1. Introduction
With the penetration of electric power in various industries, medium-voltage, high-power application scenarios become increasingly extensive [
1], such as renewable energy generation, AC–DC hybrid microgrids, electrified rail transportation, electric vehicles and charging stations, etc. However, conventional two-level converters are not adaptable to medium-voltage, high-power applications due to the rated voltage of the switching devices. Even three-level converters can only be used in low-to-medium-voltage applications (up to 3 kV) [
2]. When an engineering application has a rated voltage between 3 kV and 10 kV, the most-suitable topology is a five-level converter represented by an active neutral-point-clamped structure, as shown in
Figure 1. Without the need for an additional transformer, this kind of converter has the significant advantage of being directly connected to the distribution network (10 kV). Five-level converters based on this topology are also used commercially by international companies such as ABB Group [
3]. For these reasons, it was chosen as the study object in this article.
Five-level converters only satisfy the requirement of medium voltage at the topology level, while the requirement of high power needs to be satisfied by implementing low-switching-frequency (SF) modulations. Commonly used low-SF modulations include discontinuous modulation [
4], synchronized space vector modulation (SSVPWM) [
5], and selective harmonic elimination pulse-width modulation (SHEPWM) [
6]. These modulation strategies can effectively reduce the SF while ensuring relatively good output performance, thereby reducing switching losses, improving system efficiency, and simplifying the cooling system [
7,
8]. In particular, SHEPWM is able to completely eliminate the specified low-order harmonics and has received much attention for industrial applications and in academic research [
9]. Therefore, we propose the application of SHEPWM to five-level converters to meet the practical needs of medium-voltage, high-power applications.
However, depending on the application scenario, five-level converters may be connected to photovoltaic or wind power as grid-connected converters or linked to medium-voltage electrical motors as power drivers, requiring that the common-mode voltage (CMV) of the converter be reduced as much as possible. CMV can also cause common-mode current (CMC), adversely affecting the insulation of the loads [
10,
11]. Thus, CMV suppression has always been a hot topic of research for scholars at home and abroad.
CMV suppression is a common problem for three-phase converters; therefore, valuable solutions under high SF have been proposed by a large number of scholars. Although the specific steps to achieve CMV suppression differ depending on the converter, they can be broadly classified into two categories. The first category is based on the direct analysis of space vectors. CMV under the action of different space vectors was discussed in [
12], leading to the proposal of a new switching sequence. Since the new switching sequence directly discards the space vector that causes a high CMV, the output waveform at this point can significantly suppress the CMV [
13]. An improved fixed-switching-frequency (FSF)-based model predictive control (MPC) method was proposed to select the control voltage vectors to reduce CMV [
14]. These voltage vectors with high CMV are abandoned to limit the CMV amplitude to one-sixth of the DC-link input voltage. The second category is based on the analysis of the zero-sequence voltage in carrier modulation mode. The authors of [
15,
16] provided an in-depth analysis of the relationship between the zero-sequence voltage and CMV, leading to the proposal of a method for adjusting the zero-sequence voltage to suppress the CMV. Unfortunately, both method types are aimed at high SF modulations. The concept of the space vector does not exist under SHEPWM, and the zero-sequence voltage is difficult to freely regulate under SHEPWM. For a low switching frequency, the nearest zero CMV vector (NZCMVV) was proposed to suppress the CMV [
17]. Unlike NLM, which uses the nearest level, NZCMVV selects two candidate levels for each phase to provide eight degrees of freedom to select the zero-CMV voltage vector. It is simple to implement and does not increase the complexity due to an increasing number of levels. However, it cannot be applied to SHEPWM and significantly reduces harmonic performance.
For a long time, SHEPWM has been regarded as an independent modulation strategy, with numerous works dedicated to exploring related techniques. A segment of research, as evidenced by studies such as [
18,
19], is centered on numerical algorithms designed to optimize the calculation process of the switching angles. Attempting to relax the symmetry constraints, half-wave symmetry SHEPWM was also discussed in-depth in [
20,
21]. Moreover, a large number of scholars aim to construct a unified mathematical model and implementation method for multilevel SHEPWM, as in [
22,
23]. As for the current state of research, only a limited number of studies have delved into control problems under SHEPWM. The study presented in [
24] proposed an optimal control method for torque pulsation under SHEPWM, directly considering torque as a constraint. The implementation of low-frequency neutral point voltage suppression for three-level converters was detailed in [
25], based on the optimal third harmonic. Since the switching angle of SHEPWM is determined by the harmonics eliminated, it is inherently weakly controlled. So, CMV suppression is difficult under SHEPWM, and only a few studies have tackled this aspect.
Drawing inspiration from the concept of zero-sequence voltage injection, a CMV suppression method was introduced for three-level converters in [
26]. This approach actively incorporates the third harmonic component as a control degree of freedom into the constraint equation of SHEPWM. By combining SHEPWM and selective harmonic mitigation PWM (SHMPWM) with each other, harmonic mitigation and elimination were utilized to simultaneously control output voltage harmonic distortion and suppress CMV in [
27,
28]. While these methods currently represent the most-effective means of CMV suppression under SHEPWM, it is crucial to note that neither approach is deemed mature nor perfect. Firstly, the CMV suppression discussions in [
26,
27,
28] specifically pertain to three-level SHEPWM, and transitioning from three-level to five-level SHEPWM is far from a straightforward generalization. These two modulation strategies are fundamentally different, and this distinction will be thoroughly analyzed in a subsequent section. If a similar approach is to be employed under five-level SHEPWM, extensive research is needed. Secondly, and significantly, both methods make trade-offs between harmonic elimination performance and the degrees of freedom to suppress CMV. In [
26], the switching angles were sacrificed to control the third harmonic component, diminishing the low-order harmonics that SHEPWM can eliminate and resulting in poorer output performance. From another perspective, this implies an increase in the equivalent SF, contrary to the original intention of using SHEPWM. In [
27,
28], the limitations on the quality of harmonic elimination were relaxed, leading to inferior harmonic performance. A comparative summary of the aforementioned CMV suppression methods is provided in
Table 1.
Based on an extensive review of the existing literature and a rigorous analytical process, we propose a pioneering method for CMV suppression in five-level SHEPWM that avoids sacrificing the switching angles and decreasing quality of the elimination of the harmonics. This distinctive methodology arises from a nuanced exploration of the substantial distinctions between three- and five-level SHEPWM architectures. In the conventional three-level SHEPWM, a solitary level jump pattern prevails during the positive half-cycle, exclusively between 0 and . In stark contrast, the five-level SHEPWM introduces a multitude of level jump patterns, encompassing transitions such as 0 to , to , to , and to 0. The varied frequencies and quantities of each jump pattern give rise to multiple mode combinations, illustrating the concept of “multimode” articulated in this study. Our inquiry focuses on the meticulous analysis of the distinct multimode characteristics within five-level SHEPWM and their nuanced influence on CMV. Despite yielding an identical fundamental voltage, disparate modes exhibit markedly different switching angle trajectories, resulting in diverse CMV profiles. This scholarly exploration culminates in the identification of modes that minimize CMV under diverse operational conditions, thereby engendering a groundbreaking CMV suppression technique unique to five-level SHEPWM.
5. Experimental Verification
In order to fully verify the correctness and effectiveness of the proposed method, a small-scale prototype was built, as shown in
Figure 8. The five-level converter was constructed on the basis of discrete IGBTs (IKW50N60T, Infineon, Munich, Germany). These IGBTs are driven by driver chips (2ED020I12-F2, Infineon, Munich, Germany). The input DC power is obtained by diode rectification, for which the amplitude is regulated via an s voltage slider (220 V input and 0–250 V output). The concerned algorithms were implemented in real-time on a DSP board (TMS320F28335, TI, Dallas, TX, USA). The voltages of the DC-link capacitor and flying capacitor are read into the DSP via sensors (LV25, LEM, Geneva, Switzerland). The currents of the three-phase output and DC-link midpoint are read into the DSP via sensors (LA50, LEM, Geneva, Switzerland). The experimental results were measured directly using the hardware voltage and current probes and observed by a hardware oscilloscope.
The experimental parameters are presented in
Table 5. The operation conditions in experiment verification are organized as follows.
In order to verify the superiority of the selected modes in CMV suppression, the switching angle solutions from
and
(
) were used for the experimental comparison. The specific angles and corresponding
under the selected modulation ratio are shown in
Table 6, while the direction of level jumping can be deduced from the backwardsmode according to (
13). The sets of switching angles were stored in the LUT together with the corresponding level jumping states.
Using angles from
m = 0.66 in
Table 6 as an example firstly, during this experiment, a change of mode from mode 104
to mode 90
was forced at the instant of 0.06 s. The experimental result of the phase voltage, line current, CMV, and FFT analysis is shown in
Figure 9. Both before and after the switching modes, the level jump patterns from the phase voltage behaved as the mode set, and the unwanted lower harmonics were effectively eliminated. It can be observed that, however, the CMV of
was much less than that of
, which was as high as 73.655V for
, while only 21.663 V for
. In order to make a comprehensive analysis of the relationship between the CMV and
harmonics,
Figure 9 also shows the detailed comparison of the
harmonics. It can be observed that the lower
harmonic amplitudes in
showed a significant decrease from those in
. When looking at the higher
harmonics, there was a slight increase of the harmonic amplitudes in
compared with
, which will not affect the reduction of the overall
harmonics. Besides, the current THD in
was also lower, which means that a suppression of the CMV can be achieved by
with a good output performance at the same time.
Figure 10 shows the experimental results and FFT of the other angles in
Table 6, and the summary statistics are shown in
Table 7. The same as discussed in
Figure 9, it can be seen that all modes could achieve the set jumping levels and the desired fundamental amplitude. It is worth explaining that there was some deviation (
) between the actual fundamental amplitude (
) and the reference value (
), but this deviation is acceptable and understandable. From the perspective of software control, a possible explanation for this might be the fluctuation of the midpoint potential and suspension capacitance voltage. In order to realize the control of the voltage, the actual angle issued will deviate from the theoretical value, resulting in the difference in the amplitude of the fundamental wave. This is not the focus of the research in this paper. From the experimental platform, sensors and non-ideal switching devices can also have an effect on the output waveforms. But, as is clear, the CMV in the optimized mode is effectively suppressed because of the lower
harmonic amplitude. The specific decline is shown in percentage terms in
Table 7. The decline ratio for the CMV completely conforms to the transformation law of the
with little differences in the numerical value. For the output performance, there is no doubt that the unwanted specific harmonics are eliminated for all modes realizing the basic goal of SHEPWM. Interestingly,
also had a good performance in terms of the output current harmonics compared with
.
What emerges from the results reported here is that the harmonic characteristics of multiple modes with the same modulation ratio are quite different, including the harmonics, which are closely related to the CMV. According to the optimization method proposed in this paper, minimizing the and considering the mode switchover frequency simultaneously, the resulting mode can ensure good output performance while effectively realizing the suppression effect of the CMV.