Why are the transmission lines high-voltage, three-phase and AC? Three-Phase Circuits Why are the transmission lines high-voltage, three-phase and AC? High-Voltage Three-Phase Alternative Current Average power loss in a transmission line with impedance : the transmitted power: The loss of average power can be written as: The loss can be reduced by using a very high voltage amplitude . Under a balanced load, the torque on the generator does not fluctuate much. Therefore the vibration on the generator is less. It is easy to change the voltage value by transformers. Transformers are very efficient in 60 Hz, and require almost no maintenance. Cheap induction motors can be made which use three-phase directly . Easier to produce than DC. Under the balanced load assumption, one can reduce the number of lines, therefore three-phase is more economical.

Three-phase Generator Rotor- A magnet Stator- with three wires : aa’, bb’, cc’ The wire aa’ is the same as bb’ except the angle shift of Magnetic Flux for different phases : aa’: bb’: cc’: , constant L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits” Mc.Graw Hill, 1987, New York

Rotor is rotating with constant angular frequency: Magnetic Fluxes Voltages Phasors of voltages: L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits” Mc.Graw Hill, 1987, New York

Power System Under Balanced Load The connection n-n’ can be removed. Why? L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits” Mc.Graw Hill, 1987, New York

Reducing the analysis to one-phase! Let n be the reference node! VR VT VS IR IS IT KCL equation for n’ is Node voltage of n’ is the same as the node voltage of n. We can assume that n=n’ =0

Instantaneous Power: The total instantaneous power delivered to a balanced load is constant. Hence, the torque required for the rotor is also constant!

Analysis of Balanced Three-Phase Circuits Star 1 2 3 Triangle a b c Triangle-To-Star Star-To-Triangle zc zb za z1 z2 z3

How can one obtain the conversion relations? 1 2 3

KVL for the node sequence n-a-a’-n’-n VR VT VS IR IS IT KVL for the node sequence n-a-a’-n’-n KVL for the node sequence n-b-b’-n’-n KVL for the node sequence n-c-c’-n’-n There is a ................... between three subcircuits for different phases. If you solve one you can get the others by..........................!

A balanced three-phase circuit of 220 Volt is shown where Z=10e-j45 A balanced three-phase circuit of 220 Volt is shown where Z=10e-j45. Find the currents IR, IS and IT! IR IS IT