In abc frame, it suffices to write KCL in 3 nodes. It then becomes straight forward to get the d-q components.

Dear Vladimir,

As the currents and voltages applied to the dq-model are always the phase voltages and phase currents one has to compensate for this in the simulation and in practice. It is normal to assume the dq model as being star connected but in practice most motors are delta connected to improve the em torque by  factor of 3.

Let us consider a standard 380V (L-L) IM.

When the motor is star connected one must use the Line to neutral voltages (220v) and the Line and Phase currents are equal. Note there will be both a change in magnitude (380-220) and phase shift (0-30 degrees) between the line and phase voltages. This must be accounted for when under FOC using KVL as Mohammad notes.

Vab = Van-Vbn; Vbc=Vbn-Vbc; Vca=Vcn-Van (KVL)  -- dq voltages = Van:Vbn:Vcn = 220

Ia = Ian; Ib= Ibn; Ic = Icn ---- dq currents = Ian:Ibn:Icn

When the motor is delta connected then the one must use the Line to line voltages (380v) and as Mohammad notes KCL must be used to derive the line currents from the phase currents. Here there will be no change in either magnitude or phase for the motor voltages but the line currents will change in magnitude and phase with a phase shift of 30 degrees.

Iab = Ian-Ibn; Ibc=Ibn-Ibc; Ica=Icn-Ian (KCL) ---- dq currents =Ian:Ibn:Icn

Va = Van; Vb= Vbn; Vc = Vcn   --- dq voltages = 380

Note that regardless of connection FOC always relies on the phase voltages and currents to achieve the internal dynamic decoupling. Otherwise, whether in practice or simulation the system will perform suboptimal.

The best way to check in a simulation is to see whether the d-axis rotor flux goes to zero. If not then there is an error.

In some sectors of the machine tool industry IM motors are connected in star at low speed and when they go to high speed they are delta connected in the field weakening range to increase the stator currents to allow higher speed control of the rotor field flux.

That is why in SIMULINK (for example) one may either use the inverter pole voltages or the inverter pole-pole voltages as the inputs to the dq-model to simulate star or delta connection respectively.

If the system is balanced then one may account for both the magnitude and phase shift in the controller s/w.

Hope this helps.

Dear Dr. Gregory Diana,

Thanks a lot for the very informative response.

I would just like you give a justification of this statement: "IM motors are connected in star at low speed and when they go to high speed they are delta connected in the field weakening range to increase the stator currents to allow higher speed control of the rotor field flux."

It is evident that the delta connection will apply higher voltage to the phase windings. So why does this correspond to the flux weakening region?

What do you mean by pole voltages and pole-pole voltages?

Thanks a lot for the time you devote to responding my questions.

Hi Mohammad,

Sure. I am Mr not Dr.

ITEM 1

In the machine tool industry IM drives which run up to 60,000-150,000 rpm are used. In this case to enable such high speeds the IM must enter the field weakening region. Normally rotor field flux = 1/speed so as the speed goes very high the field current become very low and difficult to control. In such cases, where FOC is used, the motor is designed to run under "base speed" in STAR. At some point within the field weakening range (normally when Torque-star = Torquedelta) they switch from STAR to DELTA for reasons mentioned above. At very high speeds they even revert to V/F control and dispense with FOC altogether.

ITEM 2

The standard IGBT inverter normally consists of three dual IGBT modules (or legs), each with a top and bottom switch. They normally have a +DC and -DC connection and the OUTPUT. The OUTPUT is normally called the POLE VOLTAGE.

If one measures from any OUTPUT to -DC this is called the pole voltage. If one measures from OUTPUT to OUTPUT this is called the pole to pole voltage.  If the motor is STAR connected it sees the POLE to -DC and if DELTA it sees POLE to POLE.

These are important "little" details when designing PMW strategies as what the motor sees depends on how it is connected and how the PWM is applied to the inverter. The basic literature rarely mentions this or is even aware of it.

Cheers and hope this helps.

Hi Vladimir,

If you are familiar with Y connection. You can convert your delta connection to the equivalent Y connection. You don't need to care what exactly the winding scheme is in the motor. Use the equivalent parameters then you will be fine.

@Gregory: I don't think that's field weakening, correct if I'm wrong.

You need reduce the physical flux flow to achieve flux weakening. if you switch between delta and Y connection and you connect the terminals to the same grid, speeds will be almost the same, instead, either the Y connected motor produce the less torque, or the delta connected motor will generate too much heat.

I assume you actually vary the frequencies for different connection, but that's still VVVF.

Dear Hao,

Your first point is incorrect. As you correctly note it  has nothing to do with the parameters (which will remain the same as you note) but rather what voltages to apply and what currents to feedback in either connection. You can see this if you try a physical STAR/DELTA switch whether fixed or variable speed drive and there will be a physical 30 degree phase shift in voltages and currents.

On the second issue it is correct ( I am not referring to just a STAR-DELTA switch). To achieve high spindle speeds (>50/60 Hz) the motor must enter the field weakening region (by physically reducing the field flux or back emf) as you correctly note. To achieve speeds of 30000 or 60000 rpm under FOC will require stator frequencies of 500/1000 Hz (2-pole motor) and a field weakening range of 10/20:1. Normal motors can do 2/4:1 FW range. As Ids ~ 1/Wr the field current and flux drops of rapidly with speed and at 30000 is 0.1 of that at 50H and 0,02 at 60000 rpm.

To achieve this wide FW range the motor is designed to run normally in star and enters the field weakening region in this connection. At some point (when the star and delta torques are equivalent) the motor is physically switched from star to delta allowing the field weakening range to be further extended. Recall the torque in DELTA is 3 times that in STAR and thus the current loops are able to function much better. At changeover there will be a 30 degree phase shift which must be compensated for and cannot be ignored as you state.

Yes, during FW the stator frequency will increase. It is no different to a STAR/DELA starter and is widely used in the machine tool industry. Yes it is still a VVVF drive using FOC.

see http://www.mmsonline.com/articles/wyedelta-in-perspective

Hi Gregory:

I'm not sure if I stated my points clear. Considering the motor as a black box, you can always get an equivalent Y or delta circuit.

I agree with you from an application engineer's perspective. In high performance motor, the  torque capability is more restricted by the heat dissipation, while the speed is more restricted by the mechanical strength (including bearing) and the voltage.  This is a general explanation.

@Vladimi: For a driver which is capable of self-commissioning function, the driver will determine/measure the equivalent parameters based on the the built-in model, it doesn't care about the physical winding scheme.

Unless you want to research the difference between the delta and Y connections, that's another scenario. 

Hopefully I explained things clearly this time. Good luck to you guys.

 Dear Mr Gregory Diana,

I have  questions regarding Delta connected 3 Phase Indunction motor modelling. I have already built star connected Induction motor model. To make model for delta connected winding apart from phase voltage and Phase current , Do i need to make any changes in motor model ?

The dq or 2 axis model / equations remain the same. For a DELTA connection one must use the Line-Line voltages as the supply voltages. The dq or 2-axs currents will be the phase currents so to obtain the line currents one must apply Kirchhoff's current law to obtain the line currents. As noted above there will be a 30 deg phase shift between line and phase current and also a change in magnitude (Line > Phase currents).

see the following reference.

https://www.google.co.za/search?num=50&newwindow=1&site=&source=hp&q=pillay+star+and+delta+connection&oq=pillay+star+and+delta+connection&gs_l=hp.3...2425.23305.0.25465.43.38.0.0.0.0.480.5985.2-4j6j6.16.0.msedr...0...1c.1.64.hp..38.5.1948.0.k0_W-jtAj14

As the paper notes it is possible to use equivalents (as noted by Hao) but in real-time control this is not the case when one switches dynamically from STAR/DELAT etc.

Hope this helps.

Dear Mr. Gregory Diana,

I am developing an IM for application in electric vehicles with max. speed upto 20000 rpm. The inverter fed IM has a field weakening ratio of 4/5:1. Since the dimensions of the motor are restricted, i need a delta winding arrangement(higher phase voltage as compared  to star) to achieve the maximum torque during base speed region. I want to know, how big the advantage is of having star connection in the base speed and delta in the field weakening region?

Thanks in advance!