IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 28, NO. 3, JULY 2013 1909 Modelling of Dynamic Transmission Cable Temperature Considering Soil-Specific Heat, Thermal Resistivity, and Precipitation Rasmus Olsen, Student Member, IEEE, George J. Anders, Fellow, IEEE, Joachim Holboell, Senior Member, IEEE, and Unnur Stella Gudmundsdóttir, Member, IEEE Abstract—This paper presents an algorithm for the estimation of the time-dependent temperature evolution of power cables, when real-time temperature measurements of the cable surface or a point within its vicinity are available. The thermal resistivity and specific heat of the cable surroundings are varied as functions of the mois- ture content which is known to vary with time. Furthermore, issues related to the cooling effect during rainy weather are considered. The algorithm is based on the lumped parameters model and takes as input distributed temperature sensing measurements as well as the current and ambient temperature. The concept is verified by studying a laboratory setup of a 245 kV cable system. Index Terms—Cables, prediction methods, temperature, tem- perature control, transmission lines. I. INTRODUCTION T HIS PAPER describes how the temperature of power cables can be dynamically computed when the thermal models are dependent on the moisture content of the surround- ings. It is shown how simple temperature measurements from an optic fiber can be implemented in the calculations and how the developed algorithm will estimate the dynamic evolution of the cable environment. This, in turn, will allow predictions about the future development of the temperature and can be utilized in dynamic rating calculations. The background for developing the temperature estimation methodology is the decision, made by the Danish parliament, to underground all of the Danish transmission system below 400 kV and large parts of the 400 kV system as well. The decision was made based on two reports [1] and [2], which discuss different possibilities in performing such an undergrounding. Based on this decision, the Danish transmission system operator (TSO), Energinet.dk, started a research project investigating possible implementation strategies for dynamic rating of cable-based transmission grids. As Energinet.dk always installs Manuscript received December 23, 2012; revised March 25, 2013; accepted May 08, 2013. Date of publication June 13, 2013; date of current version June 20, 2013. Paper no. TPWRD-01400-2012. R. Olsen and U. S. Gudmundsdóttir are with the Section of Transmission Lines, Energinet.dk, Fredericia 7000, Denmark (e-mail: rso@energinet.dk; usg@energinet.dk). G. J. Anders is with the Department of Electrical Engineering of the Technical University of Lodz, Lodz 90-924, Poland (e-mail: george.anders@bell.net). J. Holboell is with the Department of Electrical Engineering, Technical Uni- versity of Denmark, Kgs. Lyngby 2800, Denmark (e-mail: jh@elektro.dtu.dk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2013.2263300 fibres for distributed temperature sensing (DTS) measurements together with their cables, it was decided to investigate how such measurements could be used for improving the utilisation of an almost completely undergrounded transmission system. The objective is to use the thermal models during normal operation, such that the transmission system operator can monitor the temperature of all cables in the grid. Furthermore, constant monitoring will enable estimation of the cables’ real-time loadability, including the emergency rating and, thus, the system operator will gain increased flexibility, especially during contingencies. In addition to these two purposes, the thermal models can be used for the prediction of the future thermal evolution of the ca- bles. This means that the operator, based on the forecasted gen- eration and consumption patterns, can determine if his trans- mission system can operate safely in the hours to come, or if he needs to perform control actions in order to prevent over- loadings. The latter means that valid dynamic thermal models of the cables will enable Electrothermal Coordination (ETC)- based operation of transmission grids as discussed, for example, in [3] and [4]. In order to ensure accurate thermal modelling of the indi- vidual power cables, which is a necessity for ETC to become reality, the parameters of the thermal models should be as accu- rate as possible. Different studies have taken into consideration the changes of the thermal parameters of the cable surroundings by adapting the soil thermal resistivity while assuming that other thermal parameters are static, [5] and [6]. However, it should be realised that other thermal parameters, in particular, the specific heat of the surroundings, may also change over time. The implementation of the time varying specific heat of cable surroundings in thermal modelling will be addressed in this paper. Furthermore, the effect of precipitation will be included in the analysis to improve accuracy of the thermal models. All these considerations will be implemented in the thermal models by assuming that DTS measurements are available, such as will be the case for the future Danish transmission system. In case DTS measurements are not available, as might be the case for older cable systems, the thermal model will be able to work with measurements from thermocouples, which may easily be installed after commissioning of the cable. It should be recognised that in addition to the moisture con- tent, also the temperature of the cable surroundings affects the thermal resistivity [7] and specific heat [8] of the material. In this study, this temperature dependence of the thermal resistivity and 0885-8977/$31.00 © 2013 IEEE