Impedance of an RMU
4.7 Lumped element modelling and measurement
In the RMU, two separate current paths can be distinguished. In Section 4.4 these two paths were identified. When switching in the mini-grid, these paths can be separated and mea-surements can be performed on each current path. In Figure 4-II the two separate loops are given. If the transformer connecting cables are disconnected at the transformer, the left-hand loop of Figure 4-II is formed. The right-left-hand loop of Figure 4-II is formed when the transformer is disconnected by the circuit breaker. The transformer was short circuited in the measurement of the two segments in the RMU. The impedance of a transformer is a complex system. When the transformer is a part of the circuit, this can lead to ambiguous results. Now the two segments and the transformer are measured and modelled separately and combined later. The common element in this loop is the earth connection of the trans-former connecting cables. In Figure 4.12 the results of the measurement of SegmentI are given. The elements in the model are fitted to this measurement and the values are given in Table 4-2
In the frequency range between 500 kHz and 9 MHz the measurement and theory coincide.
Above this range, the injected power is low, which causes a drop of measurement accuracy and transmission line effects begin to become significant. The impedance of the cable (Zo) corresponds to earlier results, and the connection resistance(Rconn ) is in the correct order of magnitude if the skin effect is included in this impedance. The magnitude of the radiation resistance(Rmd,l)is frequency dependent and therefore, the corresponding "antenna" length
Segment
ISegment
2Fig. 4. 11: RMU current loops of an RMU with one connected cable.
Fig. 4.12: Measured and simulated impedance of Segment 1.
element fitted value remark
Zo IOD
Rearm 4 D
Rrad ,1 corresponding to 5 m
Lself,1 93 JL H corresponds to I m x 50 cm, radius 13 cm
CTCC 2·4 nF
Cpar,1 220 pF
Table 4.2: Model results for measurement of Segment 1
is given. This length is 5 metre, which seems fairly large when compared to the size of the first segment. The radiation resistance is the effective value for all the conductors in the segment. Under the assumption that the contribution of all conductors can be added,s m is in the order of magnitude of the size of the system. The self-inductance of this segment
(Lself,I) can be modelled by a square loop ofI m by 50 cm, and an effective conductor radius of 13 cm. The radius seems very large, but in the switching equipment, the space between the rails of the three phases is in this order of magnitude. The model is very simple and does not take into account the complex structure of the compounded self-inductance of the conductors, but it gives a good indication on the order of magnitude of the self-inductance.
The capacitance of the TCC agrees with the values found in the data sheets of the cable. The parasitic capacitance has a typical magnitude that is expected in a section of this size.
The results of the measurement and modelling of section 2 of Figure 4.II are given in Fig-ure +13 and Table 4-3- The results of the measFig-urement and the model coincide very well up to a 2 MHz. Above 2 MHz some deviation arises. Segment 2 is larger than segment I, and transmission line effects become already notable at lower frequencies. Parasitic effects become more dominant when frequency increases, which makes these results less accurate.
400r--1---,---,---,---r---,---,---.---,---.
...
ol-J_~~~:.i..-_----'--_----.l_ _-'---_---'--_ __'___ _____l_~
2 3 4 5 6 7 8 9 10
frequency (Hz) x 106
-".-::-•• :7:".c;-;-",..,..,,,.;"",_ . _.. '.'.'.'.'.'.'.",....'~~""""""""""""",,,,,,,,,,-~,~
- Measurement
",' Model -3u---'---'---'---'-'---'---'.:...:i..-_---"-'-_--C1.---'---'---'---'-'---_---l.-_---':r:::==:"=:I==='d
2 3 4 5 6 7 8 9 10
frequency (Hz) x 106
-2
Fig. 4. 13:Measured and simulated impedance of Segment 2.
element fitted value remark
Rconn 5.5 D
Rrad ,2 corresponding to 7 m
Lse1f,2 2.2/-lH corresponds to 2 m x 50 cm, radius 7 cm
GTCC 2·4 nF
Gpar,2 60pF
Table4.3: Model results for measurement of Segment 2
The model can be extended by adding circuit components to compensate for these effects.
This makes the model more complex, which is unfavourable. When measuring at the con-nected cable (PLEq, the frequency range from 2 MHz and higher is not significant for the total result because of the filtering by the capacitance formed by the TCCs.
In Figure +5 a high frequency SP model for a distribution transformer is given. The com-parison between the measurement of the impedance of the transformer and the model of the transformer are presented in Figure +1+ The values for the impedances in the model are given in Table +4. These results are in agreement with [Wie04] and [Wou03]
Up to now the lumped elements in an RMU are measured and modelled separately. The
element fitted value
R 3 D
L I,2/-l H
G
1 I,2 nFG
2 13 pFTable4.4:Model results for measurement of the transformer
2 3 4 5 6
Fig. 4.14: Measured and simulated impedance of the power transformer.
final step is to perform a measurement with the complete RMU connected similar to when it is in operation, and verify the measurements with the obtained model. The injection and detection takes place at PLEC. The results of the measurement and the overall model are given in Figure4.15. Itis observed that the results coincide in the frequency range between
I MHz and 9 MHz. For higher frequencies the results of the measurements are inaccurate
400,---,---.---,---.---,----.---,---,---,---T"1
Fig. 4. 15:Comparison between thePLECmeasurement and the model.
Lself,n Lself.l R.oo.l R.oo.2 Rdiss Lself.2r···---]
Segmentn Segment 1 Segment 2 Transfonner
Fig. 4. 16:Model for an RMU with multiple connected cables.
because of the limited injected power and transmission line effects become significant. In this range, the impedance of the RMU is high, whereas most sensitive PD-detection can be done when the impedance of the RMU is low. Therefore the inaccuracy in this area is acceptable. The results show that an RMU can be modelled by a limited number oflumped impedances with sufficient accuracy for PD-online detection.