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I'm trying to solve the power flow for the WECC-9 bus reported below:

enter image description here

all generators (1,2 and 3) are behind a transformer, which has a Voltage converter ratio (e.g. 18/230) and a reactance(?), which I guess derives from the "Voltage-behind-Reactance" model.

How should I deal with the transformers for Power Flow computation, by means of Newton Rapson and the likes? should I divide the reactance by the transformer ratio or something else?

I found this other question but it is not clear to me, and the reference within seems to have been changed

Newton Raphson Load Flow of a Power System with Transformers

user3149593
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Your first step is to convert this entire problem into a per-unit system. This is exactly what the question you've linked to has indicated. When using a per-unit system, a transformer can be accurately modelled as an additional series reactance.

Firstly, we can arbitrarily choose \$S_{BASE} = 100 MVA\$. Does it need to be 100 MVA? No. It can be whatever we want but I like 100 MVA.

Following that, when you set up a per-unit system on a power system with transformers, the base voltage changes with respect to the transformers' turn ratio. In your above question, we can choose 18 kV to be the \$V_{BASE}\$ for BUS-2. This, in turn, means that:

  • BUS-2 \$V_{BASE-2} = 18 kV \$ we got to pick this one
  • BUS-7 \$V_{BASE-7} = \frac{230}{18} \times V_{BASE-2} = 230 kV\$
  • BUS-1 \$V_{BASE-1} = 16.5 kV \$ this is calculated the same way as above
  • BUS-3 \$V_{BASE-3} = 13.8 kV\$ this is calculated the same way as two above

The magic of a per-unit system is now that the primary side of the transformer is with respect to the primary voltage and the secondary side is with respect to the secondary voltage the transformer can be replaced with a reactance. Your question indicates that T1 = 5.76 %X, T2 = 6.25 %X, and T3 = 5.86 %X. Usually, I would find the new per-unit reactance by using: $$X_{T1, pu} = 0.0576 \times \frac{S_{BASE}}{S} $$

but you haven't provided the MVA rating of the transformers. Luckily, this is a well-known problem and we can find that T1 = 77 MVA, T2 = 163 MVA, and T3 = 86 MVA.

$$ X_{T1,pu} = 0.0576 \times \frac{100}{77} = 0.0748 $$ $$ X_{T2,pu} = 0.0625 \times \frac{100}{163} = 0.0383 $$ $$ X_{T3,pu} = 0.0586 \times \frac{100}{86} = 0.0681 $$

Voila! Your vertical squiggly lines can now be drawn and horizontal squiggly lines.

  • Thanks for the answer. I have a small question. The MVA rating of the transformer is ought to be given, if pu parameters are specified, right? Because it's not given in this case, so you calculate it based on some industrial standard. – Edward Jul 09 '21 at 08:46
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    @edxu96 -- yes, the MVA rating should be known. IIRC, I believe OP missed it in the question information and I substituted in some values from another WECC-9 problem. The key here is that per-unit is needed to remove the transformers for the larger power flow calculations. –  Jul 09 '21 at 13:16
  • Thanks for the quick reply. I'm implementing transformer models in power flow, and just added your answer as test case :-) – Edward Jul 09 '21 at 13:26
  • @edxu96 -- cool! Let me know if it's wrong lol –  Jul 09 '21 at 14:26
  • Your explanation in terms of changing base apparent power is very straightforward. But I do have a question regarding base voltages. You mentioned that "we got to pick this one (18kV for bus 2 and 230 kV for bus 7, corresponding to the rated voltage of the transformer)". But in most power flow softwares (including my company's product) the base voltage of any bus can be arbitrarily chosen. However, when the pu base is changed from the transformer to the grid, these base voltages are actually not used. I don't see any point of setting base voltages for buses. – Edward Jul 30 '21 at 13:36
  • @Edward -- in a pure design standpoint, you shouldn't need to, because at that point you can make the transformers whatever you want. If you've already got a 230/18kV transformer in the system, you can't change those voltages. There's also standard voltages you may need to adhere to depending on your local codes. –  Jul 30 '21 at 16:55
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    Thanks. But I'm developing software, so users might not follow local codes ;-( ... My points can be summarised by [a new question I just wrote](https://electronics.stackexchange.com/questions/579875/how-to-change-per-unit-base-before-power-flow-calculation): the base nodal voltages can be changed, but impedances in pu should be changed accordingly. – Edward Aug 02 '21 at 09:39
  • @Edward -- I added my two cents. Further to your above comment *"the base voltage of any bus can be arbitrarily chosen"*, this is true, however, my selection of 18 kV wasn't arbitrary, it was the rated voltage for the transformer. I could select 50 kV, but there would be more transformations involved to keep everything in per unit. –  Aug 03 '21 at 14:55