Support concentric neutral cables

[veronicaguo]

No description provided.

[coveralls]

Pull Request Test Coverage Report for Build 116

• 48 of 48 (100.0%) changed or added relevant lines in 2 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+4.2%) to 87.5%

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Totals
Change from base Build 79:	4.2%
Covered Lines:	126
Relevant Lines:	144

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💛 - Coveralls

[etimberg]

I think the tests should include:

1. Single/two phase cables
2. Cables with another neutral, ie phases of A, B, C, N, AN, BN, CN
3. Input validation for cases that are not supported

It might also be good to add some documentation on what the inputs are

[etimberg]

Should number_of_terms be passed through here?

[veronicaguo]

seems like it's exactly the same as in CarsonsEquations class... thinking of dropping it here

[veronicaguo]

dropped it here 53fa95f

[etimberg]

i think this new property should be tested. perhaps also deprecate the convert_geometric_model function

[AnjoMan]

it is called on the concentric neutral. its just added here because it doesn't depend on anything that Carsons doesn't have.

[veronicaguo]

exposed impedance as a stand-alone function in 723ff87

[etimberg]

I did some analysis of this code versus the underground cable impedance implementation in gridlab-d. There appear to be significant differences in the computation of the distances between phases.

It was hard to audit further since gridlab-d computes the Z matrix directly and not through carson's equations.

[etimberg]

Comparison to Gridlab-d

To try and find the issues with the impedance calculations, I audited the gridlab-d source. I think this method differs from the Gridlab-d distance calculations in the following cases.

Background

Gridlab-d appears to use the following indexes for different phases. The snippets below use these phase indexes

Index	Description
1	Phase A
2	Phase B
3	Phase C
4	Concentric Neutral A
5	Concentric Neutral B
6	Concentric Neutral C
7	Neutral Conductor

Conductor to Neutral Cable

Python Implementation

In this case, the inputs are I = {'A'}, J = {'N'}

This leads to the following:

I ^ J = {'A', 'N'}
I & J = {}

one_neutral_same_phase == False
different_phase == True
one_neutral == True

Thus the code passed the check on line 233 and returns (distance_ij**2 + r**2) ** 0.5.

Gridlab-D Implementation

However, gridlab-d does the following in the case of A -> N:

#define DIST(ph1, ph2) (has_phase(PHASE_##ph1) && has_phase(PHASE_##ph2) && config->line_spacing ? OBJECTDATA(config->line_spacing, line_spacing)->distance_##ph1##to##ph2 : 0.0)
D(1, 7) = DIST(A, N);

Solution

I think the correct solution in this case is to return distance_ij

Conductor to Own Concentric Neutral

Python Implementation

In this case, the inputs are I = {'A'}, J = {'A', 'N'}

This leads to the following:

I ^ J = {'N'}
I & J = {'A}

one_neutral_same_phase == True
different_phase == False
one_neutral == True

Thus the check on line 227 is true, and so r is returned. This value was calculated earlier on lines 200 and 201 as

(diameter_over_neutral - model.neutral_strand_diameter[phase]) / 2

Gridlab-d Distance

Gridlab-d does the following:

dia_od1 = UG_GET(A, outer_diameter);
DIA(4) = UG_GET(A, neutral_diameter);
rad_14 = (dia_od1 - DIA(4)) / 24.0;
D(1, 4) = rad_14;

Solution

Divide by 24 on line 201 instead of 2. Additionally, check that the gridlab-d outer diameter is the diameter over the neutral.

Conductor to Different Phase Concentric Neutral

Python Implementation

In this case, the inputs are I = {'A'}, J = {'B', 'N'}

This leads to the following:

I ^ J = {'A', 'B', 'N'}
I & J = {}

one_neutral_same_phase == False
different_phase == True
one_neutral == True

Thus the check on line 233 is True, and so the python code returns (distance_ij**2 + r**2) ** 0.5

Gridlab-d Implementation

D(1, 5) = D(1, 2);

In otherwords, the distance from A -> BN is the same as the distance from A -> B.

Concentric Neutral to Another Concentric Neutral

Python Implementation

In this case, the inputs are I = {'A', 'N'}, J = {'B', 'N'}

This leads to the following:

I ^ J = {'A', 'B'}
I & J = {'N'}

one_neutral_same_phase == False
different_phase == False
one_neutral == False

Thus the check on line 227 and the check on line 233 are False and so distance_ij is returned

Gridlab-d Implementation

D(4, 5) = D(1, 2);

In other words, the distance from AN -> BN is the same as the distance from A -> B. The code appears to be correct here

[veronicaguo]

Thanks for the thorough audit @etimberg ! A couple points here:

• For case Conductor to Own Concentric Neutral, I think gridlab-d divides by 24 to include unit conversion from inch to ft. We handle everything using metric units, so dividing by 2 to get radius from diameter.

• For case Conductor to Different Phase Concentric Neutral, our implementation follows the assumption and example given in the Kersting's book, approximating the concentric neutrals as one single wire directly above their respective phase conductors. So there comes the Pythagorean theorem.

[etimberg]

That makes sense @veronicaguo re 2 instead of 24. For the Conductor to Different Phase Concentric Neutral case, I'm not sure that the distance calculation is correct. It assumes all the cables are in one horizontal plane because that's the only way the triangle becomes right angle. If the cables were arranged in a geometry similar to this image, the distance from the top conductor to one of the bottom concentric neutrals is formed by a non right triangle and so the extra term from the cosine law would need to be added.

Maybe a way to simplify the code here is to calculate the position (x,y) of the concentric neutral in a prior step. Then, all you'd do here is lookup distance_ij. It might be worthwhile testing this function independently too for the following cases:

• Horizontal geometry
• Vertical geometry
• Bundled like the image above

[etimberg]

I audited this against gridlab-d. The gridlab-d implementation is shown below

GMRCN(4) = !(has_phase(PHASE_A) && strands_4 > 0) ? 0.0 : pow(GMR(4) * strands_4 * pow(rad_14, (strands_4 - 1)), (1.0 / strands_4));

Differences

• Does not bail out early in the 0 case. Perhaps check GMR_s?
• R is incorrect per the comment on the distance function.