Download EE 311: EE Junior Lab Single Phase Transformers

EE 311: EE Junior Lab
Experiment 5 Single Phase Transformers
J. Carroll
9/25/06
Objective
• The objective of this experiment is to
examine the operating characteristics of a
single phase two winding transformer
Background Theory
• Ideal Transformers - set of mutually
coupled coils N 1 , N 2
• Iron or ferromagnetic material core
• Right-hand rule dictates
– positive currents i1, i2 produce positive core flux  c
– coil flux linkages 1, 2 are related to the core
flux  c
Ideal Transformers
  N
1
1
c
 N
2
2
2
1
2
1
1
(2)
c
v    N 
v    N 
1
N
v  
N
(1)
1
2
c
c
(3)
( 4)

v  nv

2
2
N
i  
N
2
1

i  n i

1
2
1
(5)
2
2
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 Vm versus ac rms magnetizing current I m
– the ratio provides a large signal approximation of the
magnetizing reactance X m
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
– I m magnetizing current
–
–
–
–
–
–
–
Vm magnetizing voltage
R1 primary winding resistance
X 1 primary winding leakage reactance
R resistance representing core losses
X m magnetizing reactance
R2 secondary winding resistance
X 2 secondary winding leakage reactance
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 I 2 has been reversed for
convenience
• Short circuit and open circuit tests used to
measure impedances of equivalent circuit
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
– Req and X eq calculated from short circuit measurements
Req
R1  n R2 
2
X eq
2
X1  n X 2 
2
2
(9)
(10)
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 R1 and X 1 from the circuit allows
– R and X m to be calculated from the measured values
of Voc , I oc , and Poc
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
V2 open circuit  V2 load
VR 
 100 %
V2 load
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!