# Blondel's Two Reaction Theory of Synchronous Machines

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## 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.

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 ($𝐹_{𝑎}$) 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 ($𝐹_{𝑑}$).

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 ($𝐹_{q}$). The d-axis component ($𝐹_{𝑑}$) is either magnetising or de-magnetising while the q-axis component ($𝐹_{q}$) results in a cross-magnetising effect.

If ψ is the angle between the armature current ($𝐼_{𝑎}$) and the excitation voltage ($𝐸_{𝑓}$) and the amplitude of the armature MMF is given by ($𝐹_{𝑎}$), then

The d-axis component ($𝐹_{𝑑}$) is given by,

$$\mathrm{𝐹_{𝑑} = 𝐹_{𝑎}\:sin\:𝜓}$$

And the q-axis component ($𝐹_{q}$) is given by,

$$\mathrm{𝐹_{𝑞} = 𝐹_{𝑎}\:cos\:𝜓}$$

Updated on 14-Oct-2021 11:30:21