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.
Figure 2.
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.
Figure 4.
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.
Table 1.
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 |
Table 2.
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 |
Figure 6.
3D graph of energy consumption response to variations in manoeuvre time (Tm) and acceleration time (Tεε).
Table 3.
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 |
Table A1.
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 | - |