Modelling SWER (Single Wire Earth Return) - Single Phase Conductor

[SeanDO]

Hi

I'm trying find the correct way to model SWER. I'm aware some software's let you select the system type as SWER, but I'm stuck with just a 3-phase modelling software (PSS-ADEPT).

Can you represent SWER with sequence components in a 3-phase system? I've read that you can apply the Carson Equation to 1, 2, and 3 phase conductor systems, where I assume a 1 phase conductor system is identical to a SWER system?

So far I can produce the primitive impedance matrix as a 2x2 matrix: [[z_aa, z_ag],[z_ga, z_gg]], where z_aa is the self impedance of the conductor, z_ga = z_ag is the mutual impedance of the ground-conductor pair, and z_gg is the self impedance of the ground.

I have expressions for getting values for a z_aa, z_ag, z_gg from the physical parameters of the system. I can then use Kron Reduction to get rid of the neutral (is this step right, as Kron reduction requires 0 A current in the neutral and this technically isn't true because the neutral is the earth return path?) and produce a 1x1 matrix (scalar) that is the adjusted z_aa value (z_aa(new) = z_aa(old) - 2*z_ag/z_gg).

I then build the phase frame matrix [z_abc] = [[z_aa(new), 0, 0], [0, 0, 0], [0, 0, 0]]. Then proceed to do the typical thing: [z_012] = [A]^-1.[z_abc].[A]. Since the phase frame matrix is symmetrical we should expect to see 0 elements for the off-diagonal terms in the impedance matrix. This doesn't yield a meaningful result though.... so can someone explain where I might be going wrong, or what the correct approach is with SWER (and 2-phase/v-phase systems) and finding the zero, positive and negative sequence impedance.

 

[magoo2]

Symmetrical components were intended to simplify the calculations of unbalanced three phase systems. You're trying to go in an opposite direction. A SWER is just a single phase system with a phase conductor, transformers and using the earth for the return path.

I admire the fact that you've gone through a lot of work to look at the possibilities of being able to fool a three phase load flow so that it can accommodate a single phase model. I just don't think it's going to work.

I think you're better off just writing the single phase equations for a single phase system and developing your own software. You could probably make it work on a spreadsheet.

 

[SeanDO]

On page 87 (equation 4.58) shows a single phase line represented in the phase impedance/frame matrix, which makes me think it is possible to represent SWER in the 3 phase sequence component form. But like you say, the earth is the return path (so current does not equal 0), so I think that to represent SWER properly you would not do the Kron Reduction step to eliminate the neutral i.e. treat the earth return path as a separate phase conductor. Therefore, the phase frame matrix is [z_abc] = [[z_aa, z_ag, 0], [z_ga, z_gg, 0], [0, 0, 0]] - so that is just treating the ground return path as phase b (it could equally have been phase c). Do you see anything wrong with this approach?

 

[ijl]

You can model a single wire in an three-phase network with the help of a double open-line fault (phases b and c open, or broken, for example), see the attached picture. In practice, this is very much the same as a single-line-to-earth fault.