Electric Machinery PowerPoint Slides Chapter 2 Transformers to accompany Electric Machinery Sixth Edition A.E. Fitzgerald Charles Kingsley, Jr. Stephen D. Umans Chapter 2 Transformers

Transformer with open secondary. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Transformer with open secondary. Figure 2.4 2-1

No-load phasor diagram. Figure 2.5

Ideal transformer and load. Figure 2.6

Three circuits which are identical at terminals ab when the transformer is ideal. Figure 2.7

Equivalent circuits for Example 2 Equivalent circuits for Example 2.2 (a) Impedance in series with the secondary. (b) Impedance referred to the primary. Figure 2.8

Schematic view of mutual and leakage fluxes in a transformer. Figure 2.9

Steps in the development of the transformer equivalent circuit. Figure 2.10

Equivalent circuits for transformer of Example 2 Equivalent circuits for transformer of Example 2.3 referred to (a) the high-voltage side and (b) the low-voltage side. Figure 2.11

Approximate transformer equivalent circuits. Figure 2.12

Cantilever equivalent circuit for Example 2.4. Figure 2.13

(a) Equivalent circuit and (b) phasor diagram for Example 2.5. Figure 2.14

Equivalent circuit with short-circuited secondary Equivalent circuit with short-circuited secondary. (a) Complete equivalent circuit. (b) Cantilever equivalent circuit with the exciting branch at the transformer secondary. Figure 2.15

Equivalent circuit with open-circuited secondary Equivalent circuit with open-circuited secondary. (a) Complete equivalent circuit. (b) Cantilever equivalent circuit with the exciting branch at the transformer primary. Figure 2.16

(a) Two-winding transformer. (b) Connection as an autotransformer. Figure 2.17

(a) Autotransformer connection for Example 2. 7 (a) Autotransformer connection for Example 2.7. (b) Currents under rated load. Figure 2.18

Common three-phase transformer connections; the transformer windings are indicated by the heavy lines. Figure 2.19

2.8 VOLTAGE AND CURRENT TRANSFORMERS Used in instrumentation applications 765 000 Volt, 10 000 Ampers can not be measured directly Most instruments range: Voltage (Potantial) Transformers (PT) 0-120 V rms; Current Transformers (CT) 0-5 A rms Equivalent circuit for an instrumentation transformer. Figure 2.21 Rc (core loss resistance) neglected in equivalent circuit. Zb is referred to as the BURDEN on that transformer.

FOR PT: FOR CT:

Example 2.10: A 2400:120 V, 60 Hz potential transformer has the following parameter values (referred to the 2400 V winding side): Assuming a 2400 V input, which ideally should produce a voltage of 120 V at the low voltage winding, calculate the magnitude and relative phase-angle errors of the secondary voltage if the secondary winding is open-circuited. Assuming the burden impedance to be purely resistive (Zb=Rb), calculate the minimum resistance (maximum burden) that can be applied to the secondary such that the magnitude error is less than 0.5 percent. Repeat part (b) but find the minimum resistance such that the phase-angle error is less than 1 degree.

2.9 THE PER-UNIT SYSTEM Computations relating to machines, transformers, and systems of machines are often carried out in per-unit form. Quantities are expressed as ratios to chosen BASE values. V, I, P, Q, S, R, X, Z, G (conductance), B (susceptance), Y can be translated. Single Phase: Base Change:

Example 2. 12: The equivalent circuit for a 100 MVA, 7. 97 kV:79 Example 2.12: The equivalent circuit for a 100 MVA, 7.97 kV:79.7 kV transformer is shown in Fig. 2.22a. Convert the equivalent circuit parameters to per-unit using the transformer rating as base. 7.97 kV:79.7 kV

Example 2.8: Three single-phase, 50 kV 2400:240 V transformers, each identical with an impedance of 1.42+j1.82 Ohm referred to high voltage side is connected Wye-Delta in a three-phase 150 kVA bank to step down the voltage at the load end of a feeder whose impedance is 0.15+j1 Ohm/phase. The voltage at the sending end of the feeder is 4160 V line-to-line. On their secondary sides, the transformer supply a balanced three-phase load through a feeder whos impedance is 0.0005+j 0.0020 Ohm/phase. Find the line-to-line voltage at the load when the load draws rated current from the transformer at a power factor of 0.8 lagging.