1. Dynamic thermal rating of power transmission lines related to renewable resources Jiri Hosek Institute of Atmospheric Physics, Prague, Czech Rep.

2. 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

3. Dynamic thermal rating of power lines The DTR calculations are based on a heat balance equation: q c.. convective heat loss q r.. heat loss due to long wave radiation q s.. heat gain due to solar radiation I 2 R(T c ).. heat gain due to Joule heating mC p.. heat capacity of the conductor DTR may be calculated as: 1. steady state - total heat losses and gains are in equilibrium - dT c /dt=0 or 2. transient - necessary for conductor temperature calculations under varying current and/or ambient conditions

4. 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

5. Thermal model – convective heat transfer T c.. temperatures of the conductor T a.. temperature of the airstream ρ f.. air density D.. conductor diameter k f.. thermal conductivity of air K β.. 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

6. Thermal model – radiative heat transfer Solar radiation is calculated as follows: α.. Solar absorptivity Q se.. 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 Q se 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: ε.. emissivity D.. conductor diameter T c.. conductor temperature T a.. ambient air temperature

7. Thermal model – sensitivity

8. 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

9. 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 Meteorological mast at Dlouha Louka 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.

10. Conductor parameters AlFe6 120mm 2 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/m 2 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

11. 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 A 2) 17 WTs, max current delivered 356 A 3) 26 WTs, max current delivered 544 A

12. Required and available ampacity – 13 WTs

13. Required and available ampacity – 17 WTs

14. Required and available ampacity – 26 WTs

15. Wasted production, 10 - 40 WTs

16. 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