Figure 1.
Topology of a TSS with the ARB. ARB, advanced rail balancer; PSD, phase shifting device; TSS, traction substation.
Figure 2.
Block diagram of the proposed control scheme. PI, proportional integration; SOGI-PLL, second-order generalized integrator phase-locked loop.
Figure 3.
Steinmetz’s symmetrising circuit and corresponding phasor diagram illustrating the function of the electronic balancer.
Figure 4.
Timeline visualising control and modulation delay of the system.
Figure 5.
Influence of different discretisation techniques on R controller Bode’s characteristics. FOH, first-order hold.
Figure 6.
Bode’s characteristics of discrete R controllers with ARB control system latency and ideal characteristic of continuous R controller without latency. ARB, advanced rail balancer; FOH, first-order hold.
Figure 7.
Scheme of the laboratory model of ARB. ARB, advanced rail balancer.
Figure 8.
Laboratory prototype for experimental validation.
Table 1.
Parameters of the experimental model.
| Parameter | Description | Value |
|---|---|---|
| Ug12, Ug23, Ug31 | Line-line voltage | 400 VRMS/50 Hz |
| LCHB | Filtration inductor | 4 mH |
| CCHB | DC-link capacitor | 2.5 mF |
| UDC | DC-link voltage | 180 V |
| ΣUDC | DC-link voltage summation | 4 × 180 V = 720 V |
| fPWM | PWM frequency | 1 kHz |
| tdt | Dead time duration | 1 µs |
| PI: KP; TI | PI gain and time constant | 0.04, 0.2 s |
| PR(1): KP; KR | PR gain and time constant | 2; 200 |
| A load | RL load parameters | 16 Ω, 20 mH (P(1) = 8.66 kW, Q(1) = 3.4 kVAr) |
| B load | Diode rectifier load parameters | AC: 10 mH; DC: 16 Ω, 80 mH (P(1) = 6.7 kW, Q(1) = 4.3 kVAr) |
Figure 9.
RL load, ARB off, blue Ug1 [250 V/div], cyan Ig1 [10 A/div], purple Ug12 [250 V/div], green Icat [10 A/div] (aligned with Ig1). ARB, advanced rail balancer; THD, total harmonic distortion.
Figure 10.
RL load, ARB—balancing ON + harmonics filtration OFF, blue Ug1 [250 V/div], cyan Ig1 [10 A/div], purple Ug12 [250 V/div], green Icat [10A/div]. ARB, advanced rail balancer; THD, total harmonic distortion.
Figure 11.
RL load, ARB—balancing ON + harmonics filtration OFF, blue UCHB12 [250 V/div], cyan ICHB12 [10 A/div], purple ICHB23 [10 A/div], green ICHB31 [10 A/div]. ARB, advanced rail balancer.
Figure 12.
RL load, ARB—balancing ON + harmonics filtration OFF, blue Ug1 [250 V/div], cyan Ig1 [10 A/div], purple Ig2 [10 A/div], green Ig3 [10 A/div]. ARB, advanced rail balancer; THD, total harmonic distortion.
Figure 13.
RL load, ARB—balancing ON + harmonics filtration ON, common R controllers, blue Ug1 [250 V/div], cyan ICHB12 [10 A/div], purple ICHB23 [10 A/div], green ICHB31 [10 A/div]. ARB, advanced rail balancer.
Figure 14.
RL load, ARB—balancing ON + harmonics filtration ON, advanced R controllers, blue Ug1 [250 V/div], cyan Ig1 [10 A/div], purple Ig2 [10 A/div], green Ig3 [10 A/div]. ARB, advanced rail balancer; THD, total harmonic distortion.
Figure 15.
Load: Diode rectifier with RL load, ARB off, blue Ug1 [250 V/div], cyan Ig1 [10 A/div], purple Ug12 [250 V/div], green Icat [10 A/div] (aligned with Ig1). ARB, advanced rail balancer; THD, total harmonic distortion.
Figure 16.
Load: Diode rectifier with RL load, ARB—balancing ON + harmonics filtration ON with advanced R controllers, blue UCHB12 [250 V/div], cyan ICHB12 [10 A/div], purple ICHB23 [10 A/div], green ICHB31 [10 A/div]. ARB, advanced rail balancer.
Figure 17.
Load: Diode rectifier with RL load, ARB—balancing ON + harmonics filtration ON with advanced R controllers, blue Ug1 [250 V/div], cyan Ig1 [10 A/div], purple Ig2 [10 A/div], green Ig3 [10 A/div]. ARB, advanced rail balancer; THD, total harmonic distortion.