Star Connection & Delta Connection
Star Connection (Y): Three Phase Power, Voltage & Current Values
Three Phase Star Connection: Line, Phase Current, Voltages & Power in Y Configuration
Table of Contents
1. What is Star Connection (Y)?
2. Voltage, Current and Power Values in Star Connection (Y) ? ? ?
2.1 Line Voltages and Phase Voltages in Star Connection ? ? ?
2.2 Line Currents and Phase Currents in Star Connection ? ? ?
2.3 Power in Star Connection
What is Star Connection (Y)?
Star Connection (Y) System is also known as Three Phase Four Wire System (3-Phase 4 Wire) and it is the most preferred system for AC power distribution while for transmission, Delta connection is generally used.
In Star (also denoted by Y) system of interconnection, the starting ends or finishing ends (similiar ends) of three coils are connected together to form the neutral point. Or
Star Connection is obtained by connecting together similar ends of the three coils, either "Starting" or "Finishing". The other ends are joined to the line wires. The common point is called the neutral or Star Point, which is represented by N. (As shown in fig 1)
Star Connection is also called Three Phase 4 Wires (3-Phase, 4-Wires) system.
Also Read:
Delta Connection (): 3 Phase Power, Voltage & Current Values https://www.electricaltechnology.org/2014/09/delta-connection-power-voltage-current.html
Difference Between Star (Y) and Delta () Connections https://www.electricaltechnology.org/2014/09/comparison-between-star-and-delta-connections.html#google_vignette
If?a balance symmetrical load is connected across three phase voltage system in parallel, then the three currents will flow in neutral wire which quantities would be same, but they would be differ by 120°?(out of phase), hence the vector sum of these three currents = 0.i.e.
IR?+ IY?+ IB?= 0?? ……………. Victorially
The voltage between any two terminals or voltage between Line and Neutral (Star Point) is called Phase voltage or Star voltage denoted by?VPh. And the voltage between two Lines is called Line to Line Voltage or Line Voltage denoted by?VL.
?Star Connection (Y) Three Phase Power, Voltage & Current Values
?Voltage, Current and Power Values in Star Connection (Y)
Now we will find the values of Line current, Line Voltage, Phase Current, Phase Voltage and Power in three phase Star AC system.
Line Voltages and Phase Voltages in Star Connnection
We know that the Line Voltage between Line 1 and Line 2 (from fig 3a) is ?
VRY?= VR?– VY?…. (Vector Difference)
Thus, to find vector of?VY, increase the Vector of? in reverse direction as shown in the dotted form in the below fig 2. Similarly, on the both ends of vector?VR?and Vector?VY, make perpendicular (垂直的、直立的) dotted lines which look like a parallelogram (平行四边形)?as shown in fig(2). The Diagonal line which divides the parallelogram into two parts, showing the value of?VRY. The angle between?VY?and?VR?vectors is 60°.
Hence, if VR?= VY?= VB?= VPH
then VRY?= 2 x VPH?x Cos (60°/2)
? ? ? ?= 2 x VPH?x Cos 30° ? ? ? ?
= 2 x VPH?x (√3/2) …… Since Cos 30° = √3/2 VRY?= √3 VPH Similarly,
VYB?= VY?– VB
VYB?= √3 VPH
And
VBR?= VB?– VR
VBR?= √3 VPH
Hence, it is proved that?VRY?= VYB?= VBR?is line voltages (VL) in Star Connection, Therefor, in Star Connection:
VL?= √3 VPH?or VL?= √3 EPH
Line Voltages and Phase Voltages in Star Connection
It is seen from the fig 2 that:
* Line voltages are 120°?apart from each other
* Line voltages are 30°?leading from the corresponding phase voltages
* The eange? ?between line currents and respective line voltages are (30°+Ф), i.e. each line current is lagging (30°+Ф) from the corresponding line voltage.
Related Post: Star and Delta Connected Lighting Loads https://www.electricaltechnology.org/2014/09/star-and-delta-connected-lighting-loads.html
Line Currents and Phase Currents in Star Connection
It is see from below that each line is in series with indiviual phase winding, therefore, the value of line current is same as in Phase windings to which the line is connected.
i.e:
*Current in Line 1 =?IR
*Current in Line 2 =?IY
* Current in Line 3 =?IB
Since, the flowing currents in all three lines are same, and the individual current in each line is equal to the corresponding phase current, therefore:
IR?= IY?= IB?= IPH?…. The phase current
Line Current = Phase Current
IL?= IPH
In simple words, the value of Line Currents and Phase Currents are same in Star Connection. ?
Star Connection (Y): Values of Line Currents & Voltages and Phase Currents & Voltages
Also read:
Three Phase Current Values in a 3-Phase System https://www.electricaltechnology.org/2014/09/three-phase-current-values.html
Power in Star Connection In a three phase AC circuit, the total True or Active power is the sum of the three phase power. Or the sum of the all three phase powers is the total Active or True Power (https://www.electricaltechnology.org/2013/07/active-reactive-apparent-and-complex.html).
Hence, total active or true power in a three phase AC system,
Total True or Active Power = 3 Phase Power
Or
P = 3 x VPH x?IPH?x CosФ???????????????????? ….. Eq ? … (1)
We know that the values of Phase Current and Phase Voltage in Star Connection,
IL?= IPH
VPH?= VL?/√3???? ….. (From?VL?= √3 VPH)
Putting these values in power equ..... (1)
P = 3 x (VL/√3) x IL?x CosФ ?????…….…. ?????(VPH?= VL?/√3)
P = √3 x√3 x (VL/√3) x IL?x CosФ ???….…?? {3 = √3x√3}
P = √3 x VL?x IL?x CosФ
Hence proved,
Power in Star Connection,
P = 3 x VPH x?IPH?x CosФ or
P = √3 x VL?x IL?x CosФ
The same is explained in 3-Phase Circuit MCQs with explanatory Answer (MCQs No. 1)
Similarly,
Total Reactive Power =?Q = √3 x VL?x IL?x SinФ
Where?Cos Φ = Power factor?= the phase angle between Phase Voltage and Phase Current and not between Line current and Line voltage.
Good to Know: Reactive Power (https://www.electricaltechnology.org/2016/05/importance-of-reactive-power.html) of Inductive coil is taken as Positive (+) and that of a Capacitor as Negative (-).
Also, the total apparent power of the three phases,
Total Apparent Power =?S = √3 x VL?x IL?Or,
S = √ (P2?+ Q2)
Also Read:
Introduction to Series, Parallel and Series-Paralle Connections Series, Parallel and Series-Parallel Connection of Batteries Three Phase Motor Connection STAR/DELTA Without Timer. Power & Control Diagrams Star Delta 3-phase Motor Automatic starter with Timer
Delta Connection (Δ): 3 Phase Power, Voltage & Current Values
Three Phase Delta Connection: Line, Phase Current, Voltages & Power in?Δ?Configuration
1. What is Delta Connection (Δ) ?
2. Voltage, Current and Power Values in Delta Connection (Δ)
领英推荐
2.1. Line Voltages (VL) and Phase Voltage (VPh) in Delta Connection 2.2. Line Currents (IL) and Phase Currents (IPh) in Delta Connection ? 2.3. Power in Delta Connection
What is Delta Connection (Δ)?
Delta or Mesh Connection (Δ) System is also known as Three Phase Three Wire System (3-Phase 3 Wire) and it is the most preferred system for AC power transmission while for distribution, Star connection is generally used.
In Delta (also denoted by?Δ) system of interconnection, the starting ends of the three phases or coils are connected to the finishing ends of the coil. Or the starting end of the first coil is connected to the finishing end of the second coil and so on (for all three coils) and it looks like a closed mesh or circuit as shown in?fig (1).
In more clear words, all three coils are connected in series to form a close mesh or circuit. Three wires are taken out from three junctions and the all outgoing currents from junction assumed to be positive.
In Delta connection, the three windings interconnection looks like a short circuit, but this is not true, if the system is balanced, then the value of the algebraic sum of all voltages around the mesh is zero in Delta connection.
When a terminal is open in Δ, then there is no chance of flowing currents with basic frequency around the closed mesh.
Also Read:
*Star Connection (Y): Three Phase Power, Voltage & Current Values https://www.electricaltechnology.org/2014/09/star-connection-power-voltage-current.html
*Difference between Star (Y) and Delta (Δ) Connections https://www.electricaltechnology.org/2014/09/comparison-between-star-and-delta-connections.html
Good to?Remember: In Delta configuration, at any instant, the EMF value of one phase is equal to the resultant of the other two phases EMF values but in the opposite direction. ?
Fig (1). 3 Phase Power, Voltage & Current Values in Delta Connection (Δ)
Voltage, Current and Power Values in Delta Connection (Δ)
Now we will find the values of Line current, Line Voltage, Phase Current, Phase Voltages and Power in three phase Delta AC system.
Line Voltages (VL) and Phase Voltages (VPh) in Delta Connection
It is seen in fig 2 that there is only one phase winding between two terminals (i.e. there is one phase winding between two wires). Therefore, in Delta Connection, the voltage between (any pair of) two lines is equal to the phase voltage of the phase winding which is connected between two lines.
Since the phase sequence is R?→?Y?→?B, therefore, the direction of voltage from R phase towards Y phase is positive (+), and the voltage of R phase is leading by 120°?from Y phase voltage. Likewise, the voltage of Y phase is leading by 120°?from the phase voltage of B and its direction is positive from Y towards B.
If the line voltage between:
*Line 1 and Line 2 =?VRY
*Line 2 and Line 3 =?VYB
* Line 3 and Line 1 =?VBR
Then, we see that?VRY?leads?VYB?by 120°?and?VYB?leads?VBR?by 120°.
Let's suppose:
VRY?= VYB?= VBR?= VL?? …………… (Line Voltage)
Then?
VL?= VPH
I.e. in Delta connection, the Line Voltage is equal to the Phase Voltage.
* Also read: Three Phase Current Values in a 3-Phase System https://www.electricaltechnology.org/2014/09/three-phase-current-values.html
Line Currents (IL) and Phase Currents (IPh) in Delta Connection
It will be noted from the below figure that the total current of each Line is equal to the vector difference between two phase currents in Delta connection flowing through that line i.e.:
*Current in Line 1 =?I1?= IR?– IB
*Current in Line 2 =?I2?= IY?– IR?
* Current in Line 3 =?I3?= IB?– IY
Vector Difference ?
?
Figure. Line & Phase Current and Line & Phase Voltage in Delta (Δ) Connection
The current of Line 1 can be found by determining the vector difference between?IR?and?IR?and we can do that by increasing the?IB?Vector in?reverse, so that,?IR?and?IB?makes a parallelogram. The diagonal of that parallelogram shows the vector difference of?IR?and?IB?which is equal to current in Line 1 =?I1. Moreover, by reversing the vector of?IB, it may indicate as (-IB), therefore, the angle between?IR?and?IB??(IB, when reversed =?-IB) is 60°.
If,
IR?= IY?= IB?= IPH?…. The phase currents
Then;
The current flowing in Line 1 would be:
IL?or I1?= 2 x IPH?x Cos (60°/2) ?? ? ? ? ? ?
=?2 x IPH?x Cos 30° ? ? ? ? ? ?
=?2 x IPH?x (√3/2) …… Since Cos 30° = √3/2
IL= √3 IPH?
I.e. In Delta Connection, The Line current is?√3?times of Phase Current.
Similarly, we can find the reaming two Line currents as same as above i.e.,
I2?= IY?– IR?… Vector Difference = √3 IPH
I3?= IB?– IY?… Vector difference = √3 IPH
As, all the Line current are equal in magnitude i.e.
I1?= I2?= I3?= IL
Hence ?
IL?= √3 IPH
It is seen from the fig above that,
*The Line Currents are 120 apart from each other
*Line currents are lagging by 30 from their corresponding Phase Currents
*The angle?Ф?between line currents and respective line voltages is (30°+Ф), i.e. each Line current is lagging by (30°+Ф) from the corresponding line voltage.
Power in Delta Connection
We know that the power of each phase:
Power / Phase = VPH x?IPH?x CosФ
And the total power of three phases: \
Total Power = P = 3 x VPH x?IPH?x CosФ?….. (1)
We know that the values of Phase Current and Phase Voltage in Delta Connection:
IPH?= IL?/√3?? ….. (From IL?= √3 IPH)
VPH?= VL??
Putting these values in power eq...... (1)
P = 3 x VL?x ( IL/√3) x CosФ …… (IPH?= IL?/ /√3)
P = √3 x√3 x VL?x ( IL/√3) x CosФ …{ 3 = √3x√3 }
P = √3 x VLx IL?x CosФ?? …
Hence proved:
Power in Delta Connection,
P = 3 x VPH?x?IPH?x?CosФ?…. or
P = √3 x VL?x IL?x CosФ
Where?Cos Φ = Power factor?= the phase angle between Phase Voltage and Phase Current (not between Line current and line voltage).
The same is explained in 3-Phase Circuit MCQs with explanatory Answer (MCQs No. 1)
Good to Remember:
In both Star and Delta Connections, The total power on balanced load is same.
I.e. total power in a Three Phase System =?P = √3 x VL?x IL?x CosФ
Good to know:
Balanced System is a system where:
*All three phase voltages are equal in magnitude
*All phase voltages are in phase by each other i.e.?360°/3 = 120°
*All three phase Currents are equal in magnitude
*All phase Currents are in phase by each other i.e.?360°/3 = 120°
*A three phase balanced load is a system in which the load connected across three phases are identical.
Delta Connection (Δ): 3 Phase Power, Voltage & Current Values