Three Phase System and Power Measurement Method
Phase System: Any system utilising more than one winding is referred as Poly phase system. The system with two winding displaced 90 electrical degree apart is called a Two-phase system. A Three phase system consists of three independent winding displaced by 120 electrical degree from each other. For certain special jobs like Mercury Arc Rectifier, a system with Six or Twelve phase is also used.
eR + eY + eB = 0
Balanced Three Supply System: A three phase supply system is Balanced, when the line to line voltage are equal in magnitude and displaced in phase by 120° with respect to each other. In a Balanced three phase Star connected circuit, the sum of the instantaneous currents in the three-phase is always zero OR the current in the neutral conductor is zero at every instant. In a Balanced three-phase symmetrical Delta connected circuit, the circulating current in the closed delta must always be zero i.e. the sum of the instantaneous values of emf of the three phases should be zero at every instant. In a balanced load the impedance in all the phases are same.
Unbalanced Three Supply System: A three phase supply system is Unbalanced, wen either of the three voltages are unequal in magnitude or the phase angle between them is not equal to 120°. In Unbalanced load the impedance of one or more phases are different from the phases.
Phase Sequence: The order in which the phase voltages of a three phase system attain their peak or maximum positive values is called the Phase Sequence of the system. The phase sequence RYB normally means that the Red phase is followed by Yellow phase, which is followed by the Blue phase. Phase sequence of particular system can be changed by interchanging the connections of any two phases.
Single Phase Motor: The single phase motors used for domestic applications are in fractional horse power rating. These motors are not self starting, unless provided with an extra starting winding. Their efficiency and power factor is quite poor.
Three Phase Motor: A three phase induction motor having three winding on its stator displaced 120 electrical degree from each other is a self starting motor. It has much better efficiency and power factor compared to a single phase motor.
Measurement of Power:
1) One Watt-meter Method: Power in a star connected balanced load with neutral point can be measured by connecting a single watt-meter with its current coil in one line and the pressure coil between the line and the neutral point. The reading of the watt-meter thus connected give the Power per phase. Therefore:
Total Power = 3 x Power per phase = 3 x W1
2) Two Watt-meter Method: Power in a three phase three wire system with balanced or unbalanced load can be measured by using two watt-meter. The load may be Star or Delta connected. Let W1 is the power measured by first watt-meter and W2 is the power measured by second watt-meter.
Total instantaneous Power = W1 + W2
3) Three Watt-meter Method: In case the supply is three phase four wire system then for unbalanced loads the two watt-meter method cannot be used as there is current flowing in the neutral. Let Wr is the power measured by first watt-meter, Wy is the power measured by second watt-meter, and Wb is the power measure by third watt-meter.
Total Power = Wr + Wy + Wb
Reference:
V N Mittle and Arvind Mittal, "Basic Electrical Engineering," TATA McGRAW Hill, Tenth Reprint, 2009.
Author:
Paramjeet Singh Jamwal worked as an Assistant Professor in Electrical and Electronics Engineering Department of Roorkee College of Engineering (RCE), Roorkee, Uttarakhand, India (2017).
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