
Required and available ampacity – 26 WTs
Wasted production, 10 - 40 WTs
Conclusions
• dynamic thermal rating allows more line capacity than static rating
• the ampacity calculations suggest that, using DTR, it may be
possible to transport double the amount of energy in case of
favorable ambient conditions
• DTR is calculated using thermal model and measured or modeled
meteorological data
• if the line is used close to the operational limits, DTR helps to
transport the energy otherwise wasted