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# 3-phase circuit

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Engineering review on AC circuit steady state analysis.
Presentation lecture for energy engineering class.
Course: MS in Renewable Energy Engineering, Oregon institute of technology

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### 3-phase circuit

1. 1. Balance Three-Phase Voltages • A three-phase generator consists of a rotating magnet (rotor) surrounded by a stationary winding (stator). A three-phase generator The generated voltages
2. 2. Electricity generation - Hydro • The generation of electric power in the poly-phase mode is accomplished with an electric generator, which converts mechanical energy to electrical energy.
3. 3. Electricity generation – Fossil-fuel
4. 4. Electricity generation - Nuclear
5. 5. Three-Phase Circuit A system produced by a generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120°.
6. 6. Balance Three-Phase Voltages • Two possible configurations: Three-phase voltage sources: (a) Y-connected ; (b) Δ-connected
7. 7. Balance Three-Phase Voltages • Balanced phase voltages are equal in magnitude and are out of phase with each other by 120°. • The phase sequence is the time order in which the voltages pass through their respective maximum values. • A balanced load is one in which the phase impedances are equal in magnitude and in phase
8. 8. Balance Three-Phase Voltages Example 1 Determine the phase sequence of the set of voltages. van 200 cos( t 10 ) vbn 200 cos( t 230 ) vcn 200 cos( t 110 )
9. 9. Balance Three-Phase Voltages Solution: The voltages can be expressed in phasor form as Van 200 10 V Vbn 200 230 V Vcn 200 110 V We notice that Van leads Vcn by 120° and Vcn in turn leads Vbn by 120°. Hence, we have an acb sequence.
10. 10. Balance Three-Phase Connection • Four possible connections 1. Y-Y connection (Y-connected source with a Y-connected load) 2. Y-Δ connection (Y-connected source with a Δ-connected load) 3. Δ-Δ connection 4. Δ-Y connection
11. 11. Balance Three-Phase Connection • A balanced Y-Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load. VL 3V p , where Vp Van Vbn Vcn VL Vab Vbc Vca
12. 12. Balance Three-Phase Connection • A balanced Y-Δ system is a three-phase system with a balanced y-connected source and a balanced Δ-connected load. IL 3I p , where IL Ia Ip I AB Ib I BC Ic ICA
13. 13. Balance Three-Phase Connection • A balanced Δ-Δ system is a three-phase system with a balanced Δ -connected source and a balanced Δ -connected load.
14. 14. Balance Three-Phase Connection • A balanced Δ-Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load.
15. 15. Power in a balanced System • Comparing the power loss in (a) a single-phase system, and (b) a three-phase system
16. 16. If same power loss is tolerated in both system, three-phase system use only 75% of materials of a single-phase system
17. 17. Application – Residential Wiring A 120/240 household power system A typical wiring diagram of a room
18. 18. Application – Residential Wiring Single-phase three-wire residential wiring
19. 19. Since this value is well below the rated value of 170 A rms, the conductor is sized properly and we can safely add the third store.