Electric Power Systems 2: Generators, Three-phase Power, and Power Electronics, Lecture notes of Electrical Engineering

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15-830 – Electric Power Systems 2:

Generators, Three-phase Power,

and Power Electronics

J. Zico Kolter

October 9, 2012

Generators

• Basic AC Generator

Loop of Wire

Rotating Magnet

• Rotor - rotating element
• Stator - stationary element on the outside
• Armature - wires carrying the current (could be either in rotor or stator, but typically stator)
• Synchronous generator - generator moves “in sync” with power in grid - I.e., for U.S. AC power, generator spins at 60Hz = 3600 RPM (in practice, can have multiple poles in rotor magnet, allows for slower rotation)

• In practice, typically use electromagnet instead of permanent magnet in the rotor

• Needs a DC current source to create magnet (exciter), can come from seperate generator or from grid
• By increasing/decreasing exciter current, we change strength of magnet, which varies generator voltage
• Also, increase number of windings in armature, increases voltage (by fixed ratio)

• What causes “force” on rotor?

Armature Current

Induced Magnetic Field

Armature current itself creates magnetic field opposing rotor revolution, requires force to overcome

• Indirectly control reactive power via voltage

Vr = Vs

R

R + jωL

• Voltage across resistor is decreased by adding inductor
• To maintain real power, we need to increase voltage
• Effectively, generator “supplies” reactive power by increasing voltage

0 0.5 1 1.5 2 −

−0.

0

1

t/ω

Phase A Phase B Phase C

• Why three phase power?
• Hypothetical setup

Need six wires

• Can derive this from trignonometric identities, but easy to see using complex representation

• Because of this, we can bring line together and form a single “neutral” return line

Need four wires

• Attaching three wires in this manner known as a “wye” connection

(optional)Ground

A B

C

• Another common possibility is the “delta” connection, also a way of attaching loads with only three lines A B

C

• Delta connection is directly connecting two different phases together, not obvious that this produces correct current in loads
• Delta connector scales observed voltages by

• Power for three phases

(^00) 0.5 1 1.5 2

t/ω

pA(t) pB(t) pC(t)

• Three sine waves 120 degrees out of phase, add to a constant number - Mechanically, this means the generator rotor experiences constant force throughout its revolution
• True for any number of phases ≥ 3?

Power Electronics

• Equipment that converts AC-DC voltage/current or AC-AC, DC-DC (but changes voltage) AC - AC Transformer (not called power electronics) AC - DC Rectifier DC - AC Inverter DC - DC Buck/Boost Converters