Compute the susceptance matrix in higher precision

[odow]

Closes #862

[codecov]

Codecov Report

Merging #863 (174194a) into master (d417de6) will not change coverage.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master     #863   +/-   ##
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  Coverage   93.79%   93.79%           
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  Files          43       43           
  Lines        9893     9893           
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  Hits         9279     9279           
  Misses        614      614           

Impacted Files	Coverage Δ
src/core/admittance_matrix.jl	88.23% <100.00%> (ø)

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[odow]

@ccoffrin so it looks like PowerModels is veeeeery sensitive to inv(::ComplexF64). Computing them in BigFloat and then rounding back to Float64 seemed to fix the iteration limit problem on Windows.

[odow]

I spoke too soon. Previous commit passed though...

[ccoffrin]

Thanks a bunch for digging into this. Now that I understand the root cause, I am inclined to relax the test requirements rather than update these operations to big complex operations. When it comes to power systems, performance is the highest priority, so I think the default operations should use whatever Julia type will be most efficient, which I presume is the hardware-native Complex Float type.

If you have any insights into what Julia functions provide the best abstractions for processing Complex numbers (e.g, inv(x) vs 1/x), I happy to consider those changes, if they have the potential for better performance or numerical stability.

[odow]

1 / x didn't fix it, which I guess isn't surprising. Should the susceptance matrix always have a det of 0?

It seems problematic if an imprecision of eps in the input data can have a large impact on the output. Maybe there's a check other than the determinant that is more useful?

[ccoffrin]

You are right, using det as the measure was possibly not the best choice. I was looking for a single value that would be a reasonable signature for the data in the matrix. I am open to suggestion for other measures that would be more robust to numerical issues.

[odow]

What about just checking the smallest absolute eigen value?

[odow]

Closing in favor of #865