๐๐ง๐๐๐ซ๐ฌ๐ญ๐๐ง๐๐ข๐ง๐ ๐จ๐ ๐-๐๐ฑ๐ข๐ฌ ๐๐ง๐ ๐ช-๐๐ฑ๐ข๐ฌ
The d-axis (direct axis) and q-axis (quadrature axis) representation simplifies the analysis of synchronous machines by transforming the complex three-phase system into two orthogonal components:
๐๐ก๐ฒ ๐-๐ช ๐๐ฑ๐ข๐ฌ?
Simplifies rotating fields: Converts sinusoidal variations into steady-state components in a rotating reference frame.Separates fluxes: Decouples field excitation (d-axis) and torque production (q-axis).Models asymmetry: Accounts for different reactances (Xd>Xq) due to rotor construction.
๐-๐๐ฑ๐ข๐ฌ:-
Aligned with the rotorโs magnetic field (field excitation flux), responsible for reactive power.Represents the magnetizing component.Controls the reactive power flow and voltage regulation.In synchronous machines, the D-axis current (id) is responsible for producing the flux required for magnetization.
๐ช-๐๐ฑ๐ข๐ฌ:-
Perpendicular to the rotorโs field (armature flux), responsible for active power.Represents the torque-producing component.Controls the active power flow and determines the mechanical torque in the machine.The Q-axis current (iq) interacts with the rotor flux to generate electromagnetic torque (Te).
๐-๐๐ฑ๐ข๐ฌ ๐๐ง๐ ๐ -๐๐ฑ๐ข๐ฌ ๐ข๐ง ๐ฉ๐จ๐ฐ๐๐ซ ๐ฌ๐ฒ๐ฌ๐ญ๐๐ฆ ๐ฌ๐ญ๐ฎ๐๐ข๐๐ฌ
๐๐ญ๐๐๐๐ฒ-๐๐ญ๐๐ญ๐ ๐๐ง๐๐ฅ๐ฒ๐ฌ๐ข๐ฌ
D-Axis: Governs the reactive power and voltage regulation.Q-Axis: Governs the real power and torque production.
๐๐ซ๐๐ง๐ฌ๐ข๐๐ง๐ญ ๐๐ญ๐๐๐ข๐ฅ๐ข๐ญ๐ฒ
During faults or disturbances, the d-axis and q-axis reactance affect the transient (Xdโฒ,Xqโฒ) and sub transient (Xdโฒโฒ,Xqโฒโฒ) responses of the machine
If Xd is much larger than Xq, the machine will have a high synchronous reactance, limiting fault currents but reducing voltage regulation.Machines with smaller Xd and Xq provide better transient response but allow higher fault currents.
