Example 1

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# Example 1 - PowerPoint PPT Presentation

Example 1.

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Presentation Transcript
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)

Ic

E1

IF

Qc

E1

If

Im

f

IF

Ic

Im

The no load current If is needed to supply the no load

losses and to magnetize the transformer core.

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.

referred to the primary

Equivalent circuit

V1: Primary voltage (supply)

I1 : Primary current.

I2: : Secondary current

Approximate Circuit

(a)

(b)

The no load current ranges from 1% to 3% of the full load current.

Therefore, the circuit can be simplified to circuit (b).

Performance Measures
• The percent regulation
• The transformer efficiency
Efficiency
• The efficiency of the transformer is the ratio of output (secondary) power to the input (primary) power. Formally the efficiency is η:

Where,

P1 : The input power (Primary) = V1I1 cosf1

P2 : The output power (Secondary) = V2I2 cosf2

Where,

PL is the power loss in the transformer = Pcopper + Piron

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