Patent Publication Number: US-2023152260-A1

Title: Estimating The Thermal Resisitivity Of Soil Surrounding An Underground Cable

Description:
TECHNICAL FIELD 
     The invention relates to electric cables, for instance in relation to high voltages. More particularly, the invention relates to a method, arrangement, computer program and computer program product for estimating the thermal resistivity of soil. 
     BACKGROUND 
     The thermal properties of soil and especially the thermal resistivity may be important to know in relation to underground power cables. This property may for instance be of interest in cable load protection systems, such as for predicting a so-called power overload, i.e. a load that is higher than what the cable is rated for. 
     US 2015/ 0253458 describes estimating thermal properties of soil as well as using such properties for cable rating and cable reconducting. In order to determine the thermal properties of the soil a weather driven method is used that is essentially based on the difference between the temperature of the air and the soil. Also, other properties above ground are considered, such as wind speed, solar input and radiation. The way that the soil properties are determined is thereby complex and requires weather data, which can be hard to obtain. It would therefore be of interest to use a simpler way of determining the thermal resistivity, for instance one that does not depend on weather data. 
     Aspects of the invention are concerned with improvements in relation to the determination of the thermal resistivity of soil and especially one that does not need weather data. 
     SUMMARY 
     One object of the invention is therefore to provide a simple determining of the thermal resistivity of soil, for instance one that does not depend on weather data. 
     This is according to a first aspect achieved through a method for estimating the thermal resistivity of soil surrounding an underground cable, the method being performed by a thermal resistivity estimating unit and comprising:
     obtaining a first temperature from a first temperature sensor at an exterior surface of the cable,   obtaining a second temperature from a second temperature sensor placed in the soil at a distance from the cable,   obtaining a measurement of current transmitted in the cable, and   estimating the thermal resistivity of soil based on the first and the second temperatures as well as on the current measurement.   

     The object is according to a second aspect achieved through an arrangement for estimating the thermal resistivity of soil, the arrangement comprising:
     a thermal resistivity estimating unit configured to,   obtain a first temperature from a first temperature sensor at an exterior surface of the cable,   obtain a second temperature from a second temperature sensor placed in the soil at a distance from the cable,   obtain a measurement of current transmitted in the cable, and   estimate the thermal resistivity of soil based on the first and the second temperatures as well as on the current measurement.   

     The object is according to a third aspect achieved through a computer program for estimating the thermal resistivity of soil surrounding an underground cable, the computer program comprising computer program code which when run by a processor of a thermal resistivity estimating device, causes the thermal resistivity estimating device to:
     obtain a first temperature from a first temperature sensor at an exterior surface of the cable,   obtain a second temperature from a second temperature sensor placed in the soil at a distance from the cable,   obtain a measurement of current transmitted in the cable, and estimate the thermal resistivity of soil based on the first and the second temperatures as well as on the current measurement.   

     The object is according to a fourth aspect achieved through a computer program product for estimating the thermal resistivity of soil surrounding an underground cable, the computer program product comprising computer program code according to the third aspect. 
     The invention according to the above-mentioned aspects has a number of advantages. It allows safe overload operation combined with low safety margins. Thereby the cable can be more efficiently used compared with when no or an inadequate estimation of the thermal resistivity of soil is made. Furthermore, the number of sensors used can be low and also combined with use for other purposes, such as overload operations. This means that the invention can be implemented in a simple way. 
     The first temperature may be a temperature that depends on the operation of the cable, while the distance at which the second temperature sensor is placed or located may be such that the second temperature is uninfluenced by the operation of the cable. It is thus uninfluenced by changes of the first temperature caused by operation of the cable. 
     The estimation of the thermal resistivity of soil may be based on an estimate of the temperature at the exterior surface of the cable caused by power losses in the cable when the measured current is running in the cable. 
     The estimation of the thermal resistivity may additionally be based on a difference between the estimated temperature and the measured temperature at the exterior surface of the cable. 
     The estimation of the thermal resistivity of the soil may furthermore be iterative and involve predicting a following thermal resistivity of the soil based on a combination of a previous thermal resistivity of the soil and the difference between the estimated temperature and the measured temperature at the exterior surface of the cable. 
     The estimation of the resistivity of the soil may also be based on applying the current measurement and the temperatures in a thermal model of the cable and possibly also of the soil. If the soil is included, the model may consider the soil up to the previously mentioned distance at which the second temperature sensor is located. 
     The estimating may more particularly comprise applying a previous estimate of thermal resistivity of the soil in the model together with a previous current measurement and previous first and second temperatures and obtaining a following estimate of the thermal resistivity based on processing of the previous thermal resistivity, the previous current measurement and the previous first and second temperatures in the model. 
     The application in the model may provide an estimated following first temperature and the estimated following thermal resistivity may be determined as a combination of the previous thermal resistivity and an error, which error is the difference between the measured following first temperature and the estimated following first temperature. It is additionally possible that the error is amplified before being combined with the previous thermal resistivity. 
     The cable may comprise a number of layers of cable material around at least one conductor. 
     In this case the model may comprise a number of thermal resistances and a number of thermal capacitances and each cable material layer may have a corresponding thermal resistance in the model and the soil may have one or more thermal resistances in the model corresponding to one or more soil layers between the cable and the second temperature sensor. Furthermore, a first thermal capacitance may be the thermal capacitance of the conductor and a part of a first neighbouring layer, the last thermal capacitance may be the thermal capacitance of the soil at the second temperature sensor and half of a neighbouring soil layer, where the thermal capacitances in-between the first and the last thermal capacitances may be made up of the capacitances of half of two neighbouring layers. 
     The thermal resistances may be connected in series in a string, where the first thermal capacitance may be connected to a first end of the string and the last thermal capacitance may be connected to a second opposite end of the string, while the rest of the thermal capacitances may each be connected to a corresponding junction between two thermal resistances of the string. 
     The first temperature may additionally be the temperature at the junction in the model between the thermal resistance of the last layer of the cable and the thermal resistance of a first soil layer and the second temperature may be the temperature after the thermal resistance of a last soil layer. 
     The current may correspond to a heat flow being fed into the model by a heat source. The estimation of the thermal resistance of the soil may be based on the power being input into the cable by the measured current. 
     The arrangement may additionally comprise the first and the second sensor. 
     It is also possible that the arrangement comprises the control system for controlling the transmission of power through the cable. 
     The first temperature sensor may be a temperature sensor in a first group of sensors comprising at least one sensor at the exterior surface of the cable, which first group comprises at least the first temperature sensor. The second temperature sensor may be a temperature sensor in a second group of sensors placed in the soil at a distance from the cable, which second group comprises at least the second temperature sensor. The arrangement may thereby also comprise the first and the second groups of sensors. 
     The arrangement may additionally comprise the cable as well as possibly also a current sensor used for detecting the current running in the cable. 
     The arrangement may furthermore comprise an overload operation determining unit configured to determine overload operating conditions based on the estimated thermal resistivity of the soil. 
     The method may in a similar manner comprise determining overload operating conditions based on the estimated thermal resistivity of the soil. 
     The determining of overload operating conditions may comprise determining an overload power level and/or an overload time duration at which the cable may be operated in an overload operating mode. 
     It should be emphasized that the term “comprises/comprising” when used in this specification is taken to specify the presence of stated features, integers, steps or components, but does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will now be described in more detail in relation to the enclosed drawings, in which: 
         FIG.  1    schematically shows a perspective view of an end of a power cable, 
         FIG.  2    schematically shows a thermal resistivity estimating arrangement comprising a first group of temperature sensors on the surface of the power cable a second group of temperature sensor in the soil as well as a first realization of a thermal resistivity estimating device comprising a thermal resistivity estimating unit and communicating with a control system that controls the transmission of power over the power cable, 
         FIG.  3    schematically shows a second realization of thermal resistivity estimating device, 
         FIG.  4    shows a flow chart of a first embodiment of a method of estimating the thermal resistivity of the soil, which method steps are being performed in the thermal resistivity estimating unit, 
         FIG.  5    schematically shows a scheme used for estimating the thermal resistivity of the soil, 
         FIG.  6    schematically shows a thermal model of the cable employed in the estimating scheme, 
         FIG.  7    shows a flow chart of a second embodiment of a method of estimating the thermal resistivity of the soil, which method steps are being performed in the thermal resistivity estimating unit, and 
         FIG.  8    shows a computer program product in the form of a CD ROM disc with computer program instructions for implementing the thermal resistivity estimating unit. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, for purposes of explanation and not limitation, specific details are set forth such as particular architectures, interfaces, techniques, etc. in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known devices, circuits and methods are omitted so as not to obscure the description of the invention with unnecessary detail. 
     The invention is generally directed towards an electric underground cable, i.e. an underground power cable, such as a Direct Current (DC) underground cable like a High Voltage Direct Current (HVDC) underground cable, for instance operated at 100 kV and above. It should here be realized that the invention is not limited to these types of electric cables, but may also be used in relation to for instance Alternating Current (AC) underground cables and for cables at other voltage levels. The invention is more particularly concerned with estimating the thermal resistivity of soil surrounding such a cable. 
       FIG.  1    schematically shows an end portion  24  of a first such DC cable  22 . The cable is an insulated electric high voltage DC cable  22  and comprises from inside and out: a high voltage DC conductor  10 , a polymer-based insulation system  12 - 16 , a grounding layer  18 , and an outer covering or sheath  20 . In this example the insulating system comprises a first insulating layer  12  inside a second insulating layer  14  and a third insulating layer  16  outside of the second insulating layer  14 . The first insulating layer  12  may be a first semiconductive insulating layer, the second insulating layer  14  may be a main insulating layer and the third insulating layer  16  may be a second semiconductive insulating layer. It should here also be realized that the third layer, i.e. the second semiconductive insulating layer may be omitted. It is also possible with more layers in the insulating system. It can thereby be seen that the cable comprises a number of layers of cable material around the conductor. 
     Furthermore, the cable may also comprise further layers such as an inner water blocking layer and a conductor screen layer between the conductor  20  and the insulation system  12  -  16  as well as a second water blocking layer between the grounding layer  18  and the sheath  20 . 
       FIG.  2    schematically shows an arrangement for estimating the thermal resistivity of soil together with parts of a control system that controls the transmission of power over a power cable. The arrangement comprises a thermal resistivity estimating device  40  that comprises a thermal resistivity estimating unit  42  and optionally also an overload operation determining unit  44 . The thermal resistivity estimating device  40  is connected to a first temperature sensor  26  placed on the surface of a cable  22  and to a second temperature sensor  30  placed in the soil at a distance from the cable  22 . The first sensor  26  may be separated from the sheath  20  by a patch of separating material, such as a patch of polyethylene (PE). The first sensor  26  may be a sensor in a first group of sensors placed on the exterior surface of the cable  22 , where in the figure a further sensor  28  in this first group is shown. In a similar manner the second sensor  30  may be a sensor in a second group of sensors, where in the figure two further sensors  32  and  34  in the second group are shown. The distance from the cable at which each sensor in the second group is placed may be such that that temperatures detected by the sensors in the second group are uninfluenced by the operation of the cable  22 . The distance is thus such that any heating caused by the transmission of power through the cable  22  will not be able to propagate to the sensors of the second group. It should thereby be realized that the distances between individual sensors in the second group and the cable may differ slightly, as long as the temperature sensing is uninfluenced by the operation of the cable  22 . 
     The first and second groups of temperature sensors are more particularly connected to a signal collecting device  36 , which in turn is connected to a connection box  38 , where the connection box  38  is in turn connected to the thermal resistivity estimating device  40 . It can be seen that the thermal resistivity estimating device  40  receives a first temperature T s  from the first temperature sensor  26  via the signal collecting device  36  and the connection box  38  as well as a second temperature T a  from the second temperature sensors  30  via the signal collecting device  36  and the connection box  38 , where the first temperature T s  is the temperature of the exterior surface of the cable  22  and the second temperature T a  is the ambient temperature at the above-mentioned distance from the cable  22 . The thermal resistivity estimating device  40  may of course also receive temperature measurements from the other temperature sensors of the first and the second group. However, as will be seen later, these temperatures are not essential for the estimating of the thermal resistivity of the soil. Consequently, only the first and the second temperature sensor  26  and  30  may be used and the other sensors may be omitted. 
     The temperature sensors  26 ,  28 ,  30 ,  32  and  34  as well as the signal collecting device  36  and connection box  38  may or may not be a part of the thermal resistivity estimating arrangement. Also, the cable  22  may or may not be a part of the thermal resistivity estimating arrangement. 
     The thermal resistivity estimating device  40  also communicates with a high-level process control computer  46  of a process control system, which high-level process control computer may be part of a Supervisory Control and Data Acquisition (SCADA) process control system. The high-level process control computer  46  in turn communicates with a local low level control device  48  controlling a converter, which converter controls transmission of power through the cable  22 . The converter may be a line-commutated converter (LCC) employing thyristors. The control of such a converter is indicated through the local low-level control device  48  controlling a thyristor  50 . 
     It should here be realized that an LCC is merely one example of a converter that can be used. It is likewise possible with a voltage source converter (VSC) such as a two- or a multilevel converter. If a multilevel converter is used, it may additionally be a modular multilevel converter (MMC). 
     The current I c  being input to the cable is also measured by a current sensor  52 , which current sensor may report the measured current I c  to the high-level process control computer  46 , which may in turn submit the measured current I c  to the thermal resistivity estimating device  40 . 
     It is possible that one or more of the high-level process control computer  46 , local low level control device  48 , converter and current sensor  52  is a part of the thermal resistivity estimating arrangement. The control system may thereby be a part of the arrangement. However, the elements may also be external to the thermal resistivity estimating arrangement. 
     The thermal resistivity estimating unit  42  and the overload operation determining unit  44  of the thermal resistivity estimating device  40  may according to a first realization be implemented through one or more integrated circuits such as through a Programmable Logic Controller (PLC). However, also other alternatives are possible such as a digital signal processor (DSP), an Application Specific Integrated Circuit (ASIC) or a Field-Programmable Gate Array (FPGA). 
     Alternatively, the thermal resistivity estimating device  40  may according to a second realization be provided in the form of a processor with associated program memory including computer program code for performing its functionality.  FIG.  3    schematically shows such a realization where the thermal resistivity estimating device  40  is implemented as a processor PR  54  comprising a memory M  56  comprising first computer instructions CI 1   58  for implementing the thermal resistivity estimating unit  42  and second computer instructions CI 2  for implementing the overload operation determining unit  44 . 
     When using or operating a cable it may be of interest to know the thermal resistivity of the ambient soil, i.e. of the soil that surrounds the cable. 
     This may for instance be of interest if operating the cable with an overload, i.e. at power levels that are higher than those that the cable is rated for. If this resistivity is known, it is possible to safely operate at a higher power level than if the resistivity is unknown or poorly estimated. 
     Such a resistivity is also typically not fixed but may vary depending on atmospheric and seasonal weather variations. Dampness, frost in the ground and thaw are examples of weather variations that influence the thermal resistivity. 
     Aspects of the present invention are directed towards estimating the thermal resistivity of soil in a simple way with a limited number of inputs that are obtained during operation of the cable. The inputs used do furthermore not need to concern weather and temperatures above ground. Therefore, they may be obtained using sensors at or around the cable. 
     How this may be done according to a first embodiment will now be described with reference also being made to  FIG.  4   , which shows a flow chart of a number of method steps in a method of estimating the thermal resistivity of the soil surrounding the cable, which method steps are being carried out by the thermal resistivity estimating unit  42 . 
     The thermal resistivity estimating unit  42  obtains the first temperature Ts from the first temperature sensor  26  at the exterior surface of the cable  22 , S100, where the first temperature is a temperature that depends on the operation of the cable. It also obtains the second temperature T a  from the second temperature sensor  30  being placed or located at a distance from the exterior surface of the cable  22 , S 102 , which distance is such that the second temperature is uninfluenced by the operation of the cable. These temperatures may be received from the sensors  26  and  30  via the signal collection device  36  and the connection box  38 , where it is additionally possible that the connection box suppresses transients of the detected temperatures. The connection box  38  may additionally provide galvanic separation between the signal collecting device  36  and the thermal resistivity estimating device  40 . 
     The thermal resistivity estimating unit  42  also obtains a measurement of the current I c  transmitted in the cable  22 , S 104 . The current may be detected by the current sensor  52  and submitted to the high-level control computer  46 , which may in turn supply it to the thermal resistivity estimating device  40 . As an alternative it is possible that the thermal resistivity estimating device  40  communicates directly with the current sensor  52 . 
     When the thermal resistivity estimating unit  42  has obtained these measurements, it goes on and estimates the thermal resistivity of soil based on the first and the second temperatures T s , T a  as well as on the current measurement I c , S 106 . 
     The estimation of the thermal resistivity may be based on an estimate of the temperature at the exterior surface of the cable  22  caused by the power losses in the cable when the measured current runs in the cable. This may be done through applying the measured temperatures and current in a model of the cable, which model possibly also models the soil up to the previously mentioned distance. The estimation of the thermal resistivity may more particularly be based on a difference between the estimated temperature and the measured temperature at the exterior surface of the cable  22 . The estimation of the thermal resistivity may be iterative. It may more particularly be based on processing made at discrete consecutive points in time, so-called sampling times and may involve the predicting of a following thermal resistivity of the soil based on a combination of the above-mentioned difference and a previous thermal resistivity of the soil, where it is additionally possible that the difference is the difference between an estimated temperature and a measured temperature at the following point in time, where the estimation of the temperature at the following point in time has been made based on measurements made at the previous point in time. 
     A second embodiment will now be described with reference to  FIGS.  5 ,  6  and  7   , where  FIG.  5    shows a scheme used for estimating the thermal resistivity of soil implemented by the thermal resistivity estimating unit  42 ,  FIG.  6    schematically shows a thermal model of the cable employed in the estimating scheme and  FIG.  7    shows a flow chart of a second embodiment of a method of estimating the thermal resistivity of soil, which method steps are being performed in the thermal resistivity estimating unit  42 . 
     The thermal resistivity estimating unit  42  operates on measurements at different points in time. For a present point in time t, the thermal resistivity estimating unit  42  operates on measurements of both a previous point in time  t - 1  and measurements of a following point in time, which following point in time is the current or present point in time t. The thermal resistivity estimating unit  42  obtains or receives an estimated previous thermal resistivity of the soil ρ( t - 1 ) as a first input, a measured previous first temperature T s ( t - 1 ) meas  as a second input, a measured previous second temperature T a ( t - 1 ) meas  as a third input, a measured previous current input to the cable I c ( t - 1 ) as a fourth input, and a following or present measured first temperature T s (t) meas  as a fifth input, where the first, second, third and fourth inputs are inputs to a block  64  implementing a thermal model M and which as an output provides a predicted following first temperature T s (t) pred , i.e. a predicted temperature of the current point in time t, to a negative input terminal of a subtracting block  66 . The first input, i.e. the estimated previous thermal resistivity of the soil ρ( t - 1 ), is also provided to a first input terminal of an adding block  70 . The subtracting block  66  also has a positive input on which it receives the fifth input signal, i.e. the measured following first temperature T s (t) meas . The subtracting block  66  also supplies an error e to an amplifying block  68 , which amplifies the error e with a gain K and supplies the amplified error e to a second input terminal of the adding block  70 , which has an output on which it provides an estimated following thermal resistivity of the soil ρ(t), which is the thermal resistivity estimated for the current point in time t. 
       FIG.  6    shows one realization of the thermal model, which is a thermal model of the cable and the soil up to the location of the second temperature sensor  30 . 
     The model M comprises a number of thermal resistances R 1 , ..., Rn, R(n+1), ... and Rm and a number of thermal capacitances C 0 , C 1 , ..., C(n-1), Cn, C(n+1), ..., C(m-1) and Cm. Each cable material layer has a corresponding thermal resistance in the model, where in this case there are n layers and thus n thermal resistances of the layers and the soil has one or more thermal resistances in the model corresponding to one or more soil layers between the cable  22  and the second temperature sensor  30 . In the present example there are m-n soil layers and thus m-n thermal resistances of the soil and thereby the number of thermal resistances in the model is m. In  FIG.  6   , a first thermal resistance R 1  is associated with a first layer outside of the conductor  12 . There is then a thermal resistance for each following layer of the cable. There is thereby an nth and final thermal resistance Rn of the cable. Then follows m-n thermal resistances of the soil. After the last thermal resistance Rn of the cable there is a first thermal resistance R(n+1) of the soil. There are then a number of following thermal resistances up until a final thermal resistance Rm of the soil, which is also the last thermal resistance of the model. 
     The thermal resistances of the different cable layers may be known. However, the thermal resistances of soil are typically not known. 
     The model further comprises a thermal capacitance C 0  being the thermal capacitance of the conductor  10  and a part of a first neighbouring layer  12  and a last thermal capacitance Cm that is the thermal capacitance of the soil at the second temperature sensor  30  and half of a neighbouring last soil layer of the model. The thermal capacitances C 1 , ..., C(n-1), Cn, (C(n+1), ...., C(m-1) in-between the first and the last thermal capacitances C 0  and Cm are made up of the capacitances of half of two neighbouring layers. 
     As can be seen in  FIG.  6   , the thermal resistances R 1 , ...., Rn, R(n+1), ...., Rm are connected in series in a string, where the first thermal capacitance C 0  is connected to a first end of the string and the last thermal capacitance Cm is connected to a second opposite end of the string, with the rest of the thermal capacitances C 1 , ..., (Cn-1), Cn, C(n+1), ..., C(m-1) each being connected to a corresponding junction between two thermal resistances of the string. In the example of  FIG.  6   , the first thermal capacitance C 0  is thus connected to a first end of the string formed by a first end of the first thermal resistance R 1 , the thermal capacitance C 1  is connected to a first junction between a second end of the first thermal resistance R 1  and a first end of a second thermal resistance (not shown), a capacitance C(n-1) is connected to a junction between a second end of an (n-1)th resistance (not shown) and a first end of an nth resistance Rn, a capacitance Cn is connected to a junction between the second end of the nth resistance Rn and a first end of the (n+1)th resistance R(n+1), a capacitance C(n+1) is connected to a junction between the second end of the (n+1)th resistance R(n+1) and a first end of an (n+2)th resistance (not shown) etc. Finally a capacitance C(m-1) is connected to a junction between a second end of an (m-1)th resistance (not shown) and a first end of the mth resistance Rm. The last thermal capacitance Cm is connected to a second end of the string which end is opposite to the first end. The second end of the string is in this case made up of a second end of the mth thermal resistance Rm. 
     In the model, the first temperature Ts is the temperature at the junction in the model between the thermal resistance Rn of the last layer of the cable  22  and the thermal resistance R(n+1) of a first soil layer and the second temperature Ta is the temperature after the thermal resistance Rm of a last soil layer in the model, which is also the last layer of the model. 
     There is in the model also a heat source HS connected in parallel with the first thermal capacitance C 0 , which heat source HS is provided by the conductor  10  and generates a heat flow HF that is fed into the model at the first end of the string of thermal resistances, which heat flow corresponds to the current I c . 
     It should here be realized that the model may comprise more elements, such as more heat sources corresponding to other elements of the cable thermal temperature sources. 
     The model is a variation of the model defined in ELECTRA No 87,1983, “Computer method for the calculation of the response of single-core cables to a step function transient”, Paper presented by working group 21 02 of Study Committee 21 (HV Insulated Cables), which is herein incorporated by reference. 
     The estimation of the thermal resistivity in this second embodiment is iterative. This means that the estimation operates on measurements obtained at different points in time, i.e. sampling times. It also operates on previous estimates of the thermal resistivity of the soil. 
     Initially the thermal resistivity may be assigned a random non-zero value. As an alternative, the soil may originally be assigned a nominal thermal resistivity, for instance a thermal resistivity of the material obtained from general or laboratory measurements of the soil. The estimate of the resistivity is then improved with every iteration in the estimating scheme. 
     For a present time t, the thermal resistivity estimating unit  42  then operates on values of a previous time  t - 1 . It more particularly operates on a thermal resistivity estimate ρ of this previous time  t - 1 . 
     The operation may therefore involve the thermal resistivity estimating unit  42  obtaining the previous estimate of the thermal resistivity ρ( t - 1 ), S 108 , which is the estimate made at the previous time  t - 1 . 
     The thermal resistivity estimating unit  42  also obtains the first temperature T s  from the first temperature sensor  26  at the exterior surface of the cable  22  and in the present case it obtains the previous measured temperature T s ( t - 1 ) meas  at the exterior surface of the cable  22 , S 110 , which is the temperature detected by the first temperature sensor  26  and sampled at the previous point in time  t - 1 . The thermal resistivity estimating unit  42  also obtains a previous second measured temperature T a ( t - 1 ) meas  in the soil, S 112 , which is the temperature measured by the second temperature sensor  30  and sampled at time  t - 1 . The thermal resistivity estimating unit  42  also obtains a previous measurement of the current I c ( t - 1 ) transmitted in the cable  22 , S 114 , i.e. the current measured by the current sensor  52  at time  t - 1 . 
     The estimation of the thermal resistivity is in this case based on an estimate of the temperature at the exterior surface of the cable  22  caused by the power losses in the cable for the current I c  running in the conductor  10  of the cable  22 . This is done through applying the measured temperatures and current in the model M of the cable  22  and the soil provided through the thermal model implementing block  64 , S 116 . 
     In the example of the model M, a flow of heat HF corresponding to the measured current I c  is provided by heat source HS to an input formed across the first thermal capacitance C 0 . The previous estimated resistivity ρ(t-1) may be used to obtain values of the thermal resistances of the soil R(n+1), ... , Rm and the previous first and second temperatures may be input as temperatures on either side of these thermal resistances R(n+1), ... , Rm. The thermal resistivity estimating unit  42  then estimates a following first temperature T s (t) pred  using the thermal model M in thermal model implementing block  64 , S 118 . It thus enters the first, second, third and fourth inputs that are associated with the previous time  t - 1  in the model M and using this model it predicts the following first temperature T s (t) pred , which is the temperature of time t, the present time. The prediction my more particularly involve predicting the change of the first temperature due to the heat flow HF caused by the measured current I c ( t - 1 ). In this respect it can also be mentioned that as the second temperature is sensed at a distance from the cable that is uninfluenced by the heatflow HF, the second temperature will be considered to remain the same. The predicted first temperature T s (t) pred  is then provided to the subtracting block  66 . 
     The estimation of the thermal resistivity is in this case based on a difference between the estimated first temperature and the measured first temperature at the exterior surface of the cable. 
     In the present case, this is done through the thermal resistivity estimating unit  42  obtaining the following measured temperature T s (t) meas  at the exterior surface of the cable  22 , S 120 , which is the temperature detected by the first temperature sensor  26  and sampled at the present time t. This measured temperature is also provided to the subtracting block  66 . 
     The subtracting block then forms an error e as a difference between the measured and estimated following first temperatures T s (t) meas  and T s (t) pred , S 122 . This error e is then amplified with a gain K in a following optional amplification block  68 , S 124 , and the amplified error is provided to the adding block  70  as is the previously predicted thermal resistivity ρ(t-1), i.e. the thermal resistivity that was estimated at the previous point in time  t - 1 . 
     The possibly amplified error e is then combined with the previous thermal resistivity estimate ρ( t - 1 ), which combination may be an addition, where the result of the combination is the following estimated thermal resistivity ρ(t), i.e. the thermal resistivity estimated for the present time t. 
     Thereby the following thermal resistivity ρ(t) of the soil is determined as a combination of the previous estimate of the thermal resistivity ρ( t - 1 ) of the soil and the possibly amplified error e, S 126 . 
     The estimating of the following thermal resistivity of the soil in this case thus involves a combination of the previous thermal resistivity of the soil and the difference between the measured following first temperature and the predicted following first temperature, where the prediction of the following first temperature has been made based on measurements made at the previous point in time. 
     This type of operation can then continue until the prediction of the thermal resistivity stabilizes. 
     After the thermal resistivity has been estimated, it may then be used by the overload operation determining unit  44  to determining of overload operating conditions identify that can be used in an overload operating mode. The determining of overload operating conditions may comprise determining a maximum overcurrent level, an overload power level and/or an overload time duration at which the cable may be operated in the overload operating mode. The overload operation determining unit  44  may then inform the high-level control computer  46  of the overload operating conditions and the high-level control computer may then use the information of the overload operation conditions in the control of the converter made via the low-level control device  48  in order to avoid the overload operating conditions from being violated. 
     Through the estimation of the thermal resistivity of the soil, it is possible to combine safe overload operation with low safety margins, which is due to a good estimate of the thermal resistivity. Thereby the cable can be more efficiently used compared with when no or an inadequate estimation of the thermal resistivity of soil is made. Furthermore, the sensors used are often required for the overload operation. This means that the invention can be implemented in a simple way using only additional software. 
     The first and second groups of temperature sensors may be used if the stability of the temperature at the exterior surface of the cable and at the distance to the cable are desired. The temperatures of the first group may be combined, such as averaged, and the temperatures of the second group may be combined, such as averaged, in order to obtain more stable temperatures in the estimation of the thermal resistivity of the soil. 
     As was mentioned earlier, the thermal resistivity estimating device may be provided in the form of a processor with associated program memory including computer program code for performing its functionality. 
     A computer program may also be a computer program product, for instance in the form of a computer readable storage medium or data carrier, like a CD ROM disc or a memory stick, carrying a computer program with the computer program code, which will implement the functionality of the above-described thermal resistivity estimating unit when being loaded into a processor. One such computer program product in the form of a CD ROM disc  72  with the above-mentioned computer program code  58  is schematically shown in  FIG.  8   . 
     A computer program product may also be a program provided via a server and downloaded therefrom to the thermal resistivity estimating device. 
     It should here be realized that the invention can be varied in more ways than was discussed above. 
     Although the invention has been described with reference to a DC cable, it should be realized that the teachings described herein may also be applied on an AC cable, such as an AC cable comprising three cores or three conductors. 
     Moreover, the shown thermal model is merely one example of a model that may be used. It is possible to use other models of the power loss through the cable. In the estimating scheme, it is possible to use a subtracting block instead of the adding block as well as to use an adding block instead of the subtracting block. Other types of combinations of the error with the previous estimate of the thermal resistivity than addition or subtraction are also possible. It is in fact possible to have a completely different estimating scheme. 
     It should also be realized that the overload operation determining unit  44  may be omitted from the thermal resistivity estimating arrangement. It is also possible to omit the signal collection device and the connection box. 
     Therefore, while the invention has been described in connection with what is presently considered to be most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements. Therefore, the invention is only to be limited by the following claims.