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Energy Optimal Control of Electromechanical Systems: Trade-off Demands Cover

Energy Optimal Control of Electromechanical Systems: Trade-off Demands

Open Access
|Jun 2025

Figures & Tables

Figure 1.

Overall control system for verification of energy-saving control of train unit with induction motors. ENOC, energy near-optimal control; EOC, energy optimal control; FOC, field-oriented control.
Overall control system for verification of energy-saving control of train unit with induction motors. ENOC, energy near-optimal control; EOC, energy optimal control; FOC, field-oriented control.

Figure 2.

Energy-saving time profiles of the prescribed speed for EOC and ENOC. ENOC, energy near-optimal control; EOC, energy optimal control.
Energy-saving time profiles of the prescribed speed for EOC and ENOC. ENOC, energy near-optimal control; EOC, energy optimal control.

Figure 3.

Prescribed time functions of acceleration, speed and position for Tm2 = 300 s. ENOC, energy near-optimal control; EOC, energy optimal control.
Prescribed time functions of acceleration, speed and position for Tm2 = 300 s. ENOC, energy near-optimal control; EOC, energy optimal control.

Figure 4.

EOC profiles of speed, current and total energy consumption. EOC, energy optimal control.
EOC profiles of speed, current and total energy consumption. EOC, energy optimal control.

Figure 5.

ENOC profiles of speed, current and total energy consumption. ENOC, energy near-optimal control.
ENOC profiles of speed, current and total energy consumption. ENOC, energy near-optimal control.

Figure 6.

3D graph of energy consumption response to variations in manoeuvre time (Tm) and acceleration time (Tεε).
3D graph of energy consumption response to variations in manoeuvre time (Tm) and acceleration time (Tεε).

Total consumed energy_

Point colourTm (s)Tεε (s)WT (Wh)Energy increase (%)
Red (min. point)4100.02596.78821040.0
Blue2050.01248.3942157+2.52
Green1025.00624.1972409+14.5

Peak and minimum values of speed, current and energy for different manoeuvre times under the EOC strategy_

Vmax (km/h)Imax (A)Imin (A)Wsh (Wh)Wmax (Wh)WT (Wh)
Tm1 = 270 s
86.094371.8–352.34468.28052.24714.9
Tm2 = 300 s
75.858325.1–305.34062.86767.94251.8
Tm3 = 330 s
67.946289.0–268.93758.05855.73907.6

IM nominal parameters_

Nominal output powerPN720kWNominal frequencyfN50Hz
Nominal speedωN156.24rads–1Nominal voltageUN780V
Nominal currentIN650AMaximal currentImax810A
Nominal torqueΓN4929NmNominal power factorcosφN0.88-
Pole-pairs numberp2-Total resistanceRc0.0952Ω
Stator resistanceRs0.0358ΩRotor resistanceRr0.032Ω
Mutual inductanceLm15.5mHLeakage inductanceLσ12mH
Total massMu45.8tTotal moment of inertiaJr470kgm2
Wheel average diameterDwa0.91mGear ratiou3.73-

Peak and minimum values of speed, current and energy for different manoeuvre times under the ENOC strategy_

Vmax (km/h)Imax (A)Imin (A)Wsh (Wh)Wmax (Wh)WT (Wh)
Tm1 = 270 s
86.094228.1–187.84659.49293.04921.8
Tm2 = 300 s
75.858196.2–159.14207.37773.74406.7
Tm3 = 330 s
67.946170.7–135.83876.76704.54032.3
DOI: https://doi.org/10.2478/pead-2025-0012 | Journal eISSN: 2543-4292 | Journal ISSN: 2451-0262
Language: English
Page range: 177 - 188
Submitted on: Mar 3, 2025
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Accepted on: May 27, 2025
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Published on: Jun 21, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2025 Branislav Ftorek, Vladimír Vavrúš, Ján Šimon, Ján Vittek, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.