Isolated single-stage BI-directional ac-DC converters

Abstract

An exemplary bidirectional isolated single-stage AC-DC and DC-AC converter and method that can perform AC-DC and DC-AC conversion through a transformer dual active bridge converter for grid-connected bidirectional application. The bidirectional isolated single-stage AC-DC and DC-AC converter has an AC side module comprising bridges that connect at its first end to the AC source, at its second end to one another, and at its outputs between the bridges to the primary side of the transformer through a blocking capacitor. The DC side module includes a second set of bridges that connect at its first end to the DC source, at its second end to one another, and at its outputs between the bridges to the secondary side of the transformer.

Description

Attorney Docket No.10046-535WO1 8137 HUA ISOLATED SINGLE-STAGE BI-DIRECTIONAL AC-DC CONVERTERS GOVERNMENT LICENSE RIGHTS

[0001] This invention was made with government support under grant no. N00014-21-1- 2124 awarded by the Office of Naval Research. The government has certain rights in the invention. RELATED APPLICATION

[0002] This PCT application claims priority to, and the benefit of, U.S. Provisional Patent Application No.63 / 520,876, filed August 21, 2023, entitled “ISOLATED SINGLE-STAGE BI-DIRECTIONAL AC-DC CONVERTERS,” which is incorporated by reference herein in its entirety. BACKGROUND

[0003] AC-DC converters can convert alternating current (AC) from a source (e.g., mains, a generator, etc.) into regulated and controlled direct current (DC) and vice-versa and are employed in many applications. Conventional AC-DC converter designs typically convert power through multiple stages, for example, using a grid frequency transformer, active or passive rectifier circuitry, and smoothing capacitors. The AC-DC converters can first step up or step down and input AC voltage, then rectify the stepped-up or stepped-down AC voltage through a diode or diode bridge, and finally smooth the rectified input voltage using capacitors, e.g., to produce a DC output.

[0004] Bidirectional AC-DC converters often employ active switches (e.g., MOSFETs or IGBTs) to allow for DC-to-AC conversion in addition to AC-to-DC conversion rather than the diode or diode-bridge rectification components. As power requirements increase, conventional AC-DC converters can become bulky, expensive, and complex. For example, increasing the voltage operation can require additional gate drivers, power supplies, and the like, which add to size, cost, and control complexity.

[0005] These and other drawbacks can be amplified in split-phase and three-phase implementations, among others. For example, with the prevalence of renewable energy generation systems and electric vehicles, grid-connect three-phase bidirectional AC-DC converters with power factor correction (PFC) capability are of growing interest. One such common implementation is a two-stage configuration with a first-stage PFC converter, and a second-stage high-frequency (HF) isolated DC-DC converter. Another common implementation is a phase modular single-stage PFC AC-DC dual-active-bridge (DAB) withAttorney Docket No.10046-535WO1 8137 HUA variable frequency control. However, in both implementations, control is complex, and extra active unfolding bridges are needed on the AC side; therefore, the switch count can be high.

[0006] There is a benefit to improving power conversion systems. SUMMARY

[0007] An exemplary bidirectional isolated single-stage AC-DC and DC-AC converter and method thereof are disclosed that can perform AC-DC and DC-AC conversion through transformer dual active bridge converter (e.g., Y-configuration transformer dual active bridge converter) for grid-connected bidirectional application. The bidirectional isolated single- stage AC-DC and DC-AC converter has an AC side module comprising bridges that connect at its first end to the AC source or load, at its second end to one another (to be floating neutral from the AC source or load, e.g., grid neural), and at its switching nodes to the primary side of the transformer through a blocking capacitor. The DC side module includes a second set of bridges that connect at its first end to the DC source or load, at its second end to one another, and at its switching node to the secondary side of the transformer. For 3-phase operation, a Y-Configuration winding is employed on at least one of the primary side or secondary side of the transformer. The converter is highly flexible while using the minimal / optimized number of active and passive components and can operate using straightforward modulation operation. For 3-phase operation, the number of switches can, for example, be reduced by 6 devices on the AC side. In both the 1-phase and 3-phase operation, because the bridges on the AC side modules are floating neutral to the AC source or grid, no zero crossing detection nor voltage unfolding is needed for the controls.

[0008] The converter includes blocking capacitors to block DC voltage and grid frequency voltage, and provide isolation between the AC side and DC side module. The blocking capacitors can be used to operate the convert in series-resonant or non-series resonant mode.

[0009] In some embodiments, the transformer non-Y configuration side is connected to three switch bridges having two switching node connections (type 2). In some embodiments, the transformer Y-configuration side is connected to a three-switch bridge having one switching node connection (type 1).

[0010] In an example, the bidirectional isolated single-stage AC-DC and DC-AC converter is configured as a Y-Configuration Dual Active Bridge Converter (YAB) that can operate a computationally-efficient sinusoidal phase shift modulation operation. Compared to other DAB-based AC-DC converters, the YAB can achieve power factor correction (PFC)Attorney Docket No.10046-535WO1 8137 HUA with simple control while maintaining nearly full-range zero-voltage switching (ZVS) and relatively low circulating current, resulting in high efficiency.

[0011] The 1-phase or 3-phase bidirectional isolated single-stage AC-DC and DC-AC converter can directly couple to the AC and DC source and can be stacked to operate at higher voltages. The 1-phase or 3-phase bidirectional isolated single-stage AC-DC and DC- AC converter can have bridges coupled to one another and that couple to a primary side of a transformer. The exemplary bidirectional isolated single-stage AC-DC and DC-AC converter can be configured for single, split, or three-phase applications, among others, and allows for bidirectional power flow (e.g., AC-to-DC and DC-to-AC) while employing fewer power semiconductor switches and components than other bidirectional converters.

[0012] In an aspect, a system is disclosed comprising a single-stage bidirectional isolated AC-DC converter comprising: a transformer comprising (i) a primary side having two or more terminals, including at least a first terminal and a second terminal and (ii) a secondary side having two or more terminals, including at least a third terminal and a fourth terminal (e.g., wherein at least one of the primary side and the secondary side has a Y-configuration winding); an AC module having an AC switching stage comprising at least a first switching bridge (a half bridge or full bridge) and a second switching bridge, each of the first switching bridge and second switching bridge having (i) a first connection to at least one AC source and (ii) a second connection to one other, and a third connection to the primary side of the transformer (e.g., either (a) in Y-configuration winding through the primary side or (b) to a second leg of the same bridge in a half-bridge with split cap) and configured to operate in a bridge configuration with a series-linked capacitor and the transformer to generate a first AC waveform in a first power flow direction at the primary side of the transformer, wherein the DC module is configured to generate a DC waveform from an AC waveform produced at the secondary side from the first AC waveform; and the DC module, the DC module having a DC switching stage comprising at least a third switching bridge and a fourth switching bridge having (i) a first connection to each other and a DC source and (ii) a second connection to each other and the DC source, and configured to switch a DC waveform of the DC source at the secondary side to provide a modulated waveform at the primary side to establish an AC waveform, in a second power flow direction, through the series-linked capacitor and the AC module.

[0013] In some embodiments, the first switching bridge and the second switching bridge of the AC module each comprises (i) a half-bridge and a blocking capacitor, (ii) a full bridge, or (iii) a half-bridge and two splitting capacitors.Attorney Docket No.10046-535WO1 8137 HUA

[0014] In some embodiments, the third switching bridge and the fourth switching bridge of the DC module each comprises (i) a full bridge, (ii) a half-bridge, or (iii) a half bridge and two splitting capacitors.

[0015] In some embodiments, the primary side has a first Y-configuration winding, wherein the secondary side has a second Y-configuration winding.

[0016] In some embodiments, the primary side has a Y-configuration winding, wherein the second side has a non-Y configuration winding, and wherein the first switching bridge and the second switching bridge of the AC module each comprise the half-bridge and the blocking capacitor.

[0017] In some embodiments, the (i) half-bridge and the blocking capacitor, (ii) full bridge, or (iii) half-bridge and the two splitting capacitors of the DC module either comprises a set of two unidirectional switches or a set of two bidirectional switches.

[0018] In some embodiments, the primary side has a Y-configuration winding, wherein the second side has a non-Y configuration winding, and wherein the first switching bridge and the second switching bridge of the AC module each comprise the half-bridge and the blocking capacitor.

[0019] In some embodiments, for single-phase operation, the AC module is configured to bias one or more AC waveforms of the AC source to establish, via anti-paralleled diodes of the single AC switching stage to generate an AC waveform having a DC waveform component as the first AC waveform.

[0020] In some embodiments, for three-phase operation, the AC module is configured to generate a modulated sinusoidal waveform as the first AC waveform.

[0021] In some embodiments, for single-phase operation, the single AC switching stage is configured to generate a high-frequency power flow and a low-frequency power flow, wherein the series-link capacitor is configured to block the low-frequency power flow to provide low-frequency isolation between the AC module and the DC module.

[0022] In some embodiments, the series-linked capacitor and the transformer, via leakage inductance of the transformer, are configured to collectively form a series-resonant circuit.

[0023] In some embodiments, the series-linked capacitor and the transformer are configured to form a non-resonant circuit.

[0024] In some embodiments, the system further includes a second single-stage bidirectional isolated AC-DC converter operatively connected in series to the single-stage bidirectional isolated AC-DC converter, as the first single-stage bidirectional isolated AC-DC converter, in a stack configuration, wherein (i) the AC module of the first single-stageAttorney Docket No.10046-535WO1 8137 HUA bidirectional isolated AC-DC converter as a first AC module and (ii) a second AC module of the second single-stage bidirectional isolated AC-DC converter are each configured to receive a partial voltage of the AC source, and wherein components of the first AC module and the second AC module are rated for said partial voltage.

[0025] In some embodiments, the system further includes N-1 number of single-stage bidirectional isolated AC-DC converters operatively connected in series to each other and the single-stage bidirectional isolated AC-DC converter, as an Nth single-stage bidirectional isolated AC-DC converter, in a stack configuration, wherein AC modules of the N-1 and Nth single-stage bidirectional isolated AC-DC converters are each configured to receive a partial voltage of the AC source, and wherein components of the AC modules of the N-1 and Nth single-stage bidirectional isolated AC-DC converters are rated for said partial voltage.

[0026] In some embodiments, the second single-stage bidirectional isolated AC-DC converter includes a second AC module having a single AC switching stage configured to operate in a half-bridge configuration with an input capacitor to bias one or more AC waveforms of the AC source to establish, via anti-paralleled diodes of the second AC module, in another first power flow direction, a common-mode DC potential to a second DC module linked through another series-linked capacitor and another transformer; and the second DC module having a single DC switching stage configured in a half-bridge configuration with another DC capacitor to switch the DC waveform of the DC source to the AC waveform, in a second power flow direction, through the another series-linked capacitor, the another transformer, and the second AC module.

[0027] In some embodiments, the second single-stage bidirectional isolated AC-DC converter includes: a second AC module having a single AC switching stage configured to operate in a half-bridge configuration with an input capacitor to bias one or more AC waveforms of the AC source to establish, via anti-paralleled diodes of the single AC switching stage, in another first power flow direction, a common-mode DC potential to the DC module linked through the series-linked capacitor and the transformer; and the DC module of the first single-stage bidirectional isolated AC-DC converter.

[0028] In some embodiments, (i) the first AC module of the first single-stage bidirectional isolated AC-DC converter and (ii) the second AC module of the second single- stage bidirectional isolated AC-DC converter are coupled in series.

[0029] In some embodiments, (i) the first AC module of the first single-stage bidirectional isolated AC-DC converter and (ii) the second AC module of the second single- stage bidirectional isolated AC-DC converter are coupled in a series, and (i) the DC moduleAttorney Docket No.10046-535WO1 8137 HUA of the first single-stage bidirectional isolated AC-DC converter and (ii) the second DC module of the second single-stage bidirectional isolated AC-DC converter are coupled in parallel.

[0030] In some embodiments, the N single-stage bidirectional isolated AC-DC converters are identical.

[0031] In some embodiments, the N single-stage bidirectional isolated AC-DC converters are not identical.

[0032] In some embodiments, the single AC switching stage includes, for each phase of the AC source, two switching elements configured with the anti-paralleled diodes.

[0033] In some embodiments, the single DC switching stage includes, for each set of switching elements of the single AC switching stage, a corresponding set of switching elements.

[0034] In some embodiments, for a 1-phase AC input or output, the transformer comprises a core and a winding structure having a high-frequency four-winding single-phase transformer connected in between.

[0035] In some embodiments, for a 3-phase AC input or output, the transformer comprises a core and a winding structure having a high frequency six-winding three-phase transformer connected in between.

[0036] In another aspect, a method is disclosed comprising providing a single-stage bidirectional isolated AC-DC converter of any one of the above-discussed claims; operating the single-stage bidirectional isolated AC-DC converter in the first power flow direction; and operating the single-stage bidirectional isolated AC-DC converter in the second power flow direction.

[0037] In another aspect, an electric vehicle charger is disclosed having the single-stage bidirectional isolated AC-DC converter of any one of the above-discussed claims.

[0038] In another aspect, electrical substation equipment is disclosed having the single- stage bidirectional isolated AC-DC converter of any one of the above-discussed claims.

[0039] Additional features will be set forth in part in the description, which follows or may be learned by practice. The features described herein will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive, as claimed.Attorney Docket No.10046-535WO1 8137 HUA BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Various objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and / or structurally similar elements.

[0041] Figs.1A and 1B each show an example bidirectional isolated single-stage AC-DC and DC-AC converter, according to an illustrative embodiment.

[0042] Figs.1C, 1D, 1E, 1F each show a configuration of the example bidirectional isolated single-stage AC-DC and DC-AC converter as a module that can be stacked, according to some implementations.

[0043] Fig.1G shows an example bidirectional isolated single-stage AC-DC and DC-AC converter for a single-phase input, according to an illustrative embodiment.

[0044] Figs.1H, 1I, and 1J each show additional examples of a bi-directional isolated single-stage AC-DC and DC-AC converter for three-phase input, according to an illustrative embodiment.

[0045] Figs.1K and 1L each show example bridges that may be employed in the bidirectional isolated single-stage AC-DC and DC-AC converter of Figs.1A – 1J, in accordance with an illustrative embodiment.

[0046] Figs.2A and 2B each show example configurations for transformers for the example bi-directional isolated single-stage AC-DC and DC-AC converter, according to some implementations.

[0047] Figs.3A - 3B and 4A – 4B show example implementations of stacked bidirectional isolated single-stage AC-DC and DC-AC converter, according to some implementations.

[0048] Figs.5A-5G show an example three-phase method of operations of the exemplary bidirectional isolated single-stage AC-DC and DC-AC converter, according to an illustrative embodiment.

[0049] Figs.6A-6H show a second example three-phase method of operations of the exemplary bidirectional isolated single-stage AC-DC and DC-AC converter, according to another illustrative embodiment.Attorney Docket No.10046-535WO1 8137 HUA DETAILED DESCRIPTION

[0050] Each and every feature described herein, and each and every combination of two or more of such features, is included within the scope of the present invention, provided that the features included in such a combination are not mutually inconsistent.

[0051] Some references, which may include various patents, patent applications, and publications, are cited in a reference list and discussed in the disclosure provided herein. The citation and / or discussion of such references is provided merely to clarify the description of the present disclosure and is not an admission that any such reference is “prior art” to any aspects of the present disclosure described herein. In terms of notation, “[n]” corresponds to the nthreference in the list. All references cited and discussed in this specification are incorporated herein by reference in their entirety and to the same extent as if each reference was individually incorporated by reference.

[0052] Example Systems

[0053] Figs.1A and 1B each show an example bidirectional isolated single-stage AC-DC and DC-AC converter 100 (shown as 100a, 100b), according to an illustrative embodiment. In the example shown in Figs.1A and 1B, the exemplary bidirectional isolated single-stage AC-DC and DC / AC converter 100a, 100b (herein also referred to as an AC-DC / DC-AC converter 100a, 100b) is coupled to an AC source / load 101 (shown as 101a, 101b) and a DC load / source 103 and includes an AC module 102 (shown as 102a, 102b) and a DC module 104 (shown as module 104a and module 104b) coupled through series linked blocking capacitors 106 (shown as “Cra” 106a, “Crb” 106b for single phase configuration and “Cra” 106a, “Crb” 106b, “Crc” 106c for a three-phase configuration) and a transformer 108 (shown as 108a, 108b). Fig.1A shows a single / split-phase bidirectional isolated single-stage AC-DC and DC-AC converter 100a, and Fig.1B shows a three-phase bidirectional isolated single- stage AC-DC and DC-AC converter 100b. In the example shown in Fig.1A, the AC source / load 101a is a 1-phase AC source and a 1-phase AC load. In the example shown in Fig.1B, the AC source / load 101b is a 3-phase AC source and a 3-phase AC load. Other configurations may be employed, e.g., 2-phase, 4-phase, 5-phase, 6-phase, 12-phase, 18- phase, etc.

[0054] In Figs.1A and 1B, the AC module (e.g., 102a, 102b) includes an H-bridge 110 (referenced as 110a, 110b) formed, respectively, of two or three half-bridges 111 connected in parallel in which each half-bridge branch 111 is connected to an AC source (or load), shown as Va and Vb. Each of the half-bridge branch 111 includes a pair of switching devices 112 connected in series to one another and an input capacitor 114 connected in parallel to theAttorney Docket No.10046-535WO1 8137 HUA respective pair of switching device 112. For 1-phase operation (Fig.1A), the H-bridge 110a includes 2 sets 111 (shown as 111a, 111b), each having switching devices 112 (shown as “Sa+” 112a, “Sa-” 112b, “Sb+” 112c, “Sb-” 112d) and a corresponding input capacitor 114 (shown as capacitors “Ca1”114a and “Cb1” 114b). For a 3-phase operation (Fig.1B), the H- bridge 110b includes 3 half-bridge branch (shown as 111a, 111b, 111c) of switching devices 112 (shown as “Sa+” 112a, “Sa-” 112b, “Sb+” 112c, “Sb-” 112d, “Sc+” 112e, “Sc-” 112f) and corresponding input capacitor 114 (shown as “Ca” 114a, “Cb” 114b, “Cc”114c). Each of the switching devices 112 (e.g., 112a-112f) includes an internal or external anti-parallel diode 116 (shown as 116a-116d in Fig.1A and 116a-116f in Fig.1B). That is, the anti-parallel diode 116 can be either a separate component or an intrinsic feature of the switching element itself (e.g., in the case of MOSFETs). The anti-parallel diodes prevent negative voltage oninput capacitors Ca1 and Cb1; thus, a common mode DC potential with a value of ^^^^^ isestablished, which lifts the capacitor voltages to a DC level so that they can be “chopped” by the half-bridges.

[0055] The DC module (e.g., 104a, 104b) includes a second H-bridge 118 (referenced as 118a, 118b) formed of a full bridge subcircuit 119 of switching devices 120 that are collectively connected in parallel to a DC capacitor 122 (shown as “Cdc” 122). For 1-phase operation (Fig.1A), the H-bridge 118a includes 2 pairs of switching devices 120 (shown as “Sx+” 120a, “Sx-” 120b, “Sy+” 120c, “Sy-” 120d) connected in series in one another and each pair being connected in parallel to the DC capacitor 122. For a 3-phase operation (Fig.1B), the H-bridge 118b includes 3 pairs of switching devices (shown as “Sx+” 122a, “Sx-” 122b, “Sy+” 122c, “Sy-” 122d, “Sz+” 122e, “Sz-” 122f), each element within the pair connected in series to one another and the pairs being connected in parallel to the DC capacitor 122. The switching devices (e.g., 112, 122) may be a power metal-oxide field-emitting transistor (MOSFET), insulated-gate bipolar transistor (IGBT), or other power electronic switching device. As shown, the DC output is defined across Cdc. It should be appreciated, though, that a DC source can also be connected across Cdcin DC-to-AC conversion configurations.

[0056] Herein, the AC module 102 may also be referred to as the “AC side” of AC- DC / DC-AC converter 100. Likewise, the DC module 104 may also be referred to as the “DC side” of AC-DC / DC-AC converter 100.

[0057] In the example shown in Fig.1A, the transformer 108A is a high-frequency, four- winding, single-phase transformer. An example configuration of transformer 120 is shown in FIG.2A, e.g., that may be employed for a single / split phase operation. AnotherAttorney Docket No.10046-535WO1 8137 HUA configurations of transformer 108 are shown in FIG.2B, e.g., that may be employed for a three-phase operation. Specifically, with additional reference to FIG.2A, the transformer 108a includes a core 202 and four windings formed from two wires 204, 206. Generally, core 202 and wires 204, 206 are formed of known suitable materials, such as iron and copper, respectively; however, other materials may be used. Connected between AC module 102 and DC module 104, the transformer (e.g., 108a, 108b) is generally configured to step-down or step-up a voltage of an AC waveform with DC components (e.g., in a first power flow direction) or DC waveform (e.g., in a second power flow direction). As shown, a first end 208 of the first leg (e.g., wire 204) of transformer 108a is connected between the switching devices Sa+(112a) and Sa-(112b), and a second end 210 of the first leg (e.g., wire 204) is connected between the switching elements Sb+ (112c) and Sb- (112d). The corresponding leg of the transformer 108a on the DC-side of AC-DC / DC-AC converter 100a is connected between switching elements Sx+(120a) and Sx-, (120b) and Sy+(120c) and Sy-(120d), respectively.

[0058] The AC-DC / DC-AC converter (e.g., 100a, 100b) includes a series-linked blocking capacitor 106 connected in series with respective legs of transformer 108. In Fig.1A, for a single / split phase configuration, the series-linked blocking capacitor 106 includes a pair of capacitors (shown as “Cra” 106a and “Crb” 106b). In Fig.1B, for a three-phase configuration, the series-linked blocking capacitor 106 includes three capacitors (shown as “Cra” 106a, “Crb” 106b, and “Crc” 106a). The series-linked blocking capacitor 106 and transformer 108 can be configured as a series-resonant tank for resonant operation. The resonant operation can reduce the switching stress on the switching devices and increase the overall efficiency of the operations of the system. The series-linked capacitor 106 and transformer 108 can be configured as a non-resonant tank for non-resonant operation.

[0059] The series-linked blocking capacitors are configured to block low-frequency components (e.g., 60 Hz). For example, AC module 102 may generate both a high-frequency power flow and a low-frequency power flow, in which case the series-link blocking capacitors 106 can block the low-frequency power flow to provide low-frequency isolation between the AC module 102 and the DC module 104.

[0060] As noted above, AC-DC / DC-AC converter 100 generally uses fewer components (e.g., switches) than other bidirectional converters, yielding a less complex and costly solution to bidirectional AC-DC / DC-AC conversion. Conventional AC-DC converters typically include two stages: an AC-to-DC conversion stage – where an AC waveform is converted to a DC output, or vice versa – followed by a DC-to-DC stage where the DC outputAttorney Docket No.10046-535WO1 8137 HUA of the AC-to-DC stage is cleaned and manipulated (e.g., increase / decreased to a desired output level). In contrast, the exemplary AC-DC / DC-AC converter 100 achieves both of these functions in a single stage by biasing the AC waveform with a DC component through parallel capacitors Ca1 and Cb1, as discussed above. Further, the use of solid-state switches allows AC-DC / DC-AC converter 100 to operate bidirectionally, converting AC-to-DC in a first power flow direction and DC-to-AC in a second power flow direction.

[0061] More specifically, in Figs.1A and 1B, for AC-DC conversion, the AC module (e.g., 102a, 102b) is configured to establish, via the input capacitor 114, in a first power flow direction 122, two offset AC waveforms (shown as 124a, 124b) at the input capacitors 114a, 114b having a DC component. The two offset AC waveforms 126 (e.g., from source “Va” 126a, “Vb” 126b), within 1 single stage operation in the AC module 102, is rectified (128) via the anti-paralleled diodes 116 and input capacitor 114, and the switching operation, controlled by controller 130, then shifts (132) the rectified waveform 134 to a second rectified waveform (i.e., the AC waveform 124 with the DC component) having a different DC level 136 than the first 138. The AC waveform and DC components (124) are provided to the DC module 104 through the series-linked blocking capacitor 106 and transformer 108 in which the series-linked capacitor blocks the AC component of the AC waveform 120, allowing only the DC component to pass through to the DC module 104.

[0062] For DC-AC conversion, the DC module 104 uses the same link to the AC module 102 through the transformer 108 and series-linked capacitor 106 and provides, in a second direction 140 opposite of the first direction 122, a DC waveform 124 from the DC source 103 through the transformer 108 and series-linked capacitor 106 to the set of switching devices 111 in the AC module 102. The switching device 111 of the AC module 102 then switches to modulate the DC waveform as a DC bus to generate an AC waveform as an AC output of the AC module 102.

[0063] Example Stacked Modular Bidirectional Isolated Single-Stage AC-DC and DC- AC Converter

[0064] Figs.1C, 1D, 1E, and 1F each show a configuration of the example bidirectional isolated single-stage AC-DC and DC-AC converter 100 (shown as 100c, 100d, 100e, 100f respectively) as a module that can be stacked. Figs.1C, 1D, 1E each show the AC-DC / DC- AC converter (e.g., 100c, 100d, 100e, 100f), including multiple stacked AC modules 102 (shown as 102a, 102b … 102n) and / or multiple stacked DC modules 104 (shown as 104a, 104b, … 104n). Specifically, the example of Fig.1C shows N number of AC modules 102 connected in series to a single one of transformer 108 and, subsequently, a single DC moduleAttorney Docket No.10046-535WO1 8137 HUA 104. In Fig.1D, the N number of AC modules 102 is connected in series to an N number of transformers 108 and, subsequently, the N number of DC modules 104. In Fig.1E, N number of AC modules 102 are connected in series to two transformers 108 and, subsequently, two DC modules 104. Figs.3A and 3B shows an example implementation of N number of AC modules 102 connected in series to a single one of transformer 108 and, subsequently, a single DC module 104. Figs.4A and 4B shows an example implementation of N number of AC modules 102 are connected in series to an N number of transformers 108 and, subsequently, N number of DC modules 104. In Figs.3A and 4A, a single / split phase configuration is shown. In Figs.3B and 4B, a three-phase configuration is shown.

[0065] In the stacked configuration, the voltage of the AC input (e.g., for AC-to-DC operations) and the voltage of the AC output (e.g., for DC-to-AC operations) are split across each of the N number of AC modules 102. For example, a 4000 VAC input (and 4000VAC output) across ten stacked AC modules 102 would result in a 400 VACsource (and load) for each of the ten AC modules 102. In this regard, components of the AC-DC / DC-AC converter 100 could be rated for 400VAC rather than 4000 VAC. At 400VAC, the components of the AC-DC / DC-AC converter 100 would be substantively smaller and less costly. Indeed, the AC-DC / DC-AC converter 100 is readily scalable for different implementations without adding that much complexity by merely including and stacking any number of AC modules 102. In contrast, a conventional AC module (i.e., single AC module) would require sized components (e.g., higher capacity switches, capacitors, etc.) in order to be configured for higher voltages, thus adding to the cost.

[0066] In Figs.3B and 4B, the AC-DC / DC-AC converters 100b can be configured as multiple stacked “cells,” each including AC module 102, transformer 108, and DC module 104. As shown, each of DC modules 104 is connected in parallel, e.g., to a common output. It should be appreciated, as illustrated, that any number of cells, n, can be stacked. In this manner, each cell may separately convert a respective portion of an AC input (e.g., in an AC- to-DC configuration) into a DC output, resulting in a combined DC output with an increased current, and vice versa for DC-to-AC operation. It should be appreciated that each stacked cell is not necessarily identical, as shown in FIG.1D, 3B, and 4B. In Fig.1D, the AC- DC / DC-AC converter 100d is shown to be readily scalable for different implementations, e.g., by including and stacking any number of AC-DC / DC-AC converters (e.g., 100d1, 100d2, 100d3). The number N of AC-DC / DC-AC modules can be two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, etc.Attorney Docket No.10046-535WO1 8137 HUA

[0067] Fig.1E shows another configuration of the AC-DC / DC-AC converter 100e, similar to Fig.1D, in which the number of AC modules 102 and the number of DC modules 104 are different. Indeed, the AC modules 102 and DC modules 104 can be arranged for specific purposes in any combination.

[0068] The number N of AC modules 102, e.g., for converters 100c, 100d, 100e, can be one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, etc.

[0069] The number N of DC modules 104, e.g., for converters 100c, 100d, 100e, can be one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, etc.

[0070] It is contemplated that the bidirectional operation and stackable configurations of AC-DC / DC-AC converter 100 may be useful in electric vehicle (EV) charging systems and / or medium voltage power distribution systems. For example, EV chargers may receive medium voltage AC inputs (e.g., voltage > 400 VAC) that need to be converted to lower voltage DC outputs for EV charging. Thus, the modularity and scalability of AC-DC / DC-AC converter 100 can reduce the need for expensive and complex power conversion systems as currently implemented, while the bidirectionality of AC-DC / DC-AC converter allows for vehicle-to-grid power transfer (e.g., power sharing between an EV and grid). As another example, AC-DC / DC-AC converter 100 may be used in electrical substations, e.g., to convert power at transmission voltages (e.g., medium voltage, > 400 VAC) to more usable DC levels.

[0071] Medium AC voltage applications generally employ 2,400 to 69,000 VAC. Here, the converters may be stacked to provide about 1000 VAC, 2000 VAC, 3000 VAC, 4000 VAC, 5000 VAC, 6000 VAC, 7000 VAC, 8000 VAC, 9000 VAC, 10 kVAC, 11 kVAC, 12 kVAC, 13 kVAC, 14 kVAC, 15 kVAC, 16 kVAC, 17 kVAC, 18 kVAC, 19 kVAC, 20 kVAC, 21 kVAC, 22 kVAC, 23 kVAC, 24 kVAC, 25 kVAC, 26 kVAC, 27 kVAC, 28 kVAC, 29 kVAC, 30 kVAC, 31 kVAC, 32 kVAC, 33 kVAC, 34 kVAC, 35 kVAC, 36 kVAC, 37 kVAC, 38 kVAC, 39 kVAC, 40 kVAC, 41 kVAC, 42 kVAC, 43 kVAC, 44 kVAC, 45 kVAC, 46 kVAC, 47 kVAC, 48 kVAC, 49 kVAC, 50 kVAC, 51 kVAC, 52 kVAC, 53 kVAC, 54 kVAC, 55 kVAC, 56 kVAC, 57 kVAC, 58 kVAC, 59 kVAC, 60 kVAC, 61 kVAC, 62 kVAC, 63 kVAC, 64 kVAC, 65 kVAC, 66 kVAC, 67 kVAC, 68 kVAC, 69 kVAC, High AC voltage applications generally employ 115,000 to 1,100,000 VAC. The exemplary stacked AC-DC / DC-AC converter 100 can be employed for such applications, including at any intermediate voltage range described herein and can provide the corresponding current and power.Attorney Docket No.10046-535WO1 8137 HUA

[0072] Fig.1F shows the topology of Fig.1C for a single-phase input, rather than a split phase input as shown for Figs.1C, 1D, and 1E. It is contemplated that the split-phase topology, e.g., shown in Figs.1C, 1D, and 1E, and others described herein can be implemented with a single phase.

[0073] Single Phase System and Method of Operations

[0074] Fig.1G shows an example bidirectional isolated single-stage AC-DC and DC-AC converter 100 (shown as 100g) for a single-phase input, according to an illustrative embodiment.

[0075] In Fig.1G, the system 100g also includes two independent half bridges, each having an input capacitor Ca 1and Cb 1. The source of each half bridge’s low-side switch is connected, but the drain of each high side switch is NOT connected. A blocking capacitorCbis applied in series to block the line frequency voltage component applied across node a and b. The High Frequency(HF) transformer provides galvanic isolation between, where on the secondary side, a full bridge, which contains four switches, is introduced.

[0076] The AC grid voltage ^^^and ^^^is naturally clamped to be positive by the half bridge capacitor Ca 1and Cb 1with body diodes of the primary side switches, the waveform is shown in Fig.1G. One AC line cycle is long enough to pre-charge the capacitor when the grid voltage is connected. The two AC side half bridges are switched synchronously with a 0.5-duty cycle. Those two high-side switches(i.e. ^^^ାand ^^^ା) are turning ON and OFF together, and two low side switches(i.e. ^^^ିand ^^^ି) are turning ON and OFF together. The common mode high-frequency component ^^^^,^^can be expressed as ^^^^,^^^ ^^^ ൌ

[0077] Fig.5B, subpanel D shows an example AC Side Waveforms for the primary side. While the AC grid source ^^^and ^^^are in 180° reversed, the high-frequency component applied across the switching node a and b is doubled. The blocking capacitor ^^^can be served to block out the grid frequency voltage component, giving the final voltage applied across the leakage inductance vpriin Equation Set 1.(Eq. Set 1)Attorney Docket No.10046-535WO1 8137 HUA

[0078] The exemplary AC side and DC side modulation operation can provide straightforward and linear coupling dependency between controlled variables, including phase shift variables and switching frequency. With a fixed switching frequency ^^^௪and a phase shift variable ^^, which is only determined by input AC and DC voltage, the average output power ^^^ ^^^ is only linearly coupled with phase shift variable ^^. While in some other modulation strategies, i.e. variant frequency dual-phase-shift, the average output power ^^^ ^^^ is strongly coupled with three variables nonlinearly. In addition, the exemplary modulation operation can maintain a good ZVS range along the AC line cycle even with different power levels and fixed switching frequencies to provide a theoretically high single-stage AC-DC efficiency.

[0079] Additional Three-Phase Example Systems and Method of Operations

[0080] Figs.1H, 1I, 1J each show additional examples of a bi-directional isolated single- stage AC-DC and DC-AC converter 100 (shown as 100a) for three-phase input, according to an illustrative embodiment. In Fig.1H, the AC side module comprising three bridges with blocking capacitors is shown coupled via Y-configuration winding to the primary side of the transformer (e.g., 108) through a blocking capacitor. The DC side module comprising three bridges with blocking capacitors are shown coupled to the secondary side of the transformer. As shown in Fig.1H, the transformer can be configured in which at least one, or both, of the primary side or the secondary side has a Y-configuration winding.

[0081] Figs.1K and 1L each show example bridges that may be employed in the bidirectional isolated single-stage AC-DC and DC-AC converter of Figs.1A – 1J, in accordance with an illustrative embodiment. There are two major type of switch bridges that can be used: the H-bridge (Fig.1K) and the half-bridge (Fig.1L). Among the half-bridge topology (type 2), (i) a half-bridge with a blocking capacitor can be used, or (ii) a half-bridge with split capacitors. As shown in Fig.1K, the switches of the bridges can be (i) a unidirectional switch or equivalent switching performance structure or (ii) a bi-directional switch or equivalent switching performance structure.

[0082] Table 1A shows an example configuration for a three-phase system. The AC side module can be configured with any of 3 types of bridges, the DC side module can be configured with any of the 3 types of bridges. They may be connected by Y-configuration or non-Y configuration. The switch in the bridges may be unidirectional or bi-directional. The module may be configured for resonant or non-resonant mode operation. Table 1A (3 phase)Attorney Docket No.10046-535WO1 8137 HUA

[0083] Table 1B shows an example configuration for a single-phase system. The AC side module can be configured with any of 3 types of bridges, the DC side module can be configured with any of the 3 types of bridges. There is only one configuration for the transformer. The switch in the bridges may be unidirectional or bi-directional. The module may be configured for resonant or non-resonant mode operation. Table 1B (single phase)

[0084] Among the combinations, when the transformer has one Y-configuration winding, the non-Y configuration side would be connected to three switch bridges having two switching node connections (type 2). The transformer Y-configuration side could be connected to a three-switch bridge having one switching node connection (type 1). The AC side switching bridges must have the DC+ connected to grid, and their DC- must connect together.

[0085] Example Method of Operation #1

[0086] Figs.5A-5G show an example a three-phase method of operation of the exemplary bidirectional isolated single-stage AC-DC and DC-AC converter 100 (e.g., for AC-DC / DC-AC converter 100b), according to an illustrative embodiment. In Fig.5A,Attorney Docket No.10046-535WO1 8137 HUA subpanel (a), the AC-DC / DC-AC converter 100b is shown to include three half bridges on the AC side (e.g., module 102) and one three-phase full bridge on the DC side (e.g., module 104), e.g., as described in relation to Fig.1B. A three-phase three-limb HF transformer 108b with Y-Y winding configuration is connected in between. The positive ends of AC side half bridges (e.g., 111) are connected to a three-phase AC source or load (e.g., 101b), while the negative ends are connected together at joint M. The anti-paralleled diodes (e.g., 116) of MOSFETs prevent negative voltage on the input capacitors Ca, Cb, and Cc(e.g., 114a-114c) thus establishing a common mode DC potential with a value of ^^^^^, which can then lift up the DC level of the capacitor voltages to a desired level so that they can be chopped by the half bridges [2]. It may take one line period of time (not shown) to pre-charge the three capacitors (e.g., 114a-114c) at the start-up [3], then the capacitors (e.g., 114a-114c) can present steady state voltages waveform, e.g., as shown in Fig.5A, subpanel (b). Specifically, Fig.5A, subpanel (b) shows the AC source (or load) voltage va, vb, vc, and AC side DC-Link capacitor voltage vCan, vCbn, and vCcn.

[0087] The capacitance of capacitors Cra Crb Crc (106a, 106b, 106c) and the leakage inductance of transformer 108b, in this example, are selected to form series-resonant tanks. Fig.5A, subpanel (C) shows resonant capacitor voltage vCra, vCrb, vCrcfor the series-linked blocking capacitors 106a, 106b, and 106c. The capacitor can provide resonant operation and also block the 60Hz low-frequency components. Indeed, AC module 102 may generate both a high-frequency power flow and a low-frequency power flow, in which case the series-link capacitors Cra, Crb, and Crc(106a, 106b, 106c) can block the low-frequency power flow to provide low-frequency isolation between AC module 102 and DC module 104.

[0088] By aligning the space vector of the DC side and the AC side [4], the 60-Hz power flow can be blocked between the AC side (module 102) and the DC side (module 104) so that the transformer is only magnetized with switching frequency. Fig.5A, subpanel (d), shows the voltage VTa at the AC side (at node “a”) and the voltage VTX at the DC side (at node “x”), e.g., for operation as a resonant tank, and the transformer current iLAfor one phase (phase A) for one grid period. Fig.5A, subpanel (d), shows a phase shift of θ of the power transfer from the DC side node “x” to the AC side node “a.”

[0089] Example Transformer Configurations. Fig.2B shows a three-phase transformer 108b as a high-frequency, three-phase, three-limb transformer with a Y-Y winding pattern. Specifically, with reference to FIG.2B, transformer 108b is shown to include a core 210 and six windings. Generally, core 210 and the windings are formed of known suitable materials, such as iron and copper, respectively; however, other materials may be used. ConnectedAttorney Docket No.10046-535WO1 8137 HUA between AC module 102 and DC module 104, transformer 108b is configured to step-down and step-up, respectively, a voltage of an AC waveform (e.g., in a first power flow direction, e.g., AC to DC) or DC waveform (e.g., in a second power flow direction, e.g., DC to AC).

[0090] In the example shown in Fig.2B, a first winding (shown by terminal “a” 212) of the transformer 108b is connected at a node “a” located between the switching devices Sa+ (112a) and Sa-(112b) of AC module 102b; a second winding (shown by terminal “b” 214) is connected at a node “b” located between switching devices Sb+(112c) and Sb-(112d), and the third winding (shown by terminal “c” 216) is connected at a node “c” between switching devices Sc+(112e) and Sc-(112f). The corresponding legs (shown by terminals “x” 218, “y” 220, and “z” 222) of transformer 108b on the DC-side are connected at node “x” located between switching devices Sx+ (120a) and Sx- (120b), Sy+ (120c) and Sy- (120d), and Sz+ (120e) and Sz- (120f), respectively. In some implementations, transformer 108b is magnetized with a switching frequency.

[0091] Further, AC-DC / DC-AC converter 100b is shown to include capacitors Cra (106a), Crb (106b), and Crc (106c) connected in series with respective legs of transformer 108b.

[0092] Fig.2B also shows an equivalent circuit diagram 224 of transformer 108b. For each winding, the voltage ^^்versus the winding currents and their mutual inductance can be calculated as (e.g., shown with respect to winding a) per Equation 2A.(Eq.2A)

[0093] It should be appreciated that the limb and air gap can be configured such that ^^^^ൌ ^^^^and ^^^௬ൌ ^^^௭. Since ^^்ೌ^ ^^்್^ ^^^்ൌ 0 and ^^்^^ ^^^்^ ^^^்ൌ 0 holds true in Y-Y configurations, ^^்can be calculated as (e.g., shown with respect to winding a), per Equation 2B.(Eq.2B)

[0094] In Equation 2, ^^^^^^are primary and secondary side turns ratio, while ^^భ்is the reluctance seen by winding a and x. This illustrates that each phase can be decoupled from the others. Phase A can be modeled per Equation 2.Attorney Docket No.10046-535WO1 8137 HUA(Eq.3)

[0095] In Equation3, ^^^^^ ^^ ^^^ ^^^௫^ ^^ ^^^ ^^௫^^ ^^ ^^^ are the derived admittance. The model can be solved using Fast Fourier Transform (FFT) to avoid considering the complex switching mode.

[0096] Example Control Modulation. Figs.5B – 5F show control operations at various points in the AC-DC / DC-AC converter 100b in the context of a simulation of a model of the AC-DC / DC-AC converter 100b.

[0097] In the simulation, the three half-bridges of AC module 102b are switched synchronously with a duty cycle of 0.5. That is, the three high-side switches of AC module 102b (e.g., Sa+, Sb+, and Sc+) are turned “on” and “off” synchronously, in contrast to the three low-side switches (e.g., Sa-, Sb-, and Sc-). Therefore, as shown in FIG.5B, subpanel (a), the space vector of AC module 102b is reversed with each switching period. As shown, when the high-side switches (e.g., Sa+, Sb+, and Sc+) are “on,” the AC module 102b is in phase with the input power (e.g., grid power), and when the low-side switches (e.g., Sa-, Sb-, and Sc-) are “on,” the AC module 102b is out of phase with the input power. Fig.5B, subpanel (b) shows the modulation operation of DC module 104b as described in ref [4], which is incorporated by reference herein. The control operation is configured to maintain the DC side space vector (502) in phase with the AC side (504). When the grid angle is α, the space vector for AC module 102 can be synthesized by S1 and S2 per Equation 4.(Eq.4)

[0098] In Equation 4,sin ^^. To achieve this modulation, two modulation signals can be employed for each switch pair. As shown in“Region 1” of FIG. 5B, subpanel^^௬మൌ ^^^െ 1, ^^௭భൌ െ1, and ^^௭మൌ^^^^^ ^^ଶ^െ 1. In this region, the switching frequency of half bridge “y” (119b) is double the other two half bridges (119a, 119c). Repeating this analysis for Regions “1” to “6”, the modulation signal shown in FIG.5B, subpanel (c).

[0099] AC Side Modulation. The AC Side three half bridges can be switched synchronously with a duty cycle of 0.5, i.e., the high side three switches turn on and turn off together, and the low side switches operate in complementary. The generated switch node voltages ^^^ெ, ^^^ெ, and ^^^ெmay change between 0 and the upper envelopes with highAttorney Docket No.10046-535WO1 8137 HUA frequency. An example of phase A is shown in Fig.4, of which the upper envelope is ^^^^ൌ ^^^^ ^^^^^. The other two phases have the same waveform with only respective phase shifts of ^T , and ଶଷAC ଷTAC on the envelopes.

[0100] The switching node voltage VAM, VBM, and VCMare equivalent to the AC side three-phase voltage source in Fig.2B. The common mode component ^^^^,^^in this three- phase voltage source can be calculated per Equation 5. ^^ ൌ^^^ெ ^ ^^^ெ ^ ^^^ெ^^,^^ 3(Eq.5)

[0101] For a connection between M and N in which the common mode current cannot flow, the actual voltages applied on the left side of the resonant tank can be calculated per Equation 6. ^^^ேൌ ^^^ெെ ^^^^,^^^^^ேൌ ^^^ெെ ^^^^,^^^^^ேൌ ^^^ெെ ^^^^,^^(Eq.6)

[0102] From Fig.5B, subpanel D, ^^^^,^^is the switching frequency component. When the high sides switches are on, ^^^^ൌ ^^^^. When low side switches are on, ^^^^= 0. OThe local average ^^^ெof VAMmay be determined as the sum of ^^^^and a grid-frequency component ^^^^. The grid frequency component ^^^^may be calculated per Equation 7. ^^^^ൌ ^ത^ത^തതெത െത ^ത^^ത^തതത,^തത^^^^^ൌ ത ^^ത^തതெത െത ^ത^^ത^തതത,^തത^^^^^ൌ ത ^^ത^തതெത െത ^ത^^ത^തതത,^തത^(Eq.7)

[0103] The small resonant capacitors ^^^^, ^^^^, and ^^^^may be employed to prevent grid- frequency current from flowing through the transformer that can otherwise cause transformer saturation, to block such flow. Therefore, the voltage applied to the resonant tank and, thus the transformer winding are only high-frequency. The grid-frequency voltage components remain only on the resonant capacitors. Considering superposition, the grid frequency component can be ignored, and the resonant tank can be modeled considering only the high- frequency voltages ^^^^per Equation 8. ^^^^ൌ v^ேെ ^^^^^^^^ൌ v^ேെ ^^^^Attorney Docket No.10046-535WO1 8137 HUA ^^^^ൌ v^ேെ ^^^^(Eq.8)

[0104] Fig.5B, subpanel D shows the high-frequency waveforms ^^^^, ^^^^, and ^^^^with grid frequency envelope. For AC side switching state ^^ ^^^^∈ {0, 1}, the high frequency waveforms ^^^^, ^^^^, and ^^^^can be calculated per Equation 9.(Eq.9)

[0105] DC Side Modulation. In the DAB-type circuit, no grid frequency current is allowed to flow through the transformer. The control can ensure this condition by keeping the DC side voltage space vector ^⃗^^,ௗ^always tracking the AC side ^⃗^^,^^(c.f. Fig.6(a)). The space vector can be notably obtained by averaging over a switching period. To this end, any phase shift occurring within one switching period between the DC side and the AC side cannot be observed on the space vector. Consequently, synchronizing the DC side space vector with the AC side space vector does not imply zero power transmission.

[0106] To transmit power through phase shift within one switching period, with the AC side synchronous switching, a jumping vector ^⃗^^,^^may be employed with its direction jumping to the reverse and then jumping back in every switching period. Specifically, when the high-side switches are on, the vector is in phase with the grid, i.e., ϕ = ϕg. When the low- side switches are on, the vector then reverses to the opposite ϕ = ϕg + π. The length of the vector may be. Additional description of the operation for the DC side modulation may be found in in

[0018] .

[0107] When the grid angle ϕg is in section 1, ^⃗^^,ௗ^may be synthesized using ^^^and ^^ଶwithin the first half switch period and using ^^ସand ^^ହwithin the second half, e.g., per Equation Set 10.whereAttorney Docket No.10046-535WO1 8137 HUA(Eq. Set 10)

[0108] In Fig.5B, subpanel C, the switch sequence is shown as (000) → (100) → (110) → (100) → (000) → (001) → (011) → (001) → (000). The actual switching operation may be observed from the switching node voltage VxP, VyP, and VzP, which may be synchronous with the gate signal of the top switch. Within one switching period, bridge x switches once during the first half period, and bridge z switches once in the second half, while bridge y switches twice, one in the first half and one in the second. Therefore, within section 1, the switching frequency of bridge y is twice that of the other two.

[0109] To implement the control, two modulation signals ^^^భand ^^^మmay be employed where k ∈ {x, y, z} for each phase to generate the switching signal.

[0110] For a bridge leg, e.g., x, the modulation signals ^^௫భand ^^௫మmay be determined per Equation 11. ^^௫భൌ 1 െ ^ ^^^^ ^^ଶ^ ^^௫మൌ െ1 (Eq.11)

[0111] In Equation 11, the modulation signals ^^௫భand ^^௫మare compared to the bidirectional sawtooth wave to generate ^^௫భand ^^௫మ, where the sum of ^^௫భand ^^௫మmay be used to determine the gate signal for Sx+ per Equation 12. ^^௫ାൌ ^^௫భ^ ^^௫మ(Eq.12)

[0112] gx− may be determined as the complementary of gx+ with the proper deadtime. Bridge legs y and z may be similarly determined per Equations 13a and 13b., one can have: ^^௬భൌ 1 െ ^^ଶ^^௬మൌ ^^^െ 1 (Eq.13a) ^^௭భൌ െ1 ^^௭మൌ ^ ^^^^ ^^ଶ^ െ 1 (Eq.13b)Attorney Docket No.10046-535WO1 8137 HUA

[0113] The modulation operation may be similarly repeated for sections 2 to 6 to provide the modulation signals shown in Fig.5B, subpanel C to obtain the overall grid period. Indeed, there is always one and only one bridge having double switching. From section 1 to section 6 (Fig.5B, subpanel C), the phase that does double switching, in turn, may be determined as y → x → z → y → x → z.

[0114] The voltage on the transformer’s secondary side winding may be calculated per Equation 14.^^^௬ൌ ^^௬ைൌ ^^௬^െ ^^^^,ௗ^^^^௭ൌ ^^௭ைൌ ^^௭^െ ^^^^,ௗ^(Eq.14)

[0115] In Equation 14, ^^^^,ௗ^is the DC side common mode component and may be determined per Equation 15.(Eq.15)

[0116] Phase Shift and Power Flow. To transfer power from the AC side to the DC side or in reverse, a phase shift θ may be employed. For example, when the DC side leads the AC side by θ, the power may flow from the DC side to the AC side and the circuit works as an inverter. When the DC side lags the AC side by θ, the power may flow in reverse, and the circuit works as a rectifier. Fig.5B, subpanel E shows an inverter mode waveform example in one switching period. The local average power in the switching period may be determined per Equation 16.(Eq.16)

[0117] Modeling Method. The exemplary system may employ a controller that employs a frequency domain discrete model that solves for the multi-switching mode with the Fast Fourier Transform (FFT) and then recovers the waveform with the Inverse Fast Fourier Transform (IFFT). The frequency domain discrete model can substantially reduce the complexity of multi-switching-mode operations. Notably, operation among the arrays may be performed using only scalar operations, which is very efficient computationally. Additionally, computationally-straightforward fft and ifft function may be implemented rather than the complex Discrete Fourier Transform employed for other control approaches.Attorney Docket No.10046-535WO1 8137 HUA

[0118] To perform the multi-switching mode operation, the controller can divide the whole grid period into 360 sections and consider each section as a steady state. The controller may derive the AC side waveforms in a numerical way, e.g., as discussed above. The AC side three bridges may share the same modulation signal mac(t) = 0 and the same bipolar triangle carrier cac(t) and determined per Equation Set 17. The modulation signal mac(t) and carrier cac(t) may be sampled to discrete arrays macand cacwith length of Nswhere Nsis an even number for the later truncation to avoid Gibbs phenomena ^^^^ൌ ⌊0,0, … ,0⌋்(Eq. Set 17)

[0119] By calculating Equations 5-8 and Equation Set 17, the controller can determine the discrete voltage arrays ^^^^, ^^^^, and ^^^^. Similarly, the discrete DC side modulation carrier signals ^^௫భ, ^^௫మ, ^^௬భ, ^^௬మ, ^^௭భ, ^^௭మ, and the shared carrier cdc may be used by the controller to determine the discrete arrays ^^^௫, ^^^௬, and ^^^௭. For the equivalent circuit of a phase, the input voltage may be determined as ^^^= ^^^௫െ ^^^^. The controller may transform the input voltage into a Fourier coefficient array with the FFT per Equation 18. ^^^ ൌ ^ ^^^^^0^, ^^^^^1^, … , ^^^^^^^^ െ 1^^(Eq.18)

[0120] In Equation 18, ˙ ^^^^^ ^^^ ∈ {0, 1, 2, ..., Ns−1} is a complex number representing the magnitude and phase of the kth order harmonic component per Equation 19.(Eq.19)

[0121] In Equation 19, ^^^^ ^^^ may be a signal with several jump discontinuities due to the switching. According to Gibbs Phenomena, with a finite large Ns, the signal recovered from V1or any derived waveform from it would have oscillatory behavior around the switching point

[0021] as a calculation error and doesn’t exist in the real waveform. To provide accurate waveform calculation, especially at the switching points, to have the correct switching current and correct loss estimation, the controller can discard the second half of the obtained Fourier array. In doing so, when performing the IFFT, the resulting discrete waveform could be sampled at the midpoint of peaks and valleys of the digital oscillation, therefore, avoiding the oscillatory error in the result

[0022] . To allow for this optimization, Ns should be an even number.Attorney Docket No.10046-535WO1 8137 HUA

[0122] After truncating and discarding the second half, Vi may be determined per Equation 20(Eq.20)

[0123] From Equation 20, thee discrete frequency domain model for the equivalent circuit may be determined per Equation Set 21.^^ ^^ ^^^^^^^^భൌ ^^^^(Eq. Set 21)

[0124] In Equation Set 21, ω is the discrete frequency axes vector and may be calculated per Equation 22.(Eq.22)

[0125] Using Equation Set 21 and Equation 22, the controller can determine the inductor current Ir1 and resonant cap voltage ^^^^భin the discrete frequency domain per Equation Set(Eq. Set 23)

[0126] Then, by applying an IFFT operation to Ir1and ^^^^భ, the discrete time domain waveform may be obtained per Equation Set 24. ^^^^ ൌ ^ ^^^^^0^, ^^^^^1^, … , ^^^^^^^^ െ 1^^^^^^భ ൌ ^ ^^^^^0^, ^^^^^1^, … , ^^^^^^^^ െ 1^^, whereAttorney Docket No.10046-535WO1 8137 HUA ^^ ∈ 0,1, … , ^^^െ 1 (Eq. Set 24)

[0127] Modeling Results. Fig.5C shows the inverter operations with a resistive load and for a DC voltage ^^^^ൌ 400 ^^, AC phase voltage ^^^^^ൌ 277√2 ^^ , phase shift ^^ ൌ 0.07 ^^^, and total power ^^ ൌ 15 ^^ ^^. FIG.5C shows the simulation output over one grid period, including the voltage, current, and power at nodes “a,” “b,” and “c,” (diagrams 506, 508, 510), the AC side DC-Link capacitor voltage (diagram 506), the resonant series-linked blocking capacitor voltage (diagram 512), and the current in the transformer 108b (diagram 514). FIG.5C also includes a zoomed window that further shows the conduction current of AC-side switches Sa+, Sa-and DC-side switches Sx+,, resonant capacitor voltages ^^^^^, and transformer current ^^்^.

[0128] Fig.5D, subpanel A shows the resonant tank waveforms in one grid period, and Fig.5D, subpanel B shows the local average power pave,i (i ∈ a, b, c). When pave,i (i ∈ a, b, c) is low, the DC side ^^^^(i ∈ x, y, z) is a 3-level waveform, and when pave,i is high, it becomes 5-level. Fig.5E shows an example of the resonant tank voltages and current waveform. The waveform is shown zoomed in at 180°, 190°, and 210°. The AC side ^^^^(i ∈ a, b, c) maintains a 0.5 duty cycle, and its magnitude passively changes according to the grid voltage.

[0129] Using an FFT modeling method, the ZVS performance and current stress of the switches can be analyzed. The performance of the resonant configuration / operation are compared to that of a non-resonant configuration / operation described in

[0015] . In the comparison, the switching frequency, input and output voltages, phase shift θ, and the load of the two circuits are all equal. The power of two circuits is set to 15kW. Fig.5F shows the turn-on current of phase A, which implicates ZVS performance. A negative turn-on current implies that the current is flowing through the anti-parallel diode at this switching instant; therefore the turn-on voltage is zero, and the switching loss is low. Conversely, a positive turn-on current implies a hard switching and higher loss.

[0130] Figs.5F, subpanels (a)-(d) and 5F, subpanels (a)-(d) shows operation for resonant configuration / operation, and Figs.5F, subpanels (e)-(h) and 5F, subpanels (e)-(h) shows operation for non-resonant configuration / operation. In Fig.5F, subpanels (a)-(d), it is shown that the AC-side high side and low side switches have both ZVS and hard switching. The hard switching current, however, is always below 4 A, which is approximately ZCS. The DC-side high-side switch has ZVS. The low side also has a wide ZVS range, except for a very short period of hard switching during the double-switching section. Compared to theAttorney Docket No.10046-535WO1 8137 HUA non-resonant topology shown in Figs.5F, subpanels (e)-(h) and 5G, subpanels (e)-(h), the resonant topology switching stress is averagely decreased by 68% on the AC-side and 35% on the DC-side.

[0131] Also, as shown in Fig. Fig.5F, subpanels (e)-(h), the AC side top switch Sa+ and bottom switches Sa− both have partial of time doing ZVS during one grid period. For Sa+, the ZVS range is 33.3% of the whole period, while the bottom switches Sa− has around 66.6%. Compared to the non-resonant circuit results in Fig.5F, subpanels (e)-(h), the ZVS range is approximately the same. However, the switching currents of the proposed circuit are much smaller than the non-resonant circuit, for both the soft turn-on current and the hard turn-on current. With a total power of 15kW and peak conduction current around 70A, the hard switching current of Sa+ is always below 4 A, which is approximately ZCS. So the switching loss is considerably low. For Sa−, the max hard switching current is 10A, slightly higher than Sa+, but since its ZVS time ratio is higher, its switching loss is also low.

[0132] The DC side ZVS performance is observed to be excellent. For both the resonant circuit and the non-resonant circuit, the high side switch Sx+ always has ZVS. The low side switch Sx− also has a wide ZVS range, except for a very short period of hard switching when entering and leaving the double switching section.

[0133] Compared to the non-resonant topology ( Fig.5F, subpanels (e)-(h), the resonant topology results shown in Fig.5F, subpanels (a) – (d) show hard turn-on current stress on average decreasing by 62.3%, the soft turn-on current decreasing by 45%.

[0134] Fig.5G shows waveforms of the phase A switches conduction currents. In an overall grid period, the resonant circuit switches may have smaller conduction currents compared to the non-resonant circuit. At phase angles 90°and 270°, where phase A’s power is zero, all switches’ conduction currents may be at their lowest, but the non-resonant circuit may have a much higher conduction current there.

[0135] Table 2 shows the conduction currents of both the resonant and non-resonant configurations. It can be observed that the resonant topology outperforms the non-resonant topology. An efficiency higher than 98.5% is expected for this resonant converter. Table 2 – Comparison of resonant and non-resonant topologiesAttorney Docket No.10046-535WO1 8137 HUA

[0136] Simulation Results. To verify the topology and the modeling method, a simulation was implemented with PLECS. The parameters are the same as the numerical modeling. The results are shown in (Fig.5C).

[0137] The AC side capacitor voltages ^^^^, ^^^^, and ^^^^are shifted AC with a common mode DC component, of which the voltage level is equal to the peak of the AC phase voltages. Since common mode current cannot flow in a three-phase system, the voltages and current on the load are all sinusoidal AC, and therefore the output power has a good PFC shape. Active control can be employed, e.g., to dynamically change the phase shift θ and the DC side space vector length, which are constant in the present open loop operation, to significantly decrease the THD.

[0138] The resonant capacitor voltages ^^^^^, ^^^^^, and ^^^^^may include a grid frequency AC base and a resonant frequency AC ripple. The transformer current (or the resonant tank current) can match the modeling results perfectly. Fig.5C shows the waveform at phase A’s peak power . The AC side switches Sa+ Sa− and the DC side switches Sx+ Sx− are all doing ZVS at the peak power.

[0139] Components Loss and efficiency. With the same circuit parameters listed above, the semiconductor loss has been calculated based on the loss data of a 1200V SiC FET (UF3SC120009K4S). With the other two phases loss added in, the total semiconductor loss is 102.5W. Assuming a transformer efficiency of 99.5%, an overall efficiency higher than 98.8% can be expected.

[0140] Discussion. Bidirectional AC-DC power electronic conversion system with galvanic isolation may be widely used.

[0141] On electric vehicles, a three-phase AC-DC bidirectional converter with power factor correction (PFC) capability is a key component. In charging applications, it draws three-phase power from the grid with low THD and at the same time controls the DC output voltage. In the vehicle-to-grid (V2G) application, it may enable the vehicle to send active or reactive power back to the grid.

[0142] In the battery energy storage system, a bidirectional PFC AC-DC converter may be used to minimize the impact of variable power from renewable energy sources like wind, tidal, and photovoltaic (PV) to connect the battery rack and the three-phase grid. The batteryAttorney Docket No.10046-535WO1 8137 HUA storage system can be used to provide fast real and reactive power dispatch, e.g., for grid voltage and frequency support or for optimal power dispatch.

[0143] In the above application and other applications like server supply and solar micro- inverter, galvanic isolation may be employed for safety reasons or voltage level adaption. Using a high-frequency transformer instead of a grid-frequency transformer can greatly increase the overall power density.

[0144] One typical realization of a bidirectional isolated three-phase AC-DC converter is a multi-stage configuration. The first-stage AC-DC converts the grid AC voltage to a DClink, and then a second-stage high-frequency isolated DC-DC converter provides the isolation. In some applications where a wide range of DC side voltage is required, a third-stage DC-DC non-isolated converter will be added. The multi-stage configuration, however, has several shortcomings. First, the AC-DC stage is typically a hard-switching three-phase rectifier that limits the switching frequency due to high switching losses; hence, it requires a bulky DC- link capacitor to reduce the DC-link voltage ripple [5], [6]. Second, the control is complex since each stage needs to be controlled separately. The AC-DC non-isolated stage usually employs space vector modulation (SVM) and bi-loop decoupling control to keep PFC and, at the same time maintain a stable DC-link voltage. The second DC-DC isolated stage is usually a DAB converter [7] with phase shift control [8] [9], or an LLC converter with frequency control [6].

[0145] In

[0011] and

[0012] , a single-stage, phase-modular method is proposed, which achieved a good efficiency of 97.2%. However, a complex off-line optimization is required to obtain its modulation with variable frequency and double phase shifts. Another single-stage method with simple SVPWM control is discussed in

[0013] , but a Conergy NPC topology on the AC side leads to a high switch count. A topology with a reduced switch count is proposed in

[0010] , but its THD is not satisfactory, and the efficiency is low.

[0146] In contrast, the exemplary single-stage resonant mode circuit can provide good ZVS performance, high efficiency, and reduced number of magnetic components and switches. It may include three half bridges in Y-Configuration

[0014] on the AC side and a three-phase full bridge on the DC side. A TPTL-HFT with a Y-Y winding configuration may be connected in between. The positive ends of AC side half bridges may be connected to a three-phase AC source or load, while the negative ends may be connected at joint M. The anti-paralleled diodes of MOSFETs prevent negative voltage on input capacitors Ca, Cb, and Cc; thus a common mode DC potential equal to grid voltage peak ˆmay be established, which can lift the cap voltages to a DC so that they can be chopped by the half bridges

[0016] .Attorney Docket No.10046-535WO1 8137 HUA Usually, it takes one line period to pre-charge these three capacitors at the start-up

[0017] until they present a stable shifted-AC waveform. The resonant capacitors and the transformer leakage inductance may form the series-resonant tanks, e.g., to block the 60Hz low-frequency component. By aligning the space vector of the DC side and the AC side

[0018] , grid frequency magnetizing may be prevented. The transformer only magnetized with a switching frequency.

[0147] Example Method of Operation #2

[0148] Figs.6A-6G show example a three-phase method of operation of the exemplary bidirectional isolated single-stage AC-DC and DC-AC converter 100 (e.g., for AC-DC / DC- AC converter 100b) comprising a Y-Configuration Dual Active Bridge Converter (YAB) capable of single stage bidirectional AC-DC power conversion with a simple sinusoidal phase shift modulation, according to another illustrative embodiment. Compared to other DAB based AC-DC converters, the YAB achieves power factor correction (PFC) with a simpler control method while maintaining nearly full-range zero-voltage switching (ZVS) and relatively low circulating current, resulting in high efficiency. In an example, a 2.66kW YAB converter was fabricated and tested with the circuit and modeling results demonstrating an efficiency of 97.14%.

[0149] A Y-Configuration Dual Active Bridge Converter (YAB) was fabricated using the topology of Fig.6A. Experimental shows an efficiency performance of greater than 97% with a calculated peak efficiency of 97.75%.

[0150] Fig.6A shows the example YAB converter. The shaded shielded part is a DAB structure responsible for the power conversion of phase A. Three of these structures are coupled together through two Y-Configuration transformers that have (i) a low frequency (LF) Y-Configuration on the AC side half-bridges (HBs), and (ii) a high-frequency (HF) Y- configuration on the winding of high-frequency transformer (HFT). In Fig.6A, the AC side module includes HB-a, HB-b, and HB-c half bridges, while the DC side module includes HB- x1, HB-x2, HB-y1, HB-y2, HB-z1, and HB-z2 half bridges.

[0151] The positive terminals of the HB-a, HB-b, and HB-c half bridges of the AC side module are directly connected to the three-phase grid, and the negative terminals are connected together to form a neutral point M. The neutral point M is floating from the grid neutral G. Blocking capacitors CBa, CBb, and CBcare placed between the AC side half-bridges and the high frequency transformer (HFT) to block the grid frequency component. As shown in the waveform examples in Fig.1, considering phase A as an example, the grid side provides sinusoidal voltage vaand current iawith high power factor (PF), while the input capacitor voltage vCa has a camel hump shape. Then, with a synchronous 50% duty cycleAttorney Docket No.10046-535WO1 8137 HUA switching at HB-a, HB-b, and HB-c high bridges of the AC side module, a high-frequency pulse vAN with a sinusoidal envelope can be generated on the HFT’s AC side winding.

[0152] The DC side six HBs share the same DC link. For phase A, the HB-x1 and HB-x2 half bridges do a sinusoidal phase shift to generate a sinusoidal pulse width vXx. Due to the floating neutral point N, vXx may be reshaped by the other two phases into vXN as the effective voltage applied on the right side of leakage inductance. With a constant phase shift between vXNand vAN, a high PF power flow may be achieved.

[0153] The three-phase high-frequency (HF) equivalent circuit is illustrated in Fig.6A, subpanel B. Considering phase A (blue shielded part) as an example, the AC side HF voltage source is the voltage on switch Sa−, and the DC side HF voltage source is the voltage across switching nodes X and x. La and Lx are the transformer leakage inductances on the AC and DC sides, respectively. Lm is the magnetizing inductance. Phases A, B, and C are coupled together through nodes M, N, and (xyz). To simplify the analysis, the three-phase equivalent circuit can be decoupled into the single-phase equivalent circuit shown in Fig.2b. The derivation of vAN and vXN, which is detailed in

[0154] Modulation Operation with Active Clamping Startup. The HB-a HB-b HB-c half bridges of the AC side module form the three-phase Y-configuration half-bridge structure

[0013] . Before starting, all switches may be off. The body diodes and the input capacitors may form a freewheeling circuit, with which a constant common mode (CM) voltage vcm,gmay be established on Ca, Cb, Ccto keep the HB input voltage vCa,vCb,and vCcpositive (see Fig.6B).

[0155] An active clamping method discussed in [14’] may be further employed here. Starting with phase A, when the capacitor voltage vCareaches zero, the top and bottom switches on HB-a may both be turned on to clamp vCa at zero. After 60°, when vCbdecreases to zero, clamping on HB-a may be released, and the HB-b half-bridge may begin clamping. After another 120°, the clamping shifts from the HB-b half bridge to the HB-c half bridge and continues. In this way, the common-mode voltage vcm,gcan change from a constant DC to a 180Hz varying DC, and vCa, vCb, and vCc having a camel hump shape. Meanwhile, the AC phase voltages as the differential-mode (DM) components still maintain their sinusoidal shape.

[0156] AC Side Modulation Operation. Fig.6C shows the modulation operation on the AC side and the generated switching waveforms. From top to bottom, Fig.6C shows the gate signals waveform, the switching node voltage waveforms with respect to M, the AC side HF common-mode component waveform vcm,ac(i.e., vNM), the switching node voltage waveform with respect to N, and the final effective HF pulse waveform applied to the HFT winding.Attorney Docket No.10046-535WO1 8137 HUA

[0157] In Fig.6C, for every 120°, one-half bridge is clamped while the remaining two half bridges operate with synchronous 50% duty cycle switching. The generated vaM may be a unipolar pulse with an upper envelope equal to the camel hump vCa. By considering the loop M-a-A-N and applying KVL, the high-frequency pulse vAN with a sinusoidal envelope can be determined per Equation 25. ^^^ேൌ ^^^ெെ ^^^ಳೌെ ^^^^,^^(Eq.25).

[0158] In Equation 25, vcm,ac, i.e., vNM, is the HF CM component generated by vAM, vBM, and vCM, and can be calculated per Equation 26. ^^^^^ெ ^ ^^^ெ ^ ^^^ெ^^,^^ ൌ3(Eq.26)

[0159] In Fig.6C, vcm,ac has an envelope equal to the 180Hz LF CM vcm,g. By subtracting vcm,ac from vaM, the HF DM vaN may be obtained. The blocking capacitor CBa may block the 60Hz component in vaMto provide the final effective HF AC voltage vANapplied to the transformer winding, may be is decoupled from the other two phases. vBNand vCNcan be obtained similarly.

[0160] DC side modulation. The DC side modulation may be a simple sinusoidal modulation. The principle is to keep the voltage-time product equal for the switching pulses of the AC side and the DC side, i.e., keep the areas ADC = AAC (e.g., Fig.6E). For grid voltage condition, per Equation Set 27, then the DC side inner phase shifts can be determined per Equation Set 28. ^^^ൌ ^^^. cos൫2 ^^ ^^^^^൯,^^ ^^^ ^^^௪^ൌ2^^^^.2 (Eq. Set 28)Attorney Docket No.10046-535WO1 8137 HUA

[0161] In this way, the sinusoidal pulse width modulated vXx, vYy, and vZz may be generated (cf. Fig.6D). Fig.6D shows the DC side modulation method where vXx, vYy, and vZzare the voltages across the switching nodes of the full bridges. The voltages contain a common-mode component vcm,dc. By subtracting the common-mode component, the decoupled effective pulses vXN, vYN, and vZN may be obtained. Unlike an ordinary DAB, these are not the effective voltages directly applied on the leakage inductance; a common-mode component vcm,dcamong them may cause a major difference per Equation 29. ^^^^^௫ ^ ^^^௬ ^ ^^^௭^^,ௗ^ ൌ3(Eq.29)

[0162] By subtracting vcm,dc from the effective DC side pulses vXN, vYN, and vZN, the side pulses may be calculated per Equation Set 30. ^^^ேൌ ^^^௫െ ^^^^,ௗ^^^^ேൌ ^^^௬െ ^^^^,ௗ^^^^ேൌ ^^^௭െ ^^^^,ௗ^(Eq. Set 30)

[0163] With the derived AC side effective pulses vAN, vBN, vCN and DC side effective pulses vXN, vYN, vZN, the three-phase equivalent model in Fig.2a is decoupled into three single-phase models. Assuming the transformer magnetizing inductance is infinitely large, the final equivalent circuit is simplified into Fig.6A, subpanel B.

[0164] Fig.6A, subpanel B shows the Phase shift modulation of Phase A at time instant t0. The AC side is constant 50% duty cycle square pulse, with an amplitude following grid voltage va / 2. The DC side is a three-voltage level waveform with constant amplitude of VDC, while its duty cycle is sinusoidal modulated according to the principle ADC = AAC.

[0165] For phase A, the control logic is illustrated in Fig.6D. The DC side pulse width dXmay be a dependent variable determined by the grid voltage va, while the phase shiftdetermined between vAN and vXN, may be the main variable that controls the system power. Three phases share the sameand it remains constant for a given power. It changes only when the output power (voltage source load) or output voltage (resistive load) needs to be adjusted. Compared to the AC-DC DAB, which requires offline calculation for at least two variables to control power and maintain PFC, the single-variable control of the YAB may be much computationally efficient.

[0166] Steady State Modeling. Rather than using time-domain methods for steady-state modeling of DAB that can be complex in multiple switching modes, the exemplary controllerAttorney Docket No.10046-535WO1 8137 HUA can employ frequency-domain based operation to simplify the process as switching modes no longer need to be considered.

[0167] Therefore, a straightforward FFT based modeling approach proposed in [15’] is adopted here to analyze the system. Obtaining the leakage inductor current waveform is the first step. This waveform is essential for calculating device switching currents, conduction currents, transformer currents, and system instantaneous power.

[0168] One switching period is taken as the analysis object, which is the grey-shaded area in Fig.6F starting from t0 and ending at t0 +Tsw. The control may assume: 1. The grid voltage vais constant.2. The blocking capacitor voltage vCBais constant.3. The DC link capacitor voltage is constant.4. Switching transients are ignored.

[0169] The FFT model is numerical, in which all waveforms are sampled into arrays of length Ns (Ns must be even). The derivation may start with obtaining all gate signals ga+, gx1+, and gx2+. Using ga+as the reference per Equation Set 31, the other gate signals can be obtained by circularly shifting ga+.(Eq. Set 31)

[0170] Then the voltage pulses can be obtained with Equation 32.(Eq. Set.32)

[0171] The voltage applied on the leakage inductance Laxmay then be determined per Equation 33.Attorney Docket No.10046-535WO1 8137 HUA ^^^^ൌ ^^^ேെ ^^^ே(Eq.33)

[0172] Applying FFT to vL, the controller may obtain the frequency domain VLper Equation 34. ^^^^ൌ FFT^ ^^^^^ (Eq.34)

[0173] In Equation 34, the VLis a complex array with a length of Ns, where the nth component VL(n) represents the magnitude and phase of the nth harmonic. According to [15’], the components from Ns / 2thto NSthin VLmay be set to zero to avoid the Gibbs phenomenon, i.e., resonance at switching instants. Additionally, the first component may also be set to zero because the DC component in itA is zero. The frequency domain voltage may then be determined per Equation 35.(Eq.35)

[0174] The frequency domain inductor current can be calculated per Equation 36.: ^^^ ^^^^^௧^ ൌ^^ ^^ ^^௧^where ^^ ൌ 2 ^^ ^^^௪. ^0, 1, 2, … , ^^^^ (Eq.36)

[0175] Then the inductor current for one switching period may be calculated using the Inverse FFT per Equation 37. ^^௧^ ൌ FFTି^^^^^௧^^(Eq.37)

[0176] By repeating this calculation condition per Equation 38, a whole line period inductor current result may be obtained.(Eq.38)

[0177] Phase B and phase C can be obtained similarly. In actual implementation, the operation may be performed using vectorization [12’] and can be substantially efficient compared to complex time-domain multi-mode methods [1’], [16’]–[19’].Attorney Docket No.10046-535WO1 8137 HUA

[0178] In Fig.6E, the vAN, vXN, and itA may be calculated for a whole grid period. With a positive ϕ = 0.18 Tsw, i.e., vAN may lead vXN, the average power flows from the AC side to the DC side, and the system may operate in rectifier mode.

[0179] The waveforms of effective voltages and inductor current indicate the ZVS status of the three top switches Sa+, Sx1+, and Sx2+. The ZVS dot indicates ZVS, while the hard- switch dot indicates hard switching. It can be observed that all switches achieved ZVS. Only in Fig.6D, where the grid voltage is close to zero crossing, does HB-x2 half bridge of the DC module lose ZVS, while the other two HBs half bridge still maintain ZVS.

[0180] Calculation of system power. Equation Set 39 provides for three power quantities, the first is the instant power, which is the product of instant current and instant voltage. ^^^^ൌ ^^^ே^^௧^^^^^ൌ ^^^ே^^௧^^^^^ൌ ^^^ே^^௧^^^ ൌ ^^^^^ ^^^^^ ^^^^(Eq. Set 39)

[0181] The second quantity is the local averaged power with respect to a switching period. For an ideal system with a power factor of 1.0, it is constant per Equation 40. ேೞ^^^^^^^ൌ ^ ^^ ^ି^ (Eq.40)

[0182] The third quantity is the averaged power with respect to a grid period per Equation 41.(Eq.41)

[0183] In YAB, Pavemay be controlled solely by the phase shift ϕ. As shown in Fig.6A, when ϕ > 0, the power is positive, meaning power flows from the AC side to the DC side. Conversely, when ϕ <0, power flows from the DC side to the AC side. For ϕ ∈ [0,0.25Tsw], the power may increase with increasing ϕ. When ϕ exceeds 0.25Tsw, the power may decrease with increasing ϕ. This operation may be exactly the same as in a DC-DC DAB.

[0184] ZVS analysis. The criterion for determining ZVS is that the device current must be negative at the instant of turning on, i.e., the current must be flowing through the body diodeAttorney Docket No.10046-535WO1 8137 HUA so that the turn-on voltage is zero. According to Fig.6E, the turn-on current of each device can be derived per Equation Set 42. ^^ ൌ 0: ^^^ାturns on. ^^^௪,^ାൌ ^^௧^|^ୀ^^^ ൌ ^^ଶ: ^^௫^ାturns on.^^ ൌ ^^ଷ: ^^௫ଶାturns on. ^^^௪,௫ଶାൌ ^^௧^|^ୀ^ ఛయೞ்^ேೞ^(Eq. Set 42)

[0185] Because of symmetry, the switching status of the bottom switches may be the same as the top switches where isw,a− = isw,a+, isw,x1− = isw,x1+, isw,x2− = isw,x2+. To this end, only the turn-on currents of the top switches may need to be investigated. Moreover, since the HB- x1 and HB-x2 half bridges of the DC side module perform the sinusoidal phase shifts within a grid period, the turn-on currents may be considered as symmetrical within the grid period.

[0186] The turn-on current of Sa+may maintain ZVS from 0° to 90° and from 270° to 360°, where the grid voltage is positive. Hard switching may occur from 90° to 120° and from 240° to 270°. The HB-a half bridge may be clamped from 120° to 240°, during which there is no switching loss. Generally, higher output power would cause higher switching current; however, with the ZVS locations within a grid period, the switching current can remain the same for different output powers (or ϕ).

[0187] For most of the grid period, the turn-on current of Sx1+ can maintain ZVS. The hard switching distributions may vary slightly with different power levels but may last for a short duration and are located near the zero crossing. Consequently, the hard switching current is low, resulting in low switching loss.

[0188] Loss model and efficiency estimation. The major component losses may be calculated for different power levels, and the system's theoretical efficiency may be obtained accordingly. Fig.6G shows the system power Pave, efficiency η, and major loss components from phase shift ϕ. In Fig.6G, the theoretical peak efficiency of 97.75% is obtained when ϕ = 0.15. The efficiency at peak power is 97.06%. An experimental result of 97.14% was obtained at ϕ = 0.1, where the theoretical efficiency is 97.61%. The 0.47% error could be attributed to partial ZVS loss and other filter component losses.

[0189] Hardware Test. A hardware test in rectifier mode (ϕ = 0.1Tsw) with a resistive load (RL = 15.6Ω) was performed. Fig.6H shows the experimental setup and the parameters used for the test. Fig.6H shows the waveform of phase A. From top to bottom, the respective waveforms are: the line-to-line voltage vLL,abbetween phase A and phase B; the phase A inputAttorney Docket No.10046-535WO1 8137 HUA capacitor voltage vCa with active clamping shape; the grid input current ia; the voltage vSa− on switch Sa−;the voltage vSx1− on the switch and the leakage inductor currents itA,p , itA,s on the primary and secondary sides; and the DC output voltage vDC.

[0190] In Fig.6H, the switch voltages vSa−, vSx1−, and inductor currents itA,p and itA,s are also shown zoomed in to show the ZVS status. itA,p and itA,s were measured such that positive values indicate current flowing out from the HB switching node. It can be observed that ZVS was achieved for both HB-a and HB-x1 half bridges at the DC side module at 0°, 20°, 50°, and 70°. Hard switching occurred at 110°. From 130°to 180°, the HB-a half bridge is clamped while the HB-x1 half bridge maintains ZVS.

[0191] Discussion. In recent years, isolated AC-DC converters have gained significant attentions due to their wide applications in solid-state transformers, EV fast charging, PV micro-inverters, and battery energy storage systems. Among the various isolated AC-DC bidirectional topologies, the single-stage AC-DC DAB is widely adopted due to its good Zero Voltage Switching (ZVS) performance and high efficiency. The principle of the AC-DC DAB is that the AC voltage is first rectified to a 120Hz half-sine, and then the DAB converter smooths it to a constant DC. With a large DC-link capacitor on the DC side, the 120 Hz current ripple is filtered, resulting in a constant DC voltage. The sine-to-half-sine unfolding operation can be achieved with either an AC switch half-bridge or an active unfolding bridge stage.

[0192] In [1’], an AC-DC DAB with an active unfolding bridge is presented, discussing optimal ZVS modulation methods considering different ZVS criteria. This method effectively achieves full-range ZVS and a peak efficiency of 96.3%. However, the relatively high circulating current necessary to enforce the ZVS leads to higher conduction loss. Additionally, the need to consider different switching modes makes this method very complex.

[0193] In [2’] and [3’], a variable frequency with a single switching mode method is proposed. The PFC is maintained with double phase shift and varying switching frequency (DPS-VF). The switching frequency increases significantly when the AC side voltage approaches zero-crossing in order to maintain the ZVS. A similar method is adopted in [4’], where the efficiency optimization considering major losses is implemented, achieving an efficiency of 96.6% with switching frequencies ranging from 50 kHz to 300 kHz. The efficiency is not significantly increased compared to fixed frequency methods in [1’], [5’].

[0194] This might be due to the fact that true full-range ZVS is actually impossible to achieve in the hardware, and partial ZVS or hard switching is inevitable near the AC zero-Attorney Docket No.10046-535WO1 8137 HUA crossing. Therefore high switching frequency will result in an increased switching loss. Additionally, high switching frequency leads to higher transformer core loss compared to fixed frequency methods. Thus, it remains unclear whether variable frequency control truly enhances the efficiency of an AC-DC DAB, requiring more thorough modeling of partial ZVS loss and core loss under asymmetric leakage inductance. Series resonant DAB (SR- DAB) are discussed in [6’], [7’].

[0195] With the same DPS-VF modulation, the efficiency is increased from 96.6% to 97.2%. With the same power transferred within one switching period, the rising and falling edges of the current are more leading compared to a non-resonant DAB; therefore, the half bridge switching current is decreased. The disadvantage is that the ZVS is harder to achieve than a DAB due to a lower turn-on current, while the advantage is that the turn-off loss and the circulating current are effectively decreased. Variable frequency control is more effective here because it solves the trade-off between the ZVS difficulty and loss minimization. In conclusion, frequency modulation is more suitable for an SR-DAB than a DAB. The aforementioned methods all share a common flaw: it requires the implementation of an off- line or on-line modulation solver. Not only the look-up table might become computationally challenging, but it also makes close loop power flow or voltage control more difficult to achieve.

[0196] To address this problem, simpler modulation methods are widely studied. A sinusoidal duty cycle method for half-bridge AC-DC DAB is discussed in [8’], where the author applied a sinusoidal duty cycle to the DC side half-bridge while maintaining a constant phase shift between the AC side and the DC side. Under DC-AC operation, significant 3rd and 5th harmonic distortion in the AC voltage is observed. To solve this problem, the author introduced a third harmonic injection to the DC side duty cycle, reducing the THD from 9.8% to 2.3% and achieving a peak efficiency of 96.8%. While effective, the method still lacks simplicity due to the need for online calculation of the injected harmonic. Sinusoidal phase shift methods are explored in [9’], [10’], where a similar power factor distortion problem was noticed. This suggests that, unlike most DC-AC converters, DAB cannot maintain good PFC with simple sinusoidal modulation on the DC side.

[0197] In [11’], a novel high-frequency link Y-Configuration on the transformer winding was proposed, effectively solving the power factor distortion problem under DC side sinusoidal space vector modulation. However, this topology has a relatively high circulating current at zero-crossing, increasing the conduction loss.Attorney Docket No.10046-535WO1 8137 HUA

[0198] In contrast, the exemplary Y-Configuration Dual Active Bridge (YAB) converter for a three-phase AC-DC application combines the merits of the AC-DC DAB and the Y- Configuration circuit structure in [11’] to overcome the complex modulation problems of traditional AC-DC DAB. It can achieve good PFC with simple sinusoidal phase shift modulation and maintains near-full-range ZVS for different output powers. An experimental test achieved an efficiency of 97.14%. A Fast Fourier Transform (FFT) based analysis tool is developed for both the AC-DC DAB and the proposed YAB and is available on GitHub [12’].

[0199] Configuration of Certain Implementations

[0200] The construction and arrangement of the systems and methods as shown in the various implementations are illustrative only. Although only a few implementations have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes, and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative implementations. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the implementations without departing from the scope of the present disclosure.

[0201] Although the figures show a specific order of method steps, the order of the steps may differ from what is depicted. Also, two or more steps may be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.

[0202] It is to be understood that the methods and systems are not limited to specific synthetic methods, specific components, or to particular compositions. It is also to be understood that the terminology used herein is for the purpose of describing particular implementations only and is not intended to be limiting.

[0203] As used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges mayAttorney Docket No.10046-535WO1 8137 HUA be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another implementation includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another implementation. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0204] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0205] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary” means “an example of” and is not intended to convey an indication of a preferred or ideal implementation. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0206] Disclosed are components that can be used to perform the disclosed methods and systems. These and other components are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these components are disclosed that while specific reference of each various individual and collective combinations and permutation of these may not be explicitly disclosed, each is specifically contemplated and described herein, for all methods and systems. This applies to all aspects of this application including, but not limited to, steps in disclosed methods. Thus, if there are a variety of additional steps that can be performed it is understood that each of these additional steps can be performed with any specific implementation or combination of implementations of the disclosed methods.

[0207] The disclosures of each and every publication cited herein are hereby incorporated herein by reference in their entirety.

[0208] Reference List [1] T. Chen, R. Yu, and A. Q. Huang, “A bidirectional isolated dual-phase-shift variable- frequency series resonant dual-active-bridge gan ac-dc converter,” IEEE Transactions on Industrial Electronics, 2022. [2] D. Menzi, J. E. Huber, L. Kappeler, G. Zulauf, and J. W. Kolar, “New return path inductor buck–boost y-inverter motor drive with reduced current stresses,” IEEE Transactions on Power Electronics, vol.37, no.9, pp.10086–10090, 2022.Attorney Docket No.10046-535WO1 8137 HUA [3] D. Menzi, M. Zhang, J. W. Kolar, and J. Everts, “3-Φ bidirectional buck-boost sinusoidal input current three-level sic y-rectifier,” in 2021 IEEE Applied Power Electronics Conference and Exposition (APEC), 2021, pp.590–598. [4] R. Baranwal, K. V. Iyer, K. Basu, G. F. Castelino, and N. Mohan, “A reduced switch count single-stage three-phase bidirectional rectifier with high-frequency isolation,” IEEE Transactions on Power Electronics, vol.33, no.11, pp.9520–9541, 2018. [5] Z. Chen, C. Chen, H. S. Rizi, and A. Q. Huang, “A high power density 75kva air-cooled sic intelligent power stage (ips) as a universal building block for grid applications,” in 2023 IEEE Applied Power Electronics Conference and Exposition (APEC), 2023, pp. 2299–2306. [6] T. Chen, R. Yu, and A. Q. Huang, “Variable-switching-frequency singlestage bidirectional gan ac–dc converter for the grid-tied battery energy storage system,” IEEE Transactions on Industrial Electronics, vol.69, no.11, pp.10776–10786, 2022. [7] R. De Doncker, D. Divan, and M. Kheraluwala, “A three-phase soft switched high-power- density dc / dc converter for high-power applications,” IEEE Transactions on Industry Applications, vol.27, no.1, pp.63–73, 1991. [8] C. Deng, P. Chavoshipour Heris, D. T. Nguyen, P. Saraf, and A. Hanson, “Design elements of a nonlinear decentralized control scheme for modular power conversion,” in 2022 IEEE Energy Conversion Congress and Exposition (ECCE), 2022, pp.1–7. [9] S. Liu, X. Zhao, Y. Wu, L. Zhou, Y. Li, R. Mai, and Z. He, “Efficiency improvement of dual-receiver wpt systems based on partial power processing control,” IEEE Transactions on Power Electronics, vol.37, no.6, pp.7456–7469, 2021.

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[0011] T. Chen, R. Yu, and A. Q. Huang, “A bidirectional isolated dual-phase shift variable- frequency series resonant dual-active-bridge gan ac-dc converter,” IEEE Transactions on Industrial Electronics, 2022.

[0012] H. Zou, R. Yu, R. Anand, J. Tong, and A. Q. Huang, “A gan variable frequency series resonant dual-active-bridge bidirectional ac-dc converter for battery energy storage system,” in 2023 IEEE Applied Power Electronics Conference and Exposition (APEC), 2023, pp.150–157.Attorney Docket No.10046-535WO1 8137 HUA

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[0016] M. Antivachis, D. Bortis, D. Menzi, and J. W. Kolar, “Comparative evaluation of y- inverter against three-phase two-stage buck-boost dc-ac converter systems,” in 2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), 2018, pp.181–189.

[0017] D. Menzi, J. E. Huber, L. Kappeler, G. Zulauf, and J. W. Kolar, “New return path inductor buck–boost y-inverter motor drive with reduced current stresses,” IEEE Transactions on Power Electronics, vol.37, no.9, pp.10086–10090, 2022.

[0018] D. Menzi, M. Zhang, J. W. Kolar, and J. Everts, “3-Φ bidirectional buck boost sinusoidal input current three-level sic y-rectifier,” in 2021 IEEE Applied Power Electronics Conference and Exposition (APEC), 2021, pp.590–598.

[0019] R. Baranwal, K. V. Iyer, K. Basu, G. F. Castelino, and N. Mohan, “A reduced switch count single-stage three-phase bidirectional rectifier with high-frequency isolation,” IEEE Transactions on Power Electronics, vol.33, no.11, pp.9520–9541, 2018.

[0020] D. Menzi, F. Krismer, T. Ohno, J. Huber, J. Kolar, and J. Everts, “Novel bidirectional single-stage isolated three-phase buck-boost pfc rectifier system,” in 2023 IEEE Applied Power Electronics Conference and Exposition (APEC), 2023, pp.1936–1944.

[0021] M. Zhang, Z. Chen, J. Tong, H. Zou, and A. Q. Huang, “A unified numerical modeling method for dual active bridge type converter,” in 2023 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, 2023.

[0022] A. Jerri, The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations, ser. Mathematics and Its Applications. Springer US, 1998. [Online]. Available: https: / / books.google.com / books?id=y2c00LAMnFUC

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Huang, “A gan variable-frequency series resonant dual-active-bridge bidirectional acdc converter for battery energy storage system,” in 2023 IEEE Applied Power Electronics Conference and Exposition (APEC), DOI 10.1109 / APEC43580.2023.10131248, pp.150–157, 2023. [8’] T.-T. Le, J. Lee, and S. Choi, “Single-stage totem-pole ac-dc converter based on boost half-bridge structure for battery chargers,” IEEE Transactions on Power Electronics, vol.39, DOI 10.1109 / TPEL.2023.3323946, no.1, pp.1060–1073, 2024. [9’] S. Zengin and M. Boztepe, “A novel current modulation method to eliminate low- frequency harmonics in single-stage dual active bridge ac-dc converter,” IEEE Transactions on Industrial Electronics, vol.67, DOI 10.1109 / TIE.2019.2898597, no.2, pp.1048–1058, 2020. [10’] M. Zhang, H. Zou, S. Farzamkia, Z. Chen, and A. Q. Huang, “New single-stage single- phase isolated bidirectional ac-dc pfc converter,” in 2024 IEEE Applied PowerAttorney Docket No.10046-535WO1 8137 HUA Electronics Conference and Exposition (APEC), DOI 10.1109 / APEC48139.2024.10509329, pp.1962–1967, 2024. [11’] D. Menzi, F. Krismer, T. Ohno, J. Huber, J. Kolar, and J. Everts, “Novel bidirectional single-stage isolated three-phase buck-boost pfc rectifier system,” in 2023 IEEE Applied Power Electronics Conference and Exposition (APEC), DOI 10.1109 / APEC43580.2023.10131553, pp.1936–1944, 2023. [12’] M. Zhang, “Github,” 2024. [Online]. Available: https: / / github.com / MafuZhang / YAB- Analyze-Tool / tree / main [13’] M. Antivachis, N. Kleynhans, and J. W. Kolar, “Three-phase sinusoidal output buck- boost gan y-inverter for advanced variable speed ac drives,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol.10, DOI 10.1109 / JESTPE.2020.3026742, no.3, pp.3459–3476, 2022. [14’] D. Menzi, A. Yang, S. Chhawchharia, S. Coday, and J. W. Kolar, “Novel three-phase electronic transformer,” IEEE Transactions on Power Electronics, vol.39, DOI 10.1109 / TPEL.2024.3366752, no.5, pp.5027–5033, 2024. [15’] M. Zhang, J. Tong, Z. Chen, and A. Q. Huang, “A unified numerical modeling method for dual active bridge type converter,” in 2023 IEEE Energy Conversion Congress and Exposition (ECCE), DOI 10.1109 / ECCE53617.2023.10362268, pp.3035–3041, 2023. [16’] F. Krismer and J. W. Kolar, “Closed form solution for minimum conduction loss modulation of dab converters,” IEEE Transactions on Power Electronics, vol.27, DOI 10.1109 / TPEL.2011.2157976, no.1, pp.174–188, 2012. [17’] R. Baranwal, K. V. Iyer, K. Basu, G. F. Castelino, and N. Mohan, “A reduced switch count single-stage three-phase bidirectional rectifier with high-frequency isolation,” IEEE Transactions on Power Electronics, vol.33, DOI 10.1109 / TPEL.2018.2790800, no.11, pp.9520–9541, 2018. [18’] L. Shu, W. Chen, M. Shi, R. Liu, S. Gao, and F. 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Claims

Attorney Docket No.10046-535WO1 8137 HUA WHAT IS CLAIMED IS:

1. A system comprising: a single-stage bidirectional isolated AC-DC converter comprising: a transformer comprising (i) a primary side having two or more terminals, including at least a first terminal and a second terminal and (ii) a secondary side having two or more terminals, including at least a third terminal and a fourth terminal; an AC module having an AC switching stage comprising at least a first switching bridge and a second switching bridge, each of the first switching bridge and second switching bridge having (i) a first connection to at least one AC source, (ii) a second connection to one other, and (iii) a third connection to the primary side of the transformer and configured to operate in a bridge configuration with a series-linked capacitor and the transformer to generate a first AC waveform in a first power flow direction at the primary side of the transformer, wherein the DC module is configured to generate a DC waveform from an AC waveform produced at the secondary side from the first AC waveform; and the DC module, the DC module having a DC switching stage comprising at least a third switching bridge and a fourth switching bridge having (i) a first connection to a DC source, (ii) a second connection to each other, and (iii) a third connection at its switching node to the secondary side of the transformer, the DC switching stage configured to switch a DC waveform of the DC source at the secondary side to provide a modulated waveform at the primary side to establish an AC waveform, in a second power flow direction, through the series-linked capacitor and the AC module.

2. The system of claim 2, wherein the first switching bridge and the second switching bridge of the AC module each comprises (i) a half-bridge and a blocking capacitor, (ii) a full bridge, or (iii) a half-bridge and two splitting capacitors.

3. The system of claim 1 or 2, wherein the third switching bridge and the fourth switching bridge of the DC module each comprises (i) a full bridge, (ii) a half-bridge, or (iii) a half bridge and two splitting capacitors.

4. The system of any one of claims 1-3, wherein the primary side has a first Y- configuration winding, and wherein the secondary side has a second Y-configuration winding.Attorney Docket No.10046-535WO1 8137 HUA 5. The system of any one of claims 1-3, wherein the primary side has a Y- configuration winding, wherein the second side has a non-Y wiring configuration, and wherein the first switching bridge and the second switching bridge of the AC module each comprise the half- bridge and the blocking capacitor.

6. The system of claim 5, wherein the (i) half-bridge and the blocking capacitor, (ii) full bridge, or (iii) half-bridge and the two splitting capacitors either comprises a set of two unidirectional switches or a set of two bidirectional switches.

7. The system of any one of claims 1-3, wherein the primary side has a Y- configuration winding, wherein the second side has a non-Y configuration winding, and wherein the wherein the first switching bridge and the second switching bridge of the AC module each comprises the half-bridge and the blocking capacitor.

8. The system of any one of claims 1-7, wherein for single phase operation the AC module is configured to bias one or more AC waveforms of the AC source to establish, via anti-paralleled diodes of the single AC switching stage to generate an AC waveform having a DC waveform component as the first AC waveform.

9. The system of any one of claims 1-7, wherein for three-phase operation, the AC module is configured to generate a modulated sinusoidal waveform as the first AC waveform.

10. The system of any one of claims 1-7, wherein for single phase operation, the single AC switching stage is configured to generate a high-frequency power flow and a low- frequency power flow, and wherein the series-link capacitor is configured to block the low- frequency power flow to provide low-frequency isolation between the AC module and the DC module.

11. The system of any one of claims 1-7, wherein the series-linked capacitor and the transformer, via leakage inductance of the transformer, are configured to collectively form a series-resonant circuit.

12. The system of any one of claims 1-7, wherein the series-linked capacitor and the transformer are configured to form a non-resonant circuit.Attorney Docket No.10046-535WO1 8137 HUA 13. The system of any one of claims 1-12, further comprising: a second single-stage bidirectional isolated AC-DC converter operatively connected in series to the single-stage bidirectional isolated AC-DC converter, as the first single-stage bidirectional isolated AC-DC converter, in a stack configuration, wherein (i) the AC module of the first single-stage bidirectional isolated AC-DC converter as a first AC module and (ii) a second AC module of the second single-stage bidirectional isolated AC-DC converter are each configured to receive a partial voltage of the AC source, and wherein components of the first AC module and the second AC module are rated for said partial voltage.

14. The system of any one of claims 1-12, further comprising: N-1 number of single-stage bidirectional isolated AC-DC converters operatively connected in series to each other and the single-stage bidirectional isolated AC-DC converter, as an Nth single-stage bidirectional isolated AC-DC converter, in a stack configuration, wherein AC modules of the N-1 and Nth single-stage bidirectional isolated AC-DC converters are each configured to receive a partial voltage of the AC source, and wherein components of the AC modules of the N-1 and Nth single-stage bidirectional isolated AC-DC converters are rated for said partial voltage.

15. The system of claim 13 or 14, wherein the second single-stage bidirectional isolated AC-DC converter includes: a second AC module having a single AC switching stage configured to operate in a half-bridge configuration with an input capacitor to bias one or more AC waveforms of the AC source to establish, via anti-paralleled diodes of the second AC module, in another first power flow direction, a common-mode DC potential to a second DC module linked through another series-linked capacitor and another transformer; and the second DC module having a single DC switching stage configured in a half-bridge configuration with another DC capacitor to switch the DC waveform of the DC source to the AC waveform, in a second power flow direction, through another series-linked capacitor, the another transformer, and the second AC module.

16. The system of claim 13 or 14, wherein the second single-stage bidirectional isolated AC-DC converter includes:Attorney Docket No.10046-535WO1 8137 HUA a second AC module having a single AC switching stage configured to operate in a half-bridge configuration with an input capacitor to bias one or more AC waveforms of the AC source to establish, via anti-paralleled diodes of the single AC switching stage, in another first power flow direction, a common-mode DC potential to the DC module linked through the series-linked capacitor and the transformer; and the DC module of the first single-stage bidirectional isolated AC-DC converter.

17. The system of any one of claims 13-16, wherein (i) the first AC module of the first single-stage bidirectional isolated AC-DC converter and (ii) the second AC module of the second single-stage bidirectional isolated AC-DC converter are coupled in series.

18. The system of any one of claims 13-16, wherein (i) the first AC module of the first single-stage bidirectional isolated AC-DC converter and (ii) the second AC module of the second single-stage bidirectional isolated AC-DC converter are coupled in a series, and (i) the DC module of the first single-stage bidirectional isolated AC-DC converter and (ii) the second DC module of the second single-stage bidirectional isolated AC-DC converter are coupled in parallel.

19. The system of claim 14, wherein the N single-stage bidirectional isolated AC-DC converters are identical.

20. The system of claim 14, wherein the N single-stage bidirectional isolated AC-DC converters are not identical.

21. The system of any one of claims 1-20, wherein the single AC switching stage includes, for each phase of the AC source, two switching elements configured with the anti- paralleled diodes.

22. The system of any one of claims 1-21, wherein the single DC switching stage includes, for each set of switching elements of the single AC switching stage, a corresponding set of switching elements.Attorney Docket No.10046-535WO1 8137 HUA 23. The system of any one of claims 1-22, wherein, for a 1-phase AC input or output, the transformer comprises a core and a winding structure having high-frequency four-winding single-phase transformer connected in between.

24. The system of any one of claims 1-22, wherein, for a 3-phase AC input or output, the transformer comprises a core and a winding structure having high frequency six-winding three-phase transformer connected in between.

25. A method comprising: providing a single-stage bidirectional isolated AC-DC converter of any one of claims 1-24; operating the single-stage bidirectional isolated AC-DC converter in the first power flow direction; and operating the single-stage bidirectional isolated AC-DC converter in the second power flow direction.

26. An electric vehicle charger having the single-stage bidirectional isolated AC-DC converter of any one of claims 1-24.

27. Electrical substation equipment having the single-stage bidirectional isolated AC-DC converter of any one of claims 1-24.

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