Transformers2
Mahesh Lec6 S. Illindala
341 - Electric Machinery Fundamentals
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Objectives
Knowledge (repeating from memory):
Define the per-unit system of measurements Define voltage regulation
Comprehension (demonstrating understanding of terms and concepts):
Discuss the various advantages of the per-unit system Associate the resistive elements of the transformer equivalent circuit with the various losses
Application (apply learned information to solve a problem):
Calculate the per-unit quantities and plot the per-unit equivalent circuit for a transformer Examine the voltage regulation at 0.8 lagging pf, 1.0 pf and 0.8 leading pf Estimate the efficiency of the transformer at full load and a 0.8 lagging pf from its equivalent circuit
341 - Electric Machinery Fundamentals
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Per-Unit System of Measurements for 1-F Systems
Per-unit (pu) based system, when followed, eliminates the need for explicit voltage-level conversions at every transformer in the system.
In a power system, a base apparent power (Sbase) and base voltage (Vbase) are selected at a specific point in the system. The remaining values can be computed as follows for 1-F systems: Base current,
Base impedance,
Base admittance,
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Example 2-4
Calculate the p.u. quantities of the equivalent circuit parameters on transformer primary side
, = ,
=
, =
, =
Would the p.u. quantities be different on the secondary side of the transformer 341 - Electric Machinery Fundamentals
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Class Exercise
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Class Exercise
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Class Exercise
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Class - Exercise
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Class Exercise
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Class Exercise
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Voltage Regulation
Full-load voltage regulation (VR) is a quantity that compares the output voltage of the transformer at no load (|VS,nl|) with the output voltage at full load (|VS,fl|) |VS,nl|
Figure: Approx equivalent circuit of transformer as referred to the secondary side
1.0 PF
Lagging PF Leading PF
Figure: Phasor diagrams of transformer
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Example 2-5
Calculate the full-load voltage regulation at 0.8 lagging pf. 15-kVA, 2300/230-V
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Example 2-5
With the MATLAB code given in textbook we can calculate regulation at different loads for various power factors
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Transformer Taps and Voltage Regulation Example 2-6
All the power distribution transformers are provided with taps in the windings to permit small changes in the turns ratio
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Transformer Efficiency
Transformer efficiency (h) is defined as
Copper loss modeling
Pin
Losses are transformation invariant
Copper loss,
Core loss modeling
Core loss,
(including hysterisis and eddy current losses)
Figure: Approx equivalent circuit of transformer (including the excitation branch) as referred to the secondary side
Output power,
Power factor (PF), [of the load]
Figure: Transformer phasor diagram
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Example 2-5
Calculate the full-load efficiency at 0.8 lagging pf.
15-kVA, 2300/230-V
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