Wide gain narrow band bipolar llc converter based on coupled inductors and control method

Abstract

The application discloses a wide-gain narrow-band dual-polarity LLC converter based on coupled inductance and a control method. r1 , a second half-bridge module, coupled inductance, a first transformer T r2 , a second transformer T r2 , and a variable rectifier bridge. The application aims to solve the problem of narrow voltage gain range of the existing bipolar direct-current converter for charging stations. By adopting coupled inductance and a dual-mode control method, a wide voltage gain range can be realized in a narrow switching frequency range, the method can realize more than 6 times of voltage gain in a less than 2 times switching frequency range, and has the characteristics of simple topology structure and easy control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power electronics, and particularly relates to a wide-gain narrow-frequency-band bipolar LLC converter based on coupled inductance and a control method, and mainly applies to a bipolar direct-current power distribution network. BACKGROUND

[0002] With the rapid development of electric vehicles, the number of electric vehicles is growing, and the required charging voltage range of different models is not the same. In order to accommodate a large number of electric vehicles and meet the charging needs of various models, the reliability and power supply voltage range of the charging station are constantly improving. The common DC distribution network form of the charging station has two kinds of bipolarity and unipolarity. The bipolar DC distribution network is more reliable than the unipolar DC distribution network, and it is a suitable power supply scheme. However, there are few studies on bipolar DC converters for charging stations. Several related studies use non-isolated structures and have a narrow voltage gain range. How to widen the voltage gain range of the bipolar DC converter has become a major problem. One solution is to learn from the method of achieving wide voltage gain in unipolar DC converters. In unipolar DC converters, LLC converters are widely studied due to their wide voltage gain characteristics, but traditional LLC converters require a wide switching frequency range to achieve a wide voltage gain, which poses challenges to magnetic component design and converter control. Literature (G. Xu, S. Luo, J. Xu, et al. “An ISOP LLC converter with changeable equivalent magnetizing inductance utilizing coupled inductor for ultra wide input voltage range application,” in IEEE Transactions on Transportation Electrification, vol. 10, no. 2, pp. 3680-3689) adjusts the magnetizing inductance value in two modes by coupling the magnetizing inductance of two full-bridge LLC converters, thereby achieving a wide voltage range. However, it requires a large number of switching tubes and magnetic components. Literature (C. Li, H. Wang, M. Shang. “A five-switch bridge based reconfigurable LLC converter for deeply depleted PEV charging applications,” in IEEE Transactions on Power Electronics, vol. 34, no. 5, pp. 4031-4035) proposes an LLC converter with a five-switch bridge arm and two resonant cavities. By modulating the driving signal, the input voltage of the resonant cavity is changed, six working modes are obtained, and the voltage range is widened. However, this converter introduces an auxiliary switch and uses multiple working modes, resulting in increased cost and control complexity. SUMMARY

[0003] The application provides a wide-gain narrow-band bipolar LLC converter based on coupled inductance and a control method, aiming at solving the problem of narrow voltage gain range of existing bipolar direct current converters for charging stations.

[0004] To achieve the above object, the application adopts the technical scheme of:

[0005] The wide-gain narrow-band bipolar LLC converter based on coupled inductance comprises a first half-bridge module, a second half-bridge module, coupled inductance, a first transformer T r1 , a second transformer T r2 and a variable rectifier bridge.

[0006] The first half-bridge module is composed of a first input capacitor bridge arm and a first switch tube bridge arm in parallel, the first input capacitor bridge arm is composed of a first input capacitor C r1 and a second input capacitor C r2 in series, the first switch tube bridge arm is composed of a first switch tube Q1 and a second switch tube Q2 in series, and the parallel points of the first input capacitor bridge arm and the first switch tube bridge arm are connected with a positive bus P and a neutral line O of a bipolar direct current bus respectively, and the voltage between P and O is a positive bus voltage V p .

[0007] The second half-bridge module is composed of a second input capacitor bridge arm and a second switch tube bridge arm in parallel, the second input capacitor bridge arm is composed of a third input capacitor C r3 and a fourth input capacitor C r4 in series, the second switch tube bridge arm is composed of a third switch tube Q3 and a fourth switch tube Q4 in series, and the parallel points of the second input capacitor bridge arm and the second switch tube bridge arm are connected with the neutral line O and a negative bus N of the bipolar direct current bus respectively, and the voltage between O and N is a negative bus voltage V n .

[0008] The variable rectifier bridge is composed of a first diode bridge arm, a second diode bridge arm and a voltage doubling capacitor bridge arm in parallel, the first diode bridge arm is composed of a first diode D1 and a second diode D2 in series, the second diode bridge arm is composed of a third diode D3 and a fourth diode D4 in series, the voltage doubling capacitor bridge arm is composed of a first voltage doubling capacitor C o1 and a second voltage doubling capacitor C o2 in series, the variable rectifier bridge is connected with a load R L in parallel, and the voltage on the load is an output voltage V o .

[0009] The coupling inductor comprises two windings, a first winding and a second winding, the self-inductance of the first winding is L r1 , the self-inductance of the second winding is L r2 , and the mutual inductance between the first winding and the second winding is M.

[0010] The first transformer T r1 comprises a first excitation inductor L m1 , and a primary winding of the first transformer T r1 is connected at one end to a midpoint A of a bridge arm of a first switch tube and at the other end to one end of a first winding of a coupling inductor, the other end of the first winding of the coupling inductor is connected to a midpoint B of a bridge arm of a first input capacitor, and a secondary winding of the first transformer T r1 is connected at one end to a midpoint E of a bridge arm of a first diode and at the other end to a midpoint G of a bridge arm of a voltage doubling capacitor.

[0011] The second transformer T r2 comprises a first excitation inductor L m2 , and a primary winding of the second transformer T r2 is connected at one end to a midpoint C of a bridge arm of a second switch tube and at the other end to one end of a second winding of a coupling inductor, the other end of the second winding of the coupling inductor is connected to a midpoint D of a bridge arm of a second input capacitor, and a secondary winding of the second transformer T r2 is connected at one end to a midpoint F of a bridge arm of a second diode and at the other end to the midpoint G of the bridge arm of the voltage doubling capacitor.

[0012] As a preferred technical solution of the present application: the positive bus voltage V p on the bipolar DC bus is equal to the negative bus voltage V n , and V p =V n =V in , the input capacitor values are equal, and C r1 =C r2 =C r3 =C r4 =C r , and C o1 =C o2 =C o .

[0013] As a preferred technical solution of the present application: the same name end direction of the first winding and the second winding of the coupling inductor is the same, the self-inductance of the two windings is equal, and L r1 =L r2 =L r .

[0014] As a preferred technical scheme of the present application, the primary winding and the secondary winding of the first transformer T r1 have the same direction of the same name end, the primary winding and the secondary winding of the second transformer T r2 have the opposite direction of the same name end, the primary winding and the secondary winding of the first transformer T r1 and the second transformer T r2 have the turn ratio of n:1, the excitation inductance L r1 of the first transformer T r2 and the second transformer T m1 are equal to the inductance of L m2 and L m1 , m2 , m .

[0015] As a preferred technical scheme of the present application, the input capacitors C r1 , C r2 , C r3 , and C r4 participate in resonance, C r1 , C r2 and L m1 , and L r1 form a first resonance cavity, C r3 , C r4 and L m2 , and L r2 form a second resonance cavity, the current of the first resonance cavity is i r1 , and the current of the second resonance cavity is i r2 .

[0016] The control method of the wide-gain narrow-frequency-band bipolar LLC converter based on the coupling inductance, characterized in that it comprises the following steps:

[0017] The duty cycles of the driving signals of all the switching tubes in the converter are 0.5, the driving signals of the switching tubes in the same bridge arm are complementary, when the phases of the first switching tube bridge arm and the second switching tube bridge arm are the same, the converter works in the same-phase boost mode, and when the phases of the first switching tube bridge arm and the second switching tube bridge arm are opposite, the converter works in the opposite-phase buck mode.

[0018] When the converter works in the same-phase boost mode, the current i r1 of the first resonance cavity and the current i r2 of the second resonance cavity are equal in size and have the same flow direction, the currents flowing through the first winding and the second winding of the coupling inductance are equal in size and have opposite flow directions, and the equivalent resonance inductance L r_I in this working mode is represented as:

[0019] ,

[0020] Where k=M / L r The resonant frequency f in this operating mode r_I Represented as:

[0021] ;

[0022] When the converter operates in inverting buck mode, the current i in the first resonant cavity r1 With the current i in the second resonant cavity r2 When the currents flowing through the first and second windings of the coupled inductor are equal in magnitude and opposite in direction, the equivalent resonant inductance L in this operating mode is... r_O Represented as:

[0023] ,

[0024] The resonant frequency f in this operating mode r_O Represented as:

[0025] .

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. This invention uses a coupled inductor as a resonant inductor, which can reduce the number of inductors used and reduce the system size.

[0028] 2. This invention uses the input capacitor as a resonant capacitor, which can reduce the number of capacitors used and reduce the system size.

[0029] 3. This invention utilizes the characteristics of coupled inductors and employs two control methods to obtain two different resonant inductance values, thereby obtaining two different gain curves, which can achieve a wide voltage gain range within a narrow switching frequency range. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the topology in an example of the present invention;

[0031] Figure 2 The diagram shows typical drive and current waveforms of the present invention operating in in-phase boost mode.

[0032] Figure 3 This is a current path diagram for the present invention operating in in-phase boost mode one.

[0033] Figure 4 This is the current path diagram for the present invention operating in in-phase boost mode mode two;

[0034] Figure 5 The diagram shows typical drive and current waveforms of the present invention operating in reverse buck mode.

[0035] Figure 6 Current path diagram for the invention working in the reverse buck mode modality one;

[0036] Figure 7 Current path diagram for the invention working in the reverse buck mode modality two;

[0037] Figure 8 Voltage gain curve diagram for the invention. DETAILED DESCRIPTION

[0038] The invention will be further described with reference to the drawings and the specific embodiments:

[0039] As shown in the drawings, Figure 1 The embodiment of the invention proposes a wide-gain narrow-band bipolar LLC converter based on coupled inductance, which comprises a first half-bridge module, a second half-bridge module, a coupled inductor, a first transformer T r1 , a second transformer T r2 , a variable rectifier bridge,

[0040] The first half-bridge module is composed of a first input capacitor bridge arm and a first switch tube bridge arm in parallel, the first input capacitor bridge arm is composed of a first input capacitor C r1 and a second input capacitor C r2 in series, the first switch tube bridge arm is composed of a first switch tube Q1 and a second switch tube Q2 in series, the parallel points of the first input capacitor bridge arm and the first switch tube bridge arm are connected with the positive bus P and the neutral line O of the bipolar DC bus respectively, and the voltage between P and O is the positive bus voltage V p .

[0041] The second half-bridge module is composed of a second input capacitor bridge arm and a second switch tube bridge arm in parallel, the second input capacitor bridge arm is composed of a third input capacitor C r3 and a fourth input capacitor C r4 in series, the second switch tube bridge arm is composed of a third switch tube Q3 and a fourth switch tube Q4 in series, the parallel points of the second input capacitor bridge arm and the second switch tube bridge arm are connected with the neutral line O and the negative bus N of the bipolar DC bus respectively, and the voltage between O and N is the negative bus voltage V n .

[0042] The variable rectifier bridge is composed of a first diode bridge arm, a second diode bridge arm, and a voltage doubling capacitor bridge arm in parallel. The first diode bridge arm is composed of a first diode D1 and a second diode D2 in series, the second diode bridge arm is composed of a third diode D3 and a fourth diode D4 in series, and the voltage doubling capacitor bridge arm is composed of a first voltage doubling capacitor C o1 and a second voltage doubling capacitor C o2 in series. The variable rectifier bridge is connected with the load RL Parallel, the voltage on the load is the output voltage V o ;

[0043] The coupling inductor comprises two windings, a first winding and a second winding, the self-inductance of the first winding is L r1 , and the self-inductance of the second winding is L r2 , and the mutual inductance between the two windings is M.

[0044] The first transformer T r1 contains a first excitation inductance L m1 , the first transformer T r1 , one end of the primary winding is connected to the midpoint A of the first switch tube bridge arm, and the other end is connected to one end of the first winding of the coupling inductor. The other end of the first winding of the coupling inductor is connected to the midpoint B of the first input capacitor bridge arm. The first transformer T r1 , one end of the secondary winding is connected to the midpoint E of the first diode bridge arm, and the other end is connected to the midpoint G of the voltage doubling capacitor bridge arm.

[0045] The second transformer T r2 contains a first excitation inductance L m2 , the second transformer T r2 , one end of the primary winding is connected to the midpoint C of the second switch tube bridge arm, and the other end is connected to one end of the second winding of the coupling inductor. The other end of the second winding of the coupling inductor is connected to the midpoint D of the second input capacitor bridge arm. The second transformer T r2 , one end of the secondary winding is connected to the midpoint F of the second diode bridge arm, and the other end is connected to the midpoint G of the voltage doubling capacitor bridge arm.

[0046] The positive bus voltage V p on the bipolar DC bus is equal to the negative bus voltage V n , and V p =V n =V in , the input capacitor values are equal, and C r1 =C r2 =C r3 =C r4 =C r , and C o1 =C o2 =C o .

[0047] The same name end direction of the first winding and the second winding of the coupling inductor is the same, the self-inductance of the two windings is equal, and L r1 =L r2 =L r . The same name end direction of the primary winding and the secondary winding of the first transformer T r1 is the same, and the same name end direction of the primary winding and the secondary winding of the second transformer Tr2 The primary winding and the secondary winding have opposite directions at their corresponding terminals. First transformer T r1 With the second transformer T r2 The turns ratio of the primary winding to the secondary winding is n:1. The first transformer T r1 With the second transformer T r2 excitation inductance L m1 With L m2 The sensitivity values ​​are equal, and L m1 =L m2 =L m .

[0048] Input capacitor C r1 C r2 C r3 C r4 All participate in resonance, C r1 C r2 With L m1 L r1 Forming the first resonant cavity, C r3 C r4 With L m2 L r2 This forms the second resonant cavity. The current in the first resonant cavity is i. r1 The current in the second resonant cavity is i r2 .

[0049] The control method for a wide-gain, narrow-band bipolar LLC converter based on coupled inductors proposed in this invention includes the following steps:

[0050] The duty cycle of the drive signals of all switches in the converter is 0.5. The drive signals of the switches in the same bridge arm are complementary. When the first switch bridge arm and the second switch bridge arm are in phase, the converter operates in in-phase boost mode. When the first switch bridge arm and the second switch bridge arm are in opposite phase, the converter operates in in-phase buck mode.

[0051] When the converter operates in non-inverting boost mode, the current i in the first resonant cavity r1 With the current i in the second resonant cavity r2 The equivalent resonant inductance L in this operating mode is equal in magnitude and flows in the same direction, while the currents flowing through the first and second windings of the coupled inductor are equal in magnitude and flow in opposite directions. r_I Represented as:

[0052] ,

[0053] Where k=M / L r The resonant frequency f in this operating mode r_I Represented as:

[0054] ;

[0055] When the converter works in the anti-phase buck mode, the current i r1 of the first resonant cavity is equal in magnitude and opposite in direction to the current i r2 of the second resonant cavity, and the current flowing through the first winding and the second winding of the coupling inductor is equal in magnitude and same in direction, the equivalent resonant inductance L r_O of this working mode is represented as:

[0056] ,

[0057] The resonant frequency f r_O of this working mode is represented as:

[0058] .

[0059] As shown in Figure 2 , when the converter of the present application works in the same-phase boost mode, the driving signals of the first switch Q1 (the second switch Q2) and the third switch Q3 (the fourth switch Q4) are the same, i.e. the driving signals of the first switch bridge arm and the second switch bridge arm are the same in phase. Wherein i r1 is the current of the first resonant cavity, i r2 is the current of the second resonant cavity, i Lm1 is the current of the first exciting inductor, and i Lm2 is the current of the second exciting inductor. One cycle includes two working modes, the first half cycle [t0~t1] works in mode one, and the second half cycle [t1~t2] works in mode two. The current paths of the two modes are shown in Figure 3 and Figure 4 . It can be seen from Figure 2 , 3 , 4 that in the same-phase boost mode, the current i r1 of the first resonant cavity is equal in magnitude and same in direction to the current i r2 of the second resonant cavity. The current flowing through the first winding and the second winding of the coupling inductor is equal in magnitude and opposite in direction, so the equivalent resonant inductance L r_I of this working mode is represented as

[0060] ,

[0061] Wherein k=M / L r , the resonant frequency f r_I of this working mode is represented as

[0062] .

[0063] As shown in Figure 5As shown, when the converter of the application operates in the anti-phase buck mode, the driving signals of the first switch Q1 (the second switch Q2) and the third switch Q4 (the fourth switch Q3) are the same, i.e. the driving signals of the first switch bridge arm and the second switch bridge arm are in opposite phase. One cycle includes two working modes, the first half cycle [t0~t1] operates in mode one, and the second half cycle [t1~t2] operates in mode two. The current paths of the two modes are shown in Figure 6 and Figure 7 respectively. As can be seen from Figure 5 , 6 , 7, in the anti-phase buck mode, the current i r1 of the first resonant cavity and the current i r2 of the second resonant cavity are equal in size and opposite in direction. The currents flowing through the first winding and the second winding of the coupling inductor are equal in size and the same in direction, so the equivalent resonant inductance L r_O in this working mode is represented as

[0064] ,

[0065] The resonant frequency f r_O in this working mode is represented as

[0066] .

[0067] Obviously, the resonant inductance L r_I in the same-phase boost mode is smaller than the resonant inductance L r_O in the anti-phase buck mode, so the resonant frequency f r_I in the same-phase boost mode is greater than the resonant frequency f r_O in the anti-phase buck mode, and the ratio λ _I of the excitation inductance to the resonant inductance in the same-phase boost mode L m / L r_I is greater than the ratio λ _O of the excitation inductance to the resonant inductance in the anti-phase buck mode L m / L r_O . The gain curves in the two modes can be obtained from the gain relationship of the LLC resonant converter, as shown in Figure 8 , where M v represents the voltage gain, and M v =nV o / V in . In order to achieve a wide voltage gain range in a narrow switching frequency range, the range of the switching frequency f s is set between the resonant frequencies in the two working modes of the converter, i.e. f r_O <f s <f r_I . In this frequency range, when the voltage gain Mv When the voltage gain M is greater than 1, the converter operates in non-inverting boost mode. v When the value is less than 1, the converter operates in inverted buck mode. To ensure smooth switching between the two operating modes, the switching frequency range is slightly widened, i.e., a minimum switching frequency f is set. smin Less than the resonant frequency f in inverted buck mode r_O Maximum switching frequency f smax The resonant frequency f is greater than that in in-phase boost mode. r_I A slightly wider switching frequency range does not affect the voltage gain range. In summary, the converter can achieve a wide voltage gain range within a narrow switching frequency range.

[0068] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A wide gain narrow band bipolar LLC converter based on coupled inductances, characterized by: comprising a first half-bridge module, a second half-bridge module, a coupling inductance, a first transformer T r1 , a second transformer T r2 and a variable rectifier bridge, The first half-bridge module is composed of a first input capacitor bridge arm and a first switch tube bridge arm in parallel, the first input capacitor bridge arm is composed of a first input capacitor C r1 and a second input capacitor C r2 in series, the first switch tube bridge arm is composed of a first switch tube Q1 and a second switch tube Q2 in series, the parallel points of the first input capacitor bridge arm and the first switch tube bridge arm are connected with a positive bus P and a neutral line O of a bipolar direct current bus respectively, and the voltage between P and O is a positive bus voltage V p . The second half-bridge module consists of a second input capacitor bridge arm and a second switching transistor bridge arm connected in parallel. The second input capacitor bridge arm is composed of a third input capacitor C. r3 With the fourth input capacitor C r4 The second switching bridge arm is composed of a forward series connection of a third switch Q3 and a fourth switch Q4. The parallel connection point of the second input capacitor bridge arm and the second switching bridge arm is connected to the neutral line O and the negative bus N of the bipolar DC bus, respectively. The voltage between O and N is the negative bus voltage V. n ; The variable rectifier bridge is composed of a first diode bridge arm, a second diode bridge arm, and a voltage doubling capacitor bridge arm in parallel, the first diode bridge arm is composed of a first diode D1 and a second diode D2 in series, the second diode bridge arm is composed of a third diode D3 and a fourth diode D4 in series, and the voltage doubling capacitor bridge arm is composed of a first voltage doubling capacitor C o1 and a second voltage doubling capacitor C o2 in series, the variable rectifier bridge is connected with a load R L in parallel, and the voltage on the load is an output voltage V o ; The coupling inductor comprises two windings, a first winding and a second winding, the self-inductance of the first winding being L r1 , the self-inductance of the second winding being L r2 , and the mutual inductance between the first winding and the second winding being M. The first transformer T r1 The first transformer T m1 The first transformer T r1 One end of the primary winding is connected with the midpoint A of the first switch tube bridge arm, and the other end is connected with one end of the first winding of the coupling inductor, and the other end of the first winding of the coupling inductor is connected with the midpoint B of the first input capacitor bridge arm. r1 One end of the secondary winding is connected with the midpoint E of the first diode bridge arm, and the other end is connected with the midpoint G of the voltage doubling capacitor bridge arm. The second transformer T r2 comprising a first excitation inductance L m2 , the second transformer T r2 One end of the primary winding is connected with the midpoint C of the second switch tube bridge arm, and the other end is connected with one end of the second winding of the coupling inductance, and the other end of the second winding of the coupling inductance is connected with the midpoint D of the second input capacitor bridge arm, and the second transformer T r2 One end of the secondary winding is connected with the midpoint F of the second diode bridge arm, and the other end is connected with the midpoint G of the voltage doubling capacitor bridge arm.

2. The coupled-inductor-based wide-gain narrow-band dual-biased LLC converter of claim 1, wherein: The positive bus voltage V p on the bipolar DC bus is equal to the negative bus voltage V n , and V p = V n = V in , the input capacitances are equal, and C r1 = C r2 = C r3 = C r4 = C r , and C o1 = C o2 = C o .

3. The coupled-inductor-based wide-gain narrow-band dual-biased LLC converter of claim 1, wherein: The same name end direction of the first winding and the second winding of the coupling inductance is same, the self-inductance of the two windings is equal, and L r1 = L r2 = L r .

4. The coupled-inductor-based wide-gain narrow-band dual-biased LLC converter of claim 1, wherein: The primary winding of the first transformer T r1 has the same direction of the same name end as the secondary winding, the primary winding of the second transformer T r2 has the opposite direction of the same name end as the secondary winding, the primary winding of the first transformer T r1 and the secondary winding of the second transformer T r2 have the turn ratio of n:1, the excitation inductance L r1 of the first transformer T r2 is equal to the inductance L m1 of the second transformer T m2 , and L m1 =L m2 =L m .

5. The coupled-inductor-based wide-gain narrow-band dual-biased LLC converter of claim 1, wherein: The input capacitor C r1 , C r2 , C r3 , C r4 all participate in resonance, C r1 , C r2 and L m1 , L r1 form a first resonant cavity, C r3 , C r4 and L m2 , L r2 form a second resonant cavity, the current of the first resonant cavity is i r1 , and the current of the second resonant cavity is i r2 .

6. The control method of a coupled-inductor-based wide-gain narrow-band dual- polarity LLC converter according to any one of claims 1-5, characterized in that, The method comprises the following steps: The duty cycles of the driving signals of all the switch tubes in the converter are 0.5, the driving signals of the switch tubes in the same bridge arm are complementary, when the phases of the first switch tube bridge arm and the second switch tube bridge arm are the same, the converter works in the same-phase boost mode, and when the phases of the first switch tube bridge arm and the second switch tube bridge arm are opposite, the converter works in the opposite-phase buck mode; When the transformer operates in the phase-boosting mode, the current i r1 of the first resonant cavity is equal in magnitude and opposite in direction to the current i r2 of the second resonant cavity, and the current flowing through the first winding and the second winding of the coupling inductor is equal in magnitude and opposite in direction, and the equivalent resonant inductance L r_I of the transformer in this mode of operation is represented as: ， where k = M / L r the resonant frequency f r_I is expressed as: ； When the converter operates in the anti-phase buck mode, the current i r1 of the first resonant tank is equal in magnitude and opposite in direction to the current i r2 of the second resonant tank, the currents flowing through the first winding and the second winding of the coupling inductor are equal in magnitude and same in direction, and the equivalent resonant inductance L r_O of the converter in this mode of operation is represented as: ， The resonant frequency f in this mode of operation is given by: r_O is given by: 。

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