A STUDY MATERIALS FOR ELECTRICAL ENGINEERING STUDENTS
SUBJECT: ELECTRIC CIRCUITS III
3 PHASE(ᶲ) AC SYSTEM
POLYPHASE – consists of two or more similar 1 phase systems in which the maximum values of the
independent voltage does not occur at the same time.
ADVANTAGES OFPOLYPHASE SYSTEM OVER SIMPLE PHASE SYSTEM
1. Polyphase machines are simpler, cheaper and more efficient.
2. Polyphase transmission lines can deliver more power for a given weight and cost.
3. Voltage regulation of polyphase lines is inherently better.
3 PHASE SYSTEM – interconnection of three 1 phase system whose voltage waves, though similar in
amplitude and frequency are displaced 120 electrical degrees.
PHASE SEQUENCE – order of rotation of the coil voltages in a balanced polyphase system.
Example: If the phase sequence is a-b-c, this means that “vector A” comes first, followed by “B” and “C”
(also known as positive sequence).
NOTE: VECTOR is the reference vector acceleration to the given sequence vector rotation unless
provided/specified assumed to rotate in a counterclockwise direction.
Basis is CURRENT.
×3 if phase is given
√3 if line is given.
1 Phase = P= IᶲVᶲcosꝊ
3 Phase = P= 3IᶲVᶲCosꝊ
, R= ρ l/A PS is not equal to PR
VOLTAGE REGULATION – measure of change in the voltage magnitude between the sending and
receiving end of a component.
n-Phase Active Power Formula
P = nVρIρcosꝊ
Where: n = number of phase
Vρ and Iρ = phase voltage and current
cosꝊ = power factor (pf)
3 TRIANGLES
CONNECTION IN 3 – PHASE SYSTEM
1. Wye or Star Connection
2. Delta or Mesh Connection
WYE OR STAR CONNECTED 3-PHASE BALANCED SYSTEM
Ian = Ibn = Icn = Iᶲ = Iρ = phase current
Van = Vbn = Vcn = Vρ = Vᶲ = phase voltages
Vab = Vbc = Vca =VL = line voltages
Ia = Ib = Ic = IL = line currents
IL = Iᶲ
VL = √3 vρ
SUBJECT: ELECTRIC CIRCUITS III
3 PHASE(ᶲ) AC SYSTEM
POLYPHASE – consists of two or more similar 1 phase systems in which the maximum values of the
independent voltage does not occur at the same time.
ADVANTAGES OFPOLYPHASE SYSTEM OVER SIMPLE PHASE SYSTEM
1. Polyphase machines are simpler, cheaper and more efficient.
2. Polyphase transmission lines can deliver more power for a given weight and cost.
3. Voltage regulation of polyphase lines is inherently better.
3 PHASE SYSTEM – interconnection of three 1 phase system whose voltage waves, though similar in
amplitude and frequency are displaced 120 electrical degrees.
PHASE SEQUENCE – order of rotation of the coil voltages in a balanced polyphase system.
Example: If the phase sequence is a-b-c, this means that “vector A” comes first, followed by “B” and “C”
(also known as positive sequence).
NOTE: VECTOR is the reference vector acceleration to the given sequence vector rotation unless
provided/specified assumed to rotate in a counterclockwise direction.
Basis is CURRENT.
×3 if phase is given
√3 if line is given.
1 Phase = P= IᶲVᶲcosꝊ
3 Phase = P= 3IᶲVᶲCosꝊ
, R= ρ l/A PS is not equal to PR
VOLTAGE REGULATION – measure of change in the voltage magnitude between the sending and
receiving end of a component.
n-Phase Active Power Formula
P = nVρIρcosꝊ
Where: n = number of phase
Vρ and Iρ = phase voltage and current
cosꝊ = power factor (pf)
3 TRIANGLES
CONNECTION IN 3 – PHASE SYSTEM
1. Wye or Star Connection
2. Delta or Mesh Connection
WYE OR STAR CONNECTED 3-PHASE BALANCED SYSTEM
Ian = Ibn = Icn = Iᶲ = Iρ = phase current
Van = Vbn = Vcn = Vρ = Vᶲ = phase voltages
Vab = Vbc = Vca =VL = line voltages
Ia = Ib = Ic = IL = line currents
IL = Iᶲ
VL = √3 vρ
