Optimal Selection among Various Three-Phase Four-Wire Back-to-Back (BTB) Converters with Comparative Analysis for Wave Energy Converters

Abstract

Wave energy converters are attracting attention as an energy source that can respond to climate change. In order to increase the energy efficiency of the wave energy converters, efficient power converters are also required. The efficient converters require operation at a low switching frequency, which increases the weight and volume of the passive components. Therefore, in this paper, the performance of various types of topologies is compared to select the optimal power converter for wave energy converters. In order to cope with the unbalanced operation and unbalanced load of renewable energy, in this paper, the topology of the four-leg type is analyzed centrally. In addition, the analysis was performed by applying the model predictive control that can quickly respond to the rapid energy change of wave energy. In addition, model predictive control was applied to the four-leg converter analyzed in this paper because it is suitable for application to atypical topologies. For performance analysis of various types of topology, the loss and efficiency of each converter were analyzed by applying a loss analysis model, and output current harmonics and leakage current characteristics, capacitor voltage fluctuation rate, etc., were additionally analyzed at various switching frequencies. In conclusion, the three-level four-leg converter showed up to 2.28% and 2.7% higher efficiency under balanced and unbalanced operating conditions.

1. Introduction

Excessive use of fossil fuel power plants has produced abundant greenhouse gases, a major cause of climate change. Renewable energy can partially replace fossil-fueled power plants and has been proposed as an alternative to address climate change. For this reason, wave energy has been attracting attention in the past 20 years to alleviate the energy demand problem, and the development of wave energy systems has been carried out [1]. The global theoretical wave energy potential is estimated at 16,000 TWh per year [2,3], which could make a significant contribution to meeting the growing global energy demand. In particular, the temporal characteristics of wave energy can compensate for the discontinuity of other renewable energy sources, such as wind power and solar power [4,5,6].

An important goal of renewable energy is to lower the cost of electricity generation through increased energy efficiency. In other words, an efficient converter topology has been emphasized in terms of power converters due to increased energy costs and environmental concerns. One possible way to achieve higher converter efficiency is to operate at a lower switching frequency. However, wave energy converters need to reduce the volume and weight of passive components to reach high power densities due to space constraints. This requires high switching frequencies. However, a two-level converter based on IGBT (Insulated Gate Bipolar Transistor) causes excessive loss when the switching frequency is increased, but wave energy converters are still applied to most of them. Therefore, it is difficult to meet both efficiency requirements and technical performance requirements with a two-level converter, and three-level converters for wave energy converters have been discussed [7,8,9]. Excellent efficiency at higher switching frequencies due to low switching losses despite the increased complexity and high initial cost makes the three-level topology attractive for wave power applications.

From a wave power system point of view, the benefits of using a three-level converter are not limited to the converter itself. The main parts of this modern three-phase AC-DC-AC converter system are shown in Figure 1. On the grid side, electromagnetic interference (EMI) input filters are usually required to attenuate current harmonics. From there, the three-level output voltage waveform reduces the boost inductance required and, consequently, the boost inductor volume and losses. Also, on the generator side, harmonic losses are significantly reduced when a three-level voltage waveform is applied. The positive impact is reduced mechanical insulation stress and reduced overvoltage due to long motor cables [10], which can be problematic in two-level converter applications [11].

In this paper, the competitiveness of the three-level topology for wave power applications is analyzed in terms of efficiency and performance. The paper characterizes topology loss and efficiency, topology output current harmonics and leakage current. Additionally, because of the nature of wave energy converter, it is necessary to supply power to an independent load, so the analysis is focused on the four-leg topology to respond to unbalanced loads. An unbalanced load is caused by unbalance of three-phase and single-phase loads in independent operation and can occur when nonlinear loads, such as factories and warehouses (for example, island microgrids), increase rapidly. The power range considered is limited to 5–30 kW, considering a single wave power operating area. Many fields already use various topologies of multilevel converters [12] and apply control methods [13], but in this study, an analysis was performed based on the topology applied to wave power devices so far. In [12], research on obtaining fast responses by applying artificial intelligence-based indirect space vector control was also conducted. Likewise, in [13], research on cascaded H-bridge converters for large-capacity converters was conducted, but it has not yet been applied to wave power devices.

Unlike the control methods for various topologies described above, the four-leg-based power converters focused on in this study have a special configuration, so they are not suitable for conventional linear controllers (PI controller-based pulse width modulation, PI-based PWM) or three-dimensional space vector pulse widths. Complexity increases in modulation (SVPWM) application [14,15,16,17,18]. Obviously, many studies have been conducted, and applicability is not impossible, but model-based current control is more advantageous for converters with special configurations because it can configure a simple and intuitive controller [19,20]. That is, even if complex control variables exist in an unusual topology, such as a four-wire converter, it may have the advantage of being easy to apply. Recently, many academic studies have been conducted on the application of model prediction to various topologies [21,22,23].

In conclusion, we analyze the four topologies that have been widely applied to the existing wave power generation. The four-leg topology of the two-level converter and three-level neutral clamp converter [24] is for comparison. More multilevel converters may be considered in the future [25,26]. In addition, each topology was analyzed for performance by applying model predictive control to reflect unusual behavioral characteristics. This model’s predictive control is excellent in responding to rapidly changing wave energy due to its fast response. Performance for each topology compares efficiency and performance under varying conditions, including balanced load and unbalanced load conditions. In addition, the performance comparison according to the control sampling frequency affects the topology efficiency. These analyses can provide criteria for a topology suitable for wave power generation and provide guidelines for applicability.

2. Three-Phase Four-Leg Topology Configurations and Control Method

The power converter for wave energy converter consists of an AC/DC converter that converts the AC power of a generator into DC power and a DC/AC inverter that converts DC power into AC power. Along with the technological advancement of the wave energy converter, the power conversion system for wave energy converter also needs the application of a multilevel converter according to the increase in capacity. Among other renewable energy sources, wind turbines use two-level power converters for tens of kW to hundreds of kW generators, but multilevel converters are applied for generators of MW or higher. As a result, the increase in output power has made it inevitable to apply multilevel converters. Multilevel converters (three-level NPC type converters) are not only applied in various fields but also have various advantages, such as reducing harmonics according to the increase in output voltage level and reducing the size of passive filters, so they will be applied to wave power generators. Figure 1 compares the output characteristics of the two-level topology and the three-level topology under the wave power single module rating (30 kW) operating condition. The three-level topology exhibits excellent performance, such as low total harmonic distortion and low voltage stress under the same input conditions. In other words, the three-level topology may have sufficiently excellent performance in wave energy converters.

General three-wire power converters have limitations in application depending on the operating conditions of the load. In other words, normal current control is not possible in an unbalanced load operation. These limitations can be protected by the operation of a four-wire power converter. In addition, the four-wire power converter has an excellent advantage in leakage current control in terms of safety. Since the wave energy converter needs independent operation and response to unbalanced loads, in this study, a characteristic analysis was performed using a four-leg topology. Figure 1 shows a three-level, four-leg topology for application in a wave power system with leakage capacitors.

In this paper, various four-leg topologies were compared and analyzed to select a suitable topology for application to wave energy converter. Comparison is performed from a two-level topology that has been widely applied in the past to a three-level topology to improve output performance. In this study, a total of four types of topologies were compared, and Figure 2 shows the configuration of the topology applied in this study. In order to apply the wave power characteristics, the analysis was focused on the AC/DC converter related to the input energy. DC/AC inverters have similar operating characteristics and are not described separately. The topology of the four-leg type is a rectifier with a two-level three-leg four-wire structure (Figure 3a), a three-phase two-level four-leg structure rectifier (Figure 3b), and a three-level three-leg four-wire structure. It consists of a rectifier (Figure 3c) and a rectifier with a three-level, four-leg structure (Figure 3d).

In this paper, a model predictive control that can have a fast response is applied to respond to wave energy. In addition, the model predictive control can provide the convenience of control due to the characteristics of the four-leg topology having nonlinear characteristics. Furthermore, in the case of a three-level topology, the model predictive control can have sufficient advantages because the control variable increases.

In order to apply the model predictive control to the converters shown in Figure 3, the relationship between the switching state and the output voltage according to each converter must be considered. That is, it is necessary to observe the change of the control variable according to the switching state of each converter. The control of the converter consists of two parts. It can be seen in Figure 4 that a part of the capacitor voltage control is added to the three-level converter rather than the two-level converter. This part increases the complexity of the control.

The current control part of applying the model predictive control to the converter can be expressed as follows by using the R-L filter ($R_f$, $L_f$) and the input voltage ($v_{abc\_in}$) and the input current ($i_{abc\_in}$) for the input AC voltage of the converter.

$$\left[\begin{array}{c}{v}_{a\_in}\\ v_{b\_in}\\ v_{c\_in}\end{array}\right]=R_f\left[\begin{array}{c}{i}_{a\_in}\\ i_{b\_in}\\ i_{c\_in}\end{array}\right]+L_f\frac{d}{dt}\left[\begin{array}{c}{i}_{a\_in}\\ i_{b\_in}\\ i_{c\_in}\end{array}\right]+\left[\begin{array}{c}{v}_{a\_con}\\ v_{b\_con}\\ v_{c\_con}\end{array}\right]$$

(1)

Equation (1) can be expressed as follows if the next step current is predicted based on the discrete model.

$$\left[\begin{array}{c}{i}_{a\_in}\left(k+1\right)\\ i_{b\_in}\left(k+1\right)\\ i_{c\_in}\left(k+1\right)\end{array}\right]=\left(1-L_f^{-1}{T}_{sp}{R}_f\right)\left[\begin{array}{c}{i}_{a\_in}\left(k\right)\\ i_{b\_in}\left(k\right)\\ i_{c\_in}\left(k\right)\end{array}\right]+L_f^{-1}{T}_{sp}\left[\begin{array}{c}{v}_{a\_in}\left(k\right)-v_{a\_con}\left(k\right)\\ v_{b\_in}\left(k\right)-v_{b\_con}\left(k\right)\\ v_{c\_in}\left(k\right)-v_{c\_con}\left(k\right)\end{array}\right]$$

(2)

Based on Equation (2), the optimal switching state can be selected by predicting the load current of the next step using all voltage states that the converter can make and comparing it with the reference current. The magnitude of the reference current shown in Figure 4 is based on the difference between the reference DC-Link voltage and the current DC voltage, using a PI controller to configure the controller [27]. Then, the phase of the input current is extracted based on the PLL algorithm to control the power factor to one. The current reference generated in this way can obtain the predicted reference current based on Lagrange extrapolation [28].

The optimal switching state is selected through an optimization problem, and the optimization method is as follows.

$$G_{current}=\left|i_{abc\_in}^{*}\left(k+1\right)-i_{abc\_in}^{}\left(k+1\right)\right|$$

(3)

Capacitor voltage control is essential for a three-level converter, and the variability of the capacitor voltage based on the current of the capacitor is expressed as:

$$\frac{d}{dt}\left[\begin{array}{c}{V}_{cu}\\ V_{cl}\end{array}\right]=C_{dc}^{-1}\left[\begin{array}{c}{i}_{cu}\\ i_{cl}\end{array}\right]$$

(4)

$i_{\mathrm{cu}}, i_{\mathrm{cl}}$ denote currents flowing through the upper capacitor and the lower capacitor, and $C_{dc}^{-1}$ denotes the capacitance of the capacitor, respectively. If this is expressed in discrete-model like current control, the next step capacitor voltage can be calculated as follows:

$$\left[\begin{array}{c}{v}_{cu}\left(k+1\right)\\ v_{cl}\left(k+1\right)\end{array}\right]=\left[\begin{array}{c}{v}_{cu}\left(k\right)\\ v_{cl}\left(k\right)\end{array}\right]+C_{dc}^{-1}{T}_{sp}\left[\begin{array}{c}{i}_{cu}\left(k\right)\\ i_{cl}\left(k\right)\end{array}\right]$$

(5)

As a result, the optimization method of the three-level converter is as follows and consists of a part for current control and a part for capacitor voltage balancing control.

$$G_{total}=\left|i_{abc\_in}^{*}\left(k+1\right)-i_{abc\_in}^{}\left(k+1\right)\right|+{\lambda }_{cap}\left|v_{cu}\left(k+1\right)-v_{cl}\left(k+1\right)\right|$$

(6)

In the case of the three-level converter, it can be superior to the conventional two-level converter in terms of output performance, but the number of voltage vectors to be considered for current control and capacitor voltage balancing control increases significantly [29]. The voltage vectors and switching states to be considered in the converters applied in this study are shown in

Table 1. Input voltage according to the switching state of the two-level three-leg.

Voltage Vectors	Switching State	Voltage			Voltage Vectors	Switching State	Voltage
		va	vb	vc			va	vb	vc
v1	PPP	1	1	1	v5	NPP	0	1	1
v2	NNN	0	0	0	v6	PNN	1	0	0
v3	NNP	0	0	1	v7	PNP	1	0	1
v4	NPN	0	1	0	v8	PPN	1	1	0

,

Table 2. Input voltage according to the switching state of the two-level four-leg.

Voltage Vectors	Switching State	Voltage			Voltage Vectors	Switching State	Voltage
		va	vb	vc			va	vb	vc
v1	PPPP	0	0	0	v9	PPPN	1	1	1
v2	NNNP	−1	−1	−1	v10	NNNN	0	0	0
v3	PNNP	0	−1	−1	v11	PNNN	1	0	0
v4	PPNP	0	0	−1	v12	PPNN	1	1	0
v5	NPNP	−1	0	−1	v13	NPNN	0	1	0
v6	NPPP	−1	0	0	v14	NPPN	0	1	1
v7	NNPP	−1	−1	0	v15	NNPN	0	0	1
v8	PNPP	0	−1	0	v16	PNPN	1	0	1

,

Table 3. Three-level three-leg input voltage state according to the switching state.

Voltage Vectors	Switching State	Voltage			Voltage Vectors	Switching State	Voltage
		va	vb	vc			va	vb	vc
v1	PPP	0.5	0.5	0.5	v15	ONO	0	−0.5	0
v2	NNN	−0.5	−0.5	−0.5	v16	PON	0.5	0	−0.5
v3	OOO	0	0	0	v17	OPN	0	0.5	−0.5
v4	POO	0.5	0	0	v18	NPO	−0.5	0.5	0
v5	ONN	0	−0.5	−0.5	v19	NOP	−0.5	0	0.5
v6	PPO	0.5	0.5	0	v20	ONP	0	−0.5	0.5
v7	OON	0	0	−0.5	v21	PNO	0.5	−0.5	0
v8	OPO	0	0.5	0	v22	PNN	0.5	−0.5	−0.5
v9	NON	−0.5	0	−0.5	v23	PPN	0.5	0.5	−0.5
v10	OPP	0	0.5	0.5	v24	NPN	−0.5	0.5	−0.5
v11	NOO	−0.5	0	0	v25	NPP	−0.5	0.5	0.5
v12	OOP	0	0	0.5	v26	NNP	−0.5	−0.5	0.5
v13	NNO	−0.5	−0.5	0	v27	PNP	0.5	−0.5	0.5
v14	POP	0.5	0	0.5

and

Table 4. Input voltage according to the switching state of the three-level four-leg.

Voltage Vectors	Switching State	Voltage			Voltage Vectors	Switching State	Voltage
		van	vbn	vcn			van	vbn	vcn
v1	NNNN	0	0	0	v42	OOOP	−0.5	−0.5	−0.5
v2	NNNO	−0.5	−0.5	−0.5	v43	OOPN	0.5	0.5	1
v3	NNNP	−1	−1	−1	v44	OOPO	0	0	0.5
v4	NNON	0	0	0.5	v45	OOPP	−0.5	−0.5	0
v5	NNOO	−0.5	−0.5	0	v46	OPNN	0.5	1	0
v6	NNOP	−1	−1	−0.5	v47	OPNO	0	0.5	−0.5
v7	NNPN	0	0	1	v48	OPNP	−0.5	0	−1
v8	NNPO	−0.5	−0.5	0.5	v49	OPON	0.5	1	0.5
v9	NNPP	−1	−1	0	v50	OPOO	0	0.5	0
v10	NONN	0	0.5	0	v51	OPOP	−0.5	0	−0.5
v11	NONO	−0.5	0	−0.5	v52	OPPN	0.5	1	1
v12	NONP	−1	−0.5	−1	v53	OPPO	0	0.5	0.5
v13	NOON	0	0.5	0.5	v54	OPPP	−0.5	0	0
v14	NOOO	−0.5	0	0	v55	PNNN	1	0	0
v15	NOOP	−1	−0.5	−0.5	v56	PNNO	0.5	−0.5	−0.5
v16	NOPN	0	0.5	1	v57	PNNP	0	−1	−1
v17	NOPO	−0.5	0	0.5	v58	PNON	1	0	0.5
v18	NOPP	−1	−0.5	0	v59	PNOO	0.5	−0.5	0
v19	NPNN	0	1	0	v60	PNOP	0	−1	−0.5
v20	NPNO	−0.5	0.5	−0.5	v61	PNPN	1	0	1
v21	NPNP	−1	0	−1	v62	PNPO	0.5	−0.5	0.5
v22	NPON	0	1	0.5	v63	PNPP	0	−1	0
v23	NPOO	−0.5	0.5	0	v64	PONN	1	0.5	0
v24	NPOP	−1	0	−0.5	v65	PONO	0.5	0	−0.5
v25	NPPN	0	1	1	v66	PONP	0	−0.5	−1
v26	NPPO	−0.5	0.5	0.5	v67	POON	1	0.5	0.5
v27	NPPP	−1	0	0	v68	POOO	0.5	0	0
v28	ONNN	0.5	0	0	v69	POOP	0	−0.5	−0.5
v29	ONNO	0	−0.5	−0.5	v70	POPN	1	0.5	1
v30	ONNP	−0.5	−1	−1	v71	POPO	0.5	0	0.5
v31	ONON	0.5	0	0.5	v72	POPP	0	−0.5	0
v32	ONOO	0	−0.5	0	v73	PPNN	1	1	0
v33	ONOP	−0.5	−1	−0.5	v74	PPNO	0.5	0.5	−0.5
v34	ONPN	0.5	0	1	v75	PPNP	0	0	−1
v35	ONPO	0	−0.5	0.5	v76	PPON	1	1	0.5
v36	ONPP	−0.5	−1	0	v77	PPOO	0.5	0.5	0
v37	OONN	0.5	0.5	0	v78	PPOP	0	0	−0.5
v38	OONO	0	0	−0.5	v79	PPPN	1	1	1
v39	OONP	−0.5	−0.5	−1	v80	PPPO	0.5	0.5	0.5
v40	OOON	0.5	0.5	0.5	v81	PPPP	0	0	0
v41	OOOO	0	0	0

below.

3. Four-Leg Topology Loss Analysis Model

Estimating the power dissipation allows us to estimate the efficiency of each converter, and this estimate can be used to evaluate various converter topologies before assembling and testing the converter. Therefore, the power loss estimation provides the designer with an optimization method. It can also accurately estimate semiconductor thermal stresses under various operating conditions to design appropriate protection strategies to prevent excessive thermal stresses.

A simple model that describes a semiconductor in terms of voltage source drop and resistance is useful for determining conduction losses but not suitable for estimating switching losses. As an alternative to simple and complex semiconductor models, simulations with ideal switches and diodes can be fast. With an ideal switch, there is a close match between the simulated current and voltage if the conduction voltage drop of the real device is insignificant. Therefore, a method was introduced to estimate the power dissipation in the simulation using an ideal switch and then introduce a post-process to reflect the actual semiconductor behavior. A flow chart of the power device loss calculation is shown in Figure 5.

High-speed simulation by PSIM, together with the ideal model of the power device, can be used to determine the voltage and current of the switching device at the moment of switching. A post-processor program using linear equations is run to calculate total device losses based on switching energy losses and on-state voltage losses over voltage, current, and junction temperature. SiC Mosfet turn-on energy loss (E_ON), turn-off energy loss (E_OFF), and diode reverse recovery loss based on the data sheet as a function of DC voltage (V_DC), collector current (I_C), junction temperature (T_j), and gate resistance (R_g) (E_REC) is calculated. Finally, SiC Mosfet power dissipation and diode power dissipation are calculated based on the switching frequency (f_sw) [30].

A post-processor program is used to calculate semiconductor losses after a quick simulation using ideal switches and diodes. Switching moments are detected using sharp edges in voltage and current waveforms. A positive voltage edge occurs at the moment of turning off, and a negative voltage at the moment of turning on. At each switching moment, the turn-on voltage value, turn-on current, turn-off voltage and turn-off current are sensed according to the positive or negative voltage edge. At that time, the post-processor uses linear functions derived from the datasheet to calculate the SiC Mosfet turn-on energy loss (E_ON), SiC Mosfet turn-off energy loss (E_OFF) and diode turn-off energy loss (E_REC). The turn-on power (P_ON), turn-off power (P_OFF), and diode turn-off losses (P_REC) are calculated as follows:

$$P_{ON}=\frac{1}{T}\sum E_{ON}$$

(7)

$$P_{OFF}=\frac{1}{T}\sum E_{OFF}$$

(8)

$$P_{REC}=\frac{1}{T}\sum E_{REC}$$

(9)

The SiC Mosfet conduction loss (P_{SiC-Mosfet_COND}) and diode conduction loss (P_{DIODE_COND}) are calculated.

$$P_{\mathrm{SiC}-\mathrm{Mosfet}\_\_COND}=\frac{1}{T}\int V_{CE}·I_C$$

(10)

$$P_{DIODE\_COND}=\frac{1}{T}\int V_F·I_F$$

(11)

The total SiC-Mosfet losses are:

$$P_{\mathrm{SiC}-\mathrm{Mosfet}\_TOTAL}=P_{\mathrm{SiC}-\mathrm{Mosfet}\_\_COND}+P_{ON}+P_{OFF}$$

(12)

The total diode losses are computed in the same way as SiC-Mosfet losses, except diode turn-on losses, are considered to zero

$$P_{DIODE\_TOTAL}=P_{DIODE\_COND}+P_{REC}$$

(13)

CREE’s C3M0021120K (1200 V) and C3M0025065K (650 V) devices, which are silicon carbide power MOSFETs, were applied to the converter loss analysis, respectively. In addition, for the reverse diode, Silicon Carbide Schottky Diode was applied, and CREE’s C4D40120D was applied. Through this, loss analysis was performed among the operating characteristics of each converter. It derives a topology suitable for the wave power device through the efficiency analysis of each converter.

4. Comparison of Simulations and Results

In this study, four types of topologies shown in Figure 3 were compared to select a topology suitable for wave power operating conditions. The operating conditions of the wave power generation were simulated under the rated operating conditions of 30 kW. In this study, each converter performed the operation by applying the model predictive control. The parameters of the wave power generator are shown in

Table 5. Parameter for OWC-WEC Simulation.

Parameters	Values
Vin (input voltage)	432.56 V
Rin (input restistance)	0.233 Ω
Lin (input inductance)	2.0344 mH
Cdc (DC capacitance)	4400 µF
Vdc (DC voltage)	850 V

below.

Figure 6 compares the output characteristics of each converter under the wave power rating conditions shown in Table 1 to confirm the performance of each converter. Model predictive control was applied to each converter. As analyzed above, it can be seen that the three-level converter is superior to the two-level converter in input current performance or input voltage performance. Also, it can be seen that the three-level converter is excellent in leakage current performance. Among them, it can be seen that the three-level four-leg converter has the best leakage current performance. In conclusion, a three-level four-leg converter with the best input current or output performance and leakage current performance would be most suitable for a power converter for a wave power generator.

Figure 7 shows the dynamics of the input current for each converter. Since the wave energy of the wave power generation system changes rapidly, it must be able to follow the rapidly changing current. Model predictive control can quickly follow current changes. Figure 7 shows the current dynamics of each converter according to the reference current change. It can be seen that all converters follow the reference current quickly because model predictive control is applied, even if the input energy changes rapidly due to the nature of the wave power generation. In addition, it can be seen that the three-level converter more accurately tracks the reference current than the two-level converter, and the current ripple is reduced, even if all converters exhibit a fast response. That is, if the model predictive control is applied to the converter for the wave power device, an advantage can be obtained.

Figure 8 shows the components of the prototype for topology performance verification. Performance verification was compared by applying the two-level type and the three-level type, respectively. For the semiconductor switching element of each topology, CREE’s C3M0021120K was applied for the two-level type, and CREE’s C3M0025065K was applied for the three-level type. Detailed specifications of each device are shown in

Table 6. Semiconductor switching device specifications for topology performance verification.

	Applied Topology	VDS	ID (25 °C)	RDS(ON)
C3M0021120K (1200 V)	Two-Level Type	1200 V	100 A	21 mΩ
C3M0025065K (650 V)	Three-Level Type	650 V	97 A	25 mΩ

below. Each topology applied the same control board, gate driver and load system, and a picture of the applied equipment is inserted in Figure 8. Through this, a performance analysis of each topology was performed. The part about signal distortion should also be considered [31]. The load parameters and operating switching frequencies for the experiment are shown in

Table 7. Induction Motor Parameter for inverter experiment.

Parameters	Values
Rs (stator restistance)	2 Ω
Rr (rotor restistance)	1.56 Ω
Ls (stator inductance)	54 mH
Lr (rotor inductance)	54 mH
Lm (mutual inductance)	51.5 mH
Tsp (sampling period)	200 µsec

.

Figure 9 shows the output waveform to check the operation and performance of the converter hardware. Figure 9 shows that the three-phase current and three-phase line voltage appear well in normal operation. In addition, it can be confirmed that the transient response performance is appropriately controlled by the output current size change and frequency change. Through this, it was possible to verify the corresponding algorithm through each hardware. In addition, it can be confirmed through Figure 9d that the algorithm operates without problems, even under balanced load and unbalanced load conditions.

Figure 10 shows the loss distribution of each converter element during balanced operation under rated conditions. The loss distribution is shown for each element in a-phase. For the loss analysis, the method described in Part 3 was applied. It can be seen that the three-level converter shows much less loss in each device than the two-level converter. In addition, it can be seen that the loss distribution in each device is also more balanced in the three-level converter.

Figure 11 shows the loss distribution of each converter element during unbalanced operation under rated conditions. The unbalanced operation resulted in a 1.2-fold increase in the power of a-phase. Accordingly, the overall loss increased. It was confirmed that the loss of the three-level converter was much less than that of the two-level converter in the balanced operation. Also, the loss distribution in each device was more balanced in the three-level converter. However, it can be seen that the distribution of each device is relatively constant in the three-level four-leg converter that can cope with the unbalanced operation than the three-level three-leg four-wire converter.

Table 8. Power losses under symmetric and asymmetric operation for AC/DC converter in rated operation.

		Two-Level Four-Wire	Two-Level Four-Leg	Three-Level Three-Leg Four-Wire	Three-Level Four-Leg
Losses [W]	Symmetric operation	597.75	478.89	305.79	258.26
	Asymmetric operation	899.14	752.88	693.64	490.48

shows the total losses of the converter during balanced and unbalanced operations. When considered comprehensively, it can be seen that the performance of the three-level four-leg converter is the best under the wave power characteristics condition.

Figure 12 compares the input current THD, output voltage ripple, leakage current magnitude, average switching frequency, converter loss and efficiency of each converter according to the sampling frequency change. As the sampling frequency increases, it can be seen that the THD of the input current and the output voltage ripple decrease. The three-level, four-leg converter used in this study exhibits the lowest input current THD and low voltage ripple over all switching frequency ranges. In addition, even when the sampling frequency was changed, the three-level converter performed better than the two-level converter in terms of leakage current, and the three-level four-leg converter showed the best performance. It was also confirmed that the average switching frequency of the three-level four-leg converter was the lowest, and accordingly, it showed much superior performance than the conventional wave power converter in terms of loss and efficiency of the converter.

Figure 13 compares the current THD, leakage current size, power converter loss and efficiency according to the output power change. It can be seen that the current THD and leakage current decrease as the output power increases, similar to the characteristics according to the sampling frequency change. In addition, it can be seen that loss and efficiency also improve as the output power increases. Depending on the output power change, the three-level converter showed better performance than the two-level converter, and the three-level four-leg converter showed the best performance.

Figure 14 shows the distribution of losses of each inverter element under a balanced load under rated conditions. The loss distribution is shown for each element in a-phase. As in the converter analysis, it can be seen that the three-level converter shows much less loss in each device than the two-level converter. In addition, Figure 15 shows the distribution of losses of each inverter element during unbalanced operation under rated conditions. The unbalanced operation increased the overall loss because the a-phase power increased by a factor of 1.2. It was confirmed that the loss of the three-level converter was much less than that of the two-level converter in the balanced operation. Similar to the converter analysis, the three-level inverter shows lower losses than the two-level inverter. The maximum efficiency difference was 2.28% higher for the three-level four-leg converter in balanced operation and 2.7% higher in unbalanced operation.

Table 9. Total Efficiency under symmetric and asymmetric operation for DC/AC inverter in rated operation.

		Two-Level Three-Leg Four-Wire	Two-Level Four-Leg	Three-Level Three-Leg Four-Wire	Three-Level Four-Leg
Total Efficiency [%]	Symmetric operation	96.0	96.8	97.96	98.28
	Asymmetric operation	94.0	95.0	95.4	96.7

shows the efficiency of the power converter for wave power generation incorporating the converter-inverter during balanced and unbalanced operations.

5. Conclusions

In order to increase the energy efficiency of the wave power generator, it is essential to increase the efficiency of the power converter. Efficient converters must operate at low switching frequencies, which increases the weight and volume of passive components, which can exceed space constraints. Therefore, in this paper, we compare the performance of various types of topologies, from the two-level topology to the three-level topology applied to the existing wave power generation device. In particular, analysis was performed focusing on a four-leg type topology that can cope with unbalanced operation, and model predictive control was applied to apply to abrupt energy changes and atypical topologies. As a power converter for wave power generation, a three-level, four-leg topology with the best current harmonics, leakage current performance, DC voltage fluctuation rate and loss is suitable. This was the best performance of the three-level four-leg topology, even with the switching frequency change affecting the topology performance. The three-level four-leg back-to-back converter showed up to 2.28% and 2.7% higher efficiencies under balanced and unbalanced operating conditions. In conclusion, a three-level, four-leg topology is most suitable as a power converter for wave power generation under the same conditions.