Evaluation and Comprehensive Comparison of H-Bridge-Based Bidirectional Rectiﬁer and Unidirectional Rectiﬁers

: This paper presents an evaluation and comprehensive comparison for the topologies which are applied to the front stage of transformer-less cascaded multilevel converter (TCMC). The topologies investigated are targeted at the bidirectional cascaded H-bridge rectiﬁer and three unidirectional rectiﬁers, including the diode H-bridge cascaded boost rectiﬁer, cascaded bridgeless rectiﬁer and cascaded VIENNA rectiﬁer. First, the operation principles of the unidirectional rectiﬁers are discussed. Then the performances of these topologies such as power losses, e ﬃ ciency, device current stress, cost, and total harmonic distortions are analyzed and evaluated respectively. Finally, advantages and disadvantages for each topology are discussed and highlighted. The evaluation and comparison methods presented in this paper and their results are feasible and e ﬀ ective for selecting the appropriate topology in practical applications under di ﬀ erent operating conditions.


Introduction
In recent years, with the rapid development of power semiconductor devices and power electronic technologies, the transformer-less cascaded multilevel converter (TCMC) has attracted extensive attention in the medium and high voltage application [1][2][3][4][5][6][7]. As shown in Figure 1, by employing the cascade H-bridge (CHB) converter as the front (last) stage, and the high-frequency isolated bidirectional DC-DC converter as the DC/DC stage, the TCMC can not only remove the bulky and expensive line-frequency transformer, but can also be connected directly to the medium/high voltage power grid and suited for the bidirectional power flow applications, such as coal mine hoists and locomotive traction, with some features as small size and light weight.
However, the TCMC mentioned above utilizes too many fully-controlled power switches (such as IGBTs or MOSFETs), making its main circuit and control system more complicated with higher cost and lower reliability. Considering that in many practical applications, bidirectional power flow is not always necessitated, such as in the Alternating Current (AC) speed regulation systems with pumps or fans load, etc., some researchers believe that in these applications, it might be a better choice to take the unidirectional rectifier like diode H-bridge cascaded boost rectifier, cascaded bridgeless rectifier and cascaded VIENNA rectifier as the front stage of TCMC [8][9][10][11][12]. The authors of [9] investigated the possibility of using the cascaded bridgeless rectifier to construct the front stage of TCMC. The authors of [10] discussed a method of using the diode H-bridge with the cascaded boost rectifier to construct the front stage of TCMC. The authors of [11] studied the cascaded single-phase VIENNA circuit and rectifier to construct the front stage of TCMC. The authors of [11] studied the cascaded single-phase VIENNA circuit and the corresponding voltage balancing control strategy. The authors of [12] presented a hybrid cascading typology, in which the N bridgeless rectifiers and the M fully-controlled H-bridge rectifier are connected in cascading, causing the constructed front stage of TCMC to operate not only in unity power factor, but also in leading or lagging power factors. However, all the previous references are mainly directed at the power factor regulation and voltage balancing control, with no discussion about the comparison of comprehensive performance between these different unidirectional converter typologies, and between these different unidirectional rectifier typologies and H-bridge bidirectional rectifier-based TCMC, while the comprehensive performance comparison is very important for choosing the suitable typology to construct the TCMC in different industrial applications.

Sub-modules
Sub-modules In this study, the topologies are focused on the bidirectional cascaded H-bridge rectifier, and three different kinds of topologies used in unidirectional power flow, including the diode H-bridge cascaded boost rectifier, the cascaded bridgeless rectifier, and the cascaded VIENNA rectifier. These topologies are compared on the basis of the theory of operation, power losses, efficiencies, device current stress, cost, and input current THD analysis. Moreover, it needs to be emphasized that in these topologies, identical hardware and parameters are utilized to ensure the objectivity and fairness of the comparison in this paper.
The remainder of the paper is organized as follows: Section 2 presents the configuration and the operation principle of these topologies. Section 3 discusses an investigation into the loss distribution of semiconductors and the efficiency comparison. Cost comparison is proposed in Section 4. Then the device stress and THD analysis are evaluated in Section 5 and Section 6. Finally, conclusions are summarized in Section 7.

Description to Unidirectional Rectifier Topologies and Operation Principles
Since the cascaded H-bridge rectifier has already been a focus that attracts many scholars' attention and adopted in many practical applications [13][14][15][16], it will not be discussed in this section. Instead, the single-phase cascaded rectifiers with two modules in cascading will be taken as an example, and the structures and operation principles of the three types of unidirectional rectifiers will be analyzed. In this study, the topologies are focused on the bidirectional cascaded H-bridge rectifier, and three different kinds of topologies used in unidirectional power flow, including the diode H-bridge cascaded boost rectifier, the cascaded bridgeless rectifier, and the cascaded VIENNA rectifier. These topologies are compared on the basis of the theory of operation, power losses, efficiencies, device current stress, cost, and input current THD analysis. Moreover, it needs to be emphasized that in these topologies, identical hardware and parameters are utilized to ensure the objectivity and fairness of the comparison in this paper.

Diode H-Bridge Cascaded Boost Rectifier
The remainder of the paper is organized as follows: Section 2 presents the configuration and the operation principle of these topologies. Section 3 discusses an investigation into the loss distribution of semiconductors and the efficiency comparison. Cost comparison is proposed in Section 4. Then the device stress and THD analysis are evaluated in Sections 5 and 6. Finally, conclusions are summarized in Section 7.

Description to Unidirectional Rectifier Topologies and Operation Principles
Since the cascaded H-bridge rectifier has already been a focus that attracts many scholars' attention and adopted in many practical applications [13][14][15][16], it will not be discussed in this section. Instead, the single-phase cascaded rectifiers with two modules in cascading will be taken as an example, and the structures and operation principles of the three types of unidirectional rectifiers will be analyzed.

Diode H-Bridge Cascaded Boost Rectifier
The diode H-bridge cascade boost rectifier is a novel cascaded multi-level rectifier which employs fewer fully-controlled switches and can achieve a unity power factor. Its structure is the combination Electronics 2020, 9, 309 3 of 13 of a high voltage rated diode bridge D 1 -D 4 , and the cascaded boost DC/DC modules, as shown in Figure 2 [10,17].
Electronics 2020, 9, x FOR PEER REVIEW 3 of 14 The diode H-bridge cascade boost rectifier is a novel cascaded multi-level rectifier which employs fewer fully-controlled switches and can achieve a unity power factor. Its structure is the combination of a high voltage rated diode bridge D1-D4, and the cascaded boost DC/DC modules, as shown in Figure 2 [10,17]. S=1 is defined as the status when the fully-controlled power switch is turn-on, while S=0 is turnoff, and for two switches (S1, S2), there are four modes during the operation of the circuit, namely (1,1), (0,1), (1,0), (0,0). Because the positive and negative half cycles of the power supply voltage are symmetrical, only the positive half cycle is analyzed, and the current path of the four operation modes in the positive half period of AC voltage are shown in Figure 3.

Cascaded Bridgeless Rectifier
As the bridgeless topology avoids the needs for the rectifier input diode bridge, and maintains the classic boost topology, it has been studied by many scholars and widely used in power factor correction (PFC) [18][19][20][21][22]. Furthermore, the bridgeless rectifier can be cascaded as the front stage of TCMC, as shown in Figure 4. Each module is composed of two fast recovery diodes D1 and D2, two active switches S1 and S2 with inherently body diodes DS1 and DS2, and a capacitor C. With fewer active switches than H-bridge rectifier, and when compared with the diode H-bridge boost rectifier, S=1 is defined as the status when the fully-controlled power switch is turn-on, while S=0 is turn-off, and for two switches (S 1 , S 2 ), there are four modes during the operation of the circuit, namely (1,1), (0,1), (1,0), (0,0). Because the positive and negative half cycles of the power supply voltage are symmetrical, only the positive half cycle is analyzed, and the current path of the four operation modes in the positive half period of AC voltage are shown in Figure 3. The diode H-bridge cascade boost rectifier is a novel cascaded multi-level rectifier which employs fewer fully-controlled switches and can achieve a unity power factor. Its structure is the combination of a high voltage rated diode bridge D1-D4, and the cascaded boost DC/DC modules, as shown in Figure 2 [10,17]. S=1 is defined as the status when the fully-controlled power switch is turn-on, while S=0 is turnoff, and for two switches (S1, S2), there are four modes during the operation of the circuit, namely (1,1), (0,1), (1,0), (0,0). Because the positive and negative half cycles of the power supply voltage are symmetrical, only the positive half cycle is analyzed, and the current path of the four operation modes in the positive half period of AC voltage are shown in Figure 3.

Cascaded Bridgeless Rectifier
As the bridgeless topology avoids the needs for the rectifier input diode bridge, and maintains the classic boost topology, it has been studied by many scholars and widely used in power factor correction (PFC) [18][19][20][21][22]. Furthermore, the bridgeless rectifier can be cascaded as the front stage of TCMC, as shown in Figure 4. Each module is composed of two fast recovery diodes D1 and D2, two active switches S1 and S2 with inherently body diodes DS1 and DS2, and a capacitor C. With fewer active switches than H-bridge rectifier, and when compared with the diode H-bridge boost rectifier,

Cascaded Bridgeless Rectifier
As the bridgeless topology avoids the needs for the rectifier input diode bridge, and maintains the classic boost topology, it has been studied by many scholars and widely used in power factor correction (PFC) [18][19][20][21][22]. Furthermore, the bridgeless rectifier can be cascaded as the front stage of TCMC, as shown in Figure 4. Each module is composed of two fast recovery diodes D 1 and D 2 , two active switches S 1 and S 2 with inherently body diodes D S1 and D S2 , and a capacitor C. With fewer active switches than H-bridge rectifier, and when compared with the diode H-bridge boost rectifier, Electronics 2020, 9, 309 4 of 13 bridgeless rectifier can not only reduce the total number of switching devices by two, but also lessens the number of switching devices in the current path during normal operation in each module. Since the fast recovery diodes D 1 and D 2 are unidirectional conductive, the AC side combined voltage of the bridgeless rectifier is determined by the states of switches, and the polarity of the input current.
Electronics 2020, 9, x FOR PEER REVIEW 4 of 14 bridgeless rectifier can not only reduce the total number of switching devices by two, but also lessens the number of switching devices in the current path during normal operation in each module. Since the fast recovery diodes D1 and D2 are unidirectional conductive, the AC side combined voltage of the bridgeless rectifier is determined by the states of switches, and the polarity of the input current. The effective operation mode of the two-stage cascaded bridgeless rectifier can be divided into four modes according to the states of the four switches (S11, S12, S21, S22), namely (1, 1, 1, 1), (0, 0, 1, 1), (1, 1, 0, 0) and (0, 0, 0, 0). The four operation modes in the positive half period of AC voltage can be obtained in Figure 5.

Cascaded VIENNA Rectifier
The cascaded VIENNA rectifier circuit is shown in Figure 6. Due to the structural characteristics of the VIENNA rectifier, one of the most important advantage for this topology is that each semiconductor device only suffers half of the total DC bus voltage [8]. As for the structure of a single module VIENNA topology, it is comprised of one input inductor L, two output capacitors C1 and C2, one active switch S, two regular diodes D1 and D3, and four fast recovery diode D2, D4, D5 and D6. The effective operation mode of the two-stage cascaded bridgeless rectifier can be divided into four modes according to the states of the four switches (S 11 , S 12 , S 21 , S 22 ), namely (1, 1, 1, 1), (0, 0, 1, 1), (1, 1, 0, 0) and (0, 0, 0, 0). The four operation modes in the positive half period of AC voltage can be obtained in Figure 5.
Electronics 2020, 9, x FOR PEER REVIEW 4 of 14 bridgeless rectifier can not only reduce the total number of switching devices by two, but also lessens the number of switching devices in the current path during normal operation in each module. Since the fast recovery diodes D1 and D2 are unidirectional conductive, the AC side combined voltage of the bridgeless rectifier is determined by the states of switches, and the polarity of the input current. The effective operation mode of the two-stage cascaded bridgeless rectifier can be divided into four modes according to the states of the four switches (S11, S12, S21, S22), namely (1, 1, 1, 1), (0, 0, 1, 1), (1, 1, 0, 0) and (0, 0, 0, 0). The four operation modes in the positive half period of AC voltage can be obtained in Figure 5.

Cascaded VIENNA Rectifier
The cascaded VIENNA rectifier circuit is shown in Figure 6. Due to the structural characteristics of the VIENNA rectifier, one of the most important advantage for this topology is that each semiconductor device only suffers half of the total DC bus voltage [8]. As for the structure of a single module VIENNA topology, it is comprised of one input inductor L, two output capacitors C1 and C2, one active switch S, two regular diodes D1 and D3, and four fast recovery diode D2, D4, D5 and D6.

Cascaded VIENNA Rectifier
The cascaded VIENNA rectifier circuit is shown in Figure 6. Due to the structural characteristics of the VIENNA rectifier, one of the most important advantage for this topology is that each semiconductor device only suffers half of the total DC bus voltage [8]. As for the structure of a single module VIENNA topology, it is comprised of one input inductor L, two output capacitors C 1 and C 2 , one active switch S, two regular diodes D 1 and D 3 , and four fast recovery diode D 2 , D 4 , D 5 and D 6 . Depending on the switching states of the (S1, S2), there exist four operation modes under positive half period for the two-stage cascaded VIENNA rectifier, as shown in Figure 7.

Power Losses and Efficiency-Based Evaluation
Since the power losses of the power semiconductor, including the conduction and switching losses are the major contributors to the rectifier losses, the total losses only take the semiconductor power losses into consideration in the following discussion. Analysis in this section will be implemented by PLECS software on the power loss distribution of the power semiconductors and the efficiency comparison in the four types of topologies as shown in Section 2, since PLECS software has been widely used in simulation on power electronics losses, on the basis of the component datasheet [23][24][25].

Calculation of Switching and Conduction Losses
(1) Calculation of IGBT losses Switching losses are caused by the transition of the power devices between the blocking state and the conducting state, including turn-on losses and turn-off losses.
Accordingly, the switching losses Psw can be expressed in (1) as: Depending on the switching states of the (S 1 , S 2 ), there exist four operation modes under positive half period for the two-stage cascaded VIENNA rectifier, as shown in Figure 7. Depending on the switching states of the (S1, S2), there exist four operation modes under positive half period for the two-stage cascaded VIENNA rectifier, as shown in Figure 7.

Power Losses and Efficiency-Based Evaluation
Since the power losses of the power semiconductor, including the conduction and switching losses are the major contributors to the rectifier losses, the total losses only take the semiconductor power losses into consideration in the following discussion. Analysis in this section will be implemented by PLECS software on the power loss distribution of the power semiconductors and the efficiency comparison in the four types of topologies as shown in Section 2, since PLECS software has been widely used in simulation on power electronics losses, on the basis of the component datasheet [23][24][25].

Calculation of Switching and Conduction Losses
(1) Calculation of IGBT losses Switching losses are caused by the transition of the power devices between the blocking state and the conducting state, including turn-on losses and turn-off losses.
Accordingly, the switching losses Psw can be expressed in (1) as:

Power Losses and Efficiency-Based Evaluation
Since the power losses of the power semiconductor, including the conduction and switching losses are the major contributors to the rectifier losses, the total losses only take the semiconductor power losses into consideration in the following discussion. Analysis in this section will be implemented by PLECS software on the power loss distribution of the power semiconductors and the efficiency comparison in the four types of topologies as shown in Section 2, since PLECS software has been widely used in simulation on power electronics losses, on the basis of the component datasheet [23][24][25].

Calculation of Switching and Conduction Losses
(1) Calculation of IGBT losses Switching losses are caused by the transition of the power devices between the blocking state and the conducting state, including turn-on losses and turn-off losses.
Electronics 2020, 9, 309 6 of 13 Accordingly, the switching losses P sw can be expressed in (1) as: where E on and E off are the energy losses during the turn-on and turn-off of the switches and be read from a 3D look-up table, f sw represents the switching frequency. The conduction losses, caused by the on resistance of IGBTs, occur when the device is in full conduction mode. Those losses are computed by averaging the conduction losses in each switching cycle as shown in (2) as: where v ce is the forward voltage drop of the device, i ce stands for the current flowing through the device during the conduction period, and they are calculated based on second order approximation from the 2D look-up table. D is the duty cycle, T is the switching period So that the losses of a IGBT can therefore be described as: (2) Calculation of diode losses Diode losses involve conduction losses P conD and reverse recovery losses P recD . Because the turn-on time is very short and the diodes' reverse blockage current is very small, the turn-on losses and blockage losses can be neglected.
The reverse recovery losses of diode can be expressed as: where E rr indicates the turn-off losses of diode. And the conduction loss calculation of the diode is similar to that of the switch. So the losses of a diode can be denoted as (5): Thus, the total losses are calculated as follows: P loss = (P Q + P D ) = (P sw + P con + P recD + P conD )

Investigation of Power Losses and Efficiency
In order to make a fair comparison, the same hardware and parameters have been used, as shown in Table 1.  has the lowest losses, due to the topological characteristics of the VIENNA rectifier, those semiconductor devices share only half of the DC bus voltage. The cascaded bridgeless rectifier and the cascaded H-bridge rectifier do not sustain the losses of diode bridge, while they have more fullycontrolled switches, and the cascaded H-bridge rectifier has the largest losses. In light of the description of the previous section, the cascaded bridgeless rectifiers reduce half of the fullycontrolled switches compared to cascaded H-bridges rectifiers, and the total losses are 31.7% lower than that of the cascaded H-bridge rectifier, and it also has proved that the use of fewer fullycontrolled switches can do reduce the losses.

Efficiency Investigation Under Different Power Loading
The efficiency measurement is shown in Figure 9, which illustrates the efficiency of the four topologies at different load. It is obvious that the cascaded VIENNA rectifier always functions more efficiently than the other two unidirectional rectifiers and the bidirectional cascaded H-bridge rectifier, and can also achieve at a peak efficiency of 97.97%, whereas the efficiencies for the cascaded bridgeless rectifier and diode H-bridge cascaded rectifier are secondary to it. The cascaded H-bridge rectifier performs at the lowest efficiency.

Cost performance Analysis
The differences in the main electrical power components used in N-stage cascaded single-phase topologies are illustrated in Table 2. From the graph above, it can be seen that the input diode bridge accounts for a part of the total losses among the cascaded VIENNA and diode H-bridge cascaded boost rectifiers, since the forward voltage drop of the diode bridge causes high conduction losses. Since the cascaded VIENNA rectifier has the lowest losses, due to the topological characteristics of the VIENNA rectifier, those semiconductor devices share only half of the DC bus voltage. The cascaded bridgeless rectifier and the cascaded H-bridge rectifier do not sustain the losses of diode bridge, while they have more fully-controlled switches, and the cascaded H-bridge rectifier has the largest losses. In light of the description of the previous section, the cascaded bridgeless rectifiers reduce half of the fully-controlled switches compared to cascaded H-bridges rectifiers, and the total losses are 31.7% lower than that of the cascaded H-bridge rectifier, and it also has proved that the use of fewer fully-controlled switches can do reduce the losses.

Efficiency Investigation under Different Power Loading
The efficiency measurement is shown in Figure 9, which illustrates the efficiency of the four topologies at different load.
Electronics 2020, 9, x FOR PEER REVIEW 7 of 14 From the graph above, it can be seen that the input diode bridge accounts for a part of the total losses among the cascaded VIENNA and diode H-bridge cascaded boost rectifiers, since the forward voltage drop of the diode bridge causes high conduction losses. Since the cascaded VIENNA rectifier has the lowest losses, due to the topological characteristics of the VIENNA rectifier, those semiconductor devices share only half of the DC bus voltage. The cascaded bridgeless rectifier and the cascaded H-bridge rectifier do not sustain the losses of diode bridge, while they have more fullycontrolled switches, and the cascaded H-bridge rectifier has the largest losses. In light of the description of the previous section, the cascaded bridgeless rectifiers reduce half of the fullycontrolled switches compared to cascaded H-bridges rectifiers, and the total losses are 31.7% lower than that of the cascaded H-bridge rectifier, and it also has proved that the use of fewer fullycontrolled switches can do reduce the losses.

Efficiency Investigation Under Different Power Loading
The efficiency measurement is shown in Figure 9, which illustrates the efficiency of the four topologies at different load.  It is obvious that the cascaded VIENNA rectifier always functions more efficiently than the other two unidirectional rectifiers and the bidirectional cascaded H-bridge rectifier, and can also achieve at a peak efficiency of 97.97%, whereas the efficiencies for the cascaded bridgeless rectifier and diode H-bridge cascaded rectifier are secondary to it. The cascaded H-bridge rectifier performs at the lowest efficiency.

Cost performance Analysis
The differences in the main electrical power components used in N-stage cascaded single-phase topologies are illustrated in Table 2. It is obvious that the cascaded VIENNA rectifier always functions more efficiently than the other two unidirectional rectifiers and the bidirectional cascaded H-bridge rectifier, and can also achieve at a peak efficiency of 97.97%, whereas the efficiencies for the cascaded bridgeless rectifier and diode H-bridge cascaded rectifier are secondary to it. The cascaded H-bridge rectifier performs at the lowest efficiency.

Cost Performance Analysis
The differences in the main electrical power components used in N-stage cascaded single-phase topologies are illustrated in Table 2.
Generally speaking, the cost of these rectifiers depends mainly on the devices such as IGBT, diode, input inductor, and DC-link capacitor, etc. As can be seen from Table 3, the cost for the cascaded bridgeless rectifier is relatively lower, and the coat for the diode H-bridge cascaded boost rectifier is moderate, whereas the cost of the cascaded H-bridge rectifier and the cascaded VIENNA rectifier are relatively higher. Moreover, it should be noted that due to the fairness of the comparison in this paper, identical hardware is guaranteed to be utilized in these topologies. However, the semiconductor devices of the VIENNA rectifier only share half of the DC bus voltage, and accordingly the price for semiconductor devices with low withstand voltage may be decreased. Thus, the cost of VIENNA rectifier will be reduced in practical applications.

Component Stresses
In order to select and design the devices in practical applications, comparison and analysis on the stresses of devices with different topologies are conducted in this section under the following assumptions [26]: (1) All the topologies are worked at CCM mode.
(2) These circuits are supplied by an ideal AC power source with 50 Hz frequency and operate at unity power factor.

(3) The output DC voltage is stable with no voltage ripple
The inductor current is assumed as: Then, the inductor current ripple is assumed to be half of the peak inductor current: Therefore, the RMS current of inductor is: Electronics 2020, 9, 309 9 of 13 The duty cycle of the IGBT is given by: where U s , U m are the input voltage and the corresponding peak voltage, the Udc is the DC bus voltage. The instantaneous current of IGBT is: So the RMS current of IGBT can be expressed as: Then, the fast diode duty cycle is given by: So, the instantaneous current and AVG current of diode can be expressed as: The output capacitor current is calculated by: where I 0 represents the output current.
The RMS and AVG of other devices can also be calculated by the above algorithm. As a result, the device stresses for the four circuit topologies are shown in Tables 4 and 5.

THD Analysis of Input Current
In order to better analyze the difference of total harmonic distortions (THD) of the input current between the bidirectional rectifier and the unidirectional rectifier, some simulations have been performed with MATLAB /Simulink software, the results at Po = 6 kW are shown in Figure 10. From the harmonic analysis of the input current, it is evident that the THD of the unidirectional rectifiers are generally higher than that of the bidirectional rectifier. Then the scaled-down experiment prototypes are built under Po = 1650 W. The experiment results show that the input current and voltage waveforms of three different types of unidirectional rectifiers are much the same. Taking the comparison between the cascaded H-bridge rectifier and the cascaded bridgeless rectifier as an example, as shown in Figure 11, it can be seen that the unidirectional rectifiers have the zero-crossing distortion of the input current. The cause of the distortion for the input current is analyzed below. *2 represent the current stresses of D5 and D6 in VIENNA topology.

THD Analysis of Input Current
In order to better analyze the difference of total harmonic distortions (THD) of the input current between the bidirectional rectifier and the unidirectional rectifier, some simulations have been performed with MATLAB /Simulink software, the results at Po =6 kW are shown in Figure 10. From the harmonic analysis of the input current, it is evident that the THD of the unidirectional rectifiers are generally higher than that of the bidirectional rectifier. Then the scaled-down experiment prototypes are built under Po =1650 W. The experiment results show that the input current and voltage waveforms of three different types of unidirectional rectifiers are much the same. Taking the comparison between the cascaded H-bridge rectifier and the cascaded bridgeless rectifier as an example, as shown in Figure 11, it can be seen that the unidirectional rectifiers have the zero-crossing distortion of the input current. The cause of the distortion for the input current is analyzed below.   Figure 12 shows the AC side phasor diagram under unity power factor for the unidirectional rectifiers. The input voltage us is in phase with input voltage is, the voltage across the inductance uL is orthogonal to is. According to the vector addition, the AC side reference voltage u*con lags the is by θ. Therefore, the u*con needs to be opposite to is during the period of θ as depicted in Figure 13. However, due to the unidirectional power flow, the polarity of input current is should be the identical to the AC voltage ucon, so ucon can only generate a zero AC voltage during the period of θ. After u*con changes from negative to positive, is can follow i*s after a period of [12,27]. The distortions of the input current will become more severe while the leading or lagging angle is increased, so the controllability angle for unidirectional rectifier is limited.   Figure 12 shows the AC side phasor diagram under unity power factor for the unidirectional rectifiers. The input voltage u s is in phase with input voltage i s , the voltage across the inductance u L is orthogonal to i s . According to the vector addition, the AC side reference voltage u* con lags the i s by θ. Therefore, the u* con needs to be opposite to i s during the period of θ as depicted in Figure 13. However, due to the unidirectional power flow, the polarity of input current i s should be the identical to the AC voltage u con , so u con can only generate a zero AC voltage during the period of θ. After u* con changes from negative to positive, i s can follow i* s after a period of γ [12,27]. The distortions of the input current will become more severe while the leading or lagging angle is increased, so the controllability angle for unidirectional rectifier is limited.  Figure 12 shows the AC side phasor diagram under unity power factor for the unidirectional rectifiers. The input voltage us is in phase with input voltage is, the voltage across the inductance uL is orthogonal to is. According to the vector addition, the AC side reference voltage u*con lags the is by θ. Therefore, the u*con needs to be opposite to is during the period of θ as depicted in Figure 13. However, due to the unidirectional power flow, the polarity of input current is should be the identical to the AC voltage ucon, so ucon can only generate a zero AC voltage during the period of θ. After u*con changes from negative to positive, is can follow i*s after a period of [12,27]. The distortions of the input current will become more severe while the leading or lagging angle is increased, so the controllability angle for unidirectional rectifier is limited.  However, in order to improve the THD performance for the unidirectional topologies, the control methods have been modified to decrease the distortion of the input current, and to increase the controllability angle [28][29][30].

Conclusion
An evaluation and comprehensive comparison between unidirectional rectifiers and bidirectional rectifier are presented in this paper. The topologies discussed are centered on the cascaded bidirectional H-bridge rectifier, and three different types of unidirectional rectifiers. The operation principle of the rectifiers, and their power losses, efficiencies, device stress, cost, and THD of the input current are analyzed and compared. The results show that each of the topologies possesses several advantages and disadvantages. Although the bidirectional rectifier exhibits the characteristic of low THD input current, and those types of topologies are appropriate for the However, in order to improve the THD performance for the unidirectional topologies, the control methods have been modified to decrease the distortion of the input current, and to increase the controllability angle [28][29][30].

Conclusions
An evaluation and comprehensive comparison between unidirectional rectifiers and bidirectional rectifier are presented in this paper. The topologies discussed are centered on the cascaded bidirectional H-bridge rectifier, and three different types of unidirectional rectifiers. The operation principle of the rectifiers, and their power losses, efficiencies, device stress, cost, and THD of the input current are analyzed and compared. The results show that each of the topologies possesses several advantages and disadvantages. Although the bidirectional rectifier exhibits the characteristic of low THD input current, and those types of topologies are appropriate for the bidirectional power flow application, its disadvantages cannot be neglected because of its fully-controlled power switches, resulting in higher power losses, greater cost and a more complicated control system. Meanwhile, unidirectional rectifiers also have many advantages, such as lower device stress, lower power losses, higher efficiency for the cascaded VIENNA rectifier, and lower cost for cascaded bridgeless rectifier, whereas their THD of the input current is relatively higher, so that their control systems must be carefully designed. The evaluation and comparison methods presented in this paper and their results are feasible and effective for selecting the appropriate topology in practical applications under different operating conditions.