3.1.1. Substation

The configuration with a line ending at a GIS substation is depicted in Figure 3a. The chosen sensor positioning leaves a reflection symmetric configuration. This leads to equal coupling of the central sensor to the outer phase voltages. Similarly, the coupling of the outer sensors to the central phase conductors are equal. A fundamental problem, as mentioned above, relates to the fact that from calibrating by means of symmetric phase voltages it is impossible to distinguish the contribution of the

coupling to the central sensor by the central phase from the combined coupling with the outer phases. An estimate is needed including sufficient margin to accommodate for its uncertainty [10]:

$$M = \begin{pmatrix} M\_1 & M\_4 & f\_0 M\_4 \\ M\_5 - 1/2\Delta\_0 & M\_2 & M\_5 + 1/2\Delta\_0 \\ f\_0 M\_6 & M\_6 & M\_3 \end{pmatrix} \\ \text{with } M\_5 = 1/2(M\_4 + M\_6) \\ \tag{8}$$

The main couplings in Figure 3a, diagonal elements in (8), are taken independent. Although they are expected to be similar, the effect of imprecise sensor positioning on the main coupling can be accounted for. The couplings of the side sensors to the middle phase are taken independent as well. The coupling to the phase furthest away is roughly estimated to be about 30% of the neighbour couplings *M*4 and *M*6 with an uncertainty of 50% (i.e., *f* 0 = 0.30 ± 0.15, so between a fraction of 0.15 to 0.45 of the value of *M*4 and *M*6). The estimate is based on the distance ratio sensor line, which was just over a factor two. As the sensor couples to a relatively short line, its sensed electric flux is expected to decay between 1/*r* (long line) and <sup>1</sup>/*r*<sup>2</sup> (point source). The chosen range with uncertainty covers both extremes. Electrostatic field simulation [7] provided a value of 40%. For *M*5 an average value of *M*4 and *M*6 is taken as the distances are similar. With Δ2 an uncertainty is assigned in this assumption of 50% of its value (Δ2 = 1/2*M*5). As precise positioning of the sensor in front of the central phase could relatively easy be judged, the value of Δ0was taken 20% of *M*5(Δ0= 1/5*M*5).

Solving (1) with (8) as coupling matrix results in the following set of equations:

$$\begin{aligned} M\_4 &= \frac{\mathbf{1}^{1/3} \sqrt{3} (a\_1 \sin q\_0 - b\_1 \cos q\_0) + (a\_1 \cos q\_0 + b\_1 \sin q\_0)}{1 - f\_0} & M\_1 &= 2/3 \sqrt{3} (a\_1 \sin q\_0 - b\_1 \cos q\_0) + f\_0 M\_4 \\\ M\_6 &= \frac{\mathbf{1}^{1/3} \sqrt{3} (-a\_3 \sin q\_0 + b\_3 \cos q\_0) + (a\_3 \cos q\_0 + b\_3 \sin q\_0)}{1 - f\_0} & M\_3 &= 2/3 \sqrt{3} (-a\_3 \sin q\_0 + b\_3 \cos q\_0) + f\_0 M\_6 \\\ M\_2 &= 1/2 (M\_4 + M\_6) + (a\_2 \cos q\_0 + b\_2 \sin q\_0) \end{aligned} \tag{9}$$

$$2/3\sqrt{3}(-a\_2\sin\varphi\_0 + b\_2\cos\varphi\_0) - \Delta\_0 = 0\tag{10}$$

The parameters *ai* and *bi* are obtained from fitting sinusoidal functions to the last five cycles in the recordings as shown in Figure 4a (left). Equation (10) is solved numerically in φ0 and subsequently all matrix components *Mi* can be calculated. The solution depends on the stochastic variable Δ0. The other stochastic variables do not affect the solution of (1) and their effect on the coupling matrix elements can be added afterwards.

**Figure 3.** Topologies and sensor (*ui*) positioning with respect to phase voltages *Uj*: (**a**) Overhead line ending at a substation, photo shows the installation of the sensors; (**b**) Overhead line to underground power cable transition (with termination T, surge arrester S.arr. and voltage transformer V.tr.), photos show the sensor (as seen from below) and its positioning in between two terminations belonging to the same phase. The sensor heights (indicated with arrows) are always chosen such, that they remain below the height reached by the supporting structures of the terminations.

Figure 4 shows the results upon line energization from the far end of the connection and from the substation where the measurements are taken. The black lines indicate one standard deviation confidence margin and the dash-dotted lines are extrapolated steady state phase voltages. The complete waveform in Figure 4a includes the recording of the steady state power frequency established after the switching transient. The last five cycles are employed for determining the coupling matrix. The zoomed figure shows that within the confidence bounds the overvoltage magnitude remains clearly below 2 pu. The switching event in Figure 4b contains steep transients as energization takes place near the measurement location. The zoomed waveform indicates that these relate to travelling waves, which reflect on the line to cable transition point at 6.8 km distance. Also here no serious overvoltages were observed.

**Figure 4.** Reconstructed waveforms for substation measurements recorded with 5 Msample/s over a duration corresponding to ten power cycles. The curves in colour represent the three phases with confidence margins in black: (**a**) Full and 10 times zoomed waveform showing overvoltages during the first cycle from energization at the far end of the connection; (**b**) Waveform with overvoltages during the first power cycle from energization at the near end and 10 times zoomed waveform revealing initial travelling waves along the connection. The extrapolated power cycles (dash-dotted lines) indicate the 50 Hz phase angles at the moments of contact.

#### 3.1.2. Transition Point

The configuration at a transition point is depicted in Figure 3b. Each overhead line is connected with two underground cables to match transmission capacity. The sensors are placed in between the cable terminations belonging to the same phase. The huge terminations provide shielding from coupling to the other phases. Therefore, the far end couplings (*<sup>u</sup>*1 to *U*3 and *u*3 to *U*1) are small and could in principle be neglected. The configuration also suggests that the couplings of sensor *ui* to phase *Ui*+<sup>1</sup> have similar magnitudes as is the case for the couplings of sensor *ui*+1 to phase *Ui* (*i* = 1, 2):

$$\mathbf{M} = \begin{pmatrix} M\_1 & M\_4 & f\_0 M\_1 \\ M\_5 - 1/2\Delta\_0 & M\_2 & M\_4 + 1/2\Delta\_0 \\ f\_0 M\_3 & M\_5 & M\_3 \end{pmatrix} \tag{11}$$

From Figure 3b the main couplings, diagonal elements in (11), are expected to be close, but in case of imprecise sensor positioning deviations can be accounted for by allowing independent values. Symmetry in the configuration allows to define only two distinct parameters for coupling of a sensor to a neighbouring phase. A further assumption relates to the far end couplings, which are minor contributions due to the shielding by the terminations. Electrostatic field analysis provided an estimate of 2% [7], which is implemented with an uncertainty margin of 50%: Δ1 = Δ3 = 1/4*f* 0(*M*1+*M*3) with *f* 0<sup>=</sup>0.02. In the second row the uncertainty is taken 50% of the average value of the neighbour couplings, Δ2<sup>=</sup>1/4(*M*4+*M*5). The additional uncertainty Δ0, as the measurement equipment was not synchronized with the phase voltages, is taken equal to Δ2 and accounts for the uncertainty caused by φ0. This reduces **M** to five independent components.

Solving (1) with (11) results in

$$\begin{array}{ll} M\_{1} = \frac{\mathbf{z}\_{/3} \sqrt{3} (a\_{1} \sin \varphi\_{0} - b\_{1} \cos \varphi\_{0})}{1 - f\_{0}} & M\_{4} = \mathbf{1}/2M\_{1} (1 + f\_{0}) + (a\_{1} \cos \varphi\_{0} + b\_{1} \sin \varphi\_{0})\\ M\_{3} = \frac{\mathbf{z}\_{/3} \sqrt{3} (-a\_{3} \sin \varphi\_{0} + b\_{3} \cos \varphi\_{0})}{1 - f\_{0}} & M\_{5} = \mathbf{1}/2M\_{5} (1 + f\_{0}) + (a\_{3} \cos \varphi\_{0} + b\_{3} \sin \varphi\_{0})\\ M\_{2} = \mathbf{1}/2(M\_{4} + M\_{5}) + (a\_{2} \cos \varphi\_{0} + b\_{2} \sin \varphi\_{0}) \end{array} \tag{12}$$

$$2\sqrt[2]{3}\left(-a\_2\sin\varphi\_0 + b\_2\cos\varphi\_0\right) - M\_4 + M\_5 - \Delta\_0 = 0\tag{13}$$

Equations (12) and (13) can be solved numerically after fitting the power frequency parts of the recorded waveforms.

Figure 5 shows the results obtained at the transition points. In both cases the overhead line leaving from the measurement location was energized at its far end. The confidence bounds are significantly smaller compared to those obtained in the substation measurements. Apparently, shielding by the terminations at either side of the sensors reduce cross-coupling significantly. Uncertainties in the cross-coupling therefore have minor effect on the reconstructed waveforms. Also here it was confirmed that the maximum voltages remain within safe limits.

**Figure 5.** Part of the reconstructed waveforms (covering 10 cycles recorded with 5 Msample/s) around the switching moment for measurement at transition points. Coloured curves represent the phase voltages with one standard deviation confidence margins indicated in black: (**a**) Overvoltages from energization at the substation connected by 4.4 km overhead line to the transition point; (**b**) Overvoltages from energization at the substation connected via 6.8 km overhead line. Moments of contact can be observed from the extrapolated power frequency waveforms (dash-dotted lines).

#### *3.2. Reliability of the Reconstructed Waveforms*

The D/I measurement results are compared with power system simulations obtained using PSCAD. The studied connection basically consists of a double circuit with 10.8 km cable in between two overhead line sections (4.4 km and 6.8 km length). However, both the magnitude and the harmonic content of switching transient responses depend on a much more extensive part of the grid [9]. The complete Dutch EHV grid was modelled in PSCAD using frequency dependent transmission line models [7,15]. A second measurement campaign was arranged aiming for simultaneously recording using the D/I measurement system and the RC dividers present at the transition points. The comparison allows to judge the sensitivity of di fferent techniques in terms of EMC.

#### 3.2.1. Comparison with PSCAD Simulation

Measurements were conducted at both line to cable transition points and at one of the substations. At each location six switching actions were performed di ffering in the side from which the connection was energized, the operation state of the parallel circuit and the choice of the parallel circuits to be energized. A selection is presented in Figure 6, corresponding to the results in Figures 4 and 5, with the parallel circuit de-energized.

**Figure 6.** Comparison between D/I measurement (continuous lines in colour for the three phases) and PSCAD simulations (dash-dotted black lines). Generally, the maximum overvoltage value observed for each switching event and phase agree well with calculations for: (**a**) Recording at substation with energization from far end substation; (**b**) Recording and energization at the same substation; (**c**) Energization at substation 4.4 km from the observed transition point; (**d**) Energization from substation at 6.8 km from the observed transition point.

Figure 6a,b show the result obtained at the substation, where the circuit is excited from the far side and from the measurement side, respectively. Figure 6c,d provide the associated results for the transition points. The excitation of the connection is performed at the overhead line ending at the transition point where measurements are conducted. It can be concluded that measurement results confirm the simulations in large detail.

#### 3.2.2. Comparison with RC Divider Measurement

Figure 7 shows the result from simultaneous measurement with the D/I method (top figures) and an RC divider (bottom figures). In between, the PSCAD simulations are presented. The measurements are taken at both transition points with the parallel circuit in service. It is observed that oscillations occur in the divider response, which are far more severe than found in both the simulation and the D/I response. It should be noted that, although simulation and D/I response are quite similar, also here the measured oscillation immediately after energizing is somewhat stronger than simulated.

**Figure 7.** Comparison of results from D/I methodology (top figures, black lines indicate the uncertainty margins caused by uncertainty in decoupling), PSCAD simulation (middle figures) and RC-divider results (bottom figures): (**a**) Energization from substation connected by 4.4 km overhead line to the transition point; (**b**) Energization from substation connected via 6.8 km overhead line. For both switching events the high frequency oscillations are overrepresented in the divider measurement as compared to both D/I measurement and simulation.
