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Three Phase Circuits Presentation Transcript:
1.Three-phase circuits
2.Introduction
Almost all electric power generation and most of the power transmission in the world is in the form of three-phase AC circuits. A three-phase AC system consists of three-phase generators, transmission lines, and loads.
Major advantage of three-phase systems over a single-phase system:
Power delivered to a three-phase load is constant at all time, instead of pulsing as it does in a single-phase system.
3.Generation of three-phase voltages and currents
4.Each of three-phase generators can be connected to one of three identical loads.
This way the system would consist of three single-phase circuits differing in phase angle by 1200.
The current flowing to each load can be found as
5.Generation of three-phase voltages and currents
6.We can connect the negative (ground) ends of the three single-phase generators and loads together, so they share the common return line (neutral).
7.Such three-phase power systems (equal magnitude, phase differences of 1200, identical loads) are called balanced.
Phase Sequence is the order in which the voltages in the individual phases peak.
8.Such three-phase power systems (equal magnitude, phase differences of 1200, identical loads) are called balanced.
In a balanced system, the neutral is unnecessary!
Phase Sequence is the order in which the voltages in the individual phases peak.
9.Voltages and currents
Each generator and each load can be either Y- or ?-connected. Any number of Y- and ?-connected elements may be mixed in a power system.
Phase quantities - voltages and currents in a given phase.
Line quantities – voltages between the lines and currents in the lines connected to the generators.
10.Voltages and currents
11.Magnitudes of the line-to-line voltages and the line-to-neutral voltages are related as:
In addition, the line voltages are shifted by 300 with respect to the phase voltages.
In a connection with abc sequence, the voltage of a line leads the phase voltage.
12.For the connections with the abc phase sequences, the current of a line lags the corresponding phase current by 300 (see Figure below).
For the connections with the acb phase sequences, the line current leads the corresponding phase current by 300.
13.Analysis of balanced systems
We can determine voltages, currents, and powers at various points in a balanced circuit.
Consider a Y-connected generator and load via three-phase transmission line.
For a balanced Y-connected system, insertion of a neutral does not change the system.
All three phases are identical except of 1200 shift. Therefore, we can analyze a single phase (per-phase circuit).
Limitation: not valid for ?-connections…
14.A ?-connected circuit can be analyzed via the transform of impedances by the Y-? transform. For a balanced load, it states that a ?-connected load consisting of three equal impedances Z is equivalent to a Y-connected load with the impedances Z/3. This equivalence implies that the voltages, currents, and powers supplied to both loads would be the same.
15.Example 3-1:
for a 208-V three-phase ideally balanced system, find:
the magnitude of the line current IL;
The magnitude of the load’s line and phase voltages VLL and V?L;
The real, reactive, and the apparent powers consumed by the load;
The power factor of the load.
Three Phase Circuits Presentation Transcript:
1.Three-phase circuits
2.Introduction
Almost all electric power generation and most of the power transmission in the world is in the form of three-phase AC circuits. A three-phase AC system consists of three-phase generators, transmission lines, and loads.
Major advantage of three-phase systems over a single-phase system:
Power delivered to a three-phase load is constant at all time, instead of pulsing as it does in a single-phase system.
3.Generation of three-phase voltages and currents
4.Each of three-phase generators can be connected to one of three identical loads.
This way the system would consist of three single-phase circuits differing in phase angle by 1200.
The current flowing to each load can be found as
5.Generation of three-phase voltages and currents
6.We can connect the negative (ground) ends of the three single-phase generators and loads together, so they share the common return line (neutral).
7.Such three-phase power systems (equal magnitude, phase differences of 1200, identical loads) are called balanced.
Phase Sequence is the order in which the voltages in the individual phases peak.
8.Such three-phase power systems (equal magnitude, phase differences of 1200, identical loads) are called balanced.
In a balanced system, the neutral is unnecessary!
Phase Sequence is the order in which the voltages in the individual phases peak.
9.Voltages and currents
Each generator and each load can be either Y- or ?-connected. Any number of Y- and ?-connected elements may be mixed in a power system.
Phase quantities - voltages and currents in a given phase.
Line quantities – voltages between the lines and currents in the lines connected to the generators.
10.Voltages and currents
11.Magnitudes of the line-to-line voltages and the line-to-neutral voltages are related as:
In addition, the line voltages are shifted by 300 with respect to the phase voltages.
In a connection with abc sequence, the voltage of a line leads the phase voltage.
12.For the connections with the abc phase sequences, the current of a line lags the corresponding phase current by 300 (see Figure below).
For the connections with the acb phase sequences, the line current leads the corresponding phase current by 300.
13.Analysis of balanced systems
We can determine voltages, currents, and powers at various points in a balanced circuit.
Consider a Y-connected generator and load via three-phase transmission line.
For a balanced Y-connected system, insertion of a neutral does not change the system.
All three phases are identical except of 1200 shift. Therefore, we can analyze a single phase (per-phase circuit).
Limitation: not valid for ?-connections…
14.A ?-connected circuit can be analyzed via the transform of impedances by the Y-? transform. For a balanced load, it states that a ?-connected load consisting of three equal impedances Z is equivalent to a Y-connected load with the impedances Z/3. This equivalence implies that the voltages, currents, and powers supplied to both loads would be the same.
15.Example 3-1:
for a 208-V three-phase ideally balanced system, find:
the magnitude of the line current IL;
The magnitude of the load’s line and phase voltages VLL and V?L;
The real, reactive, and the apparent powers consumed by the load;
The power factor of the load.
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