Power Transformers 2
Transcript of Power Transformers 2
Power Transformers
Three Phase Transformer Connections
Three identical single phase two winding transformers may be connected to form a three phase bank
The windings may be connected as:
Y - Y
Y - ∆
∆ - Y
∆ - ∆
Three Phase Transformer Connections
Three Phase Transformer Connections
Three Phase Transformer Connections
∆ - Y commonly used as a generator step-up transformer
Advantages:
3rd harmonic magnetizing current remains trapped in the ∆ winding
Y winding provides neutral point for grounding on HV side (has an effect on the insulation requirements of the winding)
Three Phase Transformer Connections
Y - Y seldom used because of harmonics in the magnetising current
∆ - ∆ has the advantage that one phase can be removed for maintenance while the remaining phases continue to operate as a three phase bank
Operation is reduced to 58% of the original bank
Example – Exercise 3.36
Three single phase transformers each rated at 25 MVA, 34.5/13.8 kV, are connected to form a three phase ∆ - ∆ bank. A resistive Y connected load absorbs 75 MW at 13.8 kV. If one of the single phase transformers is removed (resulting in an open ∆ connection) and the load is simultaneously reduced to 43.3 MW, determine
Example – Exercise 3.36
a) The load voltages Van, Vbn and Vcn
b) Load currents Ia, Ib and Ic
c) The MVA supplied by each of the two remaining transformers
Are balanced voltages still applied to the load?
Is the open - ∆ transformer overloaded?
Exercise 3.36
Exercise 3.36
Exercise 3.36
Exercise 3.36
Exercise 3.36
Three Phase Transformer Connections
Y – Y
No phase shift for +ve sequence
∆ - ∆
Y - ∆
HV quantities lead LV quantities by 300
for +ve sequence
∆ - Y
Three Phase Transformer
Three Phase Transformer
Three Phase Transformer
All six windings placed on a common core Advantages Cores contains less iron Costs less Weighs less Less space required Slightly higher efficiency Disadvantages Winding failure requires replacement of the transformer
Equivalent Circuit of three phase two winding transformer
Y – Y or ∆ - ∆
Equivalent Circuit of three phase two winding transformer
Y – ∆ or ∆ - Y
Three Winding Transformers
Three Winding Transformers
Three Winding Transformers
For an ideal three winding transformer:
I1pu = I2pu+ I3pu
E1pu = E2pu== E3pu
Three Winding Transformers
Three Winding Transformers
For a practical three winding transformer Open circuit test determines shunt admittance (Gc and Bm) Short circuit test determines leakage impedances (Z12, Z13 and Z23 ) Z12 = pu leakage impedance measured from winding 1 with winding 2 shorted and winding 3 open Z13
Z23
Three Winding Transformers
Short Circuit Test Z12 = Z1 + Z2
Z13 = Z1 + Z3
Z23 = Z2 + Z3
Series impedances can be calculted from above using
Z1 = 1
2(Z12 + Z13 - Z23)
Z2 = 1
2(Z12 + Z23 - Z13)
Z3 = 1
2(Z13 + Z23 - Z12)
Exercise 3.51
The ratings of a three phase three winding transformer are: Primary (1): Y connected 66 kV, 15 MVA Secondary (2): Y connected 13.2 kV, 10 MVA Tertiary (3): ∆ connected 2.3 kV, 5 MVA Neglecting winding resistances and exciting current, the per unit leakage reactances are X12 = 0.08 on a 15 MVA, 66 kV base
X13 = 0.10 on a 15 MVA, 66 kV base X23 = 0.09 on a 10 MVA, 13.2 kV base
Exercise 3.51
(a) Determine the p u reactances X1 , X2 and X3
on a 15 MVA, 66 kV base at the primary terminals
(b) Purely resistive loads of 7.5 MW at 13.2 kV and 5 MW at 2.3 kV are connected to the secondary and tertiary sides of the transformer respectively. Draw the per unit impedance diagram, showing the per unit impedances on a 15 MVA, 66 kV base at the primary terminals
Exercise 3.51
Exercise 3.51
Exercise 3.51
Exercise 3.51
Exercise 3.51
Autotransformers
Two windings of a single phase transformer are connected in series.
Windings are coupled electrically and magnetically
Autotransformers
Autotransformers
Advantages
Smaller leakage impedance
Lower losses
Lower exciting current
Lower cost for small turns ratio
Disadvantages
Higher short circuit currents
Electrical coupling of windings allows transient over-voltages to pass through more easily
Transformers with off –nominal turns ratio
Transformers with off –nominal turns ratio
A transformer whose rated voltages is not in proportion to the selected base voltages is said to have an “off nominal turns ratio”.
𝑉1𝑟𝑎𝑡𝑒𝑑
𝑉2𝑟𝑎𝑡𝑒𝑑 ≠
𝑉𝑏𝑎𝑠𝑒−1
𝑉𝑏𝑎𝑠𝑒−2
Transformers with off –nominal turns ratio
𝑉1𝑟𝑎𝑡𝑒𝑑 = 𝑎𝑡 𝑉2𝑟𝑎𝑡𝑒𝑑 (1)
If the base voltages on either side of the transformer are known the
𝑉𝑏𝑎𝑠𝑒1 = b 𝑉𝑏𝑎𝑠𝑒2 (2)
Then equation (1) can be written as
𝑉1𝑟𝑎𝑡𝑒𝑑 = 𝑎𝑡 𝑉2𝑟𝑎𝑡𝑒𝑑
= b (𝑎𝑡
𝑏) 𝑉2𝑟𝑎𝑡𝑒𝑑 (3)
Letting c = 𝑎𝑡
𝑏 equation 3 becomes
𝑉1𝑟𝑎𝑡𝑒𝑑 = bc 𝑉2𝑟𝑎𝑡𝑒𝑑 (4)
𝑉1𝑟𝑎𝑡𝑒𝑑 = bc 𝑉2𝑟𝑎𝑡𝑒𝑑 can be represented by two transformers in series as shown below
Transformers with off –nominal turns ratio
Per unit equivalent circuit
Transformers with off –nominal turns ratio
π circuit representation for real c
Transformers with off –nominal turns ratio
𝐼1
−𝐼2=
𝑌11 𝑌12
𝑌21 𝑌21
𝑉1
𝑉2
Transformers with off –nominal turns ratio
Parallel connected transformers with different turns ratios
Tap changing transformers
Voltage regulating transformers
Phase angle regulating transformers
Transformers with off –nominal turns ratio
Tap changing transformers
Transformers with off –nominal turns ratio
Tap changing transformers
Example 3.12
Example 3.12
Example 3.12
Per unit equivalent circuit
Example 3.12
Example 3.12
Example 3.12
Per unit equivalent circuit
Transformers with off –nominal turns ratio
Regulating transformers
Voltage magnitude
Phase angle regulating
Voltage magnitude regulating transformer
Voltage magnitude regulating transformer
Modelling as a off nominal turns ratio transformer
c = (1 + ∆v) for voltage increase at bus abc
c = (1 + ∆v)-1 for voltage increase at bus a’b’c’
Phase angle regulating transformer
Modelling as a off nominal turns ratio transformer
c = 1∠α for a phase increase at bus abc
c = 1∠-α for a phase increase at bus a’ b’ c’
Example 3.13
Example 3.13
Example 3.13
Example 3.13
Example 3.13
Example 3.13
Example 3.13
Tutorial 4 – Exercise 3.59
The 2 lines in example 3.13 supply a balanced load with a load current of 1∠-300. Determine the real and reactive power supplied to the load bus from each parallel line with (a) no regulating transformer (b) the voltage regulating transformer in example 3.13(a), and (c) the phase angle regulating transformer in example 3.13(b), Assume that the voltage at bus abc is adjusted so that the voltage at bus a’b’c’ remains constant at 1.0∠00 per unit.