I have a a Field Oriented Control with the PI control for Speed and Current implemented for BLDC motor. After the Inv. Park transform, Carthesian to Polar tranform is used and then Space Vector Modulation performed. I am not able to understand how the limitation of the max space vector value is taken into account, which factors decide its maximum value and how its related. Is there any way i can confirm that operation of the system is within the space vector hexagon.

Thanks,
Adnan

Generally, I limit the current controller outputs, the Vd and Vq, to be within the voltage hexagon.

Thanks for reply. can you please provide details on the how the current controller need to be implemented to get the hexagon limited operation.

Limitation of the voltage vector is quite a complex topic, since the actual limit is on the voltage magnitude, while the PI current regulators generate the values of dq components.
Steady-state limitation is ensured by limiting the maximum speed reference or by means of flux-weakening, while for transient limitation there are different techniques.

A simple one, that should be OK for most applications that don't need deep flux-weakening operation, is to just saturate voltage vector magnitude to the inscribed (inside the hexagon) circle, and maintaining its phase. The two correspondent dq values (i.e. after saturation) are used as the dq current PI limits at the next step (anti-windup is needed).

what happens if you don't saturate the voltage ? I would assume using the SV-PWM you'll go into over-modulation, and eventually to direct current. if you look into the implementation on the SV-PWM in a uC, then I think you'll reach the maximum (or minimum) value of the comparator, and stay there for a while...
How do you saturate a dq value ? the amplitude of current vector is - sqrt(Id^2+Iq^2), and the same for voltage... how do you decide on the values of the saturation of each one ? do you make the saturation for d and q the same ? not very easy I would say...

However, if you're implementing a different type of vector control, where you control the amplitude and phase of the voltage vector directly - then it's easier, I think....never done that though...

A good SV-PWM modulation algorithm should correctly lead to hexagon saturation, which means you go from the linear range (inscribed circle) to six-step operation. Actually, there are different ways of managing this transition, and in many cases over-modulation is not allowed, since the torque ripple increases.

Maintaining voltage vector phase and saturating its magnitude is one of the possible choices. However, if field-weakening is working, saturation is not strictly needed. In closed-loop field-weakening, voltage saturation can even be detrimental.

As Ari says, in some techniques, when voltage saturation occurs fixed voltage magnitude is imposed, and current is controlled by means of voltage phase. One of these is called Single Current Regulator. When we simulated it, we saw that dynamics was very sensitive to regulation gains, and current control quality was not so satisfying...