# Voltage regulation in transformers at unity power factor

• mpar3
In summary, the conversation discusses the calculation of the primary current, power factor, and impedance for a transformer, as well as the application of a given resistance value. The final answer for the secondary winding resistance is 5.0743 ohms, and the primary current is divided by √3 in the calculation.
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.
 ​

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

## 1. What is voltage regulation in transformers at unity power factor?

Voltage regulation refers to the ability of a transformer to maintain a constant output voltage despite variations in the input voltage. At unity power factor, the input and output voltages are in phase, meaning that the transformer is operating at maximum efficiency.

## 2. Why is voltage regulation important in transformers at unity power factor?

Voltage regulation is important because it ensures that the output voltage remains stable, which is crucial for the proper functioning of electrical equipment. Without proper voltage regulation, fluctuations in the output voltage can damage equipment and cause power failures.

## 3. How is voltage regulation calculated in transformers at unity power factor?

Voltage regulation is calculated by taking the difference between the no-load voltage and the full-load voltage, and then dividing that by the full-load voltage. This value is then multiplied by 100 to get a percentage. A lower percentage indicates better voltage regulation.

## 4. What factors affect voltage regulation in transformers at unity power factor?

The primary factors that affect voltage regulation in transformers at unity power factor are the transformer's design, the quality of its materials, and the load it is under. Other factors such as temperature, frequency, and the type of insulation used can also impact voltage regulation.

## 5. How can voltage regulation be improved in transformers at unity power factor?

Voltage regulation can be improved by using high-quality materials in the transformer's construction, ensuring proper design and sizing for the intended load, and regularly maintaining and testing the transformer. Additionally, using voltage regulators or tap changers can help adjust the output voltage to compensate for fluctuations in the input voltage.

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