Wave-Velocity Based Real-Time Thermal Monitoring of Medium-Voltage Underground Power Cables

Underground power cables are a bottleneck in congestion management for the medium-voltage grid because their ampacity is constrained by the maximum allowed insulation temperature. Network operators usually lack real-time information on the thermal state of the cables, which is a requirement for safe dynamical loading. This paper investigates wave-velocity based thermal monitoring of medium-voltage power cables. Variation in wave velocity arises from the temperature dependent dielectric permittivity of the insulation material. A method is proposed and tested to calibrate a thermal model, which can be used to estimate the temperature of a power cable in practical network conditions. The obtained resolution for PILC is below 1 °C. For XLPE, the resolution depends on the absolute temperature, but the fast-changing relative permittivity near its maximum operating temperature suggests that there the resolution is similar. Moreover, a method to estimate the load profile from the relation between the propagation velocity and insulation temperature is provided. The model has been tested on an operational cable circuit and the estimated current aligned well with the measured current by the network operator. The resulting absolute temperature error, caused by systematic inaccuracies from calibrating, is estimated to be about 5 °C.


I. INTRODUCTION
N ETWORK operators must deal with congestion in the medium voltage (MV) grid because of increased demand for transporting and distributing electric energy.Congestion is becoming a major concern for distribution system operators (DSOs).New connections to the MV grid may not be granted, resulting in slower integration of renewable energy sources.As an example, this is illustrated with the congestion map for feeding large-scale generation in Fig. 1, indicating regions in Fig. 1.Transport congestion in the Dutch grid for feeding; the colors indicate no transport capacity (red), announced limitation (orange) and limited availability (yellow) [1].
The Netherlands where the maximum transport capacity has been reached or will be reached soon [1].Expanding the grid capacity takes time and will not resolve the congestion problem in the short term.Better exploitation of the presently available capacity could be part of the congestion policy, provided that the thermal constraints of power cable systems are respected.
The thermal state of underground power cables is ultimately limiting their current carrying capacity.Cables can be used above their rated current for short times owing to their thermal inertia, but the temperature must be carefully managed.The duration of dynamic overloading depends on the thermal cable and soil parameters, which are not all precisely known in practice.It can only be safely applied if real-time feedback on the cable temperature is available.Online cable temperature sensing can be applied by integrating optic fibers as a thermal sensor, especially in high voltage and extra high voltage cables [2].For MV cables, the application of distributed temperature sensing with optic fibers is not economically feasible.Furthermore, it is not possible to retrofit fiber technology in existing cable systems.Thermal models can be used instead to determine the operating limits for the cable current.These models are well-developed [3], [4], [5], but their predictive value may be hampered by parameter uncertainties.In particular, the thermal resistivity of the soil surrounding the cable has a pronounced effect on the thermal behavior [3], [6], [7], [8] and its value depends significantly on the moisture conditions.To accommodate this uncertainty, temperature margins need to be incorporated to guarantee safe operation.
Wave propagation, i.e., the velocity of pulse signals travelling along transmission lines such as power cables, is to some extent dependent on temperature as shown in [9], [10], [11], [12].In [11], [12], the variation of the wave velocity throughout a year with load variation and variation of the ambient temperature was presented.This paper investigates concepts to turn these observations into an accurate and reproducible method to thermally monitor MV cables over long times.It addresses practical approaches to calibrate the temperature scale.The paper also provides extensive results for MV cables in service, which were monitored over a period of up to two years.
The paper is structured as follows.Section II presents the option to employ the wave velocity of signal propagation along a cable system as a measure to monitor its temperature.Its application for paper-insulated lead-covered (PILC) and crosslinked polyethylene (XLPE) cables is discussed in Sections III and IV, respectively.Section V provides a brief discussion on future perspectives for practical application and Section VI summarizes the results.

II. METHODOLOGY
Measurement of the wave velocity is part of existing diagnostic equipment for partial discharge (PD) detection with fault location in power cable systems.The data presented in this paper are obtained with the system described in [12], [13].It employs two-sided detection and includes a pulse injection system for synchronizing the recording units at both ends.This integrated injection and detection capability provides real-time information on the pulse transit time along the monitored connection.
The wave velocity is affected by the temperature through the dielectric permittivity.This information can be compared and combined with results from thermal modelling.These methods are employed to study the thermal responses upon typically encountered load patterns.The mentioned aspects are briefly introduced below.

A. Dielectric Permittivity
The variation in a received signal U r after travelling over distance L c along a power cable at temperature T with respect to a reference at T ref in the frequency domain f can be expressed in terms of the change in the propagation coefficient γ as shown in [14], [15]: The imaginary part of γ involves the wave velocity, which is mainly determined by the per-unit-length capacitance C and inductance L of the cable via v = 1/ÝLC.In [14] it is shown, that for frequency components relevant for pulse propagation in power cables (100 kHz -10 MHz), the temperature influence on the cable inductance is small.The temperature dependency of the transit time is therefore attributed to the temperature dependency of the relative dielectric permittivity ε r of the insulation material.The factor between the square brackets in (1) represents the relative variation in the (reciprocal) wave velocity.It causes a shift in the transit time.Equation (1) can be analyzed based on a detailed model of the cable propagation coefficient as in [14].However, since the peak shape of the received waveform is found to hardly vary with temperature, the variation in transit time can also precisely be obtained from directly measuring the signal arrival time.
The thermal variation of the wave velocity depends on the type of cable insulation.This relation has been evaluated for short segments of a PILC (about 100 m) and an XLPE (about 70 m) cable by means of time-domain reflectometry (TDR) in [15].Fig. 2(a) shows that for PILC the velocity decreases close to linear with temperature, whereas for XLPE a non-linear increase is observed.The relative permittivity has also been measured for a 1.22 mm thick XLPE material sample up to a temperature of 110 °C, controlled within ±0.1 °C [16].The effect on the velocity is shown with the dashed curve.It is based on the fitted function on the data shown in Fig. 2(b).From this figure, a strong increase of the propagation velocity is expected when Fig. 3. Load profiles for a cable feeding industrial, urban, rural areas, and for a wind farm.Fig. 4. Propagation time variation for a combined three-core PILC and XLPE cable system with simultaneously recorded soil temperatures; the dashed line connects the minimum values after periods of low load, occurring weekly.
approaching the maximum temperature of 90 °C allowed for XLPE insulation.

B. Thermal Modelling
Cables heat up during loading mainly due to electric conductor (and earth screen) losses in the cable.This variation can be relatively fast, depending on the cable load pattern.Also, the temperature of the soil surrounding the cable will slowly vary due to changing weather conditions throughout the year.To analyze the thermal response of the cable on both factors, a thermo-electric equivalent (TEE) model can be employed.
The thermal behavior of the cable itself can be accurately calculated as the information about layer thicknesses and applied materials is given by the cable manufacturer and the analysis is mostly standardized [17].However, modelling the soil under loading may be complex, as the thermal resistivity and capacity of the soil is dependent on the moisture level.During loading, the soil moisture will vaporize and migrate away from the cable, which will increase the thermal resistivity [18].The extension of this dry zone is dependent on many factors such as the heat rate of the cable, soil type, the non-drying heat rate of the soil, precipitation and so on [19].These parameters are hard to estimate with high accuracy.A detailed calculation of the dried soil radius can be found, e.g., in [7], [8], [20].The TEE models and the parameters used for this paper are summarized in the Appendix.

C. Load Patterns
Load patterns depend on the type of connected producers and consumers as illustrated in Fig. 3 for a period of several weeks.Industrial, urban, and rural areas show a daily cycle, which may be less pronounced during weekends.Wind farms are characterized by temporarily high current levels.These current profiles cause specific thermal variations that affect the wave velocity.
Fig. 4 shows the thermal response of a mixed 4214 m PILC and 1133 m XLPE cable monitored throughout a year in 2021.The peaks relate to the daily load cycles typically occurring in an industrial area (see first current profile in Fig. 3), but are absent during weekends, public holidays, and the summer vacation period.Also, a slow variation throughout the year is observed that can be attributed to the soil temperature.This temperature is recorded by the Dutch meteorological institute (KNMI) [21].The variation can mainly be ascribed to the PILC section because of its longer length and the stronger temperature dependency (Fig. 2).The propagation time after the cable has cooled down to close to the soil temperature at the end of a weekend (dashed curve) follows the variation in the soil temperature published by the KNMI (red curve).The yearly variation in the propagation time corresponds to a temperature difference of about 14 °C.It is larger than the variation observed in the daily cycles, suggesting that the temperature increase caused by the cable current is lower.The precision by which the velocity is detected suggests that the corresponding temperature resolution is better than 1 °C.

III. PILC INSULATED MV CABLES
The yearly variation in the propagation velocity, during low cable load, for six PILC cables located in the same region in The Netherlands is shown in Fig. 5 for a period of two years.The patterns are similar, but the average velocities differ more than was expected from the variation in dielectric properties, e.g., related to different manufacturers or due to ageing of the insulation material.The deviations are ascribed to imprecise documented data regarding the cable lengths.This observation indicates that thermal modelling should be made immune to this kind of systematic uncertainty.This can be achieved by focusing on changes in the propagated signal with respect to a reference situation as is indicated by (1).The linear dependency with temperature of the wave velocity for PILC cables offers the prospect to use its yearly variation together with the known soil temperatures from the KNMI, [21], to calibrate the temperature scale.In Section III-A, this method is employed to determine the cable temperature profile and to reconstruct the cycling in the current based on the monitored wave velocity.It assumes that there are moments that the cable cools down to the surrounding soil temperature, which serve as the reference situation.Section III-B discusses an iterative calibration procedure that can be employed when there is no such low-load period, or it is too short for the cable to cool down completely.

A. Direct Calibration
The wave velocity varies close to linear with temperature, but the relation may not be known with sufficient accuracy.As was observed from Fig. 5, the precise cable length may differ from the documented values.Systematic uncertainties in cable (a) Ambient temperature profile (top) and (b) comparison of the variation in transit time (symbols) with the soil temperatures together with a 1 st order response on the ambient temperature for a PILC cable [11].
design parameters make that absolute modelling of the cable propagation characteristics is not a feasible approach.
As basis for calibration, the correlation between wave velocity and soil temperature throughout a year can be used.The linear relationship is applied to the instances for which it can be assumed that the cable is thermally equalized with the surrounding soil.The soil temperature profile is only representative in case it is recorded close enough to the cable location.The soil temperature can also be extracted from the ambient temperature T a (t) above ground, which is monitored on many more locations.To this end, a simplified first order response model of the cable temperature T(t), with the response time τ as parameter, can be employed [11]: The cable temperature at time t i+1 can be expressed as function of the value at time t i and the ambient temperature T a (t i+1 ): (3) Fig. 6 shows an example for a PILC cable with a length of 1195 m.During weekends this cable was hardly loaded, and it is assumed that the temperature of the cable and the surrounding soil became equal.The thermal data for T a in Fig. 6(a) are provided on an hourly basis in [21].The starting value T(t 0 ) is the value recorded at the end of the preceding year.A least square linear fit is made between wave velocity and the temperature calculated with (3) for different values of τ .The lowest variance between the measured wave velocities and values according to the linear fit was obtained for a response time τ of 378 hours (about 15 days).This variance was only 20% larger than the value based on the thermal soil data at 50 cm depth.In comparison, the soil data at 100 cm depth resulted in an over factor 3 larger variance.Typically, MV cables are indeed buried on a depth just over 50 cm.The slope of the linear fit corresponded with a sensitivity of −0.098 %/ °C.It is similar to the slope of the trendline for PILC Fig. 2(a) and agrees with the range of values found for the cables in Fig. 5 (see inset).Apparently, one can expect a variation in the order of 10% in this sensitivity.This implies that the sensitivity should be determined for each individual cable.It should be occasionally updated as it may gradually change over a timespan of several years due to cable ageing or moisture ingress.To avoid errors, one needs to employ recent reference patterns for (1), e.g., taken at moments that the cable has cooled down to the surrounding soil temperature.
The method is exemplified for a 4163 m three-phase cable with 95 mm 2 copper conductors.The soil temperatures at a depth of 50 cm shown in Fig. 7 serve as calibration data.The cable load was cyclic, but during the summer the current was appreciably lower than during the winter months.To ensure that the cable had cooled down closely to the soil temperature during the low-load periods, for establishing the relation between velocity and temperature, the data around the summer period (April to October 2021) are selected.Fig. 7 shows the reconstructed temperature profile over a complete year.The transit time of injected pulses is measured every minute and is averaged over one hour resulting in 24 times 365 data points [11].The inset depicts the variation over a single week.
It is observed that, despite the temperature rise from the cable load during the colder months is much higher, the highest temperature is reached during the summer months due to the soil temperature.As the maximum operational temperature for PILC cables is 70 °C, there is a large potential for increasing the exploitation of the cable in this specific cable system.
By employing a simplified thermal model, the cable current I(t) is retrieved to verify the consistency with the measured current by the DSO.The current is obtained from the cable temperature profile and the surrounding soil temperature: with R AC the conductor resistance (0.178 mΩ/m), C th the equivalent thermal capacitance (2.5 J/Km) and R th the equivalent thermal resistance (1.2 Km/W).The parameters are considered constant because the temperature variation was relatively small (maximum ±6 °C).For the same reason, losses in the common earth screen of the three-phase cable are not accounted for [22].The thermal parameters are taken from the datasheet provided by the cable manufacturer.In Fig. 8, the reconstructed current profile is compared with the measured value for a period of one week.The current peaks twice a day, which is characteristic for urban and rural areas (Fig. 3).Their magnitudes are reproduced within 10%.The minimum values differ more because a low current implies that heat dissipation hardly occurs and consequently there is only a minor effect on the wave velocity.

B. Iterative Calibration
It is not guaranteed that cable systems have a long enough low-load period such that they thermally equalize with the surrounding soil.This will lead to an offset between the soil temperature and the lowest temperature the cable reaches.As can be observed from Fig. 7, during the first months, the reconstructed cable temperature remains above the soil temperature.It is only a few degrees centigrade in this case but will be more when the load cycles are less pronounced and there is a relatively large base load current.A TEE model can be employed to calculate the temperature response either based on the measured current or, if not on a reconstructed profile as described in Section III-A.The thermal model only needs to provide an estimate for the correction due to the offset temperature and therefore a limited model accuracy already suffices.
For the calibration of the wave velocity relation with temperature, it is first assumed that thermal equilibrium is reached during all low-load periods.The current profile is evaluated based on this assumption.Next, a TEE model (see appendix) is used to calculate the expected cable temperature based on the current The temperature offset found at the low-load moments is then entered in the next iteration step for calibrating the wave velocity, and a new current profile is determined.The procedure is repeated until convergence is achieved.
With the procedure sketched above, there is no need to select the data for which it is assured that the cable has closely thermalized with the surrounding soil.For Fig. 9, the complete data set of Fig. 7 is employed for the calibration.Already after two iteration steps sufficient convergence is reached.The result also matches the profile based on the earlier calibration only using the low-load period between April and October.

IV. XLPE INSULATED MV CABLES
Calibration of the wave velocity as described in Section III is not possible for XLPE insulated cables, due to the non-linear dependency with temperature.Instead, it can be based on the measured relative permittivity in Fig. 2(b), as for XLPE the variation between different cables is much less.A reference situation with known temperature is still required because absolute modelling suffers from systematic uncertainties.
The wave velocity for a 3-phase XLPE cable with 5220 m length recorded over a period of one year is shown in Fig. 10, together with the soil temperature.The variation is clearly observable, despite the lower sensitivity as compared to a PILC insulated cable (for temperatures below 50 °C).The observed Fig. 10.Propagation velocity of an XLPE insulated cable and the soil temperature at 50 cm depth.velocity variation matches the soil temperature closely.Apparently, for the relatively small variation, the velocity behaves still rather linear in temperature.
For another case, the wave velocity is monitored for a singlecore XLPE cable (630 mm 2 Al conductor) connected to a windfarm located in Chili.The variation during one month of observation together with the generated current is shown in Fig. 11(a).The current profile is typical for a wind farm, showing occasionally high peak values interrupted by calmer periods.As the periods between the peaks can cover several days, it is safe to assume that the cable cools down almost completely.Such period can serve as a reference situation.The wave velocity for other temperatures is then calculated by correcting the velocity according to (1) based on the fit on the measured relative permittivity in Fig. 2(b).The increase in propagation velocity mainly happens at the end of a high current period.This is related to the thermal inertia of the cable in combination with the non-linear dependency of the XLPE permittivity, and consequently the propagation velocity, with temperature.
The temperature profiles shown in Fig. 11(b) are calculated from the load current by means of a TEE model (see appendix).It is also determined from the variation in the wave velocity, assuming a temperature of 10 °C for the cable surroundings.This guessed value has only limited influence on the temperature during the peaks since the XLPE relative permittivity hardly changes in the low temperature range.The peak temperatures deviate on average about 5 °C.Differences can be attributed to uncertainties in both methodologies.The precise dielectric behavior of the insulation material may differ from the XLPE test sample in Fig. 2(b).Categorizing the origin of XLPE insulation used by cable manufacturers in terms of their relative permittivity values may remove this uncertainty.This expectation is supported by the strong correlation found between wave velocity and soil temperature in Fig. 10.For the TEE model, bonding type and the specific soil parameters were not known, and typical values are taken instead.Soil parameters may also vary over time depending, e.g., on the soil humidity.The peak temperatures obtained from both methods agree better Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. in the first part of Fig. 11 than in the last part.As the dielectric permittivity behavior does not change on timescales of weeks or months, the observed differences may suggest that the thermal soil parameters have changed (e.g., related to soil humidity).

V. DISCUSSION AND FUTURE PERSPECTIVE
The proposed method provides information on the overall thermal behavior of a complete cable system.Local thermal bottlenecks cannot be observed and safety margins, likewise with thermal modelling, are needed.On the other hand, the method probes directly the cable insulation temperature, independently of the thermal soil condition and provides relevant feedback for DSOs on a real-time basis.It must be noted that DSOs in practice do not have detailed information on the actual state of the soil for cables in service, lowering the accuracy of predictions on TEE alone.Therefore, exploiting the synergy of both methods allows for improved congestion management of the cable transport capacity.
Implementation of wave-based thermal models on the level of individual cable sections might not be cost effective.A more promising approach is to combine cable systems with multiple cables.Long cable systems can cover several ring-main units (RMUs), each with possibly several connected cables and a distribution transformer.The currents in the cascaded cable sections may therefore be different.With the measurement of a single transit time over all cascaded cable sections between RMUs, the method becomes more challenging.An assignment of a changing signal transit time to the change in velocities in the individual sections must be made.Further investigation is needed to determine how other information sources (e.g., recorded currents for the different sections) can be integrated to achieve the desired selectivity.
Alternatively, as the used equipment is flexible and can be re-installed easily in other RMUs, the focus can be directed to the critical cable segments only by reconfiguring the locations of the detection units.Another approach is to evaluate signal reflections arising at the RMUs, potentially containing wave-velocity information on the cable segment level.This may not be straightforward as these reflections may be obscured by contributions from other components in the network.However, one only needs to focus on a shift of structures in the waveform at the expected time for the reflection from a specific RMU or from a transition between different cable types.

VI. CONCLUSION
Thermal monitoring of power cables based on the propagation velocity of injected signals can be retrofitted in existing MV cable systems.The presented option is to employ hardware already developed for continuous monitoring of power cables on PD activity and fault detection.Although this paper aims to extract thermal information as much as possible from the wave velocity data alone, it should be emphasized that a combination with thermal modelling is most promising.
It is shown that the resolution is better than 1 °C for PILC cables.The variation of the wave velocity for XLPE is smaller than for PILC at low temperatures.At a temperature above 60 °C, however, the relative permittivity of XLPE starts dropping significantly, suggesting that a similar resolution as for PILC can be achieved there.The representative value of the measured permittivity dependency with temperature on a single XLPE material sample should be investigated deeper as it may also depend on the production process, in particular concerning the cross linking.Due to systematic uncertainties, which are relevant in calibrating the temperature scale, the obtainable accuracy is estimated to be about 5 °C.Better understanding of the dielectric permittivity behavior with temperature, particularly for XLPE, may improve the accuracy further.High resolution is still important as it enables an early detection of relatively fast changing thermal conditions.APPENDIX Thermo-electro equivalent (TEE) models are used for the thermal modelling of the buried power cables.The scheme depicted in Fig. 12(a) for the single-phase XLPE cable in Section IV is based on [3], [17], [23] and the cable datasheet.As shown inside the left box, the midpoint temperature T XLPE is taken halfway the thermal resistance representing the XLPE insulation.Its thermal capacitance is modelled using the van Wormer coefficient Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.p.The modelling parameters are summarized in Table I, which provides values for the thermal capacitances and resistances related to the aluminum conductor, lead earth screen, steel armor, and the insulation between the layers and of the outer jacket.The soil surrounding the cable, shown inside the right box, is modelled with three layers, ending up at the ambient temperature T a , [5].The soil parameter values are also provided in Table I.The model for the three-phase PILC cable with copper conductors and a common earth screen in Section III is provided in Fig. 12(b) [3], [23], [24].Only one phase is indicated (inside the left box).The two other phases are similar and connected at the point where the insulation temperature T PILC is taken.The scheme for the soil is equal to the layer model in Fig. 12(a) (right boxes).The PILC model parameters are included in Table I.

Fig. 2 .
Fig. 2. (a) Relative change in propagation velocity from TDR measurement with a linear fit on the data for PILC and a curve based on the permittivity measurement for XLPE; (b) measured relative permittivity for XLPE (fitted function has no physical background; the data points represent the measured frequencies in the range from 25 kHz to 2.5 MHz for each temperature value).

Fig. 5 .
Fig. 5. Wave velocity for six PILC cables during low-load periods; the cable lengths and the derived relative changes with temperature are indicated.

Fig. 7 .
Fig. 7. Reconstructed daily temperature cycles based on the thermal soil data recorded at 50 cm depth; inset is zoomed over one week in February.

Fig. 8 .
Fig. 8.Comparison between measured cable current and the reconstructed profile based on the monitored wave velocity.

Fig. 9 .
Fig. 9. Iterative calculation of the cable temperature and comparison with a direct calibration based on the low-load periods.

Fig. 11 .
Fig. 11.(a) Current profile and propagation velocity variation for an XLPE cable connected to a wind farm; (b) cable temperature deduced from the wave velocity and from a TEE model based on the cable current.

Fig. 12 .
Fig. 12. TEE models for (a) a single-phase XLPE cable (the three phases are modelled in trefoil formation) and (b) a three-phase PILC cable.

TABLE I PARAMETERS
FOR1-CORE 630 MM 2 XLPE CABLE WITH AL CONDUCTOR, 3-CORE 95 MM 2 PILC CABLE WITH CU CONDUCTORS, AND THERMAL SOIL PARAMETERS