Overhead transmission lines are a common way of energy transportation at high voltage levels. An increasing population density over the years leads to higher energy demand. As a consequence, the extension of existing power systems is unavoidable in order to guarantee the electric power supply in the future. Currently, the application of extra high voltage (EHV) cables in power grids is popular for the extension of existing grids. People who live nearby overhead lines are reluctant to the construction of new high voltage overhead lines. The appearance of high voltage towers and lines in the landscape can have a large visual and ecological impact. Besides, in terms of an aesthetic component in this opinion, some people are concerned about electromagnetic field effects from the high voltage overhead lines to their health, because of the continuous exposure to (low frequency) electromagnetic fields from overhead lines. There is no hard evidence of adverse health effects resulting from long term exposure to electromagnetic fields produced by overhead lines.
The highest electrical field strength occurs at the conductor surface of the line. The electric field strength directly under 400 kV overhead lines lies between 7 kV/m and 10 kV/m. At a distance of 25 m from the overhead line, the field strength can be expected to be less than 5 kV/m, which is an admissible level for human exposure. In cable systems, there exists only an electric field between the inner conductor and the screen and not outside the cable, since the screen conductor of the cable is usually connected at ground potential. In this way, the electric field is enclosed between the cable core conductor and the screen. The magnetic field strength around current carrying cables is higher compared with overhead lines, but decreases more rapidly with the distance. There exist exposure limits for the magnetic flux density: in the Netherlands this limit is 0,4 μT . 
Underground cables replacing overhead lines
A number of TSO’s around the world are now studying the effect of applying EHV AC cable lines in their power grids. Energinet (Denmark) plans to apply underground cabling of the existing 132 kV and 150 kV grids by 2030. Cables can be applied to extend the grid or to replace existing overhead lines. Cables are already widely used for the lower (distribution) voltage levels. In 2005, a total length of almost 33000 km of AC land and sea cables was in service in the world. 
At voltage levels below 220 kV, more than 90% of the cables installed between 2001 and 2005 were of the XLPE insulated type. Above 220 kV, more than 40% are still of the self-contained oil-filled (SCOF) type. Currently, network planners and system operators do not have much experience with the behavior of power systems in which long EHV AC cables are integrated. At this moment, the longest EHV cable connection is in use in Japan; a length of 40 km at 500 kV.
In Denmark, a 150 kV connection to the offshore wind farm Horns Rev 2 is being installed and has a length of 100 km. 
The Danish system operator Energinet.dk has performed several studies in relation to the application of very long HV/EHV AC cables. These studies have shown that further analysis is needed to answer questions and to provide insight in the behavior of a power system with integrated cables. The stability of the grid and the security of supply are important issues in these studies.
The application of cables in power grids and mixed line-cable-line sections will influence the behavior of the power system as such in several aspects. The steady state, transient and dynamic responses of cables for both small and large disturbances differ significantly from overhead lines. This has implications for the operation of power systems with cables in terms of grid stability and security of supply. Therefore, all steady state and transient phenomena should be a subject to study before the integration of cables is realized in practice.
From the installation point of view, high voltage cables longer than 1-2 km require cross- bonding schemes to reduce induced sheath currents. For shorter lengths, single-point bonding is generally applied. From the electrical point of view, cables cannot simply be replaced by overhead lines. The electrical behavior of cables differs from that of overhead lines. An overhead line is a transmission line surrounded by air, that gives the insulation and has a dominant inductive behavior. A cable, consists of an inner and a sheath conductor with an insulating material with semiconductor layers in between, and is therefore predominantly capacitive. Cable capacitance and inductance per unit length differ from the values of overhead lines. The series inductance of a cable is five times smaller and the shunt capacitance 20 times larger than that of an overhead line. As a result, the characteristic impedance of cables is 10 times lower and the traveling wave velocity approximately two times smaller. So, the cable characteristic impedance value lies roughly between 30 and 70 Ω. This means that the characteristic impedance loading (SIL) for a cable is several times larger and is determined by the characteristic impedance and the applied voltage. Hence, a cable loaded below its SIL, behaves like a shunt capacitor. The cable loading above its SIL behaves as a shunt reactor. A large SIL can even exceed the cable ampacity. When the cable load equals its SIL, there is no net reactive power flow and this results in a flat voltage profile along the cable.
Cables, reactive power and shunt compensation
A capacitance can be regarded as a source of reactive power. Therefore, an energized cable injects reactive power to the grid. The magnitude of the capacitive current of a cable depends on the applied voltage and on the reactance, and that means on the capacitance per unit length. When the cable ampacity is consumed completely by the capacitive current, no active power can be transferred through the cable and the critical cable length is reached. Capacitive current is therefore the major limitation in the application of AC cables for long distances. The definition of the maximum operable length at thermal limit (MCLTL) is used 
as a steady state operational design criterion of cables.
The large capacitive charging current has also consequences for the cable life time. Deterioration of cables caused by their own current is an important issue when using long EHV AC cables. High voltage equipment is dominantly inductive and therefore requires reactive power. The reactive power is indispensable for operating devices that make magnetic fields to perform their function, like transformers and motors. When long cables are applied in the system, there can be an unbalance between produced and required reactive power.
Reactive power surplus in any operation condition causes power-frequency voltage rise at the cable terminations and adjacent nodes in the grid. A step voltage change of 3% is usually allowed while connecting or disconnecting a cable.
The allowable voltage step change during switching of cables is prescribed in the net code of the grid operator. To keep these stationary overvoltages below an acceptable level, compensation of reactive power is necessary. Normally, cable connections longer than 30 km require compensation and this can be achieved by fixed or variable compensation using shunt reactors. Shunt coils are usually installed at both cable ends or at the transformer tertiary winding. When there is symmetry in the line-cable-line section, meaning that the two sections of the overhead line are of equal length, fixed shunt reactors can be applied. Variable shunt reactors are installed when one overhead line section is much longer than the other. Algorithms are described to find the optimal taps of the variable shunt reactor . Shunt reactors need to be designed according to steady state operating constraints. Important criteria for shunt reactor sizing are the voltage rise at the supply node, receiving end overvoltages and rated line-charging breaking current .
Switching shunt reactors may result in an interchange of reactive power between system inductances and cable’s capacitance. These oscillations which are superimposed to the systems natural frequency can also lead to temporary voltage rise in the grid. Switching actions in shunt compensated mixed line-cable-line connections may also result in overvoltages. In , switching-off simulations were performed on a Danish operating 400 kV system for the connection between Aarhus and Aalborg with a length of 90 km. An overvoltage of 132 % was shown compared to the voltage before switching-off. This overvoltage was caused by resonances between the cable and the shunt reactor. Another Danish study for a planned 60 kV cable of 18,5 km between Albaek and Hedebo have shown no remarkable overvoltages after switching off .
Compensation causes line resonances in situations when there exists capacitive coupling between a disconnected phase and the phases remaining in service. When there is no capacitive coupling present between single core insulated cables, the risk of line resonances is greatly reduced and the compensation rate can be 100%. The degree of compensation has an influence on the cable charging current and on the voltage profile along the cable. A study for a 400-kV cable system has shown that two shunt reactors placed at both cable ends reduce the charging current at both ends to half of the largest value. Installing reactors reduces this current to 25%, four reactors to 16% and five reactors to 12,5% of the largest value . System studies for long cables recommend installing shunt reactors with a distance of 15 km to 40 km between them . The influence of shunt compensation on the voltage profile along a 400-kV cable connection was done in a feasibility study . Power flow calculations were performed under no-load condition when one cable end was opened while the voltage at the other end was set to 415 kV. The lowest compensation rate considered was 93,3% and it turned out that the voltage along the cable stayed below 420 kV. For the highest (over)compensation rate of 111,9%, it was shown that the voltage at all places along the line was less than 415 kV.
Switching overvoltages and lightning
In another study, carried out by Cigre Working Group B1.05, a cable end termination was placed in the cable-overhead line joint. This termination was a linear variation in characteristic impedance from 90 Ωto 30 Ω. It was demonstrated that an incoming wave with 2 μs front rise time, raised the cable voltage by 2%, and for an 1 μs front time, the increase was 1% . The velocity of voltage and current waves along a cable is about 50% of the velocity of overhead lines and the waves propagate between the core and sheath.
In Denmark, a 150-kV connection to the offshore wind farm Horns Rev 2 is installed and has a length of 100 km. This cable forms the connection between the wind farm and 400 kV grid. A study to line-to-line overvoltages during energization of the 150 kV cable is reported in  for different short circuit power in the 400 kV grid. This study shows that in some cases, overvoltages are higher than the maximum allowable values.
The behavior of mixed line-cable-line systems under lightning events is of importance in power system transient studies. Lightning strokes can cause very high overvoltages, that can affect equipment insulation so overvoltage protection like surge arresters must be applied. The results of a study on a mixed overhead-cable system at 380 kV level have shown that shielding failure does not represent a critical event . Furthermore, it was shown that installing surge arresters at both cable ends reduces tower foot voltage by 10 to 15%.
Current zero missing phenomenon
Another issue, related to shunt compensated cables, is the zero-missing phenomenon that normally occurs for shunt compensated cables during the energization process of the cables. The decay of the current DC component depends on the cable- and reactor- resistances that are in general small. This results in the current not crossing zero for several cycles, meaning that the opening of the circuit-breaker could be delayed.
Therefore, countermeasures must be taken to avoid the failure of circuit-breakers. In practice some methods have been proposed to minimize the occurrence of the zero- missing phenomenon by applying a pre-insertion resistor [15, 16].
Cables and overhead lines can lead to parallel paths. The lower impedance of cables gives an inequality in power flow, which even could result in overloading the cable connections. This implies that during steady state operation, compensation is required in two different ways: as compensation for the reactive power surplus and for the difference in impedance to control the flow of power. The larger capacitance of a cable has also consequences for the system resonance frequencies, which are considerably lower. Installed long HV cables compensated by shunt reactors form a parallel resonance circuit consisting of the cable capacitance and the shunt reactor inductance. Series resonance circuits are formed by the cable capacitance and the transformer leakage inductance. Both types of resonances can lead to temporary power frequency overvoltages.
Apart of affecting the steady state operation, there are also implications for transient situations when using cable. First of all, transients cause slow-front, fast-front and very- fast-front overvoltages, which depend on their origin. Slow-front overvoltages occur for instance during cable (de)-energization, line switching and fault clearing. Fast-front surges caused by lightning induced current injections in overhead lines can lead to high overvoltages. Moreover, a restrike after switching a shunt reactor may cause overvoltages.
Travelling waves and characteristic impedance
Characteristic impedances of cables, cable joints and overhead lines differ from each other, meaning that there are impedance mismatches at line-cable-line transition points. Reflections of traveling voltage and current waves will occur at junctions and result in high voltage peaks. Characteristic impedances of cables and overhead lines are frequency dependent, which means that reflection coefficients at junctions are also frequency dependent. At high frequencies, reflections can lead to doubling of the voltage amplitude at those junctions. This can also happen at the coupling point of a transformer and cable resulting in overstress of transformer insulation, leading to accelerated aging of transformer insulation.
When the cable length increases, attenuation and distortion effects increase and the maximum voltage at the cable reduces. This maximum voltage reduction depends on the core, the insulation material and the sheath conductor. Calculations were performed to study the influence of material dimensions at maximum voltage . A square pulse of 10 μs duration applied to a 145-kV cable with a copper core and 17 mm insulation thickness, and it was found that reducing the cable lead sheath from 4 mm to 2 mm resulted in a substantial reduction of the cables maximum voltage. Furthermore, it was shown that the reduction of the maximum voltage, increases by increasing cable length. In the same study, it is shown that, when frequency dependent insulation losses were considered in the calculations, paper oil insulation results in significantly more reduction of the maximum voltage than XPLE insulation.
Simulation studies of transients in cables are of great importance when performing system studies with cables. Accurate calculation of transients requires a detailed cable model. Transients in power systems can result in steep voltage wave fronts. These steep voltages contain high frequency oscillations. For a cable model for transient studies, the frequency dependence of cable parameters should be taken into account in order to obtain accurate simulation results. The modeling of a cable and the calculation of parameters for transient simulations is a rather complex and delicate task, especially with respect to the frequency dependency of the different parameters and the influence of the ground return path. The parameters have to be determined for the different cable layers, the surrounding conditions, and both the skin and proximity effects. The total series impedance and shunt admittance of a cable has to be determined as well. The shunt admittance is formed by insulating and semiconducting layers and the material properties of the admittances are modeled by complex permittivity.
In general, the accuracy of modeling an underground cable depends on the type of phenomenon that is considered. Several cable models have been developed over years, both for planning and for system studies. The available cable models can be divided into two main classes: lumped parameter models (also called PI-section models) and distributed parameter models (also called travelling wave models). For power system steady state analysis like planning studies, π-sections have been used with sufficient accuracy. For these cases, it is usually not necessary to take account for full frequency dependency of the cable parameters. The exact π-model is accurate for power frequency studies.
Distributed wave models can be subdivided into Frequency Dependent Mode Models (FDMM) and Frequency Dependent Phase Models (FDPM). Frequency Dependent Mode Models use a constant (frequency independent) transformation matrix. This approach splits a multi-phase system into mutually exclusive modes meaning that each mode is treated as a single-phase circuit. The Frequency Dependent Phase Models are frequency dependent in all parameters. These models have been implemented in EMTP-based simulation software tools.
The FDMM, developed by J.R. Marti , uses a frequency independent transformation matrix to separate multiple coupled phases into single-phase circuits. An improvement of this model was made by taking into account the frequency dependency of the transformation matrix, developed by L. Marti . To overcome the complexity with the modal transformation matrix, a Frequency Dependent Phase Model was developed . This method minimizes the computation time by using the ARMA model. A widely used cable model nowadays, is an FDPM model using the s-domain. This model is implemented in EMTDC-based simulation programs . The difficulty with the transformation matrix is circumvented when the cable model is split into a constant ideal line section and a frequency dependent loss section .
For accurate cable modeling, the total series impedance and shunt admittance have to be determined. A fundamental description of the cables’ impedance, its admittance and the semiconducting layer is described by Ametani [22, 23]. This formulation has been widely used for the calculation of cable parameters for transient studies. The evaluation of frequency dependent impedances of underground cables can be done in different ways, for example by using the finite element method is also performed .
In order to perform accurate cable modeling for transient studies, the frequency dependency of cable parameters needs to be taken into account and therefore, cable parameter determination over a wide frequency range is an important topic. A method to calculate the frequency dependent parameters of power cables, based on spatial discretization of their cross-sections, is described in . Simplifications have often to be made, such as assuming constant permeability, neglection of dielectric losses, ignoring the proximity effects and assuming coaxial arrangement of the conducting and insulation layers. Next to that, an accurate model for the earth impedance is rather complicated and requires specific data. Evaluation for cable earth impedances can be done, by applying Pollaczek’s integral , . In general, considerable approximations have to be made while calculating the earth impedance .
The best way to verify models is to compare calculated values with field measurements And for verification, a measurement set up should be made. For validation of high frequency models, a voltage with the shape of a step-function is applied at the cable termination and measurements are carried out to verify the transient cable models implemented in software like PSCAD (Power Systems Computer Aided Design). This is how the 400 kV Gistrup-Skudshale cross bonded cable system in Denmark was studied. The comparison of transient cable models with field measurements has been reported for cross bonded cables in .