Detection of Voltage Asymmetry Based on DC Link Ripple and Analysis of Its Impact on Diagnostic Processes in Complex Electric Drives

Hybrid vehicle powertrains are equipped with a three-phase voltage generation system, where the output is rectified by AC/DC converters to charge the battery and supply the DC-link of the frequency converter. The quality of this generated voltage ensures the smooth operation of the electric drive and the reliability of its dedicated diagnostic systems. However, voltage generation units are susceptible to faults, often manifesting as amplitude or phase asymmetries in the sinusoidal output. Stator winding resistance unbalance may arise from manufacturing tolerances or uneven thermal distribution within the windings. Furthermore, short-circuit failures can introduce similar resistance imbalances. Research has shown that such conditions exacerbate harmonic content – if these harmonics are utilised as symptoms for diagnosing stator, bearing, or rotor faults, they may lead to incorrect diagnostic conclusions. Analogous phenomena are observed in stationary industrial drives due to three-phase power grid asymmetries.

Hybrid vehicle powertrains utilise a combination of an internal combustion engine (ICE) and an AC generator across various topologies. Depending on the specific configuration—series, parallel, or power-split (series–parallel)—the energy management strategy varies significantly. This article focuses on the classic series hybrid architecture, the schematic of which is illustrated in Figure 1.

Figure 1.

Block diagram of the analysed series hybrid drive architecture. ICE, internal combustion engine; PMSG, permanent magnet synchronous generator.

The system under analysis utilises a permanent magnet synchronous generator (PMSG) coupled with a conventional six-pulse diode rectifier. To isolate phenomena occurring strictly within the DC-link, the study assumes the absence of intermediate DC/DC conversion stages, such as boost or buck converters, at the rectifier output. The comprehensive control architecture, including the rectifier interface, is illustrated in Figure 2.

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.

The subject of the article is closely related to the issues of Fault Tolerant Control systems (Nesri et al., 2024) and is a supplement to the issues that have been studied for years by the team of authors.

This article aims to demonstrate that signal quality issues within the DC-link significantly impact control systems and their associated subsystems. A critical area affected is the fault detection framework for electric motor drives, including induction motors and permanent magnet synchronous motors (PMSMs). Existing literature on drive diagnostics often overlooks external disturbances and secondary faults that can compromise the diagnostic accuracy for operating motors. The motivation behind the research is to utilise as few sensors as possible to obtain reliable voltage unbalance data in the hybrid electric vehicle (HEV) energy generation systems with an uncontrolled rectifier.

As evidenced by recent studies (Pietrzak et al., 2023; Skowron et al., 2022), the vast majority of PMSM fault detection methodologies rely on the frequency analysis of measured signals. Specifically, for demagnetisation (Figure 3), stator (Figure 4) and rotor degradation, the 2nd harmonic of the fundamental supply frequency is frequently considered a primary diagnostic indicator (e.g., 200 Hz in Figure 3 and 100 Hz in Figure 4). Furthermore, the 6th harmonic (600 Hz in Figure 4) serves as a significant feature for fault identification.

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.

Diagnostic frameworks for both stator-related and inverter-specific faults rely on harmonic signatures that are inherently dependent on the power source characteristics. Consequently, faults occurring during the PMSG voltage generation stage induce distortions that propagate into the DC-link. The degree to which the AC output deviates from an ideal sinusoid manifests as distinct variations in the harmonic spectrum of the DC-link voltage (U_DC). This paper demonstrates that PMSG stator asymmetry—stemming from uneven winding resistances across one or more phases—results in altered higher harmonic content within the DC circuit. These distortions can subsequently lead to the erroneous identification of motor faults, as the control system may misinterpret supply induced ripples as internal motor degradation. Furthermore, this study provides a comparative analysis with three-phase grid asymmetries to demonstrate that these phenomena are analogous to those observed in PMSG-based generation systems.

The purpose and main contribution of this paper is presentation of the DC-link ripple based voltage unbalance detection and assessment solution. The focus is not only the designing method itself but also verifying it under simulation and experimental studies. The potential of this work is the possible implementation of this method in the systems with PMSG and uncontrolled diode rectifiers. Such solution will result in lower costs implementation because of single voltage sensor approach.

The simulation model, illustrated in Figure 5, incorporates a PMSG with variable stator phase resistances, a six-pulse diode rectifier, a DC-link, and a resistive–inductive (RL) load. This configuration represents the series HEV architecture (previously shown in Figure 1), where the PMSG and AC/DC converter provide power to the RL load, which emulates the battery pack or subsequent downstream DC/DC conversion stages.

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.

The model was implemented and solved within the MATLAB/Simulink environment. To ensure numerical stability and accuracy, the Backward Euler integration method was employed with a fixed simulation step size of 10⁻⁷ s.

The initial stage of the simulations involved analysing DC-link voltage variations to characterise the behaviour of the AC/DC system under unbalanced conditions. As illustrated in Figure 6, under balanced supply voltage conditions, the ripples are periodic and regular. The dominant frequency component is observed at 300 Hz, which corresponds to the characteristic ripple frequency of a six-pulse rectifier operating with a 50 Hz AC supply (6 × f_supply).

Figure 6.

Source and DC-link voltages with frequency spectrum analysis under balanced voltage. DC-link, direct current link.

Increasing the phase B voltage by 50% induces a significant voltage source asymmetry, as illustrated in Figure 7. The transition from standard six-pulse operation (characterised by a dominant 300 Hz component) towards a behaviour resembling two-pulse operation (where the 100 Hz component becomes dominant) is clearly discernible in both the U_DC time-domain waveforms and the corresponding frequency spectrum. That phenomenon is present in the uncontrolled (diode) rectifiers as the operation of AC/DC converter switches continuous conduction mode to discontinuous one (Fang et al., 2015).

Figure 7.

Source and DC-link voltages with frequency spectrum analysis under 50% increase of phase B voltage. DC-link, direct current link.

Furthermore, the inclusion of an inverter as the load (Figure 8) does not alter the occurrence of the 100 Hz component - this frequency remains dominant in the presence of voltage asymmetry. This confirms that the characteristic ripple behaviour induced by the source unbalance persists regardless of the load type.

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.

To enhance the detection of non-linear interactions between harmonic components, a higher-order spectral analysis (HOSA) was conducted. Specifically, the bispectrum of the UDC signal was calculated based on the methodology proposed by Ewert (2020). Unlike the standard power density spectrum (PDS), which only provides information about the power of individual frequency components, the bispectrum preserves phase information and enables the identification of quadratic phase coupling (QPC). In this study, bispectral analysis is utilised to distinguish between inherent rectifier switching harmonics and those induced by supply voltage asymmetries, providing a more robust diagnostic feature than traditional frequency-domain methods. A further bispectral investigation (Figure 9), utilising the methodology proposed by Ewert (2020), demonstrates that increasing voltage asymmetry leads to a more pronounced 100 Hz UDC component relative to the 300 Hz harmonic. This HOSA confirms that the degree of source unbalance is directly correlated with the magnitude of the low-frequency ripple.

Figure 9.

Bispectrum analysis of U_DC under changes of phase B voltages. From the left: balanced voltage, 120% of phase B voltage, 140% of phase B voltage.

The bispectrum magnitude is represented on a two-dimensional frequency plane, where the axes f₁ and f₂ denote two independent frequency components. A peak at the coordinates (f₁,f₂) indicate a strong non-linear interaction or QPC between these frequencies and their resultant sum frequency (f₁ + f₂). In the context of the U_DC voltage analysis, this allows for a precise observation of how the low-frequency ripples (e.g., 100 Hz) interact with the fundamental switching harmonics (e.g., 300 Hz), providing a more detailed ‘fingerprint’ of the system’s condition than a standard one-dimensional power spectrum. In bispectral analysis of a single signal such as U_DC, the frequencies f₁ and f₂ represent coordinates in the bifrequency plane. Although only one physical signal is measured, the bispectrum evaluates the correlation between different spectral components within that signal. Specifically, it identifies QPC, where a peak at (f₁, f₂) indicates that the harmonic component at the sum frequency (f₁ + f₂) is statistically linked to the components at f₁ and f₂. This approach is particularly effective for U_DC analysis, as it distinguishes between independent noise and the structured harmonic distortions caused by rectifier non-linearities under supply unbalance.

The 2nd simulation test was conducted based on the considerably high change of PMSG phase B resistance R_b. The following analysis is performed in accordance with model schematic on Figure 5 and data presented in Table 2.

As can be seen in the Figure 10a, the 50% increase in resistance causes the overall U_DC mean value to drop. Moreover, the asymmetry between pulses is easily seen – such occurrence increases the lower order harmonics values in the DC-link voltage.

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.

In order to understand the resistance asymmetry more deeply, phase currents of PMSG are presented (Figure 10b). The stator resistance unbalance in singular phase causes asymmetrical pulses in each phase current.

The FFT analysis of both cases (Figure 11a) mentioned above provides the information on 50 Hz power supply harmonics structure of U_DC. The main 6th harmonic that is reflected by six-pulse operation of the rectifier in the state of uneven stator resistance is slightly smaller due to the lower mean value. The 2nd, 4th and 8th harmonics increase substantially in comparison to symmetrical stator winding. Those changes will affect diagnostic methods mentioned in Skowron et al. (2022) and Pietrzak et al. (2023).

Figure 11.

Comparison of U_DC harmonic amplitudes under different levels of phase B resistance asymmetry: (a) 50% resistance increase, (b) 1% and 10% resistance increase.

Further investigation was undertaken by applying smaller R_b changes (Figure 11b). Even resistance changes as low as 1% can be easily noticed in the 2nd harmonic magnitude change. Additionally, the change of 10% can be noticed in the 4th and 8th harmonic. Those observations prove that even low changes in the PMSG stator resistance symmetry can affect U_DC frequency spectrum analysis.

In order to analyse resistance unbalance even further, multiple uneven stator resistances were implemented (Figure 12). In case of the multiple phase asymmetry, as in the single one, harmonics of lower order than six (related to six-pulse rectifier operation) increase, indicating unbalanced source resistances.

Figure 12.

Comparison of harmonics values of U_DC while multiple phases resistance change.

The experimental bench consists mainly of adjustable voltage source in form of three autotransformers (Figure 14a) and AC/DC/AC converter (Figure 14b). Each autotransformer allows for independent phase voltage adjustment – making it possible to emulate source generator stator resistance asymmetry. AC/DC/AC converter provides load behaviour similar to real industrial scenarios. U_DC is measured using differential probe. Signals are recorded using dSpace 1103 with sampling frequency of 10 kHz.

Figure 14.

Test setup core components: three autotransformers (a) and AC/DC/AC converter (b). AC, alternating current; DC, direct current.

Experiment was conducted under various phase voltage values – each unbalance case was measured at 30 separate sessions in order to obtain satisfactory amount of data for method validation. During each session, harmonic magnitudes are extracted from the DC ripple data using FFT. After obtaining 30 individual frequency spectrum data, mean value for 2nd, 4th, 6th, 8th and 12th harmonics are calculated. Afterwards the procedure continues until all of desired voltage configurations are tested. The flowchart of the experiment can be seen in Figure 15.

Figure 15.

Experiment flowchart.

Initially, the balanced state of power supply is considered 100 V root mean square per each phase. In order to represent the physical analogy of stator resistance increase, phase voltage is lowered (e.g., phase B in Figure 16). The effect on the U_DC is the same as in the Figure 10a – mean DC value is lower and pulses of it are uneven.

Figure 16.

Waveforms of U_DC under DC-link B phase voltage change. DC-link, direct current link.

During the 1st stage of experimental study, the change of phase B voltage is investigated (Figure 17a). The analysis of obtained data FFT proves the results of the simulation study – as the unbalance increases 2nd and 4th harmonics of power supply voltage frequency get higher, worsening the electrical drive operating conditions and affecting other frequency-based diagnostic methods. The presence of mentioned frequency components in the balanced case is because of both power grid and load resistance asymmetries.

Figure 17.

Frequency spectrum of chosen U_DC harmonics under different B phase voltage values (a) and frequency spectrum of chosen U_DC harmonics under different A and B phase voltage values (b).

In the event of multiple phase voltage unbalance (Figure 17b) the failure mode remains the same – lower than six-pulse related harmonics are amplified.

Experimental analysis done in Section 3.2 was performed using FFT in order to obtain information on 2nd and 6th harmonics values. The less computationally complex method to perform this task is to use digital bandpass filters that extract desired harmonics (in case presented in paper – 100 Hz and 300 Hz centre frequency). The two applied filters have bandwidth of 20 Hz. By comparing filter-based approach and FFT (Figure 18), it can be seen that for balanced and unbalanced cases, both of harmonics value assessment methods provide similar results.

Figure 18.

Frequency spectrum of chosen U_DC harmonics under balanced (a) and unbalanced (b) condition. FFT, fast Fourier transform.

The complexity comparison was carried out by calculating mean execution time value of 270 runs of the both algorithms for one calculation required to obtain data (one FFT with harmonic indexing and single filtration of 2nd harmonic). In case of filter approach the mean execution time is 68 μs, as opposed to FFT solution where mean time is equal to 439 μs.

Such approach can also be implemented using analogue filters which may be incorporated into smart gate drivers as a power converter diagnostic expansion.