Add the cross-saturation compensation to the signal-injection method (#191)

Author: mhinkkan

docs/source/conf.py

@@ -26,7 +26,7 @@
 author = "Aalto Electric Drives"
 
 # The full version, including alpha/beta/rc tags
-release = "0.7.0"
+release = "0.7.1"
 
 # -- General configuration -------------------------------------------------------------
 

docs/source/model/drive/induction_machine.md

@@ -110,7 +110,7 @@ width: 100%
 align: center
 alt: Inverse-Gamma model of an induction machine
 ---
-*Figure 3:* Inverse-Γ model of an induction machine.
+*Figure 3:* Inverse-Γ model of an induction machine. If main-flux saturation is included, the parameters become nonlinear functions of the stator flux magnitude, $\Lsgm(\abspsis)$, $\RR(\abspsis)$, and $\LM(\abspsis)$.
 ```
 
 ```{figure} ../figs/im_inv_gamma.svg
@@ -120,7 +120,7 @@ width: 100%
 align: center
 alt: Inverse-Gamma model of an induction machine
 ---
-*Figure 3:* Inverse-Γ model of an induction machine.
+*Figure 3:* Inverse-Γ model of an induction machine. If main-flux saturation is included, the parameters become nonlinear functions of the stator flux magnitude, $\Lsgm(\abspsis)$, $\RR(\abspsis)$, and $\LM(\abspsis)$.
 ```
 
 If the magnetic saturation is omitted, the inverse-Γ model is mathematically identical to the Γ model {cite}`Sle1989`. The parameters can be transformed as

docs/source/model/drive/synchronous_machine.md

@@ -136,7 +136,7 @@ label: sm_flux_linkage_map
 
 ```
 
-In practice, these maps are typically realized as lookup tables or explicit mathematical functions, see, e.g., {cite}`Hin2017,Lel2024`.
+In practice, these maps can be realized as lookup tables, explicit mathematical functions {cite}`Hin2017,Woo2023,Lel2024`, or neural networks {cite}`Lee2025`.
 
 Methods for manipulating and plotting the magnetic models are provided in the classes {class}`motulator.drive.utils.MagneticModel`, {func}`motulator.drive.utils.plot_map`, and {func}`motulator.drive.utils.plot_flux_vs_current`. If the magnetic model is lossless and physically feasible, it can be numerically inverted between the two representations, see the {func}`motulator.drive.utils.MagneticModel.invert` method.
 

docs/source/model/figs/im_gamma.svg

@@ -14,7 +14,6 @@ @ARTICLE{Awa2018
 	doi = {10.1109/TIA.2018.2862410},
 }
 
-
 @ARTICLE{Awa2019a,
 	author = {Awan and Saarakkala and Hinkkanen},
 	title = {Flux-linkage-based current control of saturated synchronous motors},
@@ -232,6 +231,14 @@ @INPROCEEDINGS{Kuk2021
 	doi = {10.1109/ISGTEurope52324.2021.9640206},
 }
 
+@ARTICLE{Lee2025,
+	author = {Lee and Lee and Lee and Jin and Yoon},
+	title = {Estimation of flux saturation model for {SynRMs} using artificial neural network},
+	journal = {IEEE Trans. Ind. Appl.},
+	year = {2025},
+	doi = {10.1109/TIA.2025.3532412},
+}
+
 @INPROCEEDINGS{Lel2024,
 	author = {Lelli and Hinkkanen and {Giulii Capponi}},
 	booktitle = {Proc. ICEM},
@@ -367,3 +374,11 @@ @ARTICLE{Ver1988
 	year = {1988},
 	doi = {10.1109/41.3067},
 }
+
+@ARTICLE{Woo2023,
+	author = {Woo and Park and Choi and Lee and Yoon},
+	title = {Flux saturation model including cross saturation for synchronous reluctance machines and its identification method at standstill},
+	journal = {IEEE Trans. Ind. Electron.},
+	year = {2023},
+	doi = {10.1109/TIE.2022.3174233},
+}

docs/source/model/figs/im_inv_gamma.svg

@@ -76,13 +76,10 @@
 # Configure the control system.
 
 # Create the flux and current maps for the control system
-curr_map = fem_flux_map.invert()
-
-# In this example, the flux maps are not given to the control system. Therefore, the
-# flux linkages are iteratively computed from the currents in this example. You could
-# add the flux maps to the control system by adding `psi_s_dq_fcn=fem_flux_map` below.
-est_par = control.SaturatedSynchronousMachinePars(n_p=2, R_s=0.2, i_s_dq_fcn=curr_map)
-
+fem_curr_map = fem_flux_map.invert()
+est_par = control.SaturatedSynchronousMachinePars(
+    n_p=2, R_s=0.2, i_s_dq_fcn=fem_curr_map, psi_s_dq_fcn=fem_flux_map
+)
 # Since the inertia `J` is provided, the mechanical-model-based speed observer is used
 cfg = control.FluxVectorControllerCfg(i_s_max=2 * base.i, J=2 * 0.0042, alpha_i=0)
 vector_ctrl = control.FluxVectorController(est_par, cfg, sensorless=True)

docs/source/model/figs/sm.svg

@@ -120,7 +120,6 @@
     n_p=2, R_s=0.63, i_s_dq_fcn=est_curr_map, psi_s_dq_fcn=est_flux_map
 )
 cfg = control.FluxVectorControllerCfg(i_s_max=2 * base.i, J=0.05, alpha_i=0)
-# cfg = control.FluxVectorControllerCfg(i_s_max=2 * base.i)
 vector_ctrl = control.FluxVectorController(est_par, cfg, sensorless=True)
 speed_ctrl = control.SpeedController(J=0.05, alpha_s=2 * np.pi * 4)
 ctrl = control.VectorControlSystem(vector_ctrl, speed_ctrl)

docs/source/refs.bib

@@ -1,8 +1,10 @@
 Signal Injection
 ----------------
 
-These examples demonstrate a square-wave signal injection for low-speed operation based on [#Kim2012]_. A phase-locked loop is used to track the rotor position. For a wider speed range, signal injection could be combined to a model-based observer. The effects of magnetic saturation are not compensated for in this version.
+These examples demonstrate a square-wave signal injection for low-speed operation based on [#Kim2012]_. Cross-saturation errors are compensated for using flux maps [#You2018]_. A phase-locked loop is used to track the rotor position. For a wider speed range, signal injection could be combined to a model-based observer.
 
 .. rubric:: References
 
 .. [#Kim2012] Kim, Ha, Sul, "PWM switching frequency signal injection sensorless method in IPMSM," IEEE Trans. Ind. Appl., 2012, https://doi.org/10.1109/TIA.2012.2210175
+
+.. [#You2018] Yousefi-Talouki, Pescetto, Pellegrino, Boldea, "Combined active flux and high-frequency injection methods for sensorless direct-flux vector control of synchronous reluctance machines," IEEE Trans. Power Electron., 2018, https://doi.org/10.1109/TPEL.2017.2697209