# Three Phase Permanent Magnet Synchronous Machine

Description of the Three Phase Permanent Magnet Synchronous Machine component in Schematic Editor.

Table 1. Three Phase Permanent Magnet Synchronous Machine component in Typhoon HIL Schematic Editor
component component dialog window component parameters
• Property tabs:

A, B, and C are stator winding terminals. The stator winding uses the current source interface.

## Electrical sub-system model

The electrical part of the machine is represented by the following system of equations, modeled in the rotating dq reference frame. The dq reference frame is attached to the rotor, and the direct axis is aligned with the rotor magnets. The modeled dynamics can be represented with the following equations:

$\left[\begin{array}{c}{v}_{ds}\\ {v}_{qs}\end{array}\right]=\left[\begin{array}{cc}{R}_{s}& 0\\ 0& {R}_{s}\end{array}\right]\left[\begin{array}{c}{i}_{ds}\\ {i}_{qs}\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\psi }_{ds}\\ {\psi }_{qs}\end{array}\right]+{\omega }_{r}\left[\begin{array}{c}{-\psi }_{qs}\\ {\psi }_{ds}\end{array}\right]$

$\left[\begin{array}{c}{\psi }_{ds}\\ {\psi }_{qs}\end{array}\right]=\left[\begin{array}{cc}{L}_{d}& {0}_{}\\ {0}_{}& {L}_{q}\end{array}\right]\left[\begin{array}{c}{i}_{ds}\\ {i}_{qs}\end{array}\right]+\left[\begin{array}{c}{\psi }_{PM}\\ 0\end{array}\right]$

${T}_{e}=\frac{3}{2}p\left({\psi }_{ds}{i}_{qs}-{\psi }_{qs}{i}_{ds}\right)$

If the saturation effects are considered, the equations have the same form, but in that case fluxes are functions of stator currents:

If the saturation effects and machine's flux and torque spatial harmonics are considered, the equations also have the same form, but in that case fluxes are functions of the rotor mechanical angle and stator currents:

Table 2. Three Phase Permanent Magnet Synchronous Machine electrical subsystem model variables
symbol description
ψds Direct axis component of the stator flux [Wb]
ψqs Quadrature axis component of the stator flux [Wb]
ψPM Flux amplitude established in stator phases by rotor permanent magnets [Wb]
ids Direct axis component of the stator current [A]
iqs Quadrature axis component of the stator current [A]
vds Direct axis component of the stator voltage [V]
vqs Quadrature axis component of the stator voltage [V]
Rs Stator phase resistance [Ω]
Ld Direct axis inductance [H]
ωr Rotor electrical speed [rad/s] ( $=p{\omega }_{m}$ )
p Machine number of pole pairs
Te Machine developed electromagnetic torque [Nm]

## Mechanical sub-system model

Motion equation:

Table 3. Mechanical sub-system model variables
symbol description
Jm Combined rotor and load moment of inertia [kgm2]
Te Machine developed electromagnetic torque [Nm]
Tl Shaft mechanical load torque [Nm]
b Machine viscous friction coefficient [Nms]
Note: Motion equation is the same for all of the rotating machine models.

## Electrical

This component offers several levels of model fidelity, designated by the Model Type property. The following options are available:
• linear
• nonlinear
• nonlinear - spatial harmonic
If the selected Model Type is nonlinear, the following saturation types can be specified:
• flux vs current
• absolute inductance vs current
• incremental inductance vs current
If the selected Model Type is nonlinear - spatial harmonic, the following saturation types can be specified:
• flux vs current, theta
• current vs fluxes, theta
Table 4. Electrical parameters
symbol description
Rs Stator phase resistance [Ω]
Ld Direct axis inductance [H]
Psi_pm Flux amplitude established in stator phases by rotor permanent magnets [Wb]
id vector List of stator current direct axis component values [A]
iq vector List of stator current quadrature axis component values [A]
theta vector List of mechanical angle values [⁰]
psid vector List of stator flux direct axis component values [Wb]
psiq vector List of stator flux quadrature axis component values [Wb]
id table Table of stator current direct axis component values [A]
iq table Table of stator current quadrature axis component values [A]
psid table Table of stator flux direct axis component values [Wb]
psiq table Table of stator flux quadrature axis component values [Wb]
Ld table Table of stator inductance direct axis component values [H]
Lq table Table of stator inductance quadrature axis component values [H]
theta vector Te List of mechanical angle values used as input to the torque lookup table [⁰]
id vector Te List of stator current direct axis component values used as input to the torque lookup table [A]
iq vector Te List of stator current quadrature axis component values used as input to the torque lookup table [A]
torque table Table of torque values [Nm]

The Dynamic flux checkbox enables real-time change to the amplitude of the permanent magnet's flux linkage in the stator phase winding. When enabled, a machine input terminal is either created or extended by a new input for defining this flux value in Wb.

Note: If the selected Load source is Model and the Dynamic flux checkbox is enabled, the machine input terminal is extended to a vector of 2 elements in the following order: [model_load, Permanent magnet's flux].
Note: This property is only available if the selected Model Type is linear.

The permanent magnet synchronous machine model can include magnetic saturation effects. In that case, fluxes or inductances are defined as functions of stator currents ids and iqs. These functions are represented in the form of lookup tables. The lookup tables use linear interpolation and linear extrapolation.

Saturation can be parametrized in the following ways:
1. fluxes vs stator currents
2. absolute inductances vs stator currents
3. incremental inductances vs stator currents
In each of these cases the direct axis and quadrature axis flux or inductance can depend on both stator currents or only on the corresponding stator current. When fluxes or inductances are functions of both direct axis and quadrature axis currents, it is important to define the lookup tables as nested Python lists where the number of inner lists must be equal to the number of elements in the current id vector and the number of elements of each inner list must also be equal to the number of elements in the current iq vector.
id_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
iq_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
psid_table = [-0.0492472, -0.0433668, -0.0425532, -0.0433464, -0.0484104]
psiq_table = [-0.1330824, -0.0838922, 0.0, 0.0838828, 0.133098]
id_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
iq_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
psid_table = [[-0.0492472, -0.0433668, -0.0425532, -0.0433464, -0.0484104],
[-0.0115952, -0.0274476, -0.0330376, -0.02771, -0.0126918],
[0.032, 0.032, 0.032, 0.032, 0.032],
[0.064706, 0.0662274, 0.0593586, 0.0677826, 0.0649068],
[0.0805368, 0.0705448, 0.05448328, 0.070713, 0.0812716]]
psiq_table = [[-0.1330824, -0.0838922, 0.0, 0.0838828, 0.133098],
[-0.1313616, -0.1041012, 0.0, 0.1041148, 0.1282268],
[-0.1286288, -0.1076058, 0.0, 0.107, 0.1278272],
[-0.1175936, -0.084391, 0.0, 0.0839394, 0.1162836],
[-0.1092448, -0.0588548, 0.0, 0.0585804, 0.1084576]]
id_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
iq_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
Ld_table = [0.00186383, 0.00325188, 0.00399657, 0.00136793, 0.000562082]
Lq_table = [0.00321572, 0.00538029, 0.00779154, 0.00535, 0.00319568]
id_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
iq_vector = [-40.0, -20.0, 0.0, 20.0, 40.0]
Ld_table = [[0.00203118, 0.00188417, 0.00186383, 0.00188366, 0.00201026],
[0.00217976, 0.00297238, 0.00325188, 0.0029855, 0.00223459],
[0.00226518, 0.00283656, 0.00399657, 0.00280727, 0.00218666],
[0.0016353, 0.00171137, 0.00136793, 0.00178913, 0.00164534],
[0.00121342, 0.00096362, 0.000562082, 0.000967825, 0.00123179]]
Lq_table = [[0.00332706, 0.00419461, 0.0049565, 0.00419414, 0.00332745],
[0.00328404, 0.00520506, 0.00635444, 0.00520574, 0.00320567],
[0.00321572, 0.00538029, 0.00779154, 0.00535, 0.00319568],
[0.00293984, 0.00421955, 0.00547829, 0.00419697, 0.00290709],
[0.00273112, 0.00294274, 0.00323358, 0.00292902, 0.00271144]]

Besides the saturation, the permanent magnet synchronous machine model can include flux and torque spatial harmonics. The spatial effects are parametrized using lookup tables. Either the d- and q- axis current tables, or the d- and q- axis fluxes can be provided. In addition a torque table can be used if available.

In case current tables are used, the corresponding mechanical angle vector and d- and q- axis flux vectors should be provided. Current tables should be provided in the form of nested Python lists, as shown in Figure 5.


theta_vector = [0.0, 22.5, 45.0, 67.5, 90.0]
psid_vector = [-0.17759843289, -0.05223218269499999, 0.07313406750000001, 0.19850031769499998, 0.32386656789]
psiq_vector = [-0.32096138538, -0.16050672498000002, -5.2064580000010796e-05, 0.16040259582, 0.32085725622]
id_table = [[[-233.3333332266475, -257.7293103580557, -316.8917613233176, -333.57733038563356, -524.5012794984455],
[-214.1362540654731, -179.8644557067018, -175.6095994946196, -181.0505387996648, -215.40138388018036],
[-36.92650378240601, -69.0586289788347, -63.273581686244526, -70.17063151820344, -40.77023976035882],
[267.6898480190032, 52.86421935401373, 33.6580242832348, 51.462420971634344, 266.73575462947525],
[719.0939587350539, 504.29327242411, 327.8805498461348, 505.3208160059561, 739.8031312300301]],

[[-518.6412851693793, -311.47136454996325, -302.8497902237722, -323.26411347945736, -484.76183994292415],
[-252.47146382293585, -187.917041119209, -178.50886480262463, -187.11355282815586, -254.94255002472855],
[-27.470288415968216, -71.54367706056314, -68.17667941441388, -70.94691442014319, -21.575177136365266],
[263.634217105358, 49.99306039271444, 33.85662343644734, 50.02324023988559, 287.38372287122087],
[487.8066465303234, 475.34138513129415, 343.28954740870137, 481.09585672382536, 886.1748266387335]],

[[-1358.0867863490253, -294.7644181190118, -316.2886710922492, -333.2853796951674, -518.7741520618608],
[-221.40609547432894, -180.6126549799535, -175.32783498152025, -181.39213200802254, -219.73544940320306],
[-38.02088727721427, -69.39880536269256, -63.591831678615975, -70.03870613567662, -39.99592319412275],
[285.0269280215043, 52.55932476567479, 33.48729415990562, 51.772679745456095, 284.5939396855646],
[734.8557131136035, 496.92968546349186, 325.83589711204013, 497.4153052130295, 741.5352609429758]],

[[-481.31401210416425, -324.3217707320712, -303.1230653884171, -319.94141667622443, -522.4177238390196],
[-255.25215748840276, -187.61666345042423, -178.62561705508995, -187.38544556322825, -252.53421982058447],
[-21.136661228127362, -71.02227901516046, -68.21328231570936, -71.46227873128916, -28.007081413419538],
[287.9372590077436, 49.97715317296145, 33.84805488373838, 49.995135090980924, 263.72969918521676],
[889.7033083203972, 480.3358765356305, 343.4912680789687, 475.0335963743356, 480.71904954910747]],

[[-233.3333332266475, -257.7293103580557, -316.8917613233176, -333.57733038563356, -524.5012794984455],
[-214.1362540654731, -179.8644557067018, -175.6095994946196, -181.0505387996648, -215.40138388018036],
[-36.92650378240601, -69.0586289788347, -63.273581686244526, -70.17063151820344, -40.77023976035882],
[267.6898480190032, 52.86421935401373, 33.6580242832348, 51.462420971634344, 266.73575462947525],
[719.0939587350539, 504.29327242411, 327.8805498461348, 505.3208160059561, 739.8031312300301]]]
iq_table = [[[-505.7767327606924, -280.3879247672038, -0.004979635775945353, 81.56072354263337, 388.022701946017],
[-362.12146235920517, -65.11706948656484, -0.009006689778155635, 65.30288347665756, 360.9222744404181],
[-354.10565650294666, -56.28518525873091, -0.023007195469517627, 56.50559644760159, 354.42659138277475],
[-524.7129199636797, -63.51586774014338, -0.01907211767377474, 63.685563133071724, 523.6006117473538],
[-495.7745746168233, -223.462055435398, -0.043131396443353134, 223.51990260596656, 486.3133476657266]],

[[-385.5547021702862, -116.62652914866759, -2.4328564864150097, 91.1395141118797, 385.6202158255354],
[-348.5643372214161, -62.474866982627866, -1.6141778719715782, 63.915430122112376, 348.38827743061563],
[-344.2317951973277, -53.217841641598724, -0.2829134174492452, 53.444266829119286, 344.3158304893939],
[-559.9321686062336, -63.97847245191365, 0.007447138963719371, 63.605984497759785, 494.10502040433096],
[-744.2509414789488, -220.91783037329884, 5.646314291601746, 226.49417767658827, 426.45076352257263]],

[[-423.6191488886197, -197.28821469674918, -0.029109158152621717, 82.36933719822528, 396.7502646889574],
[-360.7616050698228, -65.10159040008985, -0.012464979197774825, 65.19745059787274, 359.1885431242987],
[-355.1172303301486, -56.04912760800942, -0.02066736464822022, 56.14819320909155, 354.974375905354],
[-501.7906358828526, -63.50620117139304, -0.018480103433047602, 63.56419813700306, 501.286806969245],
[-559.602743618543, -224.5269544340933, -0.040533278535931805, 224.41147249208652, 557.825916546207]],

[[-385.7921708213368, -91.33910828723663, 2.4258636983859017, 85.7541393098867, 384.9268913902443],
[-348.98598069158527, -64.04405447565786, 1.5924463454305111, 62.3542611407755, 347.9667145908271],
[-344.8627213215603, -53.50384725036235, 0.2523346366688757, 53.16092671197423, 343.8275503768093],
[-493.585223980637, -63.69991599380379, -0.039915498956818986, 63.89491923222919, 559.4722578117016],
[-424.3689382948914, -226.77181375007936, -5.718555609379146, 220.65695426867234, 749.2674814023829]],

[[-505.7767327606924, -280.3879247672038, -0.004979635775945353, 81.56072354263337, 388.022701946017],
[-362.12146235920517, -65.11706948656484, -0.009006689778155635, 65.30288347665756, 360.9222744404181],
[-354.10565650294666, -56.28518525873091, -0.023007195469517627, 56.50559644760159, 354.42659138277475],
[-524.7129199636797, -63.51586774014338, -0.01907211767377474, 63.685563133071724, 523.6006117473538],
[-495.7745746168233, -223.462055435398, -0.043131396443353134, 223.51990260596656, 486.3133476657266]]]

Similarly, if flux tables are used, the corresponding mechanical angle vector and d- and q- axis current vectors should be provided. Flux tables should be provided in the form of nested Python lists, as shown in Figure 6.


theta_vector = [0.0, 22.5, 45.0, 67.5, 90.0]
id_vector = [-300.0, -150.0, 0.0, 150.0, 300.0]
iq_vector = [-300.0, -150.0, 0.0, 150.0, 300.0]
psid_table = [[[-0.092992778243, -0.13237251915, -0.16322147546, -0.13199157146, -0.10096193349],
[-0.0029494444998, -0.0083929999014, -0.029282905194, -0.0076414133404, -0.0013852031402],
[0.10440490171, 0.13644154255, 0.15471253507, 0.13778940842, 0.10531066716],
[0.18806823552, 0.22325538719, 0.2895834114, 0.22386412916, 0.18914953295],
[0.24210056956, 0.29284169573, 0.31930592972, 0.29305836422, 0.24223625458]],

[[-0.091400959733, -0.13475573804, -0.1749292499, -0.13344967473, -0.091505913051],
[0.010807087209, 0.0037682080669, -0.021177885886, 0.0050580803528, 0.013865421481],
[0.092979720949, 0.12680245185, 0.15720949383, 0.12830221086, 0.087157456451],
[0.18484038315, 0.23450690007, 0.28648263093, 0.23077487949, 0.1926615474],
[0.25554160821, 0.29268163818, 0.31651723863, 0.29290688656, 0.24704807003]],

[[-0.092992778243, -0.13237251915, -0.16322147546, -0.13199157146, -0.10096193349],
[-0.0029494444998, -0.0083929999014, -0.029282905194, -0.0076414133404, -0.0013852031402],
[0.10440490171, 0.13644154255, 0.15471253507, 0.13778940842, 0.10531066716],
[0.18806823552, 0.22325538719, 0.2895834114, 0.22386412916, 0.18914953295],
[0.24210056956, 0.29284169573, 0.31930592972, 0.29305836422, 0.24223625458]],

[[-0.091739531935, -0.13328209289, -0.17463672462, -0.13547915191, -0.091106283561],
[0.013974984528, 0.0048494387289, -0.021094593366, 0.0038619542714, 0.010457400808],
[0.086814220716, 0.12836592752, 0.15721463763, 0.1268579119, 0.093560402719],
[0.19321204329, 0.23077116549, 0.28644304894, 0.23461864289, 0.18407649916],
[0.24692274285, 0.29322474181, 0.31649361144, 0.29252690265, 0.25568574595]],

[[-0.092992778243, -0.13237251915, -0.16322147546, -0.13199157146, -0.10096193349],
[-0.0029494444998, -0.0083929999014, -0.029282905194, -0.0076414133404, -0.0013852031402],
[0.10440490171, 0.13644154255, 0.15471253507, 0.13778940842, 0.10531066716],
[0.18806823552, 0.22325538719, 0.2895834114, 0.22386412916, 0.18914953295],
[0.24210056956, 0.29284169573, 0.31930592972, 0.29305836422, 0.24223625458]]]
psiq_table = [[[-0.30267057235, -0.23873204132, -3.9742242698e-05, 0.23875633211, 0.30306175105],
[-0.31253878169, -0.27121809539, -2.2774634102e-05, 0.27112438205, 0.31253416609],
[-0.30684677005, -0.259210521, 6.9890032954e-05, 0.25852469615, 0.30648202774],
[-0.27257340534, -0.21876346148, -5.6740341132e-06, 0.21818529546, 0.27195331969],
[-0.24765650006, -0.14232824489, -6.7496759671e-07, 0.14203490233, 0.24758221016]],

[[-0.30314844055, -0.23689140972, 0.006975562102, 0.23574775985, 0.30351314397],
[-0.31581755327, -0.27606985039, 0.0039708418441, 0.27758097142, 0.31729056994],
[-0.31160085409, -0.26147296559, -4.8308402859e-06, 0.25981872322, 0.31166008436],
[-0.27067568901, -0.20688026038, -0.0023277204107, 0.21045636042, 0.2674130018],
[-0.23345074332, -0.14921595542, -0.0080053069921, 0.14892982912, 0.24254256344]],

[[-0.30267057235, -0.23873204132, -3.9742242698e-05, 0.23875633211, 0.30306175105],
[-0.31253878169, -0.27121809539, -2.2774634102e-05, 0.27112438205, 0.31253416609],
[-0.30684677005, -0.259210521, 6.9890032954e-05, 0.25852469615, 0.30648202774],
[-0.27257340534, -0.21876346148, -5.6740341132e-06, 0.21818529546, 0.27195331969],
[-0.24765650006, -0.14232824489, -6.7496759671e-07, 0.14203490233, 0.24758221016]],

[[-0.30347772145, -0.23574820553, -0.0070489207773, 0.23674928558, 0.30319387316],
[-0.31728064507, -0.27756643361, -0.003993128536, 0.27608560052, 0.31584615044],
[-0.31180110856, -0.25977013167, 2.3755038513e-05, 0.26144478567, 0.31137362134],
[-0.26710307569, -0.21045301205, 0.0023337513966, 0.2067830635, 0.27114401138],
[-0.24263545724, -0.14851609547, 0.0080074775793, 0.14941882074, 0.23337278011]],

[[-0.30267057235, -0.23873204132, -3.9742242698e-05, 0.23875633211, 0.30306175105],
[-0.31253878169, -0.27121809539, -2.2774634102e-05, 0.27112438205, 0.31253416609],
[-0.30684677005, -0.259210521, 6.9890032954e-05, 0.25852469615, 0.30648202774],
[-0.27257340534, -0.21876346148, -5.6740341132e-06, 0.21818529546, 0.27195331969],
[-0.24765650006, -0.14232824489, -6.7496759671e-07, 0.14203490233, 0.24758221016]]]


If a torque table is used, the corresponding mechanical angle vector and d- and q- axis current vectors should be provided. The torque table should be provided in the form of a nested Python list, as shown in Figure 7.


theta_vector_Te = [0.0, 22.5, 45.0, 67.5, 90.0]
id_vector_Te = [-300.0, -150.0, 0.0, 150.0, 300.0]
iq_vector_Te = [-300.0, -150.0, 0.0, 150.0, 300.0]
torque_table = [[[-461.04655919, -332.8598734071429, -1.1081461012, 332.19516658214286, 417.44568224],
[-310.17034254416666, -270.33688624595237, -0.6028780509916667, 269.57222287255956, 310.7964117258333],
[-181.42294254944443, -115.84374552687302, -0.13964706623777776, 116.38231039379764, 182.8068861733333],
[-71.39653398216667, -22.090781084223217, -0.2480898520933333, 22.702675578991077, 72.44508516358334],
[-17.389187999, 3.0152441219300004, -0.31449026734, -3.308692608017501, 17.560602092]],

[[-406.5500464167241, -330.2185009995751, -7.2103075736586435, 323.99610574970444, 393.13764143206896],
[-303.17428486106326, -258.37521056718805, -1.4688384703044242, 242.9134570621413, 279.117122536839],
[-193.58256053022032, -126.93593080655926, -0.04663152688847841, 115.51015942860606, 185.61982493497604],
[-82.87228742445406, -20.587316537185636, -2.0893218356421634, 18.94765146882643, 68.77152552149352],
[-11.835865058366366, 2.80535151599267, -4.42165218217588, -6.2915582802488705, 16.960317375474148]],

[[-434.3803288555173, -329.51918068817736, -0.978479661904311, 328.7406081689655, 411.19810940724136],
[-309.23001032433905, -266.99211121801216, -0.5271894872158025, 266.1513282419253, 308.8419751629023],
[-181.02066051524906, -115.72874560938229, -0.13495381758771985, 115.85456795407985, 181.61551272879308],
[-72.77033463190806, -21.76985714980434, -0.2098273789515268, 21.9973558092166, 73.07922227660056],
[-16.708790785637927, 4.057159049915403, -0.23920637331069816, -4.498794611058943, 16.951112875275868]],

[[-395.9036097492242, -327.4350358606774, 4.104308753119819, 326.5365435651355, 404.0223042287069],
[-281.1730763519828, -244.62356556263495, 0.18221397225358488, 256.6490751091097, 300.84784955936783],
[-186.29659264766764, -116.5868949390978, -0.24199789123452298, 126.11889945284456, 193.75063811867813],
[-70.16874964458478, -19.41093047180019, 1.6817520097219076, 20.172507135146788, 81.2285505420783],
[-16.95140339243965, 5.482216391687682, 3.8769159026112012, -3.4494739236762335, 12.050726226853453]],

[[-461.04655919, -332.8598734071429, -1.1081461012, 332.19516658214286, 417.44568224],
[-310.17034254416666, -270.33688624595237, -0.6028780509916667, 269.57222287255956, 310.7964117258333],
[-181.42294254944443, -115.84374552687302, -0.13964706623777776, 116.38231039379764, 182.8068861733333],
[-71.39653398216667, -22.090781084223217, -0.2480898520933333, 22.702675578991077, 72.44508516358334],
[-17.389187999, 3.0152441219300004, -0.31449026734, -3.308692608017501, 17.560602092]]]


In all cases the mechanical angle vector must be given as a list ranging from 0 to 360/pole_pairs. The number of points available for all lookup tables used is 215. If the total number of points provided in the lookup tables exceeds this number, the tables will be rescaled to work with fewer points. The resulting tables may have lower resolution than the original ones.

If iron losses are included, the corresponding direct and quadrature axis iron loss currents are calculated as follows:

${v}_{qs}={\omega }_{r}{\psi }_{ds}$

${R}_{Fe}=\frac{3{\omega }_{r}^{2}\left({\psi }_{ds}^{2}+{\psi }_{qs}^{2}\right)}{2{P}_{Fe}}$

${i}_{d,Fe}=\frac{{v}_{ds}}{{R}_{Fe}}$

${i}_{q,Fe}=\frac{{v}_{qs}}{{R}_{Fe}}$

Direct and quadrature axis components of iron loss currents are added to the corresponding components of stator currents, which provide the machine's electromagnetic torque:

${i}_{ds}={i}_{dm}+{i}_{d,Fe}$

${i}_{qs}={i}_{qm}+{i}_{q,Fe}$

Table 5. The permanent magnet synchronous machine iron losses variables
symbol description
ψds Direct axis component of the stator flux [Wb]
ψqs Quadrature axis component of the stator flux [Wb]
vds Direct axis component of the stator voltage [V]
vqs Quadrature axis component of the stator voltage [V]
ids Direct axis component of the stator current [A]
iqs Quadrature axis component of the stator current [A]
id,Fe Direct axis component of the iron loss current [A]
iq,Fe Quadrature axis component of the iron loss current [A]
idm Direct axis component of the stator current which determines torque production [A]
iqm Quadrature axis component of the stator current which determines torque production [A]
RFe Iron loss resistance [Ω]
PFe Total iron losses [W]
ωr Rotor electrical speed [rad/s] ( $=p{\omega }_{m}$ )
Note: The iron losses option is available only if nonlinear - spatial harmonic is chosen as the model type.

An example of a PMSM model including iron losses can be found in the pmsm iron losses.tse example in our Examples Explorer [examples\models\electrical drives\pmsm iron losses].

## Mechanical

Table 6. Mechanical parameters
symbol description
pms Machine number of pole pairs
Star/delta Stator winding connection (star or delta)
Jm Combined rotor and load moment of inertia [kgm2]
Friction coefficient Machine viscous friction coefficient [Nms]
Unconstrained mechanical angle Limiting mechanical angle between 0 and 2π

symbol description
Load source Load can be set from SCADA/external or from model (in model case, one signal processing input will appear)
Load ai offset Assigned offset value to the input signal representing external torque command
Load ai gain Assigned gain value to the input signal representing external torque command

External load enables you to use an analog input signal from a HIL analog channel with the load_ai_pin address as an external torque/speed load, and to assign offset (V) and gain (Nm/V) to the input signal, according to the formula:

${T}_{l}=load_ai_gain·\left(AI\left(load_ai_pin\right)+load_ai_offset\right)$

Note: An analog input pin may be overwritten if another component uses the same analog input pin. If another property (from the same or a different component) uses the same analog input pin, the input signal value will be applied to only one of those properties. For instance, if both the load and the resolver carrier signal use the same analog input pin, the signal value will only be applied only to one of these.

## Feedback

Table 8. Feedback parameters
symbol description
Encoder ppr Incremental encoder number of pulses per revolution
Encoder Z pulse length Z digital signal pulse length in periods. Can be Quarter length or Full period (default)
Resolver pole pairs Resolver number of pole pairs
Resolver carrier source Resolver carrier signal source selection (internal or external)
External resolver carrier source type External resolver carrier signal source type selection (single ended or differential); available only if the Resolver carrier source property is set to external
Resolver carrier frequency Resolver carrier signal frequency (internal carrier) [Hz]
Resolver ai pin 1 Resolver carrier input channel 1 address (external carrier)
Resolver ai pin 2 Resolver carrier input channel 2 address (external carrier); available only if the External resolver carrier source type property is set to differential
Resolver ai offset Resolver carrier input channel offset (external carrier)
Resolver ai gain Resolver carrier input channel gain (external carrier)
Absolute encoder protocol Standardized protocol providing the absolute machine encoder position
Singleturn bits Number of machine absolute encoder singleturn bits
Enable multiturn Enable multiturn absolute encoder support
Multiturn bits Number of machine absolute encoder multiturn bits
EnDat/SSI/BiSS clock DI pin Clock digital input pin for the chosen absolute encoder protocol type
Clock DI logic Clock DI pin logic: active high/active low
EnDat data DI pin EnDat data digital input pin
Data DI logic EnDat data DI pin logic: active high/active low

If an external resolver carrier source is selected, the source signal type can be set as either single ended or differential. The single ended external resolver carrier source type enables use of an analog input signal from the HIL analog channel with the res_ai_pin_1 address as the external carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal, according to the formula:

$res_carr_src=res_ai_gain·\left(AI\left(res_ai_pin_1\right)+res_ai_offset\right)$

The differential external resolver carrier source type enables use of two analog input signals from the HIL analog channels with the res_ai_pin_1 and the res_ai_pin_2 addresses. Analog signals from these HIL analog inputs are subtracted, and the resulting signal is used as the external differential carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal (similarly to the single ended case), according to the formula:

$res_carr_src=res_ai_gain·\left(\left(AI\left(res_ai_pin_1\right)-AI\left(res_ai_pin_2\right)\right)+res_ai_offset\right)$
Note: Differential external resolver signal support is available from the 2023.1 software version. Only the single ended external resolver option was available in previous software versions.
Note: In order to get a resolver signal with an amplitude of 1 when using an external carrier signal, the offset and the gain should be chosen in such a way that the resolver carrier signal has an amplitude of 1 after the adjustment. As shown in Figure 1, the sinusoidal signal used to generate external resolver carrier source is fed to HIL analog input 1. The analog input signal is scaled in order to get the resolver signals with an amplitude of 1.
Note: An analog input pin may be overwritten if another component uses the same analog input pin. If another property (from the same or a different component) uses the same analog input pin, the input signal value will be applied to only one of those properties. E.g. if both the load and the resolver carrier signal use the same analog input pin, the signal value will be applied only to one of these.

The following expression must hold in order to properly generate the encoder signals:

$4·enc_ppr·{f}_{m}{·T}_{s}\le 1$
Table 9. Variables in the encoder limitation expression
symbol description
enc_ppr Encoder number of pulses per revolution
fm Rotor mechanical frequency [Hz]
Ts Simulation time step [s]
Note: While the machine speed is positive, the encoder channel B signal leads the encoder channel A signal.
Note: Absolute encoder protocol is not supported on HIL402 (configurations: 1, 2, 3, and 4).

symbol description
Theta_ab Position of the stationary αβ reference frame, in respect to the stator phase a axis [rad]

The machine model output variables (currents, voltages and fluxes) can be observed from a stationary reference frame. There are two widely used approaches in electrical machine modeling: in the first, the alpha axis of the stationary reference frame lags by 90 degrees in regard to the stator phase a axis (used by default, and indicated in a) Figure 6. In the second one, the alpha axis is aligned with the stator phase a axis (indicated in b) Figure 6. The user can select between these two situations.

It is important to know the value of Theta_ab when the rotor position feedback is necessary. As an example, if a model uses the mechanical angle as a feedback signal and feeds it to one of the abc to dq, alpha beta to dq, dq to abc, or dq to alpha beta transformation blocks, the same transformation angle offset value should be used in both components to ensure the expected simulation results.

Note: This property is available only on certain machine components.

## Snubber

All machines with current source based circuit interfaces have the Snubber tab in the properties window where the value of snubber resistance can be set. Snubbers are necessary in the cases when an inverter or a contactor is directly connected to the machine terminals. This value can be set to infinite (inf), but it is not recommended when a machine is directly connected to the inverter since there will be a current source directly connected to an open switch. In this case, one of each switch pairs S1 and S2, S3 and S4, and S5 and S6 will be forced closed by the circuit solver in order to avoid the topological conflicts. On the other hand, with finite snubber values, there's always a path for the currents Ia and Ib, so all inverter switches can be open in this case. Circuit representations of this circuit without and with snubber resistors are shown in Figure 4 and Figure 5 respectively. Snubbers are connected across the current sources.

Note: Snubbers exist only in the machine components that have the current source based circuit interface.
Note: Snubbers are dynamic, which means that the snubber is dynamically added to circuit modes where topological conflicts are detected.
Table 11. Snubber parameters
symbol description
Rsnb stator Stator snubber resistance value [Ω]

## Output

This block tab enables a single, vectorized signal output from the machine. The output vector contains selected machine mechanical and/or electrical variables in the same order as listed in this tab.

Note: All machine components have the Execution rate, Electrical torque, Mechanical speed, and Mechanical angle, but the rest of the signals differ from component to component.
Table 12. Output parameters
symbol description
Execution rate Signal processing output execution rate [s]
Electrical torque Machine electrical torque [Nm]
Mechanical speed Machine mechanical angular speed [rad/s]
Mechanical angle Machine mechanical angle [rad]
Stator alpha axis current Alpha axis component of the stator current [A]
Stator beta axis current Beta axis component of the stator current [A]
Stator d-axis current Direct axis component of the stator current [A]
Stator q-axis current Quadrature axis component of the stator current [A]
Stator alpha axis flux Alpha axis component of the stator flux [Wb]
Stator beta axis flux Beta axis component of the stator flux [Wb]
Stator d-axis flux Direct axis component of the stator flux [Wb]
Stator q-axis flux Quadrature axis component of the stator flux [Wb]