Three phase-circuits
28 likes18,591 views
The document discusses three-phase circuits and provides information on: - The advantages of three-phase supply systems such as higher efficiency of power transfer and smoother load characteristics. - Key concepts like phase sequence, balanced/unbalanced supply and load, and the relationships between line and phase voltages and currents. - How to calculate power in a balanced three-phase system and use two wattmeters to measure total power and power factor.
![Two Wattmeter Method to Measure 3-phase Power
The reading of wattmeter W1 is given by
P1 = |VAB|×|IA|×cos(φ +30◦
) = |V||I|cos(30◦
+φ) (1)
where |V| and |I| are the line voltage and current respectively.
The reading of wattmeter W2 is
P2 = |VCB|×|IC|×cos(30◦
−φ) = |V||I|cos(30◦
−φ) (2)
So, the sum of the two wattmeter readings is
P1 +P2 = |V|·|I|·[cos(30◦
+φ)+cos(30◦
−φ)]
= 2|V|·|I|·cos30◦
cosφ
=
√
3|V|·|I|·cosφ (3)
which is nothing but the total three-phase active power.
R S Ananda Murthy Three-phase Circuits](https://image.slidesharecdn.com/three-phase-circuits-160430042313/85/Three-phase-circuits-17-320.jpg)
![Finding Power Factor from Two Wattmeter Readings
We can also write
P1 −P2 = |V|·|I|·[cos(30◦
+φ)−cos(30◦
−φ)]
= −2|V|·|I|·sin30◦
sinφ
= −|V|·|I|·sinφ (4)
Dividing Eq.(4) by Eq. (3) we get
P1 −P2
P1 +P2
=
−tanφ
√
3
=⇒ φ = tan−1
√
3(P2 −P1)
P1 +P2
(5)
from this the load power factor cosφ of the load can be found.
But the above equation can be applied only to balanced load.
R S Ananda Murthy Three-phase Circuits](https://image.slidesharecdn.com/three-phase-circuits-160430042313/85/Three-phase-circuits-18-320.jpg)
Three phase-circuits
- 1. Three-phase Circuits Workshop on Basic Electrical Engineering held at VVCE, Mysuru, on 30-April-2016 R S Ananda Murthy Associate Professor Department of Electrical & Electronics Engineering, Sri Jayachamarajendra College of Engineering, Mysore 570 006 R S Ananda Murthy Three-phase Circuits
- 2. Learning Outcomes After completing this lecture the student should be able to – State the advantages of three-phase supply. State the meaning of phase sequence, balanced supply, balanced load, and balanced system. Derive the relationship between line and phase values of voltages and currents in a balanced system. Derive equation for the power consumed by a three-phase balanced load. Show that power in a three-phase three-wire system can be measured using two wattmeters. Find the power factor of a balanced three-phase load using two wattmeter readings. R S Ananda Murthy Three-phase Circuits
- 3. Advantages of Three-phase Supply The amount of conducting material required to transfer a given amount of power is minimum in a three-phase system. The instantaneous power in a three-phase system never falls to zero resulting in smoother and better operating characteristics of the load. Three-phase supply is required by three-phase induction motors which are widely used in industry because of their ruggedness, longer life, higher torque, low initial and maintenance costs. R S Ananda Murthy Three-phase Circuits
- 4. Advantages of Three-phase Supply Domestic as well as industrial and commercial power can be supplied from the same three-phase distribution system. Three-phase system has better voltage regulation. For a given size of the machine, the power generated by a three-phase alternator is higher. R S Ananda Murthy Three-phase Circuits
- 5. Generation of Three-phase Supply NS A1 A2 C2 Stator C1 B1 B2 vA = Vm sinωt =⇒ VA = |Vph|∠0◦ vB = Vm sin(ωt −120◦ ) =⇒ VB = |Vph|∠−120◦ vC = Vm sin(ωt −240◦ ) =⇒ VB = |Vph|∠−240◦ R S Ananda Murthy Three-phase Circuits
- 6. Meaning of Phase Sequence ABC Sequence ACB Sequence Phase sequence can be changed by reversing the direction of rotation of rotor of the alternator. R S Ananda Murthy Three-phase Circuits
- 7. Meaning of Balanced and Unbalanced Supply (a) (b) (c) (d) If |VA| = |VB| = |VC| = |Vph| and if the phase difference between VA and VB, VB and VC, VC and VA is equal to 120◦ as shown in (a) then, the supply is said to be balanced or symmetrical. Phasor diagrams (b), (c), and (d) represent unbalanced supply. Can you explain why? R S Ananda Murthy Three-phase Circuits
- 8. Meaning of Balanced/Unbalanced Load and System If the three impedances, which may be Y or ∆ connected are equal, then, the three-phase load is said to be balanced. If load and supply are both balanced, then three-phase system is said to be balanced. Under normal working conditions, a three-phase system can be taken to be balanced. R S Ananda Murthy Three-phase Circuits
- 9. Relation between Line and Phase Voltages ABC Sequence If supply is balanced, then, line voltage magnitudes will be |VAB| = |VBC| = |VCA| = √ 3|Vph| = |V|. When phase sequence is ABC, VAB leads VAN by 30◦, VBC leads VBN by 30◦, and VCA leads VCN by 30◦. R S Ananda Murthy Three-phase Circuits
- 10. Relation between Line and Phase Voltages If supply is balanced, then, line voltage magnitudes will be |VAB| = |VBC| = |VCA| = √ 3|Vph| = |V|. When phase sequence is ACB, VAB lags VAN by 30◦, VBC lags VBN by 30◦, and VCA lags VCN by 30◦. R S Ananda Murthy Three-phase Circuits
- 11. Line and Phase Currents in Three-phase Circuits Star Point Line Current Current flowing through each impedance is called phase current Current flowing through each suppy line is called line current Load can be Y or delta connected as shown above R S Ananda Murthy Three-phase Circuits
- 12. Relation between Line and Phase Currents In Y-connected load, the line current is equal to the phase current. From the phasor diagram given in the previous slide, it is clear that |IA| = 2|IAB|cos30◦ = √ 3·|IAB| = √ 3· |V| |Z| = |IB| = |IC| = |I| i.e., in a balanced ∆-connected three-phase load, the line current is √ 3×|Iph| where |Iph| = |V|/|Z|. R S Ananda Murthy Three-phase Circuits
- 13. Zero Neutral Shift Voltage in Balanced System A C B Balanced Supply Balanced Load Neutral Shift Voltage It can be shown that in a balanced system the neutral shift voltage is zero so that VAN = VAN , VBN = VBN , and VCN = VCN . R S Ananda Murthy Three-phase Circuits
- 14. Power in Balanced System A B C Balanced Three-phase Supply Total power consumed by the load is P = 3Pph = 3|Vph|·|Iph|cosφ = √ 3· √ 3|Vph|·|Iph|cosφ But √ 3|Vph| = |V| and |Iph| = |I| in a Y-connected load and ∆-connected load can always be replaced by equivalent Y. So, P = √ 3·|V|·|I|·cosφ R S Ananda Murthy Three-phase Circuits
- 15. Two Wattmeter Method to Measure 3-phase Power M L M L COM COM V V Y or Delta Connected Three-phase Balanced Load A B C N Balanced Supply Wattmeter has current coil with terminals marked as M and L, and voltage coil terminals marked as COM and V. R S Ananda Murthy Three-phase Circuits
- 16. Two Wattmeter Method to Measure 3-phase Power R S Ananda Murthy Three-phase Circuits
- 17. Two Wattmeter Method to Measure 3-phase Power The reading of wattmeter W1 is given by P1 = |VAB|×|IA|×cos(φ +30◦ ) = |V||I|cos(30◦ +φ) (1) where |V| and |I| are the line voltage and current respectively. The reading of wattmeter W2 is P2 = |VCB|×|IC|×cos(30◦ −φ) = |V||I|cos(30◦ −φ) (2) So, the sum of the two wattmeter readings is P1 +P2 = |V|·|I|·[cos(30◦ +φ)+cos(30◦ −φ)] = 2|V|·|I|·cos30◦ cosφ = √ 3|V|·|I|·cosφ (3) which is nothing but the total three-phase active power. R S Ananda Murthy Three-phase Circuits
- 18. Finding Power Factor from Two Wattmeter Readings We can also write P1 −P2 = |V|·|I|·[cos(30◦ +φ)−cos(30◦ −φ)] = −2|V|·|I|·sin30◦ sinφ = −|V|·|I|·sinφ (4) Dividing Eq.(4) by Eq. (3) we get P1 −P2 P1 +P2 = −tanφ √ 3 =⇒ φ = tan−1 √ 3(P2 −P1) P1 +P2 (5) from this the load power factor cosφ of the load can be found. But the above equation can be applied only to balanced load. R S Ananda Murthy Three-phase Circuits
- 19. License This work is licensed under a Creative Commons Attribution 4.0 International License. R S Ananda Murthy Three-phase Circuits