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Q1. For a Yd1 transformer:

(a) Draw the connection diagram

The Star - Delta connection is shown below

Star - Delta Connection Assignment.png

(b) Show how the connections must be modified to allow parallel operation with a Yd11 transformer.

Yd11 - Here 11 represents the phase displacement. This is between the HV and LV windings.

11 = 330o lagging or 30o leading

Star - Delta Connection Assignment1.png

(c) Draw a phasor diagram for the modified connection.

Star - Delta Connection Assignment2.png

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Q2. In your own words, state the three essential and two highly desirable conditions which must be fulfilled for two 3-phase transformers to operate satisfactorily in parallel. State briefly what you think may be the possible consequences of not complying with these conditions.

The assumptions are

a) Both the transformers should have same phase shift.

b) Paralleling via distribution or transmission circuits which consists of cables and overhead lines.

c) When connected in no phase shift condition the primary and secondary are in phase. But when connected differently, the secondary voltage waveforms will differ from the primary voltage waveforms by 30 degrees. And is called a 30 degree phase shift. Parallel connected transformers will have same phase shift.

d) For satisfactory operation the voltage ratios could be same

e) The leakage impedance is inversely proportional to the KVA rating

f) Proper connection of transformers that means the polarities is more important. If polarities are reversed it can lead to damage of transformer.

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Q3. (a) Two single-phase transformers have the following impedances referred to the secondary side. Unit A rated 250 kVA (0.09 + j2.7) Ω Unit B rated 400 kVA (0.04 + j1.6) Ω. Determine the load taken by each machine as a percentage of its rating when they share a common load of 500 kVA at 0.73 p.f. lag.

To calculate -

Unit A rated 250 kVA (0.09 + j2.7) Ω

Unit B rated 400 kVA (0.04 + j1.6) Ω

Common load of 500 kVA at 0.73 p.f. lag

Unit A

Unit B

(0.09 + j2.7) Ω =2.7015L30

(0.04 + j1.6) Ω


Choose a base = (250/400)x(0.04 + j1.6)

0.625(0.04 + j1.6) = 0.025+ j1

= 1.0003L40

The load taken by each machine as a percentage of its rating

S = 250x(2.7015/1.0003) = 675.17KVA

S = 400x(2.7015/1.0003) = 675.17KVA = 1080.27KVA

Q3. (b) Transformer A is rated at 300 kVA with an impedance of (0.09 + j0.18) Ω. Transformer B is rated at 200 kVA with an impedance of (0.09 + j0.23) Ω. If these transformers are connected in parallel to supply a common load, determine the percentage overload on B when A supplies its full load at p.f. 0.45 lag.

To calculate -

Transformer A is rated at 300 kVA with an impedance of (0.09 + j0.18) Ω.

Transformer B is rated at 200 kVA with an impedance of (0.09 + j0.23) Ω.

Transformer A

Transformer B

(0.09 + j0.18) Ω = 0.2012L61.36

(0.09 + j0.23) Ω


Choose a base = (300/200)x(0.09 + j0.23)

1.5(0.09 + j0.23) = 0.135+ j0.345

= 0.3705L67.63

The load taken by each machine as a percentage of its rating

S = 300 x (0.2012/0.3705) = 162.91KVA

S = 200x(0.2012/0.3705) = 108.61 KVA

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Q4. From the operating chart shown determine the following performance limitations for a generator:

Star - Delta Connection Assignment3.png

(a) where the power limit and the MVA limit coincide;

(i) the power factor = 0.83

(ii) The load angle = 24.59

(iii) The MVAr output = 0.12

(b) where the power limit and the stability margin coincide;

 (i) The p.u. excitation = -0.7-j0.83

(ii) The MVA output = √(0.832+.122) = 0.8417.

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Q5. A 3-phase synchronous generator rated at 570 MVA is connected to an infinite busbar. Using the data given in the table below, plot the capacity chart of the generator.

Quantity

Value

Synchronised Reactance

2.0 p.u

Excitation Limit

2.8 p.u

Maximum Margin

570 MVA

Turbine Power Limit

500 MW

Stability Margin

10% Full Load Power

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