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1. ECE 530 – Analysis Techniques for Large-Scale Electrical Systems

   Lecture 26: Geomagnetic Disturbance (GMD) Modeling Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign overbye@illinois.edu
2. Announcements HW 8 is due today HW 9 should be done before the exam but need not be turned in Final Wed. Dec 18 from 1:30 to 4:30pm in EL 260 Closed book, closed notes; you may bring in one new note sheet and your exam 1 note sheet, along with simple calculators
3. In the News: Ice and Power Lines Quebec Ice Storm,January 1998;Some places gotmore than threeinches of ice! Image source: http://i.imwx.com/web/spia-index-web.jpg
4. High Impact, Low Frequency Events Over the last several years NERC has been considering high-impact, low frequency events (HILFs) These are events that can cause wide-scale, catastrophic damage, beyond that caused the more frequent events like ice storms and hurricanes Several types of HILFs identified by NERC in June 2010 report: 1) Coordinated Attack, 2) Pandemic, 3) Geomagnetic Disturbances (GMDs), 4) Electromagnetic Pulse (EMP) Here at UIUC we have been focused on GMDs, with some work planned on EMPs
5. GMD References NERC Interim GMD Report issued in late Feb 2012 available at http://www.nerc.com/files/2012GMD.pdf IEEE Spectrum, Feb. 2012 A wide variety of papers are available; one place to start is T.J. Overbye, K.S. Shetye, T.R. Hutchins, Q. Qiu, J.D. Weber, "Power Grid Sensitivity Analysis of Geomagnetically Induced Currents," IEEE Transactions on Power Systems, vol. 28, pp. 4821-4828, November 2013
6. GMD Overview Geomagnetic disturbances (GMDs) have the potential to severely disrupt operations of the electric grid, yet power engineers have had few tools to help them assess the impact of GMDs on their systems Recent research and development is helping to move GMD assessment into the realm of power system planning and operations engineers Guiding motto: “All models are wrong but some are useful,” George Box, 1979
7. Geomagnetic Disturbances (GMDs) Solar events can cause changes in the earth’s magnetic field (i.e., dB/dt). These changes in turn produces an electric field at the surface Changes in the magnetic flux are usually expressed in nT/minute; from a 60 Hz perspective an almost dc electric field 1989 North America storm produced a change of 500 nT/minute, while a stronger storm (e.g., 1921) could produce more than 5000 nT/minute variation Storm “footprint” can be continental in scale For reference, Earth’s magnetic field is normally between 25,000 and 65,000 nT, with higher values near the poles Image source: J. Kappenman, “A Perfect Storm of Planetary Proportions,” IEEE Spectrum, Feb 2012, page 29
8. March 8-9, 2012 “Event” Below example shows results for a relatively small storm that occurred in March 2012 (Ottawaat 45.4N) Less than100 dB/dt,compared to 500 forthe 1989 event and5000 in 1921 Image source: www.intermagnet.org/apps/plt/plot_result_int_e.php
9. March 1989 Storm that Caused Quebec Blackout
10. Electric Fields and Geomagnetically Induced Currents As described by Faraday’s law, changes in the magnetic flux intensity produce a (non-uniform) electric field on the surface; values are impacted by ground conductivity Electric fields are vectors with a magnitude and direction; values are in units of volts/mile (or volts/km); A 2400 nT/minute storm could produce 5 to 10 volts/mile. The electric fields cause geomagnetically induced currents (GICs) to flow in electrical conductors such as the high voltage transmission grid Currents are quasi-DC (frequencies much below 1 Hz)
11. Electric Fields and Geomagnetically Induced Currents Three phases appear to be in parallel to GIC The induced voltages that drive the GICs can be modeled as dc voltages in the transmission lines. The magnitude of the dc voltage is determined by integrating the electric field variation along the line As long as the electric field is uniform, the integration is path independentSo the electric field tangential to the line is With the voltage then
12. Geomagnetically Induced Currents (GICs)
13. Uniform vs. NonuniformElectric Fields For some situations uniform electric field models can be used (i.e., constant magnitude and direction) The actual electric fields produced by a GMD will be nonuniform, and depend, in part, upon the ground resistivity Because of the low frequency, currents can penetrate 100's of kms into the ground One dimensional models are commonly used, but there is actually quite a bit of uncertainty in the underlying ground resistivity
14. 1D Conductivity Example
15. Maximum Electric Field and Latitude Note,magneticlatitudeis notthe sameas geographiclatitude Image Source: http://www.nerc.com/comm/PC/Geomagnetic%20Disturbance%20Task%20Force%20GMDTF%202013/Day2_all_final.pdf
16. Magnetic Latitude Note thatalmostall of the US andEurope are above 40 degreesmagneticlatitude Image Source: http://hfradio.org/swp_proplab/maglat00.gif
17. An Example Nonuniform Field
18. Power System Impacts of GICs The dc GICs are superimposed upon the ac currents. In transformers this can push the flux into saturation for part of the ac cycle This can cause largeharmonics; in the positive sequence(e.g., power flow and transient stability) theseharmonics can be represented by increased reactive power losses on the transformer.
19. Mapping Transformer GICs to Transformer Reactive Power Losses Transformer specific, and can vary widely depending upon the core type Single phase, shell, 3-legged, 5-legged Ideally this information would need to be supplied by the transformer owner Currently support default values or a user specified linear mapping For large system studies default data is used when nothing else is available. Values change with core type Still debate in the industry with respect to the magnitude of damage GICs would cause in transformers (from slightly age to permanently destroy)
20. Four Bus Example The line and transformer resistance and current values are per phase so the total. Substation grounding values are total resistance. Brown arrows show GIC flow.
21. The Impact of a Large GMD From an Operations Perspective There would be a day or so warning but without specifics on the actual magnitude It could strike quickly (they move at millions of miles per hour) with rises times of less than a minute, rapidly covering a good chunk of the continent Reactive power loadings on hundreds of transformers could sky rocket, causing heating issues and potential large-scale voltage collapses Power system software like state estimation could fail Control room personnel would be overwhelmed The storm could last for days with varying intensity
22. GMD Enhanced Power Analysis Software By integrating GIC calculations directly within power analysis software (like power flow) power engineers can readily see the impact of GICs on their systems, and consider mitigation options GIC calculations use many of the existing model parameters such as line resistance. But some non-standard values are also needed; power engineers would be in the best position to provide these values, but all can be estimated when actual values are not available Substation grounding resistance, transformer grounding configuration, transformer coil resistance, whether auto-transformer, whether three-winding transformer, generator step-up transformer parameters
23. GIC G-Matrix With knowledge of the pertinent transmission system parameters and the GMD-induced line voltages, the dc bus voltages and GIC flows can be calculated by solving a linear equation I = G V The G matrix is similar to the Ybus except 1) it is augmented to include substation neutrals, and 2) it is just conductances The current vector contains the Norton injections associated with the GMD-induced line voltages Factoring the sparse G matrix and doing the forward/backward substitution takes about 1 second for the 62,600 bus Eastern Interconnect Model
24. Four Bus Case G Matrix Below image shows the G matrix for the four bus case
25. GIC Transformer Modeling How the transformers are grounded is quite important for GIC studies No flow through the delta windings, or ungrounded wyes Common for generator step-up transformers (GSUs) is grounded-wye high side, delta low side At the transmission to distribution common configuration is delta high, grounded-wye low Transmission autotransformers are usually grounded-wye with a delta tertiary
26. Autotransformer Example The below figure is a one-line for a four bus system with an autotransformer between buses 2 and 3 G Matrix T.J. Overbye, K.S. Shetye, T.R. Hutchins, Q. Qiu, J.D. Weber, "Power Grid Sensitivity Analysis of Geomagnetically Induced Currents," IEEE Transactions on Power Systems, vol. 28, pp. 4821-4828, November 2013
27. Determining GMD Storm Scenarios The starting point for the GIC analysis in the power flow is an assumed storm scenario; this is used to determine the transmission line dc voltages Feb 2012 NERC report recommended for planning purposes a similar approach could be used Uniform electric field: All locations experience the same electric field; induced voltages depend on assumed direction Maximum value in 1989 was 1.7 V/km (2.7 V/mile) We also consider a more detailed non-uniform model Non-uniform electric field: Magnitude of electric field varies according a some function; induced voltages in lines depend on magnitude and assumed direction
28. GIC Flows in Eastern Interconnect for a Uniform 2.5 V/Mile, N-S Field
29. GIC Visualization for EPRI Test System – East Field Case is described in: R. Horton, D. Boteler, T.J. Overbye, R. Pirjola, R.C. Dugan, "A Test Case for the Calculation of Geomagnetically Induced Currents," IEEE Transactions on Power Delivery, vol. 27, pp. 2368-2373, October 2012.
30. GIC Visualization for EPRI Test System – North Field
31. Integrated Geographic Information The potentially time-varying GMD induced dc voltages are determined by knowing the latitude and longitude of the transmission lines Just knowing the geo-coordinates of the terminal buses should be sufficient Actual transmission path isn't usually needed Hence buses need to be mapped to substations, and substations to their geo-coordinates
32. Power Flow Convergence Issues Integrated GIC modeling can certainly impact power flow convergence since the GIC induced reactive power losses simultaneously add lots of reactive power. Several techniques can help prevent divergence Just calculating the GICs without solving the power flow Not calculating GMD induced voltages for equivalent lines Gradually increasing the assumed electric fields to avoid simultaneously adding too much reactive power at one time Only calculating the GIC transformer reactive power losses for specified areas; reactive power doesn’t tend to travel far Limiting the size of the GMD Freezing the transformer taps and switched shunts in certain problematic areas
33. Integrating GIC Calculations into Power System Planning A large GMD could cause substantially different power system flows and voltages Studies allow for testing various mitigation strategies Operational (short-term) changes include redispatching generation to avoid long distance power transfers and reducing transformer loading values, and strategically opening devices to limit GIC flows Longer-term mitigation actions include the installation of GIC blocking devices on the transformer neutrals (such as capacitors) and/or increased series capacitor compensation on long transmission lines There are many potential research directions to pursue
34. Research Example: Determining Mitigation Strategies GIC flows can be reduced both through operational strategies such as strategically opening lines, and through longer term approaches such as installing blocking devices Algorithms are needed to provide power engineers with techniques that go beyond trial-and-error Such approaches require a coupling between the GIC calculations and the power flow solutions For example, determining lines that would 1) substantially reduce the GIC flows and 2) are not crucial from an operational perspective
35. GIC Source Sensitivity Analysis Sensitivities of the effective GIC for a transformer (or set of transformers) to the assumed transmission line GMD-induced electric fields can be easily calculated Sensitivities are derived by first writing the effective GIC for transformer r in matrix formwhere G is the GIC conductance matrix, ET are the input fields tangential to each line, B relates the voltages to the Norton current injections, and Cr relates the voltages to the effective current G, B, Cr are sparse, hence quick computation
36. GIC Sensitivity Analysis, cont. Sensitivities, telling which voltage inputs contribute to the current, are determined just by differentiating the previous equation Each entry k in ST,rtells how IEffective for transformer r would vary for a 1 V/km variation in the electric field tangential to the kth transmission line
37. Observations Because of sparsity the computation is trivial Simple scaling of entries in ST,r accounts for nonuniform, nontangential fields Simple summation tells which lines actually contributed to the value
38. Four Bus Example Transpose of STvectors for the four bus system
39. Observations, cont. Sum of absolute values of entries in ST,r(i.e., the 1-norm) tells the worst case uniform field current that could occur in transformer r Define to quantify difference between actual current and the worst case current (low for interior values, high for edge values)
40. Twenty Bus Test Case Example Consider at XF 18-17 (upper left) and 20-5 (middle)
41. Twenty Bus Case Results
42. Extended to Multiple Transformers Analysis can be easily extended to multiple transformers by including their contributions in the C vector
43. Large Case Results In the Eastern Interconnectexample, usually very few lines contribute the GICs for each transformerFor AEP’s 60 transformerswith the largest effective currents about50% of the GICs are contributed by just 10 lines (out of 57,000 in thecase); 76% by just 20 lines; 99% by 1% ofthe lines Conclusion is detailed electricfield values are only needed forthe contributing lines
44. Small System Operational Mitigation Example The system on the right shows how the GIC impacts can be reduced by doing generation dispatch to allow opening a 345 kV line Research is needed to determine optimal solutions