EESM: Correction / Introduction of transfer ratios between rotor and stator #234

max-schenke · 2024-04-23T08:58:04Z

Refers to #233.

max-schenke · 2024-04-23T09:09:37Z

Could @MpenaLea elaborate on the theory a little bit?

M-Pena · 2024-04-23T14:03:29Z

Could @MpenaLea elaborate on the theory a little bit?

https://github.com/upb-lea/gym-electric-motor/blame/5443a5157f1320a9d3f8852efc37ae9e77bc619c/gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py#L98
#### Parameters taken from DOI: 10.1109/ICELMACH.2014.6960287 (C. D. Nguyen; W. Hofmann)
The source considers a stator-referred model for the rotor variables and parameters, obtained from [D. Schröder, "Elektrische Antriebe, Regelung von Antriebssystemen," Springer-Verlag, 3. Auflage, 2008], where it is stated: "die rotorseitigen Parameter sind auf den Statorkreis umgerechnet;".

A transformation is required to relate the model rotor parameters and variables to their physical counterpart. This transformation is not unique. It can be done, for example, as detailed in [C. Ong, Dynamic Simulation of Electric Machinery: Using MATLAB/SIMULINK. Prentice Hall PTR, 1998, isbn: 9780137237852, p. 267 and following], neglecting the effect of q-axis and damping windings in the rotor. From this transformation, one obtains:

i_F = (2/3)(N_f/N_s) * i_f
u_F = (N_s/N_f) * u_f
Psi_F = (N_s/N_f) * Psi_f
R_F = (3/2)(N_s/N_f)^2 * R_f
L_F = (3/2)(N_s/N_f)^2 * L_f
L_dF = L_Fd = (3/2)(N_s/N_f) * L_df

where the parameters and variables with "f" refer to the physical values, and with "F" these are referred to the stator circuit. N_s and N_f are the stator and field winding number of turns, respectively. The system of equations with rotor variables referred to the stator (F) results in a symmetrical coupling between d and F (L_dF = L_Fd), as is currently internally considered in the model. Appropriate transformations based on the above must be applied to have a valid physical interpretation of the results obtained from the model. Alternatively, the differential equations considered can be modified to only consider physical parameters and variables, e.g., as Q. K. Nguyen, et. al. DOI: [10.1109/ICPE.2015.7168165]

XyDrKRulof

Based on what @M-Pena wrote I think the formulas look correct (besides the magic 77). I would request @bhk11 to also have a deeper look at the model_constants matrix as it is quite difficult to dig through it. I just wonder whether parameters such as r_s and l_d do not have to be transformed?

Also, as a general note, I would like to know whether these changes we introduce here can be expected to be in favor for everyone using GEM or if it is only important for this specific motor parameter set? Or in other words: Should we make this transformation optional inside GEM? Couldn't users do the transformation themselves? What is the most common case here - to transform or not to transform?

XyDrKRulof · 2024-04-24T08:17:26Z

gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py

    r_s                    mOhm        15.55         Stator resistance
    r_e                    mOhm        7.2           Excitation resistance
    l_d                    mH          1.66          Direct axis inductance
    l_q                    mH          0.35          Quadrature axis inductance
    l_m                    mH          1.589         Mutual inductance
    l_e                    mH          1.74          Excitation inductance
    p                      1           3             Pole pair number
+    k                      1           65.21         Transfer ratio of number of windings (N_s / N_e)


Why do we introduce k as a parameter instead of N_s and N_e? Is that a common approach for EESM simulations?

XyDrKRulof · 2024-04-24T08:21:02Z

gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py

+        mp['l_E'] = mp['k'] ** 2 * 3/2 * mp['l_e']
+
+        mp['i_k_rs'] = 2 / 3 / mp['k'] # ratio (i_E / i_e)
+        mp['sigma'] = 1 - mp['l_M'] ** 2 / (mp['l_d'] * mp['l_E']) * 77


What does the 77 here stand for?

I intended to check whether this is caught by any unit tests 😁
Apparently its not...

Forgot to delete afterwards

bhk11 · 2024-04-24T12:28:37Z

gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py

+        mp['l_E'] = mp['k'] ** 2 * 3/2 * mp['l_e']
+
+        mp['i_k_rs'] = 2 / 3 / mp['k'] # ratio (i_E / i_e)
+        mp['sigma'] = 1 - mp['l_M'] ** 2 / (mp['l_d'] * mp['l_E']) * 77


magic number

bhk11 · 2024-04-24T12:29:55Z

gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py

+            [                     0,                          -mp['r_s'] / mp['sigma'],          0, mp['l_M'] * mp['r_E'] / (mp['sigma'] * mp['l_E']) * mp['i_k_rs'],                        1 / mp['sigma'],   0, -mp['l_M'] * mp['k'] / (mp['sigma'] * mp['l_E']),                    0,                            mp['l_q'] * mp['p'] / mp['sigma'],                                   0],
+            [                     0,                                                 0, -mp['r_s'],                                                                0,                                      0,   1,                                                0, -mp['l_d'] * mp['p'],                                                            0, -mp['p'] * mp['l_M'] * mp['i_k_rs']],
+            [                     0, mp['l_M'] * mp['r_s'] / (mp['sigma'] * mp['l_d']),          0,                          -mp['r_E'] / mp['sigma'] * mp['i_k_rs'], -mp['l_M'] / (mp['sigma'] * mp['l_d']),   0,                            mp['k'] / mp['sigma'],                    0, -mp['p'] * mp['l_M'] * mp['l_q'] / (mp['sigma'] * mp['l_d']),                                   0],
+            [               mp['p'],                                                 0,          0,                                                                0,                                      0,   0,                                                0,                    0,                                                            0,                                   0],


When I use the linear model, which Mario provide to us, the matrix should look like:
self._model_constants = np.array([ # omega, i_d, i_q, i_e, u_d, u_q, u_e, omega * i_d, omega * i_q, omega * i_e [ 0, -mp['r_s'] / (mp['sigma'] * mp['l_d']), 0, mp['l_M'] * mp['r_E'] / (mp['sigma'] * mp['l_E'] * mp['l_d']) * mp['i_k_rs'], 1 / (mp['sigma'] * mp['l_d']), 0, -mp['l_M'] * mp['k'] / (mp['sigma'] * mp['l_E'] * mp['l_d']), 0, mp['l_q'] * mp['p'] / (mp['sigma'] * mp['l_d']), 0], [ 0, 0, -mp['r_s'] / (mp['l_q']), 0, 0, 1 / (mp['l_q']), 0, -mp['l_d'] * mp['p'] / (mp['l_q']), 0, -mp['p'] * mp['l_M'] * mp['i_k_rs'] / (mp['l_q'])], [ 0, mp['l_M'] * mp['r_s'] / (mp['sigma'] * mp['l_d'] * mp['l_E']), 0, -mp['r_E'] / (mp['sigma'] * mp['l_E']) * mp['i_k_rs'], -mp['l_M'] / (mp['sigma'] * mp['l_d'] * mp['l_E']), 0, mp['k'] / (mp['sigma'] * mp['l_E']), 0, -mp['p'] * mp['l_M'] * mp['l_q'] / (mp['sigma'] * mp['l_d'] * mp['l_E']), 0], [ mp['p'], 0, 0, 0, 0, 0, 0, 0, 0, 0], ])
to my opinion.

The latest changes look correct as far as I can tell, accounting for the modifications done in lines 144-146. In your suggestion, I am missing some parameters in the equations for d(i_e)/dt. That whole matrix row must be divided by mp['i_k_rs']

I would agree. According to my notes, I have written down the equation for di_E/dt.

That should be correct now:

self._model_constants = np.array([ # omega, i_d, i_q, i_e, u_d, u_q, u_e, omega * i_d, omega * i_q, omega * i_e
[ 0, -mp['r_s'] / (mp['sigma'] * mp['l_d']), 0, mp['l_M'] * mp['r_E'] / (mp['sigma'] * mp['l_E'] * mp['l_d']) * mp['i_k_rs'], 1 / (mp['sigma'] * mp['l_d']), 0, -mp['l_M'] * mp['k'] / (mp['sigma'] * mp['l_E'] * mp['l_d']), 0, mp['l_q'] * mp['p'] / (mp['sigma'] * mp['l_d']), 0],
[ 0, 0, -mp['r_s'] / (mp['l_q']), 0, 0, 1 / (mp['l_q']), 0, -mp['l_d'] * mp['p'] / (mp['l_q']), 0, -mp['p'] * mp['l_M'] * mp['i_k_rs'] / (mp['l_q'])],
[ 0, mp['l_M'] * mp['r_s'] / (mp['sigma'] * mp['l_d'] * mp['l_E'] * mp['i_k_rs']), 0, -mp['r_E'] / (mp['sigma'] * mp['l_E']), -mp['l_M'] / (mp['sigma'] * mp['l_d'] * mp['l_E'] * mp['i_k_rs']), 0, mp['k'] / (mp['sigma'] * mp['l_E'] * mp['i_k_rs']), 0, -mp['p'] * mp['l_M'] * mp['l_q'] / (mp['sigma'] * mp['l_d'] * mp['l_E'] * mp['i_k_rs']), 0],
[ mp['p'], 0, 0, 0, 0, 0, 0, 0, 0, 0],
])

bhk11

I didn't check the Jacobian yet. Would you agree to the changes for the _model_constants?

XyDrKRulof · 2024-05-13T08:45:58Z

I am still somewhat questioning why we introduce the transfer ratio of number of windings instead of the number of windings themselves. Especially because all other motor parameters are actual physical properties. I don't mind as long as the logic is now correct, though.

XyDrKRulof · 2024-05-13T08:47:01Z

Mistakenly closed this pull request. Sorry

M-Pena · 2024-05-14T17:14:34Z

gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py

+                [                       -mp['r_s'] / (mp['l_d'] * mp['sigma']),                          mp['l_q'] / (mp['sigma'] * mp['l_d']) * omega * mp['p'], mp['l_M'] * mp['r_e'] / (mp['sigma'] * mp['l_d'] * mp['l_E']) * mp['i_k_rs'], 0],
+                [                     -mp['l_d'] / mp['l_q'] * omega * mp['p'],                                                           -mp['r_s'] / mp['l_q'],                      -omega * mp['p'] * mp['l_E'] / mp['l_q'] * mp['i_k_rs'], 0],
+                [mp['l_M'] * mp['r_s'] / (mp['sigma'] * mp['l_d'] * mp['l_E']), -omega * mp['p'] * mp['l_M'] * mp['l_q'] / (mp['sigma'] * mp['l_d'] * mp['l_E']),                                        -mp['r_E'] / mp['l_E'] * mp['i_k_rs'], 0],
+                [                                                            0,                                                                                0,                                                                            0, 0],
            ]),


I believe lines 198-201 should be replaced with
[ -mp['r_s'] / (mp['l_d'] * mp['sigma']), mp['l_q'] / (mp['sigma'] * mp['l_d']) * omega * mp['p'], mp['l_M'] * mp['r_E'] / (mp['sigma'] * mp['l_d'] * mp['l_E']) * mp['i_k_rs'], 0],
[ -mp['l_d'] / mp['l_q'] * omega * mp['p'], -mp['r_s'] / mp['l_q'], -omega * mp['p'] * mp['l_M'] / mp['l_q'] * mp['i_k_rs'], 0],
[mp['l_M'] * mp['r_s'] / (mp['sigma'] * mp['l_d'] * mp['l_E']* mp['i_k_rs']), -omega * mp['p'] * mp['l_M'] * mp['l_q'] / (mp['sigma'] * mp['l_d'] * mp['l_E']* mp['i_k_rs']), -mp['r_E'] / (mp['sigma'] * mp['l_E'])], 0],
[ 0, 0, 0, 0],

I have the same solution.

M-Pena · 2024-05-14T17:20:12Z

gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py

-                -mp['p'] * mp['l_d'] / mp['l_q'] * state[self.I_SD_IDX] - mp['p'] * mp['l_m'] / mp['l_q'] * state[self.I_E_IDX],
-                -mp['p'],
+                -mp['p'] * mp['l_d'] / mp['l_q'] * state[self.I_SD_IDX] - mp['p'] * mp['l_M'] / mp['l_q'] * state[self.I_E_IDX] * mp['i_k_rs'],
+                -mp['p'] * mp['l_M'] * mp['l_q'] / (mp['sigma'] * mp['l_d'] * mp['l_E']),


Correction to line 206
-mp['p'] * mp['l_M'] * mp['l_q'] / (mp['sigma'] * mp['l_d'] * mp['l_E'] * mp['i_k_rs']) * state[self.I_SQ_IDX],

Isn't there a / mp['sigma'] missing in line 204?

M-Pena · 2024-05-14T17:25:09Z

gym_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py

-                1.5 * mp['p'] * (mp['l_e'] * state[self.I_E_IDX] + (mp['l_d'] - mp['l_q']) * state[self.I_SD_IDX]),
-                1.5 * mp['p'] * mp['l_e'] * state[self.I_SQ_IDX],
+                1.5 * mp['p'] * (mp['l_E'] * state[self.I_E_IDX] * mp['i_k_rs'] + (mp['l_d'] - mp['l_q']) * state[self.I_SD_IDX]),
+                1.5 * mp['p'] * mp['l_E'] * state[self.I_SQ_IDX],
                0,


Lines 211 and 212
1.5 * mp['p'] * (mp['l_M'] * state[self.I_E_IDX] * mp['i_k_rs'] + (mp['l_d'] - mp['l_q']) * state[self.I_SD_IDX]),

1.5 * mp['p'] * mp['l_M'] * mp['i_k_rs'] * state[self.I_SQ_IDX],

This correction looks also fine to me.

bhk11

Looks correct to me.

introduce transfer ratio k between rotor and stator windings

40c3367

max-schenke requested review from atra94, XyDrKRulof and M-Pena April 23, 2024 08:58

max-schenke requested review from bhk11 and removed request for atra94 April 23, 2024 09:10

XyDrKRulof requested changes Apr 24, 2024

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bhk11 reviewed Apr 24, 2024

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bhk11 requested changes Apr 24, 2024

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max-schenke changed the base branch from master to nightly April 25, 2024 07:08

remove magic number

3977a58

max-schenke requested a review from XyDrKRulof May 13, 2024 07:36

XyDrKRulof closed this May 13, 2024

XyDrKRulof reopened this May 13, 2024

XyDrKRulof approved these changes May 13, 2024

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M-Pena reviewed May 14, 2024

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fixes to EESM ODE and jacobian

124b7b6

bhk11 approved these changes May 15, 2024

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max-schenke and others added 3 commits May 15, 2024 15:43

merge with current nightly

e363003

update python version requirement to >=3.9

eb00223

Merge branch 'nightly' into EESM_transformations

e7406f6

max-schenke merged commit 4ee85c4 into nightly May 17, 2024
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max-schenke mentioned this pull request May 17, 2024

EESM: rotor quantities differ from the physical system #233

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EESM: Correction / Introduction of transfer ratios between rotor and stator #234

EESM: Correction / Introduction of transfer ratios between rotor and stator #234

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EESM: Correction / Introduction of transfer ratios between rotor and stator #234

EESM: Correction / Introduction of transfer ratios between rotor and stator #234

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