EE212 Passive AC Circuits

1. EE212 Passive AC Circuits Lecture Notes 5a Three Phase Systems EE 212 2010-2011

2. Three Phase Systems EE 212 2010-2011

3. Three Phase Systems Bulk power generation and transmission systems are three-phase (3-f) systems. Generation and transmission of electrical power are more efficient in 3-f systems than in 1-f systems. • Generation: • steady power (1-f power is fluctuating) • more efficient conversion of mechanical power to electrical power (3 times power with additional armature windings and slightly more torque) • Transmission: • More efficient transmission of power (steady power) • less conducting material required to transmit power (delta transmission – no return conductor) • 3-f transformers are more efficient EE 212 2010-2011

4. 2SinA.SinB = Cos(A-B) - Cos(A+B) p(t) = cos θ – cos(2wt-θ) Single Phase Power Fluctuates with Time i(t) v(t) = Vmsin wt volts i(t) = Imsin(wt-θ) amperes v(t) Instantaneous Power, p(t) = v(t) x i(t) p(t) = Vmsin wt . Imsin(wt-θ) 1st term is constant (equal to the average or real power) 2nd term is sinusoidal at twice the excitation frequency. EE 212 2010-2011

5. Three Phase Systems Three phase power does not vary with time. Consumption: 3-f machines start and run more efficiently. Industrial loads, larger motors require 3- fsupply. Most lighting loads, heating loads and small motors require 1-fsupply. EE 212 2010-2011

6. N S 1-f Power Generation: 3-f Power Generation: Phase Sequence is a-b-c Phase Sequence: the order in which the voltages of the individual phases reach their maximum values EE 212 2010-2011

7. Va = /00 Vb = /-1200 /1200 Vc = Vc 1200 Va -1200 Vb Voltages in the three phases (1200 out of phase): Phase a va = Vm sin wt Phase b vb = Vm sin (wt – 1200) Phase c vc = Vm sin (wt – 2400) = Vm sin (wt + 1200) In Phasor Form, 3 Phases: a-b-c, R-Y-B, L1-L2-L3 EE 212 2010-2011

8. Types of Three Phase Systems • Balanced Systems: • - 3 phases (V & I) are equal in magnitude and 1200 out of phase • Unbalanced Systems: • 3 phases (V or I) are unequal in magnitude EE 212 2010-2011

9. Types of Three Phase Systems (continued) Three Phase Systems are connected either in: - Y (wye or star) connection (3 phase 3 wire, or 3 phase 4 wire) - D (delta) connection EE 212 2010-2011

10. Line and Phase Parameters Y (wye or star) connection (3 phase 3 or 4 wire) D (delta) connection Phase parameters usually not easily accessible EE 212 2010-2011

11. B a b A Za Zb n Zc c C Vca Vcn Vab -Vbn 300 Van Vbn Vbc Balanced Y System Phase voltages, Vp: |Van| = |Vbn| = |Vcn| Phase currents, Ip: |I an| = |I bn| = |I cn| Phase sequence a-b-c Vab= Van + Vnb= Van– Vbn EE 212 2010-2011

12. a A Zab Zca Zbc c b C B Ic Ica Iab 300 Ibc Ia -Ica Ib BalancedD System Phase voltages, Vp: |Vab| = |Vbc| = |Vca| Phase currents, Ip: |I ab| = |I bc| = |I ca| Line voltages, VL: |Vab| = |Vbc| = |Vca| Line currents, IL: |I a| = |I b| = |I c| Phase sequence a-b-c Ia = Iab + Iac= Iab - Ica From phasor diagram: cos 300 = (½|Ia|) / |Iab|= 3/2 i.e. |Ia| = 3 |Iab| andIa lags Iab by 300 Vline = Vphase|Iline| = 3 |Iphase| EE 212 2010-2011

13. Balanced 3-Phase Systems Y |VL| = 3 |Vph|, IL = Iph, Vab(line) leads Van(ph) by 300 D VL = Vph, |IL| = 3 |Iph|, Ia(line) lags Iab(ph) by 300 Power Factor of a 3-f load cos  where,  is the angle between the phase current and the phase voltage 3-phase power = 3 x Per phase power P (3- f) = 3 |Vph|.|Iph|. cos  = 3.|VL|.|IL|. cos  Q (3- f) = 3 |Vph|.|Iph|.sin  = 3.|VL|. |IL|. sin  S (3- f) = 3 |Vph|.|Iph| = 3.|VL|. |IL|) EE 212 2010-2011