### Author Topic: Modelling a 3-phase supply  (Read 1347 times)

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#### 741

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##### Modelling a 3-phase supply
« on: September 16, 2020, 10:44:02 am »
I'd like to make an LTSpice model showing the main features of a 3-phase supply starting with the 3 wire overhead transmission lines. As I understand it, those 3 phases end in 3 transformers at the sub-station in a Y configuration; the centre/common of those transformers is grounded and then the out-going supply is L1, L2, L3 and Earth/Neutral (PEN conductor). Thus I'd need an idea of combined impedance for the (Lx,N) connections. Having done this, I'd then go on to load the supply with various simulated loads, some Y, some Delta.

I think that I can define three AC voltages to represent the 3 wires that are sometimes seen strung atop wooden poles. I do not know what voltage these are at (11kv?). Then, add 3 transformers (need to know the inductances for the windings). The outputs of these are 230V, with 415V between phases.

#### Jay_Diddy_B

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##### Re: Modelling a 3-phase supply
« Reply #1 on: September 16, 2020, 11:52:28 am »
Hi,

Here is a start for you:

[attachimg=1]

There is a three-phase source that has a soft-start feature so the phase ramp over 200ms.

I have dimensioned the source for 1 MVA.

There is a 100 kVA, 33 kVA per phase transformer that give the 230 / 400V output.

[attachimg=2]

The source impedance is 1% losses at each stage, so 2% total losses.

I have attached the LTspice model.

Regards,
Jay_Diddy_B

[attachurl=3]

« Last Edit: September 16, 2020, 12:03:28 pm by Jay_Diddy_B »

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#### 741

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##### Re: Modelling a 3-phase supply
« Reply #2 on: September 16, 2020, 12:33:51 pm »
Hey - a very big thank you

I'll be looking at this soon.

Out of interest, where did you get the values (like 43.7mH, 160uH etc) from?
« Last Edit: September 16, 2020, 12:40:36 pm by 741 »

#### Jay_Diddy_B

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##### Re: Modelling a 3-phase supply
« Reply #3 on: September 16, 2020, 01:28:23 pm »
Hi,

Transformer Inductances

I chose Lpri to be 100H.

This was based on the magnetizing current was 10% of the full load current. This may be a bit high. However, a magnetizing current of 10% results in a PF of 0.995 with a resistive load.

The turn ratio is 11kV /230 = 47.8

The secondary inductance = Primary Inductance / (Np/Ns)2

= 100 /(47.2 = 43.7mH

Source Inductance

The source resistance determines the efficiency.
The source resistance and source inductance determine the regulation and fault currents.

I chose Rs for 1% loss at full power.

I made XL = 2.5 x Rs

This is all a guesstimate. Every installation is different, but the targets for efficiency, regulation and fault currents are similar.

( I studied Electrical Engineering in the 80's at Imperial College and I can still remember some of this stuff  )

Regards,
Jay_Diddy_B

#### 741

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##### Re: Modelling a 3-phase supply
« Reply #4 on: October 14, 2020, 07:49:12 pm »
Is is correct to say that 33 kVA per phase / 230 is "only" 144A, (which is not many houses if some have EV chargers going)?

#### TimFox

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##### Re: Modelling a 3-phase supply
« Reply #5 on: October 14, 2020, 09:10:46 pm »
The three K values in your Spice listing are correct if you have three separate single-phase transformers.  The non-idealness is included in the leakage inductances on the secondary side of the circuit.  Alternatively, you could eliminate those three inductors and reduce the K value to something less than unity.
For a single three-phase transformer (with only one core), you also need K values between the three primary windings, since they are wound on a single core.  I'm not sure, but I think that K's between the three secondary windings may be redundant if you have the three primary-primary K's.  PSpice has specific models for three-phase transformers for Y-Y and Y-delta.
« Last Edit: October 14, 2020, 09:33:53 pm by TimFox »

#### Jay_Diddy_B

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##### Re: Modelling a 3-phase supply
« Reply #6 on: October 14, 2020, 09:38:47 pm »
The three K values in your Spice listing are correct if you have three separate single-phase transformers.  The non-idealness is included in the leakage inductances on the secondary side of the circuit.  Alternatively, you could eliminate those three inductors and reduce the K value to something less than unity.
For a single three-phase transformer, you also need K values between the three primary windings, since they are wound on a single core.  I'm not sure, but I think that K's between the three secondary windings may be redundant if you have the three primary-primary K's.  PSpice has specific models for three-phase transformers for Y-Y and Y-delta.

Hi,
in general you can model the leakage inductance either as discrete inductor or by reducing the K, the coupling factor from unity. In my experience, the models will run faster if the K is set to 1 and the leakage inductance is modelled separately. The end results are the same.

I disagree with you that the three-phase transformer should be modelled as a single core. A typical three phase transformer has three limbs. Around each limb there are a pair of windings. The flux in the limb is derived from Faradays Law of Induction:

V = N d(Phi) /dt

Since the voltages are 120 degrees apart, the flux waveforms will also be 120 degrees apart. Since the flux waveforms are not in phase, the three limbs should be considered separately.

You can't make a three phase transformer like this:

[attachimg=1]

The picture is from here:

https://electronics.stackexchange.com/questions/331109/why-dont-three-phase-transformers-use-toroidal-cores

Regards,
Jay_Diddy_B

#### Jay_Diddy_B

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##### Re: Modelling a 3-phase supply
« Reply #7 on: October 14, 2020, 09:42:48 pm »
Is is correct to say that 33 kVA per phase / 230 is "only" 144A, (which is not many houses if some have EV chargers going)?

Yes, you are right it is only 144A per phase.

And yes, if everybody drove electric cars, there wouldn't be enough electricity to charge them, something politicians overlook.

Jay_Diddy_B

#### TimFox

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##### Re: Modelling a 3-phase supply
« Reply #8 on: October 14, 2020, 09:46:44 pm »
The references I can find generally show a core as in this paper from Signal:  https://www.digikey.com/Site/Global/Layouts/DownloadPdf.ashx?pdfUrl=0AC53F51FED048708BD5A0BBFF6B5638
I could not find any mention of the transformer model, with leakage and coupling, but just looking at two primary windings of this transformer, there will be a mutual inductance M between them.  k = M/(L1L2)1/2.
The phasing between the voltages you discuss is due to the applied voltages, and not the transformer model itself.
« Last Edit: October 14, 2020, 10:28:36 pm by TimFox »

#### 741

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##### Re: Modelling a 3-phase supply
« Reply #9 on: October 28, 2020, 05:49:33 pm »
What range of substation KVA exist out there? E.g. 33 kVA per phase was mentioned, do there exist significantly larger kVA substations - or is there some deliberate limit meaning 33KVA is a sensible maximum (for some reason)?

Smf