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The tables generated for the Spatial Harmonics model plot Phase Inductance, Phase Total Flux, and Torque values along the three following axes:
Axis | Description |
|---|---|
Theta | Mechanical angle of the rotor. |
Beta | Polar angle of the [Id, Iq] vector in the DQ reference frame, where Id is Direct Axis Current and Iq is Quadrature Axis Current. JMAG uses the power invariant DQ transform convention where the D axis is aligned with Phase A at Theta = 0. |
Iamp | Amplitude of the [Id, Iq] vector in the DQ reference frame, where Id is Direct Axis Current and Iq is Quadrature Axis Current |
The tables are formatted as follows:
Parameter | Number of Tables | Theta Axis Minimum Length | Beta Axis Minimum Length | lamp Axis Minimum Length |
|---|---|---|---|---|
Phase Inductance | 9 | 65 samples [0 ... 180/Number of Pole Pairs] | 33 samples or more [0 ... 360] | 32 samples or more [0 ... 3*maximum peak phase current] |
Phase Total Flux | 3 | 129 samples [0 ... 360/Number of Pole Pairs] | 33 samples or more [0 ... 360] | 32 samples or more [0 ... 3*maximum peak phase current] |
Torque | 1 | 65 samples [0 ... 180/Number of Pole Pairs] | 33 samples or more [0 ... 360] | 32 samples or more [0 ... 3*maximum peak phase current] |
The information in brackets represents the allowable range of values for the axis.
| Note |
|---|
To obtain accuracy, it is important to have a sufficient number of samples per axis. The The recommended axis lengths shown above are minimum values and longer axes can be used. |
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It is important to respect the recommended boundaries of the axes because missing table sections may lead to unexpected model behavior. The PMSM SH model in particular can demonstrate noticeable stiffness if the currents exceed the axis limits and the LUT output is being saturated.
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The model does not support the use of any symmetry options for the generation of data (for example, generating one third of the data since phase A is symmetrical in regards to B with a 120deg electrical difference). This This is valid for inductance/flux and torque (slot symmetry for torque).
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Before they are transferred to the machine model on the FPGA, the data tables are reshaped using a trilinear interpolation method. The The resulting tables are made up of equally spaced samples and are resized according to the parameters described below. The size of each table is dependent on the version of the PMSM SH model, as well as the number of enabled machines in the simulation. Because the data in the resized tables is equally spaced, the resolution across each axis can be calculated by dividing the maximum possible value along the axis by the number of samples used.
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The memory space of the PMSM SH model core is shared between the two machine models. When a single machine is enabled, the full size of the table is available to model the machine. The default number of samples for each axis is shown below.
PMSM SH v2 | |||
|---|---|---|---|
Theta Axis (Electrical angle) | Beta Axis | Iamp Axis | |
Phase Inductance | 65 samples per half-electrical turn (Resolution 2.77 deg) | 33 (Resolution 10.9 deg) | 32 (Resolution IampMax / 32 Amps) |
Phase Total Flux | 65 samples per full-electrical turn (Resolution 5.54 deg) | 33 (Resolution 10.9 deg) | 32 (Resolution IampMax / 32 Amps) |
Torque | 65 samples per slot (1/6 of electrical turn) (Resolution 0.92 deg) | 33 (Resolution 10.9 deg) | 32 (Resolution IampMax / 32 Amps) |
PMSM SH v1 | |||
|---|---|---|---|
Theta Axis (Electrical angle) | Beta Axis | Iamp Axis | |
Phase Inductance | 33 samples per half-electrical turn (Resolution 5.45 deg) | 33 (Resolution 10.9 deg) | 16 (Resolution = IampMax / 16 Amps) |
Phase Total Flux | 65 samples per full-electrical turn (Resolution 5.54 deg) | 33 (Resolution 10.9 deg) | 16 (Resolution = IampMax / 16 Amps) |
Torque | 33 samples per half-electrical turn (Resolution 5.45 deg) | 33 (Resolution 10.9 deg) | 16 (Resolution = IampMax / 16 Amps) |
Dual Machine Mode
When both PMSM SH machines are enabled, the total allocated FPGA memory is divided between the two machine models. The The default number of samples for each axis is shown below.
PMSM SH v2 | |||
|---|---|---|---|
Theta Axis (Electrical angle) | Beta Axis | Iamp Axis | |
Phase Inductance | 33 samples per half-electrical turn (Resolution 5.45 deg) | 33 (Resolution 10.9 deg) | 32 (Resolution = IampMax / 32 Amps) |
Phase Total Flux | 33 samples per full-electrical turn (Resolution 10.9 deg) | 33 (Resolution 10.9 deg) | 32 (Resolution = IampMax / 32 Amps) |
Torque | 33 samples per slot (1/6 of electrical turn) (Resolution 1.98 deg) | 33 (Resolution 10.9 deg) | 32 (Resolution = IampMax / 32 Amps) |
PMSM SH v1 | |||
|---|---|---|---|
Theta Axis (Electrical angle) | Beta Axis | Iamp Axis | |
Phase Inductance | 33 samples per half-electrical turn (Resolution 5.45 deg) | 17 (Resolution 21.17 deg) | 16 (Resolution = IampMax / 16 Amps) |
Phase Total Flux | 65 samples per full-electrical turn (Resolution 5.54 deg) | 17 (Resolution 21.17 deg) | 16 (Resolution = IampMax / 16 Amps) |
Torque | 33 samples per half-electrical turn (Resolution 5.45 deg) | 17 (Resolution 21.17 deg) | 16 (Resolution = IampMax / 16 Amps) |
Data Interpolation Performed During Simulation
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