Table 1.
Comparison of voltage unbalance detection and measurement methods.
| Article | Signals used | Amount of sensors required | Sampling frequency | Tested for DC-link capacitance change | Uncontrolled rectifier specific |
|---|---|---|---|---|---|
| Widagdo et al. (2024) | Load phase currents | 3 | Unknown | No | No |
| Li et al. (2022) | Phase voltages | 3 | 8,000 Hz | No | No |
| Al-Naimi et al. (2021) | Phase voltages | 3 | 1,000 Hz | No | No |
| Sun et al. (2013) | Phase voltages | 3 | 600 Hz | No | No |
| Bogarra et al. (2022) | DC-link voltage ripple | 1 | 50,000 Hz | No | Yes |
| This paper | DC-link voltage ripple | 1 | 10,000 Hz | Yes | Yes |
Figure 1.
Block diagram of the analysed series hybrid drive architecture. ICE, internal combustion engine; PMSG, permanent magnet synchronous generator.
Figure 2.
Detailed architecture of the series powertrain featuring a six-pulse rectifier and DC-link circuit. DC-link, direct current link; ICE, internal combustion engine; PMSG, permanent magnet synchronous generator.
Figure 3.
Stator current spectrum - PMSM rotor damage with diagnostic frequencies marked by arrows (Skowron et al., 2022). PMSMs, permanent magnet synchronous motors.
Figure 4.
Amplitude of the stator current (spectrum analysis) - PMSM stator damage – N meaning the amount of short-circuited winding turns (Pietrzak et al., 2023). PMSMs, permanent magnet synchronous motors.
Figure 5.
Schematic of the series HEV simulation model. DC-link, direct current link; HEV, hybrid electric vehicle; PMSG, permanent magnet synchronous generator; RL load, resistive–inductive load.
Figure 6.
Source and DC-link voltages with frequency spectrum analysis under balanced voltage. DC-link, direct current link.
Figure 7.
Source and DC-link voltages with frequency spectrum analysis under 50% increase of phase B voltage. DC-link, direct current link.
Figure 8.
Source, DC-link voltages with frequency spectrum analysis and AC/DC input currents under 50% increase of phase B voltage with inverter as a load. AC, alternating current; DC, direct current; DC-link, direct current link.
Figure 9.
Bispectrum analysis of UDC under changes of phase B voltages. From the left: balanced voltage, 120% of phase B voltage, 140% of phase B voltage.
Table 2.
Simulation model parameters
| Parameters | Value |
|---|---|
| Stator single phase resistance | 2.875 Ω |
| Stator single phase inductance | 9.5 mH |
| Generator voltage frequency | 50 Hz |
| DC-link capacitance | 4.7 mF |
| Load inductance | 1 mH |
| Load resistance | 100 Ω |
Figure 10.
DC-link voltage waveforms for symmetrical stator resistances and increased phase B resistance (a) and PMSG stator phase currents under balanced and unbalanced conditions (b). DC-link, direct current link; PMSG, permanent magnet synchronous generator.
Figure 11.
Comparison of UDC harmonic amplitudes under different levels of phase B resistance asymmetry: (a) 50% resistance increase, (b) 1% and 10% resistance increase.
Figure 12.
Comparison of harmonics values of UDC while multiple phases resistance change.
Figure 13.
Schematic of experimental setup. DC-link, direct current link.
Figure 14.
Test setup core components: three autotransformers (a) and AC/DC/AC converter (b). AC, alternating current; DC, direct current.
Figure 15.
Experiment flowchart.
Figure 16.
Waveforms of UDC under DC-link B phase voltage change. DC-link, direct current link.
Figure 17.
Frequency spectrum of chosen UDC harmonics under different B phase voltage values (a) and frequency spectrum of chosen UDC harmonics under different A and B phase voltage values (b).
Figure 18.
Frequency spectrum of chosen UDC harmonics under balanced (a) and unbalanced (b) condition. FFT, fast Fourier transform.
Figure 19.
VRUF value in respect to the phase B voltage change. FFT, fast Fourier transform; VRUF, voltage ripple unbalance factor.
Table 3.
DC-link capacitance values under the test
| Case number | Total capacitance (μF) |
|---|---|
| 1 | 1175 |
| 2 | 1044 |
| 3 | 940 |
| 4 | 881 |
| 5 | 705 |
Figure 20.
VRUF value in respect to the DC-link capacitance change. DC-link, direct current link;. FFT, fast Fourier transform; VRUF, voltage ripple unbalance factor.
Figure 21.
Boxplots of VRUF values for the FFT (a) and filter (b) approaches. FFT, fast Fourier transform; VRUF, voltage ripple unbalance factor.