Modelling Considerations in steady-state GMD Simulations. L. Marti Hydro One Networks Inc. Ontario, Canada

Transcription

1 1 Modelling Considerations in steady-state GMD Simulations L. Marti Hydro One Networks Inc. Ontario, Canada

2 2 Synopsis Earth models in steady-state and time domain calculations Frequency dependence Laterally uniform earth modelling Piecewise laterally uniform earth modelling Determination of peak geoelectric field for steady-state studies Examples from system studies

3 Geomagnetic and Geoelectric fields Using the plane wave method, the geoelectric field E in the frequency domain is related to the geomagnetic field at ground level with the following expressions µ B Z H Z E o = = o j Z C µ = B j G = µ G C B j j Z E o = = x y y x G C E G C E = = dbt/dt in the frequency domain

4 Geomagnetic and Geoelectric fields in the time domain In the time domain, the geoelectric field Et is related to the geomagnetic field at ground level Bt with the following expressions x y y x G C E G C E = = t g t c t E t g t c t E x y y x = = dt t db t g dt t db t g x x y y = = where * denotes convolution

5 The earth coupling function C Assuming laterally uniform earth C is frequency dependent Roughly proportional to 1/sqrt

6 Plane wave method is applicable in a region with uniform geomagnetic field and laterally uniform earth Induced geoelectric field vt on a line is In other words, the sum of the contributions of the geoelectric field in each zone accounting for relative line/field orientation Piecewise laterally uniform modelling 1,, 1 t E y t E x t v n k k y k k x n k k = = + =

7 Time domain simulations Arguably, simulations in the time domain are simpler that in steady-state Consider the following example

8 Hydro One 500 kv and 230 kv network

9 Time domain example Based on the measured geomagnetic at the Ottawa observatory March Scaled up to produce 8 V/km with the average Ontario/Quebec earth model Sampling rate = 10 s Same geomagnetic field in the whole system Geoelectric field assumed to be piecewise laterally uniform Seven distinct zones earth models Zone 1 is similar to the average Ontario/Quebec model

10 Scaled geomagnetic field measurements. March 1989 GMD event

11 Seven distinct zones and earth models

12 C per zone Zone 5b Zone 6 Zone 1 Zone 3

13 Calculated geoelectric field

14 Calculated geoelectric field

15 Calculated geoelectric field

16 In the time domain Simulations are straightforward if the geomagnetic field is assumed to be spatially uniform GICt is calculated from the solution of the dc network where the geoelectric field in each zone is calculated according to its earth model More computationally challenging in real time with a 1 s geomagnetic field sampling rate But only 30 ms computational cycle including var loss and transformer heating calculations ms with data transfer

17 Steady-state GIC studies If the geomagnetic field Bt during a GMD event is assumed to be spatially uniform, And the earth model is assumed to be laterally uniform in the entire system under consideration Then It is sufficient to define the peak geoelectric field as V/km EW and NS Induced geoelectric field on a transmission circuit just depends on relative line/field orientation and line end the geographical location of its end points

18 Steady-state GIC studies If the geomagnetic field during a GMD event is assumed to be spatially uniform, and multiple earth models exist in a network Then In steady-state analysis, IT IS NOT sufficient to define the peak geoelectric field as V/km EW and NS The geoelectric field for each zone must be established Defining the peak geoelectric field for each zone and earth model is not straightforward.

19 Defining the geoelectric field in steady-state GIC studies Two ways to define peak geoelectric field: Obtain the peak geoelectric for each earth model in the time domain using a specific Bt. Not necessarily valid for all GMD events Calculate the relative values of C using one earth model as reference Reference peak geoelectric field is assigned to the reference zone Peak geoelectric fields in other zones can then be obtained at one frequency only

20 Selecting peak geoelectric fields Zone 6 Zone 1 reference

21 Selecting geoelectric fields Zone 5b Zone 6 Zone 1 Zone 3

22 Defining the geoelectric field in steady-state GIC studies It is necessary to select a frequency range For instance 1mHz to 100 mhz No unique GIC peak value in every transformer, but rather a range Must decide which earth model or zone is the point of reference to define reference peak V/km A reasonable choice is the zone with the most transmission circuits Differences in field orientations for worst-case

23 Maximum GIC does not necessarily occur at any one frequency GIC/phase mhz 1 mhz

24 Not all transformers are affected in the same way GIC/phase n mhz 1 mhz

25 Analyzing the results in steady-state GIC studies Although C decreases with frequency, what matters are the relative magnitudes of C for each earth model In this example GIC decreases in some transformers as the frequency decreases but increases in others. C decreases at higher frequencies, however C i / C j may increase or decrease with frequency Generalizations seem futile since each system configuration and earth models are different

26 C per zone Zone 5b Zone 6 Zone 1 Zone 3

27 Transformers with circuits spanning multiple zones show more extreme changes 100 GIC1mHz/GIC100mHz Transformer id

28 Final observations Assuming a single laterally uniform earth model is quite possibly a gross oversimplification in some cases Taking into account multiple earth models is challenging in steady-state GIC simulations. In the example shown, steady-state GIC can change by up to 40% between 1 mhz and 100 mhz for transformers gith large GIC Single-value GIC studies can carry large uncertainty bars Multi-frequency steady-state studies should define a GIC range for each transformer rather than a single value. More work ahead for methods and tools