# Voltage regulation in transformers at unity power factor

• mpar3

#### mpar3

Homework Statement
A 415V to 11 kV transformer has a rating of 200 kVA. The winding resistance
and leakage reactance when referred to the primary are 0.014 Ω and 0.057 Ω
respectively.
(a) Determine the % regulation of the transformer at 0.8 power factor lagging.
(b) In designing a particular 415V to 11 kV, 200 kVA transformer, the primary
winding resistance is to be 10 mΩ. Find the maximum winding resistance of the
secondary winding if the transformer is to have 2% regulation at unity power
factor.
Relevant Equations
%Reg = 100% * (I(R * cosθ ± X * sinθ))/E
So I've done part a)
Primary current = 200000/415=481.9
Cos θ = -0.8
Sin θ = 0.6
Reg=(481.9 ( 0.014*-0.8 + 0.057*0.6))/415
= 0.0267
Reg% = 2.67%

Part b I simply used the same equation but for secondary:
@ unity p.f., cos θ =1, sin θ = 0
secondary current = 200000/11000 = 18.18

18.18(R*cosθ)/11000=0.02
solved for R gives R=12.1Ω

However, this hasn't utilised the 10mΩ given in the question so I assume it can't be as simple as that. I've seen a couple of threads with this question in from a few years ago but the explanations just didn't make sense to me

So I've now tried using the same equation for the primary side, and got the primary impedance to be 0.0172. I've then taken the 10 milliohm off from that so 0.0072, and divided this by n squared to give a secondary winding resistance of 5.06 ohms. I still don't have enough confidence in this answer to submit it though

Primary current = 200000/415/√3=278.24 A ; COSθ=0.8 ; SINθ=-0.6

Vsec/Vp=Zsec*Isec/Zp*Ip ; Zsec/Zp=Vsec/Vp*Ip/Isec=Vsec^2/Vp^2
Zp=Zsec*Vp^2/Vsec^2 [secondary impedance seen from primary].
The new total transformer resistance referred to primary will be Rx=Rp+Rsec*Vp^2/Vsec^2

I am sorry I did not remark your final answer. My calculation result was 5.0743 ,indeed.
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Primary current = 200000/415/√3=278.24 A ; COSθ=0.8 ; SINθ=-0.6
Hi sorry I've been away so long, things have been manic here. I can see my mistake with cos theta, why is the primary current over root 3?

Usually, 0.415/11 kV it is about a three-phase transformer where the primary is 415/240 V. However, if it is about a single phase -it was not specified-you don't need then √3