Bidirectional Resonant Converter for DC Microgrid Applications

: A bidirectional resonant converter is presented and veriﬁed in this paper for an electric vehicle battery charger/discharger system. The presented circuit can achieve forward and backward power operation, low switching losses on active devices, and wide output voltage operation. The circuit structure of the presented converter includes two resonant circuits on the primary and secondary sides of an isolated transformer. The frequency modulation approach is adopted to control the studied circuit. Owing to the resonant circuit characteristic, active devices for both forward (battery charge) and backward (battery discharge) power operation can be turned on at zero voltage switching. In order to implement a universal battery charger for different kinds of electric vehicle applications, the DC converter is demanded to have a wide output voltage range capability. The topology morphing between a full bridge resonant circuit and half bridge resonant circuit is selected to obtain high- and low-output voltage range operations so that the 200–500 V output voltage range is realized in the presented resonant converter. Compared to the conventional bidirectional converters, the proposed can be operated under a wide voltage range operation. In the end, a 1 kW laboratory prototype circuit is built, and experiments are provided to demonstrate the validity and performance of the presented bidirectional resonant converter.


Introduction
For the development of renewable energy, the DC microgrid or nanogrid systems have been widely studied to support one of local power distribution networks. The DC/DC converters or AC/DC converters [1][2][3][4][5] are demanded to convert unstable DC voltage from solar power or fuel cell power or unstable AC voltage from wind power into a stable DC bus voltage. Then, the DC bus voltage on the DC microgrid can supply power to residential houses, commercial buildings, and industry factories. Normally, DC/DC converters or DC/AC converters are needed to convert the DC bus voltage into low DC voltage for commercial or personal power units or AC voltage for motor drives. In order to reduce oil demand and air pollution, electric vehicles have been widely developed in recent years with using battery packs instead of gasoline as their power source. Therefore, the bidirectional AC/DC or DC/DC converters are demanded [6][7][8] to achieve battery charge and discharge. In [9,10], the phase-shift pulse-width modulation (PWM) converter has been proposed to achieve buck/boost operation under forward/backward power flow operation. However, this circuit topology has high circulating current loss at freewheeling state and low circuit efficiency at low duty cycle operation if the wide voltage range is demanded. In [11][12][13][14], dual active bridge (DAB) PWM converters have been developed and implemented to have bidirectional power operation with V o = 300-450 V voltage range. The phase shift technique and duty cycle control are used in DAB converters to control power flow between input and output terminals. However, the phase angle between two terminals and duty cycle PWM signals are more complicated to calculate and derived compared to these other bidirectional power converters. In [15,16], the symmetric resonant converters have been studied and achieved to realize bidirectional power operation using the frequency modulation approach. Therefore, the active devices can be turned on at zero voltage switching. However, the input or output voltage of this circuit topology is limited at a finite range such as 400-600 V input or 300-450 V output voltage range. The advantage of the resonant converter is the low switching loss on active devices and has been discussed in [15,16]. However, the symmetric resonant converter cannot achieve well if the wide voltage range operation is demanded for universal battery charge/discharge circuit.
A bidirectional DC/DC converter is presented to have low switching loss on active devices, forward/backward power operation, and wide voltage operation for battery charge/discharge applications on a DC microgrid system. The input voltage of the presented converter is from DC bus voltage on DC microgrid system. For forward power operation, power flow is from DC microgrid to battery. For backward power operation, power flows is from battery to DC microgrid. Two full bridge resonant circuits are used in the studied converter to achieve bidirectional power flow capability. The power flow and voltage regulation are controlled by using a frequency modulation approach. The adopted resonant circuit has a soft switching characteristic for all power switches. Thus, the switching loss on active devices is reduced. The variable half/full bridge resonant circuit structure is used in the presented converter to solve limit voltage gain disadvantage on conventional bidirectional resonant converters. When low voltage output is requested, the half bridge resonant circuit is operated to achieve low voltage gain. If the high output is demanded in the proposed converter, full bridge resonant circuit is operated to realize high voltage gain. Thus, a wide output voltage operation is implemented in the studied circuit. The presented bidirectional DC/DC converter can be applied to a universal battery charge/discharge system in electric vehicle systems or battery charge stations. The circuit schematic is presented in Section 2. The operation of principle is discussed in Section 3. The circuit analysis and design example are provided in Section 4. Experiments are provided in Section 5 to verify the performance of the proposed converter. In Section 6, a conclusion of the studied DC converter is provided. Figure 1 shows the block diagrams of the simplified DC nanogrid or microgrid system. Normally, the DC microgrid inputs can be DC power (solar power, fuel cell power, or HVDC transmission supply) or AC power (AC transmission supply or wind power). The microgrid outputs may be AC loads (motor drives), DC loads (personal computers or server systems), or battery stacks in electric vehicle applications. For residential house or industry factory applications, the bus voltage of DC microgrid system is normally controlled at 380 V. For modern battery charger/discharger system in electric vehicle applications, the bidirectional DC/DC converter is demanded to achieve grid-to-vehicle (G2V) and vehicleto-grid (V2G) power flow operations. The conventional buck/boost converter shown in Figure 2a is used to realize forward and backward power flows for battery charge and discharge operations. However, no electric isolation is given in bidirectional buck/boost converter. Figure 2b gives the circuit diagram of a dual active bridge converter to achieve bidirectional power operation. By controlling the phase-angle between the leg voltages V ab and V cd , the forward or backward power can be regulated and controlled between input and output terminals. However, dual active bridge converter has the circulating current losses at the freewheeling state. Figure 2c gives the circuit diagram of a dual resonant converter to realize bidirectional power flow operations. The symmetric resonant circuits are adopted on the primary and secondary sides so that the converter operated at forward power and backward power operations has similar circuit characteristics. The advantages of the resonant converters [17,18] are low switching losses on power devices and low electromagnetic interference. However, the dual resonant converter has less voltage gain so that the available input or output voltage is limited at a finite range.   The circuit schematic of the presented converter is shown in Figure 3a. Compared to the conventional dual resonant converter, the proposed converter has more wide output voltage range operation with bidirectional power flow operation and soft switching operation on all active devices. Full bridge circuit and one additional ac switch Sac are adopted   The circuit schematic of the presented converter is shown in Figure 3a. Compared to the conventional dual resonant converter, the proposed converter has more wide output voltage range operation with bidirectional power flow operation and soft switching operation on all active devices. Full bridge circuit and one additional ac switch Sac are adopted The circuit schematic of the presented converter is shown in Figure 3a. Compared to the conventional dual resonant converter, the proposed converter has more wide output voltage range operation with bidirectional power flow operation and soft switching operation on all active devices. Full bridge circuit and one additional ac switch S ac are adopted on the input voltage terminal. Similarly, the other full bridge circuit is adopted on the output voltage terminal in the proposed circuit. For forward power operation, S 5 -S 8 are off so that the secondary side circuit is similar to a full bridge diode rectifier. When low-output voltage range is demanded to charge the battery stack, S ac is on and S 3 and S 4 are off. Only S 1 and S 2 are controlled by the frequency modulation scheme. Figure 3b gives the equivalent circuit structure of the presented converter operated at low-output voltage range and forward power operation. One can observe that the equivalent circuit in Figure 3b is a half bridge resonant circuit. When high-output voltage range is requested to charge battery stack, S ac is off and S 1 -S 4 are controlled with frequency modulation scheme. The equivalent circuit of the presented converter operated at forward power operation and high-output voltage range is shown in Figure 3c. Basically, the circuit in Figure 3c is a full bridge resonant converter. Since the leg voltage V ab in Figure 3c (full bridge resonant circuit) is two times that of the leg voltage V ac in Figure 3b (half bridge resonant circuit), the presented converter has a larger output voltage under full bridge resonant structure ( Figure 3c) than half bridge resonant structure (Figure 3b). For backward power operation, the switches S 5 -S 8 are controlled with variable frequency modulation to transfer power from V o side to V in . Since the V o is discharged from a high-voltage level, full bridge diode rectifier is adopted on the left hand side of the proposed circuit. Therefore, S 5 -S 8 and S ac are all off and the equivalent circuit under backward power operation is shown in Figure 3d.

Circuit Schematic of the Presented Converter
Processes 2021, 9, x FOR PEER REVIEW 4 of 21 on the input voltage terminal. Similarly, the other full bridge circuit is adopted on the output voltage terminal in the proposed circuit. For forward power operation, S5-S8 are off so that the secondary side circuit is similar to a full bridge diode rectifier. When lowoutput voltage range is demanded to charge the battery stack, Sac is on and S3 and S4 are off. Only S1 and S2 are controlled by the frequency modulation scheme. Figure 3b gives the equivalent circuit structure of the presented converter operated at low-output voltage range and forward power operation. One can observe that the equivalent circuit in Figure  3b is a half bridge resonant circuit. When high-output voltage range is requested to charge battery stack, Sac is off and S1-S4 are controlled with frequency modulation scheme. The equivalent circuit of the presented converter operated at forward power operation and high-output voltage range is shown in Figure 3c. Basically, the circuit in Figure 3c is a full bridge resonant converter. Since the leg voltage Vab in Figure 3c (full bridge resonant circuit) is two times that of the leg voltage Vac in Figure 3b (half bridge resonant circuit), the presented converter has a larger output voltage under full bridge resonant structure (Figure 3c) than half bridge resonant structure (Figure 3b). For backward power operation, the switches S5-S8 are controlled with variable frequency modulation to transfer power from Vo side to Vin. Since the Vo is discharged from a high-voltage level, full bridge diode rectifier is adopted on the left hand side of the proposed circuit. Therefore, S5-S8 and Sac are all off and the equivalent circuit under backward power operation is shown in Figure  3d.

Principle of Operation
The presented circuit has three different operation modes as shown in Figure 3b-d to achieve bidirectional power operation and wide output voltage operation. Three operation modes are presented in the following discussions. Figure 4 gives the voltage and current waveforms for these three operation modes. For every switching cycle, there are eight operating states according to the conducting status of switches and diodes.

Principle of Operation
The presented circuit has three different operation modes as shown in Figure 3b-d to achieve bidirectional power operation and wide output voltage operation. Three operation modes are presented in the following discussions. Figure 4 gives the voltage and current waveforms for these three operation modes. For every switching cycle, there are eight operating states according to the conducting status of switches and diodes. v S1,g i Lm,1

Low-Output Voltage Range under Forward Power Operation
If the battery stack is at a low-voltage level, the proposed converter is needed to output low voltage. In order to achieve wide output voltage range operation, the half bridge resonant circuit as shown in Figure 3b is adopted to accomplish forward power operation. Switch S ac is on and S 3 , S 4 and S 5 -S 8 are off. Only S 1 and S 2 are controlled with frequency modulation approach. The secondary side is similar to a full bridge diode rectifier. According to the status of active switches and diodes, eight switching states are observed in every switching cycle as shown in Figure 4a if f sw < f r (resonant frequency). To simplify the circuit discussion, the circuit components are assumed as C r,1 = C r,2 /n 2 and L r,1 = n 2 L r,2 where n = n p /n s so that the converter has same resonant frequency for both forward and backward power operations. Figure 5 gives the circuits of these eight switching states.

State 1 [t 0 , t 1 ]
: v CS1 = 0 at t 0 . Since i Lr,1 (t 0 ) < 0, the anti-parallel diode D S1 conducts. Therefore, switch S 1 turns on at this moment to achieve zero voltage switching. The current i Lr,2 increases and D S5 and D S8 are forward biased. State 2 [t 1 , t 2 ]: At t 1 , i Lr,1 > 0 so that diode D S1 becomes off and i Lr,1 flows through S 1 instead of D S1 . Power is transferred from V C1 to V o in this state. The input and output leg voltages are V ac = V C1 = V in /2 and V de = V o . In this state, the resonant frequency is Thus, D S5 and D S8 are off. Since C 1 >> C r,1 , the resonant frequency in state 3 is given as f p = 1/(2π C r,1 (L m,1 + L r,1 )). State 4 [t 3 , t 4 ]: S 1 turns off at t 3 . Then, i Lr,1 will charge C S1 and discharge C S2 . If the current i Lr,1 (t 3 ) = i Lm,1,peak > V in 2C S,1 /L r,1 where C S,1 = C S1 = C S2 = C S3 = C S4 and i Lm,1,peak is the peak value of i Lm,1 , then C S2 can be discharged to zero voltage.

State 5 [t 4 , t 5 ]
: v CS2 = 0 at t 4 . Since i Lr,1 (t 4 ) > 0, the anti-parallel diode D S2 conducts. Therefore, S 2 can be turned on at this moment to realize zero voltage switching. The current i Lr,2 decreases so that D S6 and D S7 are conducting. State 6 [t 5 , t 6 ]: At t 5 , i Lr,1 < 0 so that D S2 is off. i Lr,1 flows through S 2 . Power is transferred from V C2 to V o in state 6. The resonant frequency in state 6 is f r = 1/(2π L r,1 C r,1 ). State 7 [t 6 , t 7 ]: At time t 6 , i Lr,2 = 0. Then, D S6 and D S7 become off. Since C 2 >> C r,1 , the resonant frequency in state 7 is f p = 1/(2π C r,1 (L m,1 + L r,1 )). State 8 [t 7 , T sw + t 0 ]: At time t 7 , S 2 is turned off. Since i Lr,1 (t 7 ) < 0, C S1 (C S2 ) is discharged (charged) in this state. This switching cycle is ended at time T sw + t 0 .

Low-Output Voltage Range under Forward Power Operation
If the battery stack is at a low-voltage level, the proposed converter is needed to output low voltage. In order to achieve wide output voltage range operation, the half bridge resonant circuit as shown in Figure 3b is adopted to accomplish forward power operation. Switch Sac is on and S3, S4 and S5-S8 are off. Only S1 and S2 are controlled with frequency modulation approach. The secondary side is similar to a full bridge diode rectifier. According to the status of active switches and diodes, eight switching states are observed in every switching cycle as shown in Figure 4a if fsw < fr (resonant frequency). To simplify the circuit discussion, the circuit components are assumed as Cr,1 = Cr,2/n 2 and Lr,1 = n 2 Lr,2 where n = np/ns so that the converter has same resonant frequency for both forward and backward power operations. Figure 5 gives the circuits of these eight switching states.

High-Output Voltage Range under Forward Power Operation
When high-output voltage range is demanded in the proposed converter, the full bridge resonant converter is selected on the primary side to achieve high voltage gain. Therefore, Sac is off and S1-S4 are controlled with frequency modulation to regulate the load

High-Output Voltage Range under Forward Power Operation
When high-output voltage range is demanded in the proposed converter, the full bridge resonant converter is selected on the primary side to achieve high voltage gain. Therefore, S ac is off and S 1 -S 4 are controlled with frequency modulation to regulate the load voltage. Switches S 5 -S 8 are off and the secondary side operates as a full bridge diode rectifier. Owing to the status of S 1 -S 4 and D S5 -D S8 , eight switching states are operated in every switching cycle as shown in Figure 4b. The circuits of these eight switching states are provided in Figure 6. Since the full bridge resonant circuit in Figure 6 and half bridge resonant circuit in Figure 5 have the similar operation states with differnent voltage gains, the state operations of the presented converter operated at high-output voltage range under forward power operation are neglected in this subsection.
Processes 2021, 9, x FOR PEER REVIEW 8 of 21 voltage. Switches S5-S8 are off and the secondary side operates as a full bridge diode rectifier. Owing to the status of S1-S4 and DS5-DS8, eight switching states are operated in every switching cycle as shown in Figure 4b. The circuits of these eight switching states are provided in Figure 6. Since the full bridge resonant circuit in Figure 6 and half bridge resonant circuit in Figure 5 have the similar operation states with differnent voltage gains, the state operations of the presented converter operated at high-output voltage range under forward power operation are neglected in this subsection.

Under Backward Power Operation
When the presented converter is demanded to achieve backward power operation, the circuit operation under reverse power transfer from Vo to Vin is given in Figure 3d. Switch Sac and S1-S4 are off and S5-S8 are controlled with frequency modulation. The full bridge diode rectifier and full bridge resonant circuit are operated on the left and right hand sides, respectively, of the presented circuit. Based on status of S5-S8 and DS1-DS4, the proposed converter operated in Figure 3d where iLm,2,peak is the peak value of iLm,2 and

Under Backward Power Operation
When the presented converter is demanded to achieve backward power operation, the circuit operation under reverse power transfer from V o to V in is given in Figure 3d. Switch S ac and S 1 -S 4 are off and S 5 -S 8 are controlled with frequency modulation. The full bridge diode rectifier and full bridge resonant circuit are operated on the left and right hand sides, respectively, of the presented circuit. Based on status of S 5 -S 8 and D S1 -D S4 , the proposed converter operated in Figure 3d has eight switching states (Figure 4c) in every switching cycle. Figure 7 provides eight state circuits under backward power operation.

State 1 [t 0 , t 1 ]:
At time t 0 , v CS5 = v CS8 = 0. Owing to i Lr,2 (t 0 ) < 0, D S5 anf D S8 are conducting. S 5 and S 8 turn on at this moment to accomplish zero voltage switching. On the left hand side, i Lr,1 > 0 and D S1 and D S4 are conducting. State 2 [t 1 , t 2 ]: At time t 1 , i Lr,2 becomes positive and D S5 and D S8 are off. Therefore, the positive current i Lr,2 flows through S 5 and S 8 . Power is transferred from V o to V in in this state. The leg voltages are V ab = V in and V de = V o . In state 2, the resonant frequency is f r = 1/(2π L r,2 C r,2 ). State 3 [t 2 , t 3 ]: If f r > f sw , the current i Lr,1 will be decreased to 0 at time t 2 . Then, D S1 and D S4 become off. The resonant frequency in state 3 is expressed as f p = 1/(2π C r,2 (L m,2 + L r,2 )). State 4 [t 3 , t 4 ]: At time t 3 , S 5 and S 8 are turned off. The current i Lr,2 discharge C S6 and C S7 . If the current i Lr,2 (t 3 ) = i Lm,2,peak > V o 2C S,2 /L r,2 where i Lm,2,peak is the peak value of i Lm,2 and C S,2 = C S5 = C S6 = C S7 = C S8 , then C S6 and C S7 are discharged to zero voltage.

State 5 [t 4 , t 5 ]:
At time t 4 , v CS6 = v CS7 = 0. Owing to i Lr,2 (t 4 ) > 0, D S6 and D S7 are conducting. S 6 and S 7 turn on at this moment to realize zero voltage switching. The current i Lr,1 (t) < 0 and D S2 and D S3 are conducting. State 6 [t 5 , t 6 ]: At time t 5 , i Lr,2 becomes negative and D S6 and D S7 are off. The current i Lr,2 flows through S 6 and S 7 . Power is transferred from V o to V in in state 6. State 7 [t 6 , t 7 ]: At time t 6 , i Lr,1 = 0 so that D S2 and D S3 are off. The resonant frequency in state 7 is f p = 1/(2π C r,2 (L m,2 + L r,2 )). State 8 [t 7 , T sw + t 0 ]: At time t 7 , S 6 and S 7 are off. The current i Lr,2 discharges C S5 and C S8 . This switching cycle is ended at time T sw + t 0 when v CS5 = v CS8 = 0.

Circuit Analysis and Design Procedures
The presented converter has three operation modes: forward power operation with low-output voltage range, forward power operation with high-output voltage range, and backward power operation as shown in Figures 3-6. The frequency modulation is selected to control active devices and regulate load voltage. Therefore, the voltage gain of the presented converter is related to the switching frequency. The equivalent resonant circuits based on the fundamental switching frequency analysis are shown in Figure 8 for three operation modes. For low-and high-output voltage range modes under forward power operation, the input terminal voltages are Vac = Vin/2 and Vab = Vin, respectively. The root-

Circuit Analysis and Design Procedures
The presented converter has three operation modes: forward power operation with low-output voltage range, forward power operation with high-output voltage range, and backward power operation as shown in Figures 3-6. The frequency modulation is selected to control active devices and regulate load voltage. Therefore, the voltage gain of the presented converter is related to the switching frequency. The equivalent resonant circuits based on the fundamental switching frequency analysis are shown in Figure 8 for three operation modes. For low-and high-output voltage range modes under forward power operation, the input terminal voltages are V ac = ±V in /2 and V ab = ±V in , respectively. The root-mean-square leg voltages are expressed as V ac,F = √ 2V in /π and V ab,F = 2 √ 2V in /π. The equivalent load resistance R o,ac at fundamental switching frequency under forward power operation is given as R o,ac = 8n 2 R o /π 2 . For backward power operation, the leg voltage V de = ±V o and the equivalent resistance R in,ac at fundamental switching frequency is expressed as R in,ac = 8R in /(π 2 n 2 ). Similarly, the fundamental leg voltage V de,F = 2 √ 2V o /π.

Circuit Analysis and Design Procedures
The presented converter has three operation modes: forward power operation with low-output voltage range, forward power operation with high-output voltage range, and backward power operation as shown in Figures 3-6. The frequency modulation is selected to control active devices and regulate load voltage. Therefore, the voltage gain of the presented converter is related to the switching frequency. The equivalent resonant circuits based on the fundamental switching frequency analysis are shown in Figure 8 for three operation modes. For low-and high-output voltage range modes under forward power operation, the input terminal voltages are Vac = Vin/2 and Vab = Vin, respectively. The root- M ac,B (s) = nV ab,F /n V de,F 2V o /π = sL m,2 // sL r,1 /n 2 + 1 sn 2 C r,1 +R in,ac sL r,2 + 1 sC r,2 + sL m,2 // sL r,1 /n 2 + 1 sn 2 C r,1 +R in,ac × R in,ac sL r,1 /n 2 + 1 If the following parameters are defined as Q = L r,1 /C r,1 /R o,ac , Q = L r,2 /C r,2 /R in,ac , K = L m,1 /L r,1 , K = L m,2 /L r,2 = K, and F = F = f sw / f r , then Equations (1)-(3) can be rewritten in Equations (4)-(6) for forward power operation under low-output voltage range, forward power operation under high-output voltage range, and backward power operation, respectively.
One can observe that the voltage transfer functions in Equations (4)-(6) are similar. Figure  9a gives the voltage transfer function under K = 5. The design procedures of the presented converter are provided in this section to obtain the circuit components in the laboratory prototype. The input voltage V in = 400 V, the output battery voltage V o = 200-450 V, the rated power P o,rated = 1 kW, the rated load current I o,rated = 2.3 A, and the resonant frequency f r = 70 kHz. The constant current or constant voltage is selected to charge the battery stack. If the battery stack voltage is in a low voltage range V o = 200-310 V, the half bridge resonant circuit (S ac on; S 3 and S 4 off) is operated on the left hand side of the converter. If the output battery stack voltage is in the high voltage range V o = 310-450 V, the full bridge resonant circuit (S ac off) is operated on the proposed converter to achieve battery charge (forward power operation). For backword power operation (battery discharge from V o to V in ), the load voltage (V in ) is regulated at 400 V. Since the voltage transfer functions in (4)-(6) have the same circuit characteristics for both forward and backward power operations, the circuit components of the presented converter are derived from forward power operation and low-output voltage range (V o = 200-310 V). In Equation (4), the voltage gain is related to the output voltage. The high-output voltage will result in large dc voltage gain. In this design example, the assumed minimum voltage gain |M ac,F,Low | min = 1 at V o,min = 400 V and V o = 200 V. From Equation (4), the transformer turns ratio n can be expressed in Equation (7).
In this prototype circuit, the selected primary windings (N p ) are 90 turns and secondary windings (N s ) are 90 turns. The transformer T is implemented with magnetic core PC40/EE40. According to the selected turn ratio n, the maximum voltage gain in Equation (4) can be obtained as. Figure 9b illustrates gain curves under K = 5 condition. From the given minimum and maximum dc voltage gains, one can observe the voltage gain |M ac,F,Low | curves under quality factor Q < 0.3 are greater than 1.55. That means the corresponding switching frequency index F can be obtained from V o,min = 200 V to V o,max = 310 V to control load voltage. Therefore, Q = 0.3 is used in this design example to obtain the other circuit components. R o,ac at full load can be derived in Equation (9).
From the given Q and R o,ac , the primary passive components are derived in Equations (10)- (12).
Then, the secondary resonant components of the proposed converter are obtained as: C r,2 = n 2 C r,1 = 97 nF (13) L r,2 = L r,1 /n 2 = 53 µH The resonant inductors L r,1 and L r,2 are implemented with magnetic cores PC40/EER35. Power switches FGH60N60UFD with 600 V/60 A rating are used for switches S 1 -S 8 . Power switch 6R125P6 with 650 V/19 A rating is used for switch S ac . The input and output capacitances are C 1 = C 2 = 2. In Equation (4), the voltage gain is related to the output voltage. The high-output voltage will result in large dc voltage gain. In this design example, the assumed minimum voltage   Figures 11-14 give the experimental waveforms of the proposed converter operated at forward power flow. Figure 15 shows the measured waveforms of the proposed converter operated at backward power flow. Figure 11 shows the measured waveforms of the proposed converter operated at V o = 200 V and the rated load current I o = 2.3 A. Figure 11a gives the measured input voltage, output voltage, and load current. Since the half bridge resonant circuit is operated under V o = 200 V, the switches S 3 and S 4 are off and S ac is on. S 1 and S 2 are controlled with frequency modulation. The measured switch signals of S 1 and S 2 and the resonant waveforms v Cr1 and i Lr1 on the primary side are given in Figure 11b. Since the voltage gain of the converter at V o = 200 V is unity, the switching frequency is close to the resonant frequency. Therefore, the resonant current waveform i Lr1 approximates a sinusoidal signal. The measured v Cr2 , i Lr2 , i DS5 , and i DS7 on the secondary side are provided in Figure 11c. Figure 11d gives the switch voltage and current of S 1 . One can observe that S 1 is turned on at zero voltage so that the turn-on switching loss is eliminated. Figure 12 gives the experimental results of the proposed converter operated at half bridge resonant mode (Figure 3b) under V o = 310 V and the rated current I o = 2.3 A with constant current mode control. Since the converter has higher voltage gain at V o = 310 V, the switching frequency is less than the resonant frequency, as shown in Figure 9b. The primary resonant current i Lr1 approximates a quasi-sinusoidal waveform (Figure 12b). In Figure 12c, the voltage v Cr2 is constant during i Lr2 = 0 because no current flows through C r2 . The diodes D S5 and D S7 are turned off at zero current switching. In Figure 12d, S 1 is turned on at zero voltage switching. In Figures 13 and 14, the proposed converter is operated at the full bridge resonant circuit (Figure 3c) under V o = 450 V and I o = 2.3 A and 1.15 A, respectively, with constant voltage mode control. Figures 13b and 14b show the switching signals of S 1 -S 4 under 100% and 50% rated load current. Figures 13c and 14c give the measured leg voltage v ab and resonant waveforms v Cr1 and i Lr1 on the primary side for 100% and 50% rated load current. Similarly, the measured resonant waveforms and diode currents on the secondary side are provided in Figures 13d and 14d. The diodes D S5 and D S7 are turned off at zero current switching. In Figures 13e and 14e, one can observe that S 1 is turned on at zero voltage switching for both 100% and 50% rated load current. Figure 15 gives the measured waveforms of the proposed converter operated at backward power operation from V o = 450 V to V in = 400 V. Under backward power operation, all switches on the primary side are off and S 5 -S 8 are controlled with frequency modulation. Figure 15a gives the experimental waveforms of V o , V in , and I in at full power condition. Figure 15b shows the switching signals of S 5 -S 8 . The leg voltage v de and resonant waveforms v Cr2 and i Lr2 on the secondary side are measured and provided in Figure 15c. The primary side resonant waveforms i Lr1 and v Cr1 and diode currents i DS1 and i DS3 are provided in Figure 15d. In Figure 15e, it is clear that S 5 is turned on at zero voltage switching. The measured efficiencies of the proposed converter are 92.3%, 93.5%, and 91.5% at V o = 200 V, 310 V, and 450 V, respectively, under the rated load current with constant current mode control. Figure 16 gives a picture of the prototype circuit. The comparisons between the conventioal dual active bridge converter, CLLC converters, and the studied converter are provided in Table 1. It is clear that two more power switches and split capacitors are used in the proposed circuit. However, more wide output voltage can be operated in the studied circuuit.   (b) v S1,g , v S2,g , v Cr1 , and i Lr1 ; (c) v Cr2 , i Lr2 , i DS5 , and i DS7 ; (d) v S1,g , v S1,d , and i S1 .

Conclusions
A bidirectional resonant converter is proposed, analyzed, and implemented for wide voltage range battery charger/discharger applications. The proposed converter can be used between the DC microgrid system and the electric vehicle charge station to realize G2V charge and V2G discharge operations. The proposed converter has symmetric resonant circuits on the primary and secondary sides to realize bidirectional power flow control. By selecting the half bridge or full bridge circuit structure operation, the proposed circuit can achieve low or high voltage gain. Therefore, the wide output voltage control can be implemented in the proposed converter to avoid wide switching frequency variation in conventional bidirectional resonant converters. Due to the resonant circuit behaviors, the power switches are turned on at zero voltage switching so that the switching loss can be reduced. The circuit operation principle, system analysis, circuit characteristics, and design example of the prototype circuit are provided in this paper. The experiments are also provided to validate the performance of the presented converter.

Conclusions
A bidirectional resonant converter is proposed, analyzed, and implemented for wide voltage range battery charger/discharger applications. The proposed converter can be used between the DC microgrid system and the electric vehicle charge station to realize G2V charge and V2G discharge operations. The proposed converter has symmetric resonant circuits on the primary and secondary sides to realize bidirectional power flow control. By selecting the half bridge or full bridge circuit structure operation, the proposed circuit can achieve low or high voltage gain. Therefore, the wide output voltage control can be implemented in the proposed converter to avoid wide switching frequency variation in conventional bidirectional resonant converters. Due to the resonant circuit behaviors, the power switches are turned on at zero voltage switching so that the switching loss can be reduced. The circuit operation principle, system analysis, circuit characteristics, and design example of the prototype circuit are provided in this paper. The experiments are also provided to validate the performance of the presented converter.