* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture_AC_Circuits
Audio power wikipedia , lookup
Mercury-arc valve wikipedia , lookup
Pulse-width modulation wikipedia , lookup
Current source wikipedia , lookup
Power inverter wikipedia , lookup
Ground (electricity) wikipedia , lookup
Power factor wikipedia , lookup
Opto-isolator wikipedia , lookup
Electrification wikipedia , lookup
Variable-frequency drive wikipedia , lookup
Earthing system wikipedia , lookup
Buck converter wikipedia , lookup
Electric power transmission wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Stray voltage wikipedia , lookup
Single-wire earth return wikipedia , lookup
Electric power system wikipedia , lookup
Voltage optimisation wikipedia , lookup
Electrical substation wikipedia , lookup
Amtrak's 25 Hz traction power system wikipedia , lookup
Power electronics wikipedia , lookup
Electrical wiring in the United Kingdom wikipedia , lookup
Power engineering wikipedia , lookup
History of electric power transmission wikipedia , lookup
Mains electricity wikipedia , lookup
Three-Phase AC Circuits Appendix: A (p.681) Significant Features of Three-Phase AC Circuits • Almost all ac power generation and transmission is in the form of threephase ac circuits • AC power systems have a great advantage over DC systems in that their voltage levels can be changed with transformers to reduce transmission losses. • Three-phase (3f) ac power system consists of – 3f ac generators – 3f transmission lines – 3f loads • Advantages of having 3f power systems over 1f ones: – More power per pound of metal of electrical machines of 3f. – Power delivered to a 3f load is constant, instead of pulsating as it does in a 1f system. Generation of 3f Voltages and Currents A 3f generator consists of three 1f generators: - voltage of all phases are equal in amagnitude - differing in phase angle from each aother by 120o. Three-Phases of the Generator Connected to Three identical Loads VC VA VB Phasor diagram showing the voltages in each phase Currents in the Three Phases and the Neutral Currents flowing in the three phases V0 0 Ia I Z V 120 0 Ib I 120 0 Z V 240 0 Ic I 240 0 Z It is possible to connect the negative ends of these three single phase generators and the loads together, so that they share a common return line, called neutral. I N Ia Ib Ic I I 1200 I 2400 cos j sin cos 1200 j sin 1200 I cos 2400 j sin 2400 0 As long as the three loads are equal, the return current in the neutral is zero. Balanced Power Systems • In a balanced power system: – Three generators have same voltage magnitude and phase difference is 120o. – Three loads are equal and magnitude and angle. • abc phase sequence: the voltages in the three phases peak in the order a, b and c. It is possible to have acb phase sequence. Y and Connections Ib + Va A connection of this sort is called Wye-connection. - Ia + Vb - - Z In Z Z Vc + Ic Ia Va + Another possible connection is delta-connection, in which the generators are connected head to tail. - - Vb Z + - + Z Z Ib Vc Ic Voltages and Currents in a Y-Connected 3f Circuit Phase quantities: voltages and currents in a given phase Line quantities: voltages between lines and current in the lines + If + Van - + V bc Vbn - n + - Ib Vab + - Ia (=IL) Resistive Load Vca Vcn - + Ic Van Vf 0 0 I a I f 0 0 Vbn Vf 120 0 I b I f 120 0 Vcn Vf 120 0 I c I f 240 0 Vab Van Vbn Vf00 Vf 1200 3Vf300 Voltages and Currents in a Y-Connected 3f Circuit (cont’d) The relationship between the magnitude of the line-to-line voltage and the line-to-neutral (phase) voltage in a Y-connected generator or load VLL 3Vf In a Y-connected generator or load, the current in any line is the same as the current in the corresponding phase. I L If Vcn Vab Vca Van Vbn Vbc Voltages and Currents in a -Connected 3f Circuit Iab In a delta-connected generator or load, the line-to-line voltage between any two lines will be the same as the voltage in the corresponding phase. VA + I a - VLL Vf - VB Ib + Ic + VC Ibc Ica In a delta-connected generator or load, the relationship between the magnitudes of the line and phase currents: Ic Ica I L 3I f Iab Ib Ibc Ia Power Relationship in 3f Circuits The 3f voltages applied to this load: van t 2V sint 2V sint 2400 vbn t 2V sin t 1200 vcn t The 3f currents flowing in this load: ia t 2 I sint 2 I sint 2400 ib t 2 I sin t 1200 ic t A balanced Y-connected load. Instantaneous power supplied to each of the three phases: Pa t van t ia t 2VI sint sint VI cos cos2t Pc t vcn t ic t 2VI sint 2400 sint 2400 VI cos cos2t 4800 Pb t vbn t ib t 2VI sin t 1200 sin t 1200 VI cos cos 2t 2400 Total power supplied to the 3f load: Ptotal t P3f Pa t Pa t Pa t 3VI cos 3 P1f 3f Power Equations Involving Phase Quantities The 1f power equations: S1f Vf I f P1f Vf I f cos Q1f Vf I f sin The 3f power equations: S3f 3Vf I f P3f 3Vf I f cos Q3f 3Vf I f sin S Q=Ssin 90o P=Scos 3f Power Equations Involving Line Quantities For a Y-connected load: I L If and VLL 3Vf V P3f 3Vf I f cos 3 LL I L cos 3VLL I L cos 3 For a delta-connected load: I L 3If and VLL Vf 90o IL P3f 3Vf I f cos 3VLL cos 3VLL I L cos 3 Therefore, regardless of the connection of the load: P3f 3VLL I L cos Q3f 3VLL I L sin S3f 3VLL I L Analysis of Balanced 3f Systems If a three-phase power system is balanced, it is possible to determine voltages and currents at various points in the circuit with a per phase equivalent circuit. • Neutral wire can be inserted, as no current would be flowing through it, thus, system is not affected. • Three phases are identical except for 120o phase shift for each phases. • It is thus possible to analyze circuit consists of one phase and neutral. • Results would be valid for other two phases as well if 120o phase shift is included. Wye-Delta Transformation • Above analysis if OK for Y-connected sources and loads, but no neutral can be connected for delta-connected sources and loads. • As a result, the standard approach is to transform the impedances by using the delta-wye transform of elementary circuit theory.