SUMMARY: how to perform per phase analysis of 3φ circuits
•
When analyzing balanced three-phased circuits, the first step is to transform
any ∆
connections
into
Y
equivalents,
so
that
the
overall
circuit
is
of
the
Y‐Y
configuration.
•
A
single‐phase
equivalent
circuit
is
used
to
calculate
the
line
current
and
the
phase
voltage
in
one
phase
of
the
Y‐Y
structure.
The
a‐phase
is
normally
chosen
for
this
purpose.
•
Once
we
know
the
line
current
and
phase
voltage
in
the
a‐phase
equivalent
circuit,
we
can
take
analytical
short‐cuts
to
find
any
current
or
voltage
in
a
balanced
three‐
phase
circuit,
based
on
the
following
facts:

The b- and c-phase currents and voltages are identical to the aphase current and voltage except for a 120°
shift
in
phase.
In
a
positive‐sequence
circuit,
the
b‐phase
quantity
lags
the
a‐phase
quantity
by
120°,
and
the
c‐phase
quantity
leads
the
a‐phase
quantity
by
120°.
For
a
negative
sequence
circuit,
phases
b
and
c
are
interchanged
with
respect
to
phase
a.
•
The set of line voltages is out of phase with the set of phase
voltages by ±30°.
The
plus
or
minus
sign
corresponds
to
positive
and
negative
sequence,
respectively.
•
In
a
Y‐Y
circuit
the
magnitude
of
a
line
voltage
is
√3
times
the
magnitude
of
a
phase
voltage.
•
The set of line currents is out of phase with the set of phase
currents in ∆‐connected
sources
and
loads
by
±30°.
The
minus
or
plus
sign
corresponds
to
positive
and
negative
sequence,
respectively.
•
The
magnitude
of
a
line
current
is
√3
times
the
magnitude
of
a
phase
current
in
a
∆‐connected
source
or
load.
•
The
techniques
for
calculating
per‐phase
average
power,
reactive
power,
and
complex
power
are
the
same
as
for
a
one
phase
circuit.
•
The
total
real,
reactive,
and
complex
power
can
be
determined
either
by
multiplying
the
corresponding
per
phase
quantity
by
3
or
by
using
the
expressions
based
on
line
current
and
line
voltage.
•
The
total
instantaneous
power
in
a
balanced
three‐phase
circuit
is
constant
and
equals
1.5
times
the
average
power
per
phase.
•
A
wattmeter
measures
the
average
poser
delivered
to
a
load
by
using
a
current
coil
connected
in
series
with
the
load
and
a
potential
coil
connected
in
parallel
with
the
load.
•
The total average power in a balanced three-phase circuit can be measured by
summing the readings of two wattmeters connected in two different phases of
the circuit.