1 Introduction

In recent decades, multilevel converters have been studied and applied in various medium-voltage industrial applications, including renewable energy, motor drives, and power transmission, owing to their high power density, high power quality, low dv/dt, and low voltage stress in the switches [1,2,3,4,5]. Among these converters are neutral-point-clamped (NPC) inverters, which do not require flying capacitors (FCs) or isolated DC-link sources when compared to cascaded H-bridge multilevel inverters [6]. However, the number of diodes increases when the output voltage level increases. As a result, a large number of passive switches can lead to unevenly distributed switching losses and reduced inverter efficiency.

To address the above-mentioned drawbacks, hybrid NPC inverters have been recently reported in the literature and employed in some industries [7,8,9,10,11]. The five-level hybrid active neutral-point-clamped (ANPC) inverter topology was first proposed in [12]. This topology has attracted considerable attention since it requires fewer active switching devices and fewer FCs. It was built as an extension of the well-known three-level hybrid active NPC inverter with the inclusion of two additional active switches, which results in a total of eight active switches, and one FC per phase, as shown in Fig. 1 [13,14,15].

Fig. 1
figure 1

Circuit topology of a five-level hybrid ANPC inverter

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However, in this topology, the voltage stresses in the switches are unequal [16,17,18]. Switching devices (Sx1–4, x = a, b, or c phase) must bear half of the applied DC-link voltage to form the five-level output voltage. This becomes a major challenge in medium-voltage applications unless double-switching devices are connected in series. Nevertheless, this results in a voltage-sharing problem [19].

To resolve this issue, Sx1–4 needs to be controlled at the fundamental frequency (50 or 60 Hz), whereas the switching devices Sx5–8 can be controlled at a higher switching frequency.

Various pulse width modulation (PWM) techniques have been reported to control five-level hybrid ANPC inverters, such as selective-harmonics-elimination PWM (SHE-PWM) [20], phase-disposition PWM (PD-PWM) [21], and phase-shift PWM (PS-PWM) [22]. Although SHE-PWM has the ability for voltage balancing across the FCs, it is very complex and requires a predefined lookup table to store the appropriate angles, which can lead to a slow-response control [20]. In contrast, the PD-PWM modulation technique offers a very fast response control with a low computational burden when compared to SHE-PWM [21]. However, it produces a more distorted output voltage in the five-level hybrid active NPC inverter with non-uniformly distributed switching and conducting losses. The PS-PWM modulation technique is capable of naturally balancing the FCs when compared to the PD-PWM modulation technique [22]. Consequently, a five-level output pole voltage is formed. However, the charging and discharging capabilities of the FCs are critical for high-frequency (HF) modulation.

A few methods have been reported in the literature for capacitor charging and discharging. However, they have the following issues. (1) High-voltage switching and high-voltage resistance are required for pre-charging the capacitor through the main circuit, which increases the system size and complexity. (2) Overvoltage can occur in the switching devices due to the charging of the capacitor bus. Then the voltage across the FC is controlled by the modulation technique to slowly charge and discharge the FC. An FC self-pre-charging approach was proposed in [23] to transfer the main circuit into a booster to charge the FCs to their reference values in the back-to-back five-level hybrid ANPC topology without the need for external hardware. However, the possibility of doubling the voltage stress on some of the switching devices increases dramatically.

Generally, the DC link of an inverter topology utilizes aluminum electrolytic capacitors or film capacitors. Aluminum electrolytic capacitors are preferred for applications that requiring minimal DC-link voltage ripples since they have higher capacitance-to-volume ratios. However, they have an extremely high equivalent series resistance (ESR) and a very low ripple current rating [24]. Their ESR values are significantly influenced by the voltage amplitude, frequency, and operating temperature [24]. In contrast, film capacitors have very low ESR values and higher root mean square (RMS) current ratings, which allows them to operate at higher voltage levels. These features make their lifespans longer than those of electrolytic capacitors. Therefore, they are well suited for various applications where currents and voltage ripples are high at the DC link.

A novel analysis of the effects of FC size and type on the performance of a five-level hybrid ANPC inverter is presented in this paper. A detailed calculation of the FC size is shown for operating inverters in the HF range (i.e., ≥ 30 kHz) to maintain a low harmonic distortion. Both electrolytic and film capacitors are compared during low-frequency (LF) and high-frequency HF operation of the five-level hybrid ANPC inverter under the PS-PWM modulation scheme, which has the natural balancing capability of FCs.

The rest of this paper is organized as follows. Section 2 presents the structure of a five-level hybrid ANPC inverter along with its operational principle and PS-PWM modulation scheme. The effect of FC size and type on the performance of the five-level hybrid ANPC inverter is explained in Sect. 3. Sections 4 and 5 present extensive simulation results and experimental validations, respectively. Finally, Sect. 6 concludes the paper.

In this section, the structure of the five-level hybrid ANPC inverter, its operational principle, and the PS-PWM modulation technique are extensively detailed.

2 Five-level hybrid ANPC inverter

2.1 Structure and operational principle

As shown in Fig. 1, the circuit topology of a three-phase five-level hybrid ANPC inverter mainly consists of twelve Si insulated-gate bipolar transistors (IGBTs, Sx1–4), twelve SiC metal–oxide–semiconductor field-effect transistors (MOSFETs, Sx5–8), two DC-link capacitors (C1 and C2), and three FCs (Cfx). The main advantage of this topology is its simple structure, since it requires fewer switching devices and two DC-link capacitors with a better switching loss distribution when compared to the other five-level topologies.

This inverter operates at two different frequencies, the fundamental frequency for Sx1–4 and the PWM switching frequency for Sx5–8. Therefore, to operate this topology at high PWM switching frequencies, SiC-MOSFETs are regarded as suitable choices for Sx5–8, and Si-IGBT devices are recommended for Sx1–4. This structure can have excellent performance with minimized switching losses when compared to using all Si-IGBTs. In addition, it is cost-effective when compared with all SiC-MOSFET topologies [7]. In addition, this topology requires only two capacitors for the DC-link voltage (VDC), which are separated by a neutral point and a single Cfx per phase.

Cfx needs to be charged and discharged within an allowable range that is close to its reference value, which is 1/4 of the applied VDC. This can be achieved by the PS-PWM modulation scheme, which can control the switching states of the five-level hybrid ANPC inverter, as illustrated in Table 1. Sx1 and Sx3 work in a manner that is complementary to Sx2 and Sx4, respectively. Similarly, Sx5 and Sx7 switch in a manner that is complementary to Sx6 and Sx8, respectively.

Table 1 Switching states of a five-level hybrid ANPC inverter
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There are eight possible switching states for the five-level hybrid ANPC inverter, as shown in Fig. 2. Switching states I–IV are responsible for forming the half-positive cycle of the output pole voltage Vxn. Meanwhile, the negative-half cycle is generated from switching states V–VIII. From Table 1 and Fig. 2, switching states II–III and VI–VII are responsible for the charging and discharging of Cfx, respectively. Switching states III–VI are responsible for controlling the VDC across the neutral point.

Fig. 2
figure 2

Eight switching states of five-level hybrid ANPC inverter

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2.2 PS-PWM switching scheme based on offset voltage injection

Unlike the other modulation schemes used to control five-level hybrid ANPC inverters, PS-PWM is one of the best candidates owing to its robust and natural ability to balance the voltage across Cfx. In addition, the switching losses are equally distributed among all the switching devices due to the ability of SiC-MOSFETs to operate with minimum switching losses at HF. First, the three-phase reference pole voltages (V*xn) must be generated by injecting an offset voltage (Vsn), which switches at three times the line frequency (i.e., the fundamental frequency), as shown in Fig. 3. This allows for the extension of the modulation index (MI) by 15.5% and improves the total harmonic distortion (THD) [25].

Fig. 3
figure 3

Process for generating reference three-phase pole voltages

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Therefore, V*xn can be expressed as in (1):

$$V_{{{\text{xn}}}}^{*} = V_{{{\text{xs}}}}^{*} + V_{{{\text{sn}}}}$$
(1)

where V*xs. is the reference phase voltage, and Vsn is the offset voltage, which can work as a third-harmonic injected triangle-wave signal, and can be calculated as in (2):

$$V_{{{\text{sn}}}} = - \left( {\frac{{V_{{{\text{max}}}} + V_{{{\text{min}}}} }}{2}} \right)$$
(2)

where Vmax and Vmin denote the maximum and minimum values of the three-phase reference voltages, respectively.

To satisfy the requirements for generating Vxn, two PWM carriers must be included in the PS-PWM switching scheme, with a 180° phase shift. As mentioned in the previous subsection, the switching principle for Si-IGBT switching devices (Sx1–4) depends on the reference signal. Therefore, they are switched in the same manner as the fundamental frequency, which is either 50 Hz or 60 Hz, depending on the country. Hence, the switching rules are given by (3):

$$S_{{{\text{x}}1}} {, }S_{{{\text{x}}3}} ,\overline{S}_{{{\text{x}}2}} ,{\text{and }}\overline{S}_{{{\text{x}}4}} = \left\{ \begin{gathered} 1, \, T_{{\text{x}}} < 1 \hfill \\ 0, \, T_{{\text{x}}} \ge 1 \hfill \\ \end{gathered} \right.$$
(3)

where Tx represents the reference signal.

Similarly, the SiC-MOSFET switching devices Sx5–8 are turned ON and OFF in a complementary manner by comparing the normalized reference signals (Tx_normalized) with the PWM carriers, as shown in Fig. 4, which is expressed as in (4).

$$\begin{gathered} S_{{{\text{x}}5}} {\text{ and }}\overline{S}_{{{\text{x}}6}} = \left\{ \begin{gathered} 1, \, T_{{{\text{x}}\_{\text{normalized}}}} \ge {\text{PWM carrier }}1 \hfill \\ 0, \, T_{{{\text{x}}\_{\text{normalized}}}} < {\text{PWM carrier }}1 \hfill \\ \end{gathered} \right. \hfill \\ S_{{{\text{x}}7}} {\text{ and }}\overline{S}_{{{\text{x}}8}} = \left\{ \begin{gathered} 1, \, T_{{{\text{x}}\_{\text{normalized}}}} \ge {\text{PWM carrier }}2 \hfill \\ 0, \, T_{{{\text{x}}\_{\text{normalized}}}} < {\text{PWM carrier }}2 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$$
(4)
Fig. 4
figure 4

Working principle of PS-PWM in generating output switching signals

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Moreover, this switching scheme ensures that a five-level output voltage can be generated with a balanced voltage across Cfx as well as the DC-link capacitors C1 and C2.

3 FC influence on five-level hybrid ANPC inverter performance

Figure 5 shows a comparison of different types of capacitors. Capacitors may be suitable for high-voltage or high-capacity applications, depending on the dielectric material. Capacitors made from ceramics and electrolytes are mainly used in power electronic applications owing to their high voltage and capacitance. Polymer films, as dielectric materials, are often used on offshore platforms as capacitors with different types of dielectrics. Capacitors based on polymer films exhibit excellent self-healing characteristics and have a reasonable cost [27]. Thus, film capacitors are considered to be a good candidates for use as FCs in five-level hybrid ANPC topologies.

Fig. 5
figure 5

Voltage ranges versus capacitance ranges of different types of capacitors [26]

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Figures 6 and 7 illustrate the electrical series-equivalent circuit models of both FCs. This model, which is the most commonly used, is rather simple, and gives a good frequency response [28], where Celectrolytic and Cfilm are the capacitance of both electrolytic and film FCs, respectively. Rleakage and Risolation are the parallel-connected leakage current and isolation resistances, respectively. Rl and L are the series-connected resistance and inductance, respectively. Figure 6 can be simplified and represented in a vector diagram as shown in Fig. 7. It can be seen to be a serial combination of the equivalent series resistance (RESR) and the inductance (LESL). Finally, the capacitance can be estimated as in (5),

$$C = \left\{ \begin{gathered} C_{{{\text{electrolytic}}}} \cdot \left( {1 + \frac{1}{{C_{{{\text{electrolytic}}}}^{2} \cdot R_{{{\text{leakage}}}}^{2} \cdot \omega^{2} }}} \right) \hfill \\ C_{{{\text{film}}}} \cdot \left( {1 + \frac{1}{{C_{{{\text{film}}}}^{2} \cdot R_{{{\text{isolation}}}}^{2} \cdot \omega^{2} }}} \right) \hfill \\ \end{gathered} \right.\,$$
(5)

where ω is the impedance (Z) angular frequency. In addition, both RESR and LESL can be calculated as in (6) and (7), respectively,

$$R_{{{\text{ESR}}}} = R_{{\text{l}}} + \frac{{R_{{{\text{leakage}}}} }}{{1 + C_{{{\text{electrolytic}}}}^{2} \cdot R_{{{\text{leakage}}}}^{2} \cdot \omega^{2} }}\,$$
(6)
$$L_{{{\text{ESL}}}} = L$$
(7)
Fig. 6
figure 6

Series-equivalent circuit model. a Electrolytic FC; b film FC

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Fig. 7
figure 7

FC representation. a Simplified Series-equivalent circuit b vector diagram

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It is worth noting that the dissipation factor (tan δ) is very important in film capacitors, since it measures the quality of resonance, as shown in Fig. 7b. Hence, the tan δ is mentioned in most film capacitors datasheet instead of RESR. On the other hand, the electrolytic FC RESR increases when Celectrolytic decreases. Therefore, film FCs are considered to be a better candidate for the HF operation of the five-level hybrid ANPC inverters.

FCs are responsible for generating the five-level Vxn in five-level hybrid ANPC inverter topologies. This is only achieved when the voltage across the FCs reaches VDC/4. Several factors affect the amount of time required for FCs to reach their reference values, which include the switching frequency of the Sx5–8 switching devices (fc) and size of the FC.

As mentioned in Sect. 2, the Sx5–8 switching devices are set to operate at a HF (i.e., fc = 30 kHz) to enhance the THD of the output three-phase current, which significantly reduces the ripple of the current. However, the size of the FC needs to be sufficiently large to limit the maximum voltage ripple (ΔVFC_max) that appears across it. This can be calculated as in (8):

$$\Delta V_{{{\text{FC}}\_\max }} \, = \,\frac{{\max (D_{{{\text{FC}}}} \times I_{{{\text{FC}}}} )}}{{C_{{{\text{FC}}}} \times 2 \times f_{{\text{c}}} }}$$
(8)

where IFC, DFC, and CFC are the FC, current duty cycle, and capacitance, respectively.

To simplify the design process, the worst-case scenario for ΔVFC_max is considered and used to approximate the FC value as in (9):

$$\Delta V_{{{\text{FC\_max(worst case)}}}} \approx \frac{{I_{{{\text{pk}}}} }}{{C_{{{\text{FC}}}} \times 2 \times f_{{\text{c}}} }}$$
(9)

where Ipk is the peak current at the full modulation index (MI). Therefore, the possible FC value is calculated as in (10):

$$C_{{{\text{FC}}}} = \frac{{I_{{{\text{pk}}}} }}{{\Delta V_{{{\text{FC\_max(worst case)}}}} \times 2 \times f_{{\text{c}}} }}$$
(10)

Assuming the maximum voltage ripple does not exceed the 20 V of the steady-state value of the VFC voltage at full values of the MI and the rated power, CFC is set as in (11):

$$C_{{{\text{FC}}}} \, \ge \,\frac{{34.5{\text{A}}}}{{20{\text{V}} \times 2 \times 30{\text{kHz}}}}\,\,\, \ge 28.75\,{\mu F}{.}$$
(11)

4 Simulation verification

Comprehensive simulation results obtained from the PSIM Simulation Tool are presented in this section. The effectiveness of proper FC selection is evident in the performance of the five-level hybrid ANPC inverter during HF operation. The system parameters are listed in Table 2. In this study, fc was set as low as 1.5 kHz. Meanwhile, it was set to 30 kHz for HF operation. In addition, the fundamental frequency was maintained at 60 Hz during all of the operations.

Table 2 System parameters
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The simulation results shown in Fig. 8 were used to evaluate the performance of the five-level hybrid ANPC during LF and HF operations using two different capacitors. From Fig. 8a, b it can be seen that the 220 µF electrolytic FC has better performance than the 30 µF film FC at fc = 1.5 kHz. However, the 220 µF electrolytic FC has a slower startup control to form a five-level output voltage. In addition, LF operation degrades the system performance due to the high distortions in the output current and voltage.

Fig. 8
figure 8

Simulation performance evaluation results of a five-level hybrid ANPC inverter under two types of FC at low and high PWM switching frequencies. a 220 µF electrolytic FC at fc = 1.5 kHz; b 30 µF film FC at fc = 1.5 kHz; c 220 µF electrolytic FC at fc = 30 kHz; d 30 µF film FC at fc = 30 kHz

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To improve the system performance, fc was increased from 1.5 to 30 kHz, as shown in Fig. 8c and Fig. 8d. During HF operation, the 30 µF film FC outperformed the 220 µF electrolytic FC. This is due to the natural material of the film capacitor and its small capacitance. As a result, the three-phase FCs reached their reference value (i.e., 75 V) in only 0.7 s due to the fast charging and discharging capability of the film capacitor.

The magnified simulation results of Fig. 6 with additional analysis are shown in Fig. 9. From Fig. 9a, it can be seen that the 220 µF electrolytic FC resulted in the full formation of the five-level output voltage (Van). However, a high THD was obtained during LF operation. A Fast Fourier transform (FFT) analysis of Ia shows that the distortion is high when fc = 1.5 kHz. If the 220 µF electrolytic FC is replaced by the 30 µF film FC during LF operation, more distortion occurs in addition to the high voltage ripple across the FCs, as shown in Fig. 9b.

Fig. 9
figure 9

Magnified simulation performance evaluation results of a five-level hybrid ANPC inverter under two types of FC at low and high PWM switching frequencies. a 220 µF electrolytic FC at fc = 1.5 kHz; b 30 µF film FC at fc = 1.5 kHz; c 220 µF electrolytic FC at fc = 30 kHz; d 30 µF film FC at fc = 30 kHz

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Nevertheless, when fc = 30 kHz, the THD of Ia is significantly reduced when using either FC type. When using the 220 µF electrolytic FC, the performance is similar to that of a three-level hybrid ANPC, as shown in Fig. 9c. This is due to the slow charging and discharging properties of this type of FC. Consequently, a higher THD of Van is obtained. To enhance the performance of five-level hybrid ANPC inverters during HF operation, a film FC was used instead of an electrolytic FC. As shown in Fig. 9d, Van and Vab were fully formed at the five and nine levels. In addition, the three-phase FC voltages were regulated at 75 V. Moreover, the THD of the three-phase output current was minimized to 0.41%, which is excellent and desirable in many industrial applications.

To further investigate the performances of the 220 µF electrolytic and 30 µF film FCs, comparative charts are presented in Fig. 10. These charts indicate that the 30 µF film FC is slightly better than the 220 µF electrolytic FC in terms of minimizing the THD of the three-phase output current during HF operation. In addition, a significant reduction in the THD of Van during various operations was observed, which includes variations in MI and fc, particularly in the low MI and HF ranges, as shown in Fig. 10b.

Fig. 10
figure 10

Simulation comparison for different values of fc and MI. a THD of ia; b THD of Van

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5 Experimental validation

Validation of the proposed 30 µF film FC for enhancing the five-level hybrid ANPC inverter performance in HF operation was extensively demonstrated by some experiments comparing it with the 220 µF electrolytic FC. Using an electrolytic FC with a small capacitance (i.e., ~ 30 µF) would result in very poor system performance, and might lead to serious damage of the capacitor, and unbalanced voltages across the FC due to its small capacitance and large ESR. Therefore, two different types of FCs (i.e., 30 µF film and 220 µF electrolytic) were used in experimental trials at fc = 30 kHz. As shown in Fig. 11, these experiments were performed using a five-level hybrid ANPC inverter and a TMS320f28377s digital signal processor (developed by Texas Instruments) that was operated as the main control board for executing the experimental code in a code composer studio environment. LF was excluded from the experimental verification due to the large ripples present across the FCs, as shown in Fig. 9a and Fig. 9b. Therefore, fc was fixed at 30 kHz during experimental trials. In addition, a resistor was used to ensure that the FCs were fully discharged before each experiment. Table 3 presents a detailed list of the 220 µF electrolytic and 30 µF film FCs used in this study. This table shows that the 30 µF film FCs outperformed the 220 µF electrolytic FCs in terms of many features, including size, price, and reliability in the HF range. In addition, the very low ESR of the 30 µF film FC resulted in a very long lifespan when compared to the 220 µF electrolytic.

Fig. 11
figure 11

Experimental setup of a five-level hybrid ANPC inverter

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Table 3 Experimental FC Specifications [29, 30]
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Figure 12 shows experimental results for the performance evaluation of a five-level hybrid ANPC inverter using a 220-µF electrolytic FC at fc = 30 kHz with two different zones for the magnified results. This figure shows that the five-level hybrid ANPC inverter cannot operate as desired to form a Van with five discrete levels. As a result, a high THD of Van was observed, particularly in zone-1. In zone-2, the performance of the system was similar to that of zone-1 with a 1 s of delay for charging the 220 µF electrolytic FC. Therefore, this type of FC requires a very long time to ensure that the five-level hybrid ANPC inverter operates as desired.

Fig. 12
figure 12

Experimental results for a performance evaluation of a five-level hybrid ANPC inverter using a 220 µF electrolytic FC at fc = 30 kHz: magnified zones. a 1; b 2

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Consequently, the performance of the five-level hybrid ANPC inverter was improved when a 30 µF film FC was used. Due to its physical properties when operating in HF applications and under a small capacitance, the charging capability was very quick when compared to that of the 220 µF electrolytic FC. As a result, a considerably better performance was achieved, as shown in Fig. 13. Initially, the 30 µF film FC was fully discharged at the startup of the five-level hybrid ANPC inverter, as shown in Fig. 13a. After 1 s of natural quick charging, the performance of the five-level hybrid ANPC inverter was as desired, as shown in Fig. 13b. As a result, the Van THD was minimized, as shown in Fig. 12. Hence, the 30-µF film FC is strongly recommended for enhancing the performance of five-level hybrid ANPC inverters.

Fig. 13
figure 13

Experimental results for a performance evaluation of a five-level hybrid ANPC inverter using a 30 µF film FC at fc = 30 kHz: magnified zones a 1; b 2

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6 Conclusion

In this study, a novel and comprehensive analysis was presented for the proper selection of a FC for the performance enhancement of a five-level hybrid ANPC inverter. Among the different FC types, the film FC was recommended due to its excellent operation, particularly in the HF range. Extensive simulations and experiments were conducted to verify its effectiveness in improving the overall performance of a five-level hybrid ANPC inverter. When compared to electrolytic FCs, film FCs significantly enhanced the capability of the system for five-level operating performance with low THD values in the output pole voltage and phase current. Hence, the required filter size can be reduced when it is implemented in various applications. Therefore, film FCs are desirable for enhancing the operation of five-level hybrid ANPC inverters, particularly in the HF range.