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

csc

prc TRIqdt

dTmCqq 2

Dynamic thermal rating of power lines

The DTR calculations are basedon a heat balance equation:

qc .. convective heat lossqr .. heat loss due to long wave radiationqs .. heat gain due to solar radiation I2R(Tc) .. heat gain due to Joule heatingmCp .. heat capacity of the conductor

DTR may be calculated as:

1. steady state

- total heat losses and gains are in equilibrium- dTc/dt=0

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

25.175.05.0 )(0205.0 acfc TTDq

qc Ck fK (Tc Ta )

)2sin(38.0)2cos(194.0)sin(194.1 K

Thermal model – convective heat transfer

Tc .. temperatures of the conductor Ta .. temperature of the airstreamρf .. air densityD .. conductor diameterkf .. thermal conductivity of air Kβ .. wind direction factor

The wind direction factor is calculated as follows:

β .. angle between wind direction and normal to the line

Convective heat transfer consists of either:

1. Natural convection heat loss: 2. Forced convective heat loss:

• 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

Thermal model – radiative heat transfer

Solar radiation is calculated as follows:

')sin( AQq ses

α .. Solar absorptivity Qse .. Total solar and sky radiation (elevation corrected)θ .. Angle of incidence of sun raysA’ .. 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:

44

100

15.273

100

15.2730178.0 ac

r

TTDq

ε .. emissivityD .. conductor diameterTc .. conductor temperatureTa .. ambient air temperature

Thermal model – sensitivity

Instantaneous vs. average inputs

• wind speed is typically averaged over a specified interval

• 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

instantaneous

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

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.

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 - setup

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DT

R a

mp

acit

y [A

]

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DTR ampacity [A]

WT production [kW]

Benefits of DTR for WE production

Case study• the line capacity considered blocked with 240A, leaving 180A available

• three cases studied:1) 13 WTs, max current delivered 272 A2) 17 WTs, max current delivered 356 A3) 26 WTs, max current delivered 544 A

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