Principles & Applications Electricity Principles & Applications Sixth Edition Richard J. Fowler Chapter 12 Transformers ©2003 Glencoe/McGraw-Hill

INTRODUCTION Transformer Fundamentals Transformer Efficiency Loaded Transformers Three-phase Transformers Impedance Matching

Facts About Transformers Transformers operate on mutual inductance. A transformer has a primary winding and a secondary winding. The coefficient of coupling is the portion of primary flux that links the secondary. With 100% coupling, the turns-per-volt ratio is the same for all windings. Transformers can have hysteresis, eddy current, and copper (I2R) losses.

More Facts About Transformers Transformer losses can be reduced by using silicon steel cores, laminated cores, and small gage wires. As the load on a transformer increases, angle theta decreases. Three-phase transformers use a three-legged core. Transformer windings can be connected in series or parallel.

Transformer Fundamentals Primary Secondary Load - + + - A transformer has a primary coil and a secondary coil. The primary is connected to a source. The secondary is connected to a load. During the first half-cycle, the flux builds up and collapses. This creates a half-cycle of induced voltage in the secondary.

Transformer Fundamentals Primary Secondary Load - + + - During the next half-cycle, the flux again builds up and collapses. This creates another half-cycle of induced voltage in the secondary. Notice that the primary and secondary voltages are out-of-phase.

Primary-Secondary Terminology Transformers are bidirectional devices. 120 V Primary Source 90 V Secondary Load This transformer was designed to step 120 V down to 90 V. 120 V Secondary Load Source 90 V Primary However, either winding can be used as the primary.

Turns-Per-Volt Ratio _ + 0.25 V + 1.0 V _ _ 0.75 V + The 4-turn primary with a 1 volt source provides 4 turns-per-volt; therefore, each turn has 0.25 V across it. Each turn will produces a specific amount of flux in the core. This same flux will, in turn, produce 0.25 V in each secondary turn. Thus, a 1 turn secondary provides 0.25 V, and a 3 turn secondary provides 0.75 V.

Eddy Current Illustration If an eddy current is induced in the core, one will also be induced in the aluminum disk placed on top of the core. The eddy current in the aluminum disk will produce a magnetic field that opposes the field that created the eddy current. Eddy current Aluminum disk Coil connected to a 60-Hz supply The next slide shows the results of the eddy current in the aluminum.

Click on the image to run the display. To rerun the display, click again on the image.

Transformer Losses Copper (I2R) loss B H Hysteresis loss (green area of the hysteresis loop) Eddy current loss (I2R in the core) These losses are minimized by a narrow hystersis loop, thin laminations, and large diameter wire.

Transformer Efficiency Source provides 1640 W Transformer 90 W loss (heat loss) Load 1550 W consumed The transformer core and copper losses cause the transformer to heat up as electric energy is converted to heat energy. Efficiency = 1550 W / 1640 W = 0.945

Transformer-Action Quiz The ____ coil of a transformer is connected to the source. primary Flux builds and collapses in a core ____ time(s) each cycle. two A transformer provides ____ degrees of phase shift between its two windings. 180 Any winding of a transformer can be used as the ____ winding. primary (or secondary) Core losses can be reduced by using ____ laminations. thinner Transformer inefficiency is caused by core and ____ losses. copper

Primary Current Load Iref Ipri With no load, Ipri is the Vpri Vpri Ipri Ien Ipri With no load, Ipri is the energizing current (Ien). With a load, Ipri is composed of Ien and Iref . The transformer acts like an inductor. Iref is the resistive load current reflected from the secondary to the primary. Theta is large; power is low.

There is no phase-1 flux because phase-1 current is zero. Flux in a Three-Phase Core Core Phase 3 Phase 1 Phase 2 Time 1 Phase 1 coil 2 3 At time 1, flux created by phase 2 and phase 3 join together. There is no phase-1 flux because phase-1 current is zero.

Flux in a Three-Phase Core (Time 2) Core Phase 3 Phase 1 Phase 2 Time 2 Phase 1 coil 2 3 At time 2, flux created by phase 2 and phase 3 still join together. Also, flux created by phase 1 and phase 2 join together.

Flux in a Three-Phase Core (Time 3) Core Phase 3 Phase 1 Phase 2 Phase 1 coil 2 3 Time 3 At time 3, flux created by phase 1 and phase 2 still join together. Also, flux created by phase 1 and phase 3 join together.

Flux in a Three-Phase Core (Time 4) Core Phase 3 Phase 1 Phase 2 Phase 1 coil 2 3 Time 4 At time 4, flux created by phase 1 and phase 3 still join together. Also, flux created by phase 2 and phase 3 join together.

Primary-Current Quiz The no-load primary current is called the ____ current. energizing The additional primary current caused by loading the transformer is called the ____ current. reflected (or resistive) Angle theta ____ when a load is connected to a transformer. decreases A transformer with no load acts like a(n) ____. inductor In a three-phase transformer, at least ____ primary coils are creating flux at any instant. two

Series-Opposing Windings 120 V + _ 8 V 2 A 6 V 3 A 2 V _ + 2 A Connect two terminals with the same instantaneous polarities. Take the output from the other two terminals. The output voltage equals the difference between the two voltages. The current is limited to the lesser of the two winding currents.

Series-Aiding Windings 120 V + _ 8 V 2 A 6 V 3 A 14 V _ + 2 A Connect two terminals that have opposite instantaneous polarities. Take the output from the other two terminals. The output voltage equals the sum of the two winding voltages. The current is limited to the lesser of the two winding currents.

Parallel Secondary Windings 120 V + _ 9 V 4 A 9 V _ + 8 A The two windings must have equal voltage ratings. The two windings should have equal current ratings. Connect the negative terminals and the positive terminals. Take the output from the negative and positive terminals. Voutput = Vwinding and Ioutput = 2 x Iwinding

Impedance Matching 10:1 ratio 100 W 1 W 0.1 A 1 A 10 V 1 V 20 V 100 W Notice the source in both circuits provides 0.1 A at 10 V. Thus, the transformer makes the 1-W resistor act like a 100-W resistor in terms of the load on the source.

Series and Parallel-Windings Quiz Series-opposing windings produce a voltage equal to the ____ of the voltages of the two windings. difference series- The current rating of ____ connected windings is that of the winding with the smallest current rating. A 12-V, 2-A secondary series aiding a 6-V, 3-A secondary will provide ____ V and ____ A. 18, 2 For parallel windings, ____ instantaneous polarities should be connected together. like Parallel windings must have equal ____ ratings. voltage A transformer used to make a load appear to be other than its true value is called a(n) ____ ____ transformer. impedance- matching

REVIEW Transformer Fundamentals Transformer Efficiency Loaded Transformers Three-phase Transformers Impedance Matching