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Blondel's Two Reaction Theory of Synchronous Machines
Magnetic Axes of Rotor
The figure shows the direct axis and the quadrature axis of a rotor −
Direct Axis
The axis of symmetry of the magnetic poles of the rotor is called as direct axis or d-axis. The axis of symmetry of the north magnetic poles of the rotor is known as the positive d-axis while the axis of symmetry of the south magnetic poles is known as the negative d-axis.
Quadrature Axis
The axis of symmetry halfway between the adjacent north and south poles is known as quadrature axis or q-axis. The q-axis lagging the north pole is taken as the positive q-axis. The quadrature axis is so name since it is 90° electrical or one-quarter cycle away from the direct axis.
Blondel’s Two Reaction Theory
Andre Blondel proposed the Two Reaction Theory of synchronous machines. The two reaction theory was proposed to resolve the given armature MMF ($πΉ_{π}$) into two mutually perpendicular components, with one located along the d-axis of the salient-pole rotor. This component is known as the direct axis or d-axis component and is denoted by ($πΉ_{π}$).
The other component is located perpendicular to the d-axis of the salient pole rotor. It is known as the quadrature axis or q-axis component and denoted by ($πΉ_{q}$). The d-axis component ($πΉ_{π}$) is either magnetising or de-magnetising while the q-axis component ($πΉ_{q}$) results in a cross-magnetising effect.
If ψ is the angle between the armature current ($πΌ_{π}$) and the excitation voltage ($πΈ_{π}$) and the amplitude of the armature MMF is given by ($πΉ_{π}$), then
The d-axis component ($πΉ_{π}$) is given by,
$$\mathrm{πΉ_{π} = πΉ_{π}\:sin\:π}$$
And the q-axis component ($πΉ_{q}$) is given by,
$$\mathrm{πΉ_{π} = πΉ_{π}\:cos\:π}$$
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