# How to design an induction machine

The Induction Machine (IM) is the most widely used type of electrical machine. By some estimates it accounts for 90% of all small size motors (10 – 750W) and 60 -70% of medium size motors (0.75 – 375 kW). This is mainly due to their reliability, low cost and wide range of torque / speed characteristics. The IM is also used as a generator, especially for small and medium-size applications and where the requirement for the rotor to operate over a wide range of speeds is significant, like in the case of wind turbines, where the speed of the wind is always varying.

Although these machines have been in production and have been optimized for many decades, a stricter requirement for increased efficiency of electrical machines -both motors and generators ­means further improvements can only be achieved by an in-depth knowledge of the detailed electromagnetic effects in the machine at various operating points.

Because of the difference in frequency, the behaviour of the Induction Machine cannot be captured by static simulations (or frozen flux paths). The different stator and rotor frequencies can be simulated either by including motion, and thus directly accounting for the effects of slip, or by assuming some simplifying hypothesis that allows modelling the dynamic effects at a single frequency for the entire machine. Being able to analyse the machine without the inclusion of motion helps reduce the simulation time.

Using Opera’s 2d and 3d solvers, users can solve the full motional analysis, with the stator conductors running at the supply frequency and the rotor at various slip speeds. When running as an Induction generator, the user can define a fixed speed, which corresponds to a given slip speed. Because of the difference in field frequencies, eddy currents will be induced in the rotor bars.

On the other hand, when running as an Induction Motor, slip speed will be an output of the analysis, depending on the load on the rotor. Opera offers the facilities to define a rotational analysis where the position of the rotor is calculated based on the torque produced, the rotor inertia, friction and viscous coefficients.

The load can be varied in time, allowing users to define real life scenarios, like start-ups, faults and varying load.

During transient simulations, the software will log circuit values, like voltages, currents and state of switches, as well as torque and rotor position at every timestep. These are available while the analysis is progressing and allow the users to check on the progress of the solution.

Once the analysis is completed, the model and solution can be interrogated using the Opera Post-Processor and further calculations and derivation of field values can be computed, and fields can be displayed on the structure and on any 2d surface, straight line or arc.

By modifying the rotation speed of the rotor (and implicitly the slip), the induction machine can be made to switch from motor to generator mode, thus modelling the entire operation mode, in different quadrants.

In the above image, the phase shift in the current in the stator conductors between the motor and generator operating modes is plotted. In the case of the motoring mode, the rotor speed is 75 rpm, whereas in the case of the generator mode, the speed is 2475 rpm (corresponding to a slip of 0.95 and -0.65 respectively). The black dotted line represents the normalized voltage and gives the reference for the phase shift.

Depending on the topology of the machine, a 2d analysis through the cross-section can be sufficient to obtain all of the desired outputs. The benefit of this is obviously the solving speed and by extension the ease of using these models in an optimization process. The 2d solvers will also allow the inclusion of such 3d effects as skewing, of the rotor and stator parts, by solving multiple slices through the machine and combining the results into one

Although 2d solutions can yield very accurate operating characteristics, there are situations where 3d effects are significant and for this we need to build a full 3d machine, including the end windings and any other 3 dimensional features. Opera makes this process easy, by using the existing 3d Modeller with all its model building facilities or by importing the geometry either from a CAD package or from an Opera-2d file and extruding it. Automatic meshing, robust gap re-meshing and a library of conductor topologies make the definition of a 3d model very fast and efficient.

We can see above the torque characteristic for an induction machine in both generator and motor operation. The effect of the skew on the rotor (modelled using 5 slices in the Opera-2d model) can be seen in the reduction of the torque ripple. The peak torque value remains around the same value for both cases and the start-up transients are equally long.

From the point of view of the model setup, the user only needs to define the skew angle and the number of slices they would like to model. The rotor bars in the individual slices are electrically connected, so that the correct current flow is established in the bars.

Solving a skewed model with its defined slices adds a small time penalty as compared to the non-skewed device and the solver calculates the total field values as well as the individual ones on each slice. The user is then able to visualise field values on any of the slices using the Opera-2d Post-Processor. Integrated values, such as torque and losses will automatically return the total value over the entire machine.

Whereas the skew in a machine can be solved using a 3d model, the option available in Opera-2d significantly improves the modelling and solving times required and expands the type of models that can be analysed as a 2d representation. This option is available for all electromagnetic solvers, be they static, time-transient or harmonic.

An additional feature in the Opera-3d software is the existence of a so called ‘2d slice option’. Once a 3d model has been built, users can get a quick estimation of the characteristics of the machine by using this option, which is applied as a boundary condition on the geometry. As such, the full 3d model is still retained and once the 2d slice solution has been solved and interrogated in the Post-Processor, users can go back to their original model by simply modifying the imposed boundary conditions.

As expected, the solution time when using the 2d slice boundary condition on a 3d model is very similar to that of a 2d solution, while the results are identical. The advantage is that we now have a full 3d model to which we can go back to and carry on with the full 3d analysis.

For the simulation of Induction Machines in steady-state conditions, users can further speed-up their simulations by using a harmonic solver solution instead of the time-transient one. A harmonic solution solves eddy current models where the driving currents or voltages vary sinusoidally in time. It can analyse skin effect, quasi-non-linear materials and circuit connected conductors.

The solution is much faster than a transient electromagnetic with motion, since there is no time-stepping and no movement of the rotor involved. For looking at the steady-state conditions of electromagnetic devices, the harmonic solver is the best solution in both 2d and 3d analyses.

The simplification introduced by this type of analysis means that effects such as slot ripple and higher harmonic effects due to non-sinusoidal currents are not included. Once a steady-state model is solved, fields can be investigated at different angles of the AC cycle. Other options are also available, such as peak fields and time-averaged solutions.

The torque vs. slip characteristic can be easily computed, as long as the induced currents in the rotor conductors are correctly captured. This will mean that the stator and rotor conductors will need to see fields at different frequencies. Since the harmonic solver considers the field in the entire model to be at one particular frequency, Opera can simulate the correct behaviour of an Induction Machine by altering the circuit properties of the rotor circuit, such that the correct field interaction is obtained.

As such, the rotor bar conductivities are scaled by the ratio of the rotor frequency to that of the stator, or the slip value.

Another possible method, when we are solving a 2d model, is to drive the entire machine at the slip frequency. This will result in the value of variables such as the back-emf to be reduced by the ratio of the slip frequency to the synchronous frequency. This can be remedied by scaling the length of the machine with the ratio defined below.

Also, the phase resistance per unit length and the end inductance of the winding will need to be divided by the same ratio. In the graph on the right hand side, the torque vs. slip characteristic from a series of harmonic (or steady-state) analyses is presented, along with 5 points (shown in red) obtained from dynamic analyses with motion. As it can be seen, the steady-state estimation is quite close to the results obtained from the motional analyses, the slight difference being given by the contribution of the higher harmonics in the machine.
Here we see a comparison of the solution time for the same model, using different solvers and model representations. Please note the logarithmical scale.

The design of an IM can be improved by using the Opera Optimizer and Opera’s model parametrization options. The Opera Optimizer tool can assist users in achieving optimal designs for their devices analysed using Opera. It is fully integrated with Opera and can be coupled with any of the 2d or 3d solvers. It can enable quick and easy investigations of possible design spaces for multi-physics problems. It uses an efficient optimization algorithm that combines deterministic and stochastic methods, used to solve single and multi-objective optimization problems.

Users can define their own optimization variables (be they geometrical, material properties or drive properties) and can define any of the outputs available in the Post-Processor as the objective functions.