EE 311: EE Junior Lab Experiment 5 -

Single Phase TransformersJ. Carroll

9/25/06

Objective• The objective of this experiment is to examine

the operating characteristics of a single phase two winding transformer

• Ideal Transformers - set of mutually coupled coils ,

• Iron or ferromagnetic material core

• Right-hand rule dictates– positive currents , produce positive core flux– coil flux linkages , are related to the core flux

Background Theory

1i c

2i

c

1 2

1N 2N

Ideal Transformers

)2(

)1(

22

11

c

c

N

N

)4(

)3(

222

111

c

c

Nv

Nv

)5(22

2

1

1nvv

N

Nv

2

1

2

1

2

1ini

N

Ni

Equivalent Circuits

Hysteresis and Saturation• Ferromagnetics are permeable but exhibit

hysteresis and saturation, limiting operation– magnetic field intensity, H, versus flux density B

Steady-state AC Performance• AC saturation curve plots ac rms magnetizing

voltage versus ac rms magnetizing current– the ratio provides a large signal approximation of the

magnetizing reactance mX

mV mI

Effects on the Equivalent Circuit

• Magnetizing current, hysteresis effects and core losses are modeled by a shunt resistor

Symbols Used in Eq. Circuit• Definition of symbols in Figure 8

– magnetizing current– magnetizing voltage– primary winding resistance– primary winding leakage reactance– resistance representing core losses– magnetizing reactance– secondary winding resistance– secondary winding leakage reactance

mI

mV

1R

1XR

mX

2R

2X

Remarks• This is a phasor equivalent circuit valid at a

particular frequency– phasor quantities are required in the solution of this

circuit, but all measurements are magnitudes

– be careful to keep track of the difference

• An ideal transformer appears as a part of this equivalent circuit

• The direction of has been reversed for convenience

• Short circuit and open circuit tests used to measure impedances of equivalent circuit

2I

Short Circuit Test • Rated current is applied to a winding from

variable source with other winding short-circuited– voltage, current and power are measured

Simplified Short-Circuit Eq. Circuit• Short circuit reflected across the ideal transformer

– and calculated from short circuit measurements

)10(2

)9(2

2

2

1

2

2

1

eq

eq

XXnX

RRnR

eqR eqX

Open Circuit Test • One winding is open circuited, and rated voltage is

applied to the other winding– current and power flow are measured

Simplified Open-Circuit Eq. Circuit • Neglecting and from the circuit allows

– and to be calculated from the measured values of , , and

1R 1X

ocV ocI ocPmXR

Voltage Regulation • An important consideration is ability to keep

frequency and voltage in proper range– As load increases, voltage will go down– A measure of ``goodness'' is amount of voltage drop at

full load, quantified by the voltage regulation

%100V load 2

load 2circuitopen 2

VV

VR

Procedures: Polarity Test• Apply a small voltage across P1 and P2 of test

transformer to determine polarity of secondary (S)

Hysteresis and Magnetizing Current • Plot channel 1 input versus channel 2 input, or magnetizing current

versus flux linkage, with one cycle of the input corresponding to one cycle around the B-H curve, observe proper scaling

Final Transformer Comments • Transformers are extremely versatile

– can change voltage and current levels– provide isolation between two windings, e.g., instrumentation

amplifiers– pass AC signals from one winding to the other while ``filtering

out'' the DC component

• Transformer ratings range from– a fraction of a volt-amp in printed circuit boards– giga volt-amp range in power transmission systems

• Used in constant frequency applications, such as in power systems, and also in variable frequency applications, such as audio or RF amplifiers

SAFETY• This experiment involves medium-level voltages; you

must know and follow the procedures in your Laboratory Safety Manual!– have TA check all circuits before energizing– lab partners share responsibility for lab safety– good procedure is for one partner to wire circuits, while the

other partner verifies the wiring– be aware of the lab procedures at all times!– follow lab procedures for even minor circuit changes– protective eyewear is to be worn at all times

SAFETY

– predict signal levels and adjust meter ranges before energizing circuits to prevent meter overloads

– energize circuits with zero variac output voltage, increase output slowly while monitoring circuit for over-currents

– arrange experiments so meter leads do not need to be moved while circuit energized circuit

– prevent energized leads from accidental contacts– do not touch energized circuits!