P.u. Representation is based on the rated value of the system parameter and doesn't have any units

thank you all for your valuable answers.

now all this is known, what i must change to convert my model implemented in Simulink (SI) to pu?

It should convert mathematical model of physical units to relative units. The first step is to choose a consistent set of base units. This concerns not only the voltage and current, but also, for example, resistance, and speed and time. Then, every mathematical equation is divided side by side to the equation specified in base units. The results is p.u. equation.

I presume you are using Simpower or the Power Systems blockset which has two such Asynchronous Machine models available. One for SI and the other for PU.

The internal machine models are identical and will provide the same results the only difference is that the SI unit model requires one to enter the model parameters both electrical and mechanical in actual SI engineering units, kW, amps, ohms, Henries etc whereas the pu requires the same SI parameters be converted from SI units and entered in pu.

To help you the developers of the blockset provides a conversion tool which allows you to enter the standard nameplate machine parameters in SI and will convert to SI or pu for you see

power_AsynchronousMachineParams

just type this in the Matlab command line and the menu will pop up.

You can then use these in both the SI and pu models and both should give the same results.

Once you have done this I then suggest that study the PU system that the developers of the blockset use and try and do the same exercise by hand.

Thank you Stefan an Diana.

Diana how about if i want to develop the model my self?

I can show you simple model of DC Drive - only the electrical equation.

From SI model to pu model - i hope this is clear :-)

The best approach is to use the two-axis or DQ model of a symmetric three phase induction machine plus the mechanical system. Put this into state space format and enter into Simulink using the STATE SPACE block. This allows you to define the machine parameters as matrices which you can enter as an m-file. This version will actually run faster than those provided in the blockset and may be easily linearised and the eigenvalues and pole zero plots obtained if required.

You may then use this model and take the parameters from the examples provided and run and see that you get the exact same response both in SI and pu and also in all three reference frames.

The pu system is not as straight forward as you think and when dealing with AC motors there are various options that one make may such as;

1 Orthogonal or non orthogonal Parks transform.

2 Direction of rotation.

3 Refer all parameters to an equivalent two pole machine or work in the mechanical frame of reference.

4 time base

5 Peak or RMS bases

The choice of Parks transform and direction of rotation go hand-hand. If you use the orthogonal or power invariant form then all your machine parameters in abc will be the same as in DQ (ie 1 ohm abc = 1 ohm DQ). If you choose the power invariant form then 1 ohm abc = 1.5 ohm DQ).

Once you convert in pu both will give the same results but if you are going to actually implement a controller then the orthogonal form gives one to one correspondence with actual machine and controller parameters.

The choice of time base also impacts and you may choose Tb= 1 sec and Wb = 1 or Tb = 1/Wno. and Wb = Wno. The former allows the pu speed and time and actual speed to be the same as simulation time whereas the latter does time scaling and which was very popular when analogue computers were used to do simulation.

If you use peak bases for current and voltage then the actual and simulated responses will be identical and need no scaling, but then this affects the pu torque scaling factor. You will see some pu torque equations in the journal literature have 1 some 1/2 some 1/3 some 2/3 and the question is why does this arise.

As you see there are many issues all of which are important and all of which you must go through, understand and implement as part of your learning process. Just being told or being given the answers achieves very little and what I am telling you might take a month or two to get to grips to and implement, but once done you will only then see and realise the benefits and reward in doing so. Welcome to the apprenticeship of post graduate studies ( I presume)

All the above is embedded in the models provided in the blockset and more.

i would recommend to use the pu system in simulation . it is more accurate than SI system

@Abdulaziz Alshareef

Can you reasons, why pu model is more accurate? IMHO it was true for fixed point calculation, but Matlab is using 64-bits floating point mathematics...

In theory PU and SI should always provide exactly the same results. However, when simulating machines and / or complex power systems which might involve systems with both small and large or should I say very disparate time constants (stiff systems) then one runs into numerical precision problems. As smart as we think Simulink is (and it has some of the best numerical integration solvers) one still encounters problems with accuracy for stiff systems such as power electronic converters and power systems combined.

As such the numbers in pu can become very small (ie 1 ohm SI opposed to 0.0001 pu) and thus due to numerical precision (ill conditioning) will lead to greater error as Abdulaziz points out and where SI may provide better numerical benefits as it works with significantly larger number. Remember that all numerical integration algorithms involve some degree of error in part due to the inaccuracy of the algorithm itself and in part due to numerical precision. One typically finds that at very small time steps (even 64 bit) the numerical precision error will become dominant whereas at large time steps the algorithm error dominates with both leading to inaccuracy or even instability. Such error will propagate with time and thus lead to the inaccuracies Abdulaziz refers to.

For a simple induction machine this should however not be a problem but is very important to note and be aware of.

Thank you a lot dear colleagues it's very clear now