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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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