Dynamics and Control of Electric Transmission and Microgrids

DSymmetrical Components and Per‐Unit Representation

D.1 Symmetrical Component Representation of Three‐Phase Systems

The generation, transmission, and distribution of electrical power is predominantly done using balanced three‐phase sinusoidal AC systems, except at the downstream end of distribution systems that cater to small, low‐voltage single‐phase loads. Three‐phase systems offer several advantages over single‐phase AC systems. The additional complexity in the analysis, design, and engineering of three‐phase systems is modest and manageable. Polyphase systems of order higher than three can also be built, but they generally involve greater complexity and therefore have not found widespread application. The advantages of balanced three‐phase AC systems over single‐phase AC systems are:

1. The total power in a three‐phase system is constant while it pulsates at twice the AC frequency in a single‐phase system. This also manifests as pulsating electrical torque in single‐phase machines, while the torque is constant in three‐phase machines.
2. Space and material can usually be better utilized in three‐phase equipment. A separate return conductor for each phase in the transmission line is not necessary because the sum of currents in a three‐phase balanced system is zero.
3. Some lower‐order harmonics in power‐electronic converters can be eliminated due to the three‐phase connections.
4. Three‐phase motors have a rotating magnetic field which is advantageous for starting. These motors generally ...