Abstractâ Geomagnetically induced currents (GIC) can pose a problem for power system operation. To assess the geomagnetic threat requires modelling of the ...
Equivalent Circuits for Modelling Geomagnetically Induced Currents from a Neighbouring Network D.H. Boteler and A.J.C. Lackey Natural Resources Canada Ottawa, Canada Abstract— Geomagnetically induced currents (GIC) can pose a problem for power system operation. To assess the geomagnetic threat requires modelling of the GIC in the power system. However, as well as the characteristics of the system itself, GIC are affected by connections to neighbouring systems. This paper considers three choices of equivalent circuit for a neighbouring system. Model calculations are made for the Ontario system wih equivalent circuits for the neighbouring Manitoba system, and vice versa. Values from these calculations are compared with the exact values determined from model calculations for the combined Ontario and Manitoba systems. The calculations with equivalent circuits produce errors in the GIC at substations that diminish with increasing distance of the substation from the connection to the neighbour. Comparison of the results showed that the best choice for an equivalent circuit comprises the induced voltage and resistance for the first transmission line into the neighbouring system. Index Terms—Circuit Analysis, Geomagnetism, Power Grids, Power Transmission
I. INTRODUCTION During geomagnetic disturbances the magnetic field variations induce electric fields in the transmission lines of a power system that drive quasi-dc currents in the system. These geomagnetically induced currents (GIC) cause halfcycle saturation of transformers resulting in generation of harmonics and increased reactive power requirements that can cause improper operation of protective relays, voltage sag and system stability problems [1,2]. Increasing concern that an extreme geomagnetic disturbance could cause widespread power blackouts [3] has prompted new work to assess the GIC that could occur [4]. GIC can be modelled using specialised software or by adapting standard network modelling techniques [5,6,7]. The network is represented by the resistances of the transmission lines and the transformers and the substation grounding resistances. The induced electric fields are represented by voltage sources in the transmission lines [8]. Network matrix equations are then solved to give the GIC in the network. Calculations for a northward and eastward electric field can be scaled and combined to give the GIC produced by any amplitude and direction of a uniform electric field. [9] This work was done by Natural Resources Canada’s Public Safety Geoscience program with additional support from the Energy Sector of Natural Resources Canada and the Canadian Space Agency.
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L.Marti Hydro One Toronto, Canada
S. Shelemy Manitoba Hydro Winnipeg, Canada
GIC can flow in or out of the network from/to neighbouring networks and accurate modelling requires including the effects of these neighbouring systems. Unless the complete neighbouring system (and its neighbours) is to be included in the GIC modelling, it is necessary to represent the neighbouring system by an equivalent circuit. This paper examines three choices for equivalent circuit and tests the accuracy of the GIC values obtained by comparison with the values from "exact" calculations made using the complete neighbouring system. II. TEST SITUATION The tests of the equivalent circuits are made by modelling GIC in the Manitoba and Ontario power systems. Both systems include lines at 500kV, 230kV, and 115kV. The lines on the Ontario side near the connection point are 230kV while the lines on the Manitoba side are a combination of 230kV and 115kV. The networks are connected by a 230kV line running approximately east-west between the Whiteshell (Manitoba) substation and the Kenora (Ontario) substation (Fig. 1). "Exact" calculations are made using a model of the combined power networks. Model calculations are then made for the Manitoba network with an equivalent circuit used to represent the connection to the Ontario network; and for the Ontario network with an equivalent circuit used to represent the connection to the Manitoba network.
Figure 1. Exact Network with Areas of Manitoba (green) and Ontario (blue) Highlighted to show regions that are affected by Adjacent Grid GIC
III. EQUIVALENT CIRCUITS The neighbouring system can be represented by its Thevenin equivalent circuit, so the decision is needed for the choice of Thevenin voltage and Thevenin resistance. Three equivalent circuits were tested for each network: A. Equivalent Circuit 1 (EQC-1) The first choice is to ignore the neighbouring network and leave the connection as an open circuit, as in Fig. 2. This is the approach used most commonly as it is the simplest method and requires the least amount of information from the neighbouring grid. An equivalent circuit for the connected network doesn’t exist. As such Rth and Vth 0 .
Figure 2. Equivalent Circuit 1
B. Equivalent Circuit 2 (EQC-2) Secondly the neighbouring network can be represented as the line to the first substation and it’s resistance to ground. The circuit can be seen in Fig. 3. In this case the Thevenin equivalent circuit is comprised of the voltage induced in the line Vth = VL and the combined resistance of the substation and the line Rth = RS + RL .
Figure 4. Equivalent Circuit 3
D. Exact Equivalent Circuit The exact equivalent circuit of a network can be calculated by determining the open circuit voltage, VOC at the connection point and the short-circuit current, I SC obtained if the connection point was grounded. The Thevenin equivalent circuit values are then given by: Vth = VOC and Rth = VOC / I SC . The GIC modeling program was run to calculate the node voltages for the open circuit case. The short circuit current was found by shorting the connection to ground (0.01 Ω to ground) and running the GIC modeling program to obtain the current value. The equivalent circuits were calculated for two cases: (1) a northward electric field of 1 V/km and (2) an eastward electric field of 1 V/km. The equivalent circuit values for the Manitoba network are shown in Table I and those for the Ontario networks are shown in Table II. These show that the EQC-2 values are closest to those for the real equivalent circuit and that the EQC-1 values are the most different. Table I. Equivalent Circuit values for the Manitoba Network Thev Circuit EQC-1 EQC-2 EQC-3 Exact North Vth 0.0 -34.0362 -34.0362 -35.0990 Rth ∞ 1.8998 1.5454 1.8195 East Vth 0.0 117.8394 117.8394 117.8394 Rth ∞ 1.8998 1.5454 1.7801 Table II. Equivalent Circuit values for the Ontario Network Thev Circuit EQC-1 EQC-2 EQC-3 Exact North Vth 0.0 34.0362 34.0362 41.4969 Rth ∞ 2.2839 1.5454 2.1875 East Vth 0.0 -117.8394 -117.8394 -131.0909 Rth ∞ 2.2839 1.5454 2.1870
Figure 3. Equivalent Circuit 2
C. Equivalent Circuit 3 (EQC-3) The final equivalent circuit was intended to represent the neighbouring network as an infinitely long line. The appendix shows that, when RL >> RS this leads to an equivalent circuit with Vth = VL and Rth = RL , as seen in Fig. 4.
IV. AFFECTS OF DIFFERENT EQUIVALENT CIRCUITS Model calculations were made of the GIC in each network while representing the neighbouring network with the equivalent circuits using the values from Tables I and II. Calculations were made for two cases: (1) a northward electric field of 1 V/km and (2) an eastward electric field of 1 V/km. The values obtained were compared to the "exact" GIC values obtained from a model of the combined Manitoba and Ontario network.
The GIC from a neighbouring network will only affect the system to a certain extent. At substations far from the connection point the differences from the exact values were less than 1% and are not considered further. Closer to the connection the differences were greater than 1% and these are shown in Table III to VI and Figs. 5 to 8. The best case is considered as EQC-3 (red lines) and the worst case is EQC-1 (green lines). Modelling GIC in the Ontario Network Figs. 5 and 6 show the errors for GIC in the lines. Comparing these plots it is seen that there are more errors for an eastwards electric field than a northwards electric field. Tables III and IV show the values obtained using different equivalent circuits for the Manitoba system. In this case modeling the network as an infinite line (EGC-3) does not work so well because of the orientation of the Manitoba grid in relationship to the electric fields. Manitoba branches many times close to the border between the networks therefore allowing more paths for current to flow into ground. This means that modeling the network as a single station (EQC-2) is more accurate then modeling it as an infinite line (EQC-3).
Table IV. GIC Values for Ontario, North Electric Field Station EQC-1 EQC-2 EQC-3 Exact Kenora
10.103
-4.085
-6.384
-5.915
Fort Fra
-12.409
-13.267
-13.406
-13.210
Dryden
9.143
7.925
7.728
8.006
Mackenzie
-2.088
-2.152
-2.162
-2.147
Lakehead
-6.580
-6.583
-6.582
-6.582
Marathon
16.142
16.142
16.142
16.142
Modelling GIC in the Manitoba Network Fig. 7 and Fig. 8 depict the affect that GIC from the Ontario grid have on the Manitoba system. In Table V and VI the calculated values for the affected substations are presented. The Manitoba system is much more complex near the border between the two systems. More stations are affected by GIC coming from the Ontario system but to a lesser magnitude. The Manitoba stations are similarly affected by both the Northern and Eastern electric fields with only minor differences in affected stations.
Figure 5. Affect of GIC in lines with an East Electric Field for Best Case (Red) and Worst Case (Green) Equivalent Circuits Table III. GIC values for Ontario, East Electric Field Station EQC-1 EQC-2 EQC-3 Exact Kenora
-17.945
26.875
34.137
28.364
Fort Fra
-7.544
-4.833
-4.394
-4.584
Dryden
5.211
9.056
9.679
9.402
Mackenzie
-6.300
-6.100
-6.068
-6.082
Lakehead
2.364
2.370
2.371
2.371
Marathon
1.310
1.310
1.310
1.310
Figure 6. Affect of line GIC with a North Electric Field for Best Case (Red) and Worst Case (Green) Equivalent Circuits
Figure 7. Affect of GIC in lines with an East Electric Field for Best Case (Red) and Worst Case (Green) Equivalent Circuits Table VI. GIC values for Manitoba, East Electric Field Substation EQC-1 EQC-2 EQC-3 Exact Whiteshell 115
7.338
-21.205
-33.217
Seven Sisters
6.565
-7.861
-13.931
-24.383 -9.467
McArthur Falls
1.724
-1.354
-2.649
-1.696
St. Vital 115
14.459
14.332
14.279
14.318
Harrow
3.809
3.762
3.742
3.756
Mohawk
15.305
15.288
15.282
15.287
Richer
13.725
13.715
13.710
13.714
St. Boniface
6.810
6.759
6.737
6.753
Wilkes
-1.490
-1.529
-1.546
-1.533
In Tables III-VI some stations have a very small difference in the magnitude of current. They are still displayed because all stations that were affected by more than 1% compared to the exact system are included. Fig. 9 and Fig. 10 show the percentage of stations with error greater then 1% compared to the “exact” GIC values obtained from the combined model.
Figure 8. Affect of GIC in lines with a North Electric Field for Best Case (Red) and Worst Case (Green) Equivalent Circuits
Table V. GIC values for Manitoba, North Electric Field Substation EQC-1 EQC-2 EQC-3 Exact Whiteshell 115
-2.999
5.319
8.820
7.647
Seven Sisters
-1.040
3.164
4.933
4.340
McArthur Falls
9.628
10.525
10.902
10.776
St. Vital 115
-4.846
-4.809
-4.793
-4.799
Harrow
0.611
0.625
0.630
0.628
Dakota
-9.240
-9.199
-9.182
-9.187
Mohawk
-2.678
-2.674
-2.672
-2.672
Richer
1.064
1.067
1.068
1.068
St. Boniface
0.621
0.636
0.643
0.641
Wilkes
0.269
0.280
0.284
0.283
Figure 10. Stations affected in the Ontario network when using Manitoba Equivalent Circuits
An accuracy progression can be seen in Fig. 9 with the different modeling scenarios for the equivalent Ontario circuit. The most accurate equivalent circuit was the infinite line (EQC-3). The least accurate equivalent circuit was to ignore the neighbouring network (EQC-1). The accuracies of the modeling scenarios for the Manitoba equivalent circuit are shown in Fig. 10. This shows that EQC-1 gives the worst results, but there is no difference in the accuracies between EQC-2 and EQC-3. V. DETAILS REQUIRED FOR ACCURATE MODELING To increase the accuracy of modeling the GIC coming from an external network, the more information about that network the better. In adding more detail to the neighbouring network the GIC values calculated will be closer to the exact values. To assess the increased accuracy of GIC for the amount of detail added simulations were done for each station added. Each station was added to the existing network in three different ways. First is EQC-1 where just the line resistance was included. Second is EQC-2 where you know the line resistance and station resistance. Third is EQC-3 to represent the rest of the network as an infinitely long line. For each subsequent station added the previous station was then considered as part of the original network.
Figure 9. Stations affected in the Manitoba network when using Ontario Equivalent circuits
Fig. 11 and Fig. 12 show how the accuracy improves as more stations of the neighbouring network are added. The Yaxis represents how accurate the GIC in the original Manitoba network are compared to the exact network.
APPENDIX For a long line with line resistances, RL and substation resistances RS, as shown in Figure 12, the Thevenin equivalent circuit for the end section is Vth VL and Rth = RS + RL . When RL >> RS , as is often the case, then Rth RL . Connecting this to the next section and calculating the new Thevenin equivalent circuit gives
R 2 Rs Vth VL L R L Rs
(1),
R 2 Rs Rth RL L RL Rs
(2),
For the case being considered where RL >> RS then these reduce to Vth VL and Rth RL . If this is used as the connection to another section then the calculations repeat and the same Thevenin equivalent circuit parameters are obtained regardless of the number of sections in the line.
Figure 11. Accuracy of GIC in the Manitoba Network as a function of the number of stations included from the Ontario Network
Figure 12. Line with multiple sections
It is seen that the blue EQC3 line is consistently more accurate than the two other methods. However all three methods are very accurate 4 substations into the system. This is beneficial as it gives an indication of how much detail is required to properly simulate GIC’s coming from a neighbouring network.
VII. REFERENCES
VI. CONCLUSIONS Model calculations of GIC in the connected Manitoba and Ontario networks show that the use of different equivalent circuits for the neighbouring network affects the GIC values up to four substations away from the connection. The best choice of the equivalent circuits considered was using the connecting line voltage and line resistance as the Thevenin equivalent circuit. Ignoring the neighbouring network gave the worst results. Adding substations from the neighbouring network increased the accuracy of GIC values obtained. Completely accurate values for the Manitiba system were obtained after adding four substations from the Ontario system to the model for Manitoba.
[1] [2]
[3] [4] [5] [6] [7] [8]
[9]
T. S. Molinski, Why utilities respect geomagnetically induced currents, Journal of Atmospheric and Solar-Terrestrial Physics, 64, 16, 17651778, 2002. J. G. Kappenman, Geomagnetic Disturbances and Impacts upon Power System Operation, In: The Electric Power Engineering Handbook, L. L. Grigsby (Ed.), CRC Press/IEEE Press, 2nd Edition, Chapter 16, 16-1 - 16-22, 2007. J.G. Kappenman, Geomagnetic Storms and their Impacts on the U.S. Power Grid, Report Meta-R-319, prepared for Oak Ridge National Laboratory, January 2010. A. A. Pulkkinen, E. Bernabeu, J. Eichner, C. Beggan, and A. W. P. Thompson, "Generation of 100-year geomagnetically induced current scenarios," Space Weather, vol. doi:10.1029/2011SW000750, 2012. M. Lehtinen, and R. Pirjola, "Currents induced in earthed conductor networks by geomagnetically-induced electric fields", Annales Geophysicae, 3, 479-484, 1985. A. Foss and D.H. Boteler, "GIC Simulation using network modeling”, Paper 806, Proc. Canadian Conference on Electrical and Computer Engineering (CCECE), Ottawa, Canada, May 7-10, 2006, 4pp., 2006. R. Horton, D. H. Boteler, and S. Black, “A Primer for the Calciulation of GIC in Bulk Power Systems”, Proc. 2013 IEEE Power Engineering Society General Meeting. R. Horton, D. H. Boteler, T. J. Overbye, R. J. Pirjola, R. Dugan, “A Test Case for the Calculation of Geomagnetically Induced Currents”, IEEE Transactions on Power Delivery, Vol. 27, Issue: 4, October, 2012, pp.2368-2373. D.H. Boteler, “The Use of Linear Superposition in Modelling Geomagnetically Induced Currents”, Proc. 2013 IEEE Power Engineering Society General Meeting.
