example 1 a 9375 kva, 13,800 kv, 60 hz, two pole, y-connected synchronous generator is delivering...
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Example 1
A 9375 kVA, 13,800 kV, 60 Hz, two pole, Y-connected
synchronous generator is delivering rated current at rated
voltage and unity PF. Find the armature resistance and
synchronous reactance given that the filed excitation
voltage is 11935.44 V and leads the terminal voltage by an
angle 47.96°.
Example 2
A cylindrical rotor machine is delivering active power of
0.8 p.u. and reactive power of 0.6 p.u. at a terminal
voltage of 1 p.u. If the power angle is 20°, compute the
excitation voltage and the machine’s synchronous
reactance.
Announcement
Quiz I : Next Tuesday (April 5, 2011) at 12:00 in
H11
Assignment I: will be posted today and due
Next Tuesday (April 5, 2011) at 12:00 in H11
Power Transformers
Transformation ratio
Primary (supply) Secondary (Load)
Transformers at no load
The no load current I is needed to supply the no load
losses and to magnetize the transformer core.
Im
Ic E1
I
c
E1
I
I
Ic Im
Transformer losses
The transformer losses are divided into electrical losses
(copper losses) and Magnetic losses (Iron losses).
Copper losses in both the primary and secondary windings.
Magnetic losses, these losses are divided into eddy current
losses and hysteresis losses.
2221
21 RIRI
mhysteriseseddymag IVPPP 1
Loaded Transformer
Z2’ is the load impedancereferred to the primary
Equivalent circuit
V1: Primary voltage (supply)I1 : Primary current.V2: Secondary voltage (load)I2: : Secondary current
Exact Circuit
Approximate Circuit
The no load current ranges from 1% to 3% of the full load current.Therefore, the circuit can be simplified to circuit (b).
(a) (b)
Phasor Diagram
)('2'21 eqeq jXRIVV
Performance Measures
The percent regulation
The transformer efficiency
Voltage Regulation
sincos '2
'2
'21 eqeq XIRIVVVR
Efficiency
The efficiency of the transformer is the ratio of output (secondary)
power to the input (primary) power. Formally the efficiency is η:
1
2
P
P
LPPP 21
Where,
P2 : The output power (Secondary) = V2I2 cos2
P1 : The input power (Primary) = V1I1 cos1
Where,
PL is the power loss in the transformer = Pcopper + Piron
ironeq PRIIV
IV
2'22
'2
'2
2'2
'2
cos
cos
Example
A 100-kVA, 400/2000 V, single-phase transformer has the following parameters
R1 = 0.01 R2 = 0.25 ohms
X1 = 0.03 ohms X2 = 0.75 ohms
The transformer supplies a load of 90 kVA at 2000 V and 0.8 PF lagging.
Calculate the primary voltage and current using the simplest equivalent circuit.
Find also the V.R. and efficiency for the transformer
Solution
Voltage Regulation
sincos '2
'2
'21 eqeq XIRIVVVR
%84.296.411
7.11%
7.11
6.006.02258.002.0225
VR
VVR
VR
Efficiency