# Zero resistance transmission lines?

I am using the IEEE 14 bus test system for a simulation and was wondering why some of the resistances of lines are set to zero, e.g. see lines (4,7), (4,9), (5,6) below (only part of the full data is shown below).

From  To   R           X           B
Bus   Bus  pu          pu          pu
2     5    0.05695     0.17388     0.0346
3     4    0.06701     0.17103     0.0128
4     5    0.01335     0.04211     0.0
4     7    0.0         0.20912     0.0
4     9    0.0         0.55618     0.0
5     6    0.0         0.25202     0.0
6    11    0.09498     0.19890     0.0


I thought all lines have some resistance; is a zero resistance line just an approximation for a very small resistance?

• Most likely the resistances were just smaller than 0.000005 and rounded down to 0.0. Commented Nov 20, 2014 at 17:08
• maybe the distance between the two buses is to small to have some resistance. Commented Nov 20, 2014 at 19:39

In many cases, if you encounter zero reactance or zero impedance, this often represents bus ties or breakers. However, for the IEEE 14-bus test system, that is not the case.

As you can see from the numbers, the reactance is quite high. Obviously a breaker or a short cable can not have zero resistance and a high reactance. Reactors used for reactive power compensation are usually modeled at the buses and not at the branches. It could, as Li-aung suggests be a series reactor used for limiting fault currents. However, it seems to be a bit large for that purpose. Also, I believe these are usually used between breakers and loads, not between different buses in a meshed grid.

Although it's not a physically correct representation, these numbers represent transformers. Transformers do of course have resistance, but compared to the reactance this is close to negligible (at least when it comes to power flow).

From  To   R           X           B
Bus   Bus  pu          pu          pu
4     7    0.0         0.20912     0.0
4     9    0.0         0.55618     0.0
5     6    0.0         0.25202     0.0


As you can see from the single line diagram below, the branches with zero resistance are transformers.

A common problem in power flow calculations is when impedance values are set to zero. This is because the current through a branch in general is given by the voltage difference divided by the impedance. When the impedance is zero, this gives an infinite current, thus an unfeasible power flow solution. It is common practice to set the impedance values to a very small value in such cases (for instance R = 0, X = 0.0001 pu). In AC systems, zero resistance is often not a problem, but zero reactance is, as this will cause the decoupled load flow, and the DC load flow algorithms to fail.

• Ha, I didn't think of them being transformers. Nice catch. As a sidenote, the ratio of transformer resistance to reactance ranges from about 5 (for very small transformers) to 50 (for very large transformers), so assuming zero resistance is reasonable for large enough transformers. Commented Nov 26, 2014 at 3:59
• Further comment on re-reading: "Also, I believe these are usually used between breakers and loads, not between different buses in a meshed grid." - I have seen reactors applied for fault-limiting between switchboards; it's an effective way to reduce prospective fault currents on a downstream switchboard (at the expense of losses and voltage regulation.) Commented Oct 14, 2015 at 16:01

The 'zero resistance transmission lines' are probably bus-ties between physically adjacent busbars, which are only a few metres long and thus have negligible resistance.

For example, in the picture shown below, the "MINE SWITCHBOARD" is an 11kV switchboard with two sections. I would model this as two busbars joined by a zero-impedance bus tie. Note the bus tie panel is only about 800mm wide, so its resistance is truly negligible.

Edit:

On a second read of the question, I see that the lines in question are not zero impedance - they have a zero resistance but nonzero reactance.

I would say that these are modelling an actual reactor element (a.k.a. inductor, line choke). We do use series reactors for fault current limiting in distribution networks. The reactor does have non-zero resistance in real life, but for simulation purposes the resistance is small enough that we usually ignore it.