use N42 Permanent magnet material , good B.

May I know your simulation software? Different software has different setup options.

I'm using Matlab/Simulink.

There are many possible reasons for the error. For example:

1. the default unit of the angle in MATLAB is radian.

2. If you want id=0, then the torque angle (angle between the d-axis and current phasor) is 90deg. Is this setup correctly?

3. The solver and time step for the Simulink.

All these could be the possible reasons. It is hard to judge just from your description.

Wei send me your Simulink model and I will have a look.

Hi Gregory, Thanks for being willing to help. I have attached the Simulink model. The parameters are in the following: R = 0.97; Ld = 0.0159; Lq = 0.037; p = 2; lambda_f = 0.008812; The rated power, speed and line voltage are 5kW, 1500rpm and 400V respectively. I used two PI controllers to regulated the dq axis currents, with hopes of controlling Id to be zero. But it failed. I don't know why...

Hi Peng, what do you mean default unit in Matlab? I am using the model in the Simulink library. I built the model myself and I think all the units are consistent. I tried other solvers. The results didn't change much.

Hi Wei,

I have just had a quick look and note the following;

1 The PI controllers cater for saturation but will not work. The reason is that you must stop the integrators from integrating when their outputs are saturated or reach limit. This is called wind-up of the integrators and stopping the integrator while the controller output is in limit is called anti-windup control. The standard Simulink PI controllers has this feature so I suggest you try it until you get your PI control acts the same. It is good that you are trying to do this yourself and get to understand the detail. Your scope and Scope 2 should be the same. Also your controller output only allows +VE output signals whereas it must be unidirectional.

2 I also note that the electrical Torque (Te) is -VE but your current reference for Iq is +VE. Have you defined stator currents as -VE in which case this is correct. Also you must multiply Te by the number of poles to convert from 2 pole to 4 pole torque.

3 If it is a generator then it must be driven by a prime-mover. In your case you have a constant torque prime mover (Teng = 50) but you have no initial speed on your integrator in your mechanical part. The initial speed should be 1500 rpm which assumes the generator is already running. I understand you are trying to say the generator is running and it has a step input of mechanical torque applied and the controller must then counteract.

4 If you can send your model equations in word it would be great.

I will try and run the model and get back.

Dear Wei,

Any generator must be fixed to either an electrical load or an existing power system / infinite bus into which it is going to generate power. You are trying to use PI controllers to generate the terminal voltages in order to try and develop torque to match the mechanical torque (Teng).

Generators develop an electrical torque in response to the prime mover developing torque to respond to the electrical load placed on the generator terminals.

Your Vd, Vq would have to be connected to a an electrical source and this cannot be done using state space model as you are doing and why you must use the Power System toolbox.

When simulating generators a first step is to get the system to run in steady state for a given and well known load. In such cases all variables should be dc in the DQ frame of reference.

In your model you have Vd,Vq as inputs whereas they are outputs. If it were a motor then they would be inputs and you could control the input voltages to achieve a desired response. Here you are trying to control the outputs as if they were inputs which cannot be done.

A motor takes electrical energy and converts to mechanical whereas a generator takes mechanical energy and converts to electrical. You are trying to control the PMSM machine like a motor yet running it as a generator

Hi Gregory,

Thank you so much for the detailed answer! I have attached the governing equations below. The sign of all the variables should be positive.

In my understanding, the two PI controllers can be used to establish Vd and Vq acting as variable electric loads applied to the generator. At least it is mathematically correct, if not physically implemented like this. Isn't it?

I have tried to run the model in steady state without the two PI controllers, i.e. setting up the Vd, Vq and we to be values corresponding to zero id in steady state, but the resulting id value was not zero.

Wei,

I have attached a modified model with a simple mechanical governor which ensures the system is able to settle down into steady state operation. I have created a states file called gdxFinal which gets saved at the end of each simulation run and which is loaded at the next run to ensure the states are saved. it appears to work ok. I have saved as *.mdl as I have ver 2013 which saves as *.slx.

Try it and see how it goes. It uses Vd = 500*sqrt(2) and Vq=0. In this case Iq 0.

Check the mechanical part as I have modified Te to now be correct and multiplied by 3/2*p

In steady state the states are

[157.0796;43.5977;59.9076:-11.0792]

[ Wr:Teng:Iq;Id ]

It is possible to choose Vd and Vq such that Id =0 but you can do this from the steady state equations by hand.

Thank you SO MUCH! Gregory.