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Energy Optimal Control of Electromechanical Systems: Trade-off Demands

Branislav Ftorek

Branislav Ftorek

Department of Applied Mathematics, Faculty of Mechanical Engineering, University of ŽilinaŽilina, Slovakia
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Ftorek, Branislav
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Vladimír Vavrúš

Vladimír Vavrúš

Department of Power Systems and Electric Drives, Faculty of Electrical Engineering and Information Technology, University of ŽilinaŽilina, Slovakia
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Vavrúš, Vladimír
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Ján Šimon

Ján Šimon

Department of Applied Mathematics, Faculty of Mechanical Engineering, University of ŽilinaŽilina, Slovakia
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Šimon, Ján
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Ján Vittek

Ján Vittek

Department of Applied Mathematics, Faculty of Mechanical Engineering, University of ŽilinaŽilina, Slovakia
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Vittek, Ján
  
Jun 21, 2025
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Article Category: Research Paper
Published Online: Jun 21, 2025
Page range: 177 - 188
Received: Mar 03, 2025
Accepted: May 27, 2025
DOI: https://doi.org/10.2478/pead-2025-0012
Keywords
© 2025 Branislav Ftorek et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

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 colour Tm (s) Tεε (s) WT (Wh) Energy increase (%)
Red (min. point) 4100.025 96.788 2104 0.0
Blue 2050.012 48.394 2157 +2.52
Green 1025.006 24.197 2409 +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
86.094 371.8 –352.3 4468.2 8052.2 4714.9
Tm2 = 300 s
75.858 325.1 –305.3 4062.8 6767.9 4251.8
Tm3 = 330 s
67.946 289.0 –268.9 3758.0 5855.7 3907.6

IM nominal parameters_

Nominal output power PN 720 kW Nominal frequency fN 50 Hz
Nominal speed ωN 156.24 rads–1 Nominal voltage UN 780 V
Nominal current IN 650 A Maximal current Imax 810 A
Nominal torque ΓN 4929 Nm Nominal power factor cosφN 0.88 -
Pole-pairs number p 2 - Total resistance Rc 0.0952 Ω
Stator resistance Rs 0.0358 Ω Rotor resistance Rr 0.032 Ω
Mutual inductance Lm 15.5 mH Leakage inductance Lσ 12 mH
Total mass Mu 45.8 t Total moment of inertia Jr 470 kgm2
Wheel average diameter Dwa 0.91 m Gear ratio u 3.73 -

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
86.094 228.1 –187.8 4659.4 9293.0 4921.8
Tm2 = 300 s
75.858 196.2 –159.1 4207.3 7773.7 4406.7
Tm3 = 330 s
67.946 170.7 –135.8 3876.7 6704.5 4032.3
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