Vector Clarke Transform

Functions
static __INLINE void	arm_clarke_f32 (float32_t Ia, float32_t Ib, float32_t *pIalpha, float32_t *pIbeta)
	Floating-point Clarke transform.
static __INLINE void	arm_clarke_q31 (q31_t Ia, q31_t Ib, q31_t *pIalpha, q31_t *pIbeta)
	Clarke transform for Q31 version.

Description

Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector. Generally the Clarke transform uses three-phase currents Ia, Ib and Ic to calculate currents in the two-phase orthogonal stator axis Ialpha and Ibeta. When Ialpha is superposed with Ia as shown in the figure below

Stator current space vector and its components in (a,b).

and Ia + Ib + Ic = 0, in this condition Ialpha and Ibeta can be calculated using only Ia and Ib.

The function operates on a single sample of data and each call to the function returns the processed output. The library provides separate functions for Q31 and floating-point data types.

Algorithm

where Ia and Ib are the instantaneous stator phases and pIalpha and pIbeta are the two coordinates of time invariant vector.

Fixed-Point Behavior

Care must be taken when using the Q31 version of the Clarke transform. In particular, the overflow and saturation behavior of the accumulator used must be considered. Refer to the function specific documentation below for usage guidelines.

Function Documentation

static __INLINE void arm_clarke_f32 ( float32_t  Ia, float32_t  Ib, float32_t *  pIalpha, float32_t *  pIbeta  )

static

Parameters

[in]	Ia	input three-phase coordinate a
[in]	Ib	input three-phase coordinate b
[out]	*pIalpha	points to output two-phase orthogonal vector axis alpha
[out]	*pIbeta	points to output two-phase orthogonal vector axis beta

Returns

none.

static __INLINE void arm_clarke_q31 ( q31_t  Ia, q31_t  Ib, q31_t *  pIalpha, q31_t *  pIbeta  )

static

Parameters

[in]	Ia	input three-phase coordinate a
[in]	Ib	input three-phase coordinate b
[out]	*pIalpha	points to output two-phase orthogonal vector axis alpha
[out]	*pIbeta	points to output two-phase orthogonal vector axis beta

Returns

none.

Scaling and Overflow Behavior:

The function is implemented using an internal 32-bit accumulator. The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. There is saturation on the addition, hence there is no risk of overflow.