Device and method for a bidirectional and scalable multilevel converter

Abstract

A switched-capacitor cell for use in a bidirectional and scalable multilevel converter is provided. The switched-capacitor cell comprises: a first capacitor (Ca) connected between a first input node (A1) and a first cell node (A0); a 5 second capacitor (Cb) connected between the first cell node (A0) and a second input node (A2); a first unipolar bidirectional switch (Sc) connected between the first input node (A1) and a second cell node (B0); a second unipolar bidirectional switch (Sd) connected between the second cell node (B0) and the second input node (A2); a first bipolar switch (Sa) connected between the first 10 input node (A1) and a first output node (B1) of the first switched-capacitor cell; and a second bipolar switch (Sb) connected between the second input node (A2) and a second output node (B2) of the first switched-capacitor cell.

Description

TITLE: DEVICE AND METHOD FOR A BIDIRECTIONAL AND SCALABLE MULTILEVEL CONVERTERCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of United States Provisional Patent Application No. 63 / 568,860 filed March 22, 2024, and the entire contents of United States Provisional Patent Application No. 63 / 568,860 are hereby incorporated herein in its entirety.FIELD

[0002] Various embodiments are described herein that generally relate to a device and a method for a direct current (DC) - alternating current (AC) converter and in particular to a device and a method for a bidirectional and scalable multilevel DC-AC converter.BACKGROUND

[0003] The following paragraphs are provided by way of background to the present disclosure. They are not however an admission that anything discussed therein is prior art or part of the knowledge of a person of skill in the art.

[0004] Bidirectional multilevel converters can provide bidirectional power conversion between DC power and AC power. Bidirectional multilevel converters can be used for bidirectional power conversion between DC systems including renewable energy systems (e.g., photovoltaic systems, wind turbine systems, etc.), energy storage systems (e.g., batteries) etc. and AC systems (e.g., an electric utility grid, AC loads including motors etc.).

[0005] Bidirectional multilevel converters may be used in grid-tied or off-grid applications. Grid-tied converters are designed to match the frequency and voltage of the electrical grid to which they are connected. In contrast, off-grid converters do not adjust their AC output to match an interconnected grid, but rather produce power at a set voltage and frequency.

[0006] Performance metrics for bidirectional multilevel converters can include the maximum voltage gain (ratio of peak magnitude of AC output voltage to DC input voltage) and number of voltage levels for the AC outputvoltage. Higher values of maximum voltage gain and number of voltage levels may be desirable in many applications. For example, higher values of the maximum voltage gain can enable reduction in DC input voltage requirements corresponding to a desired AC output voltage, or an increase in the AC voltage magnitude for a given DC voltage level. As another example, higher values of the number of voltage levels for the AC output voltage can enable reduction in filtering requirements of the AC output voltage. This may reduce the weight, volume and / or cost associated with the filters.SUMMARY OF VARIOUS EMBODIMENTS

[0007] In a broad aspect, in accordance with the teachings herein, there is provided at least one embodiment of a switched-capacitor cell for use in a bidirectional and scalable multilevel converter. The switched-capacitor cell comprises: a first capacitor (Ca) connected between a first input node (A1) and a first cell node (AO); a second capacitor (Cb) connected between the first cell node (AO) and a second input node (A2); a first unipolar bidirectional switch (Sc) connected between the first input node (A1) and a second cell node (BO); a second unipolar bidirectional switch (Sd) connected between the second cell node (BO) and the second input node (A2); a first bipolar switch (Sa) connected between the first input node (A1) and a first output node (B1) of the first switched-capacitor cell; and a second bipolar switch (Sb) connected between the second input node (A2) and a second output node (B2) of the first switched- capacitor cell.

[0008] In another broad aspect, in accordance with the teachings herein, there is provided at least one embodiment of a bidirectional and scalable multilevel converter comprising a first switched-capacitor cell, a second switched capacitor cell, and a control system. A first output node (B1) of the first switched-capacitor cell is connected to a first input node (A1 ) of the second switched-capacitor cell; a second output node (B2) of the first switched- capacitor cell is connected to a second input node (A2) of the second switched- capacitor cell; and a second cell node (B0) of the first switched-capacitor cell is connected to a first cell node (A0) of the second switched-capacitor cell. Thecontrol system is configured to control switching of (i) a first unipolar bidirectional switch (Sc) and a second unipolar bidirectional switch (Sd) of each switched-capacitor cell, (ii) a first bipolar switch (Sa), and (iii) a second bipolar switch (Sb) to control a voltage gain and a number of voltage levels of an AC output voltage, wherein: an AC output for providing the AC output voltage is provided between a second cell node (BO) of the second switched-capacitor cell and a first cell node (AO) of the first switched-capacitor cell; and a voltage gain of the converter is defined with reference to a DC input voltage connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell.

[0009] In at least one embodiment, the control system may be configured to control the switching based on a first control mode, wherein a first capacitor and a second capacitor of each switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage, the AC output voltage of the first control mode having a maximum of five voltage levels and a maximum voltage gain of 1 .

[0010] In at least one embodiment, the control system may be configured to control the switching based on a second control mode, wherein: the first capacitor and the second capacitor of the first switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage; and the first capacitor and the second capacitor of the second switched-capacitor cell are charged to a voltage equal to the DC input voltage, the AC output voltage of the second control mode having a maximum of four voltage levels and a maximum voltage gain of 1.5.

[0011] In at least one embodiment, one or more of (i) the first unipolar bidirectional switch (Sc) and the second unipolar bidirectional switch (Sd) of each switched-capacitor cell, (ii) the first bipolar switch (Sa), and (iii) the second bipolar switch (Sb) may include semiconductor switching devices.

[0012] In at least one embodiment, the DC input voltage may be provided by a renewable energy source, an energy storage device, a DC link from a front-end converter, or a DC microgrid.

[0013] In at least one embodiment, the AC output may be connected to an electric utility grid or an AC load.

[0014] In at least one embodiment, the bidirectional and scalable multilevel converter may further comprise a filter connecting the AC output to the electric utility grid or the AC load.

[0015] In at least one embodiment, the filter may be a LCL filter.

[0016] In another broad aspect, in accordance with the teachings herein, there is provided at least one embodiment of a bidirectional and scalable multilevel converter comprising a series of switched-capacitor cells and a control system. The series of switched-capacitor cells includes a first switched- capacitor cell, one or more intermediate switched-capacitor cells and a terminal switched-capacitor cell. The series of switched-capacitor cells is formed by: connecting a first output node (B1 ) of the first switched-capacitor cell and each of the intermediate switched-capacitor cells to a first input node (A1) of a subsequent switched-capacitor cell in the series of switched-capacitor cells; connecting a second output node (B2) of the first switched-capacitor cell and each of the intermediate switched-capacitor cells to a second input node (A2) of the subsequent switched-capacitor cell in the series of switched-capacitor cells; and connecting a second cell node (B0) of the first switched-capacitor cell and each of the intermediate switched-capacitor cells to a first cell node (A0) of the subsequent switched-capacitor cell in the series of switched-capacitor cells. The control system is coupled to the series of switched-capacitor cells and is configured to control switching of a first unipolar bidirectional switch (Sc), a second unipolar bidirectional switch (Sd), a first bipolar switch (Sa), and a second bipolar switch (Sb) of each switched-capacitor cell to control a voltage gain and a number of voltage levels of an AC output voltage, wherein: an AC output for providing the AC output voltage is provided between the second cell node (B0) of the terminal switched-capacitor cell and the first cell node (A0) of the first switched-capacitor cell; and a voltage gain of the convertor is defined with reference to a DC input voltage connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell.

[0017] In at least one embodiment, the series of switched-capacitor cells may include a single intermediate switched-capacitor cell, and the control system may be configured to control the switching based on a first control mode, wherein a first capacitor and a second capacitor of each switched- capacitor cell are charged to a voltage of 0.5 times the DC input voltage, the AC output voltage of the first control mode having a maximum of seven voltage levels and a maximum voltage gain of 1 .5.

[0018] In at least one embodiment, the series of switched-capacitor cells may include a single intermediate switched-capacitor cell, and the control system may be configured to control the switching based on a second control mode, wherein: a first capacitor and a second capacitor of the first switched- capacitor cell are charged to a voltage of 0.5 times the DC input voltage; a first capacitor and a second capacitor of the single intermediate switched-capacitor cell are charged to a voltage equal to the DC input voltage; and a first capacitor and a second capacitor of the terminal switched-capacitor cell are charged to a voltage equal to twice the DC input voltage, and the AC output voltage during the second control mode has a maximum of eight voltage levels and a maximum voltage gain of 3.5.

[0019] In at least one embodiment, one or more of (i) the first unipolar bidirectional switch (Sc), (ii) the second unipolar bidirectional switch (Sd), (iii) the first bipolar switch (Sa), and (iv) the second bipolar switch (Sb) of each switched-capacitor cell may include semiconductor switching devices.

[0020] In at least one embodiment, the DC input voltage may be provided by a renewable energy source, an energy storage device, a DC link from a front-end converter, or a DC microgrid.

[0021] In at least one embodiment, the AC output voltage may be connected to an electric utility grid or an AC load.

[0022] In at least one embodiment, the bidirectional and scalable multilevel converter may further comprise a filter connecting the AC output of the converter to the electric utility grid or the AC load.

[0023] In at least one embodiment, the filter may be a LCL filter.

[0024] In another broad aspect, in accordance with the teachings herein, there is provided at least one embodiment of a method of controlling a voltage gain and a number of voltage levels of an AC output voltage of a bidirectional and scalable multilevel converter comprising a control system and a series of switched-capacitor cells including a first switched-capacitor cell and a terminal switched-capacitor cell. The method comprises: connecting the series of switched-capacitor cells formed by: connecting a first output node (B1) of the first switched-capacitor cell to a first input node (A1 ) of a subsequent switched- capacitor cell in the series of switched-capacitor cells; connecting a second output node (B2) of the first switched-capacitor cell to a second input node (A2) of the subsequent switched-capacitor cell in the series of switched-capacitor cells; and connecting a second cell node (BO) of the first switched-capacitor cell to a first cell node (AO) of the subsequently switched-capacitor cell in the series of switched-capacitor cells; and selecting a control mode of operation for the control system to control switching of the first unipolar bidirectional switch (Sc), the second unipolar bidirectional switch (Sd), the first bipolar switch (Sa), and the second bipolar switch (Sb) of each switched-capacitor cell, wherein: an AC output for providing an AC output voltage is between the second cell node (BO) of the terminal switched-capacitor cell and the first cell node (AO) of the first switched-capacitor cell; and the voltage gain is defined with reference to a DC input voltage connected between the first input node (A1 ) and the second input node (A2) of the first switched-capacitor cell.

[0025] In at least one embodiment, the series of switched-capacitor cells may further include one or more intermediate switched-capacitor cells, wherein the method further comprises: selecting a number of the intermediate switched- capacitor cells; and connecting the series of switched-capacitor cells formed by: connecting a first output node (B1) of each of the intermediate switched- capacitor cells to a first input node (A1 ) of a subsequent switched-capacitor cell in the series of switched-capacitor cells; connecting a second output node (B2) of each of the intermediate switched-capacitor cells to a second input node (A2)of the subsequent switched-capacitor cell in the series of switched-capacitor cells; and connecting a second cell node (BO) of each of the intermediate switched-capacitor cells to a first cell node (AO) of the subsequently switched- capacitor cell in the series of switched-capacitor cells.

[0026] In at least one embodiment, the series of switched-capacitor cells may include two or more intermediate switched-capacitor cells, and the method may comprise controlling the switching based on a first control mode, wherein a first capacitor and a second capacitor of each switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage, and the AC output voltage during the first control mode has a maximum number of voltage levels greater than seven and there is a maximum voltage gain greater than 1 .5.

[0027] In at least one embodiment, the series of switched-capacitor cells may include two or more intermediate switched-capacitor cells, and the method may comprise controlling the switching based on a second control mode, wherein: a first capacitor and a second capacitor of the first switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage; a first capacitor and a second capacitor of each intermediate switched-capacitor cell and the terminal switched-capacitor cell are charged to a voltage equal to twice the voltage of the first capacitor and a second capacitor of corresponding previous switched-capacitor cell, and the AC output voltage of the second control mode has a maximum number of voltage levels greater than eight and a maximum voltage gain that is greater than 3.5.

[0028] In at least one embodiment, the method may comprise obtaining the DC input voltage from a renewable energy source, an energy storage device, a DC link from a front-end converter, or a DC microgrid.

[0029] In at least one embodiment, the method may comprise coupling the AC output to an electric utility grid or an AC load.

[0030] In at least one embodiment, the method may comprise connecting a filter between the AC output of the converter and the electric utility grid or the AC load.

[0031] In another broad aspect, in accordance with the teachings herein, there is provided at least one embodiment of a multi-phase bidirectional and scalable multilevel converter comprising multiple series of switched-capacitor cells and a control system that is coupled to the multiple series of switched- capacitor cells. Each series of switched-capacitor cells includes a first switched- capacitor cell and a terminal switched-capacitor cell. Each series of switched- capacitor cells is formed by: connecting a first output node (B1 ) of the first switched-capacitor cell to a first input node (A1 ) of a subsequent switched- capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of the first switched-capacitor cell to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched-capacitor cells; and connecting a second cell node (BO) of the first switched-capacitor cell to a first cell node (AO) of the subsequent switched-capacitor cell in that series of switched-capacitor cells. The control system is configured to control switching of the first unipolar bidirectional switch (Sc), the second unipolar bidirectional switch (Sd), the first bipolar switch (Sa), and the second bipolar switch (Sb) of each switched-capacitor cell to control a voltage gain and a number of voltage levels of a multi-phase AC output voltage, wherein each phase of the multi-phase AC output voltage is provided by the second cell node (BO) of the terminal switched-capacitor cell of a corresponding series of switched-capacitor cells; and wherein the voltage gain is defined with reference to a DC input voltage that is connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell of each series of switched-capacitor cells.

[0032] In at least one embodiment, each series of switched-capacitor cells may include one or more intermediate switched-capacitor cells, and each series of switched-capacitor cells may be formed by: connecting a first output node (B1) of each of the intermediate switched-capacitor cells to a first input node (A1 ) of a subsequent switched-capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of each of the intermediate switched-capacitor cells to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched-capacitor cells; andconnecting a second cell node (BO) of each of the intermediate switched- capacitor cells to a first cell node (AO) of the subsequent switched-capacitor cell in that series of switched-capacitor cells.

[0033] In another broad aspect, in accordance with the teachings herein, there is provided at least one embodiment of a method of controlling a voltage gain and a number of voltage levels of a multi-phase AC output voltage of a multi-phase bidirectional and scalable multilevel converter comprising a control system and multiple series of switched-capacitor cells. Each series of switched- capacitor cells includes a first switched-capacitor cell and a terminal switched- capacitor cell. The method comprises: forming each series of switched- capacitor cells by: connecting a first output node (B1) of the first switched- capacitor cell to a first input node (A1 ) of a subsequent switched-capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of the first switched-capacitor cell to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched-capacitor cells; and connecting a second cell node (BO) of the first switched-capacitor cell to a first cell node (AO) of the subsequently switched-capacitor cell in that series of switched-capacitor cells; and selecting a control mode of operation for configuring the control system to control switching of the first unipolar bidirectional switch (Sc), the second unipolar bidirectional switch (Sd), the first bipolar switch (Sa), and the second bipolar switch (Sb) of each switched- capacitor cell, wherein each phase of the multi-phase AC output voltage is provided by the second cell node (BO) of the terminal switched-capacitor cell of a corresponding series of switched-capacitor cells; and wherein the voltage gain is defined with reference to a DC input voltage that is connected between the first input node (A1) and the second input node (A2) of the first switched- capacitor cell of each series of switched-capacitor cells.

[0034] In at least one embodiment, each series of switched-capacitor cells may further include one or more intermediate switched-capacitor cells, wherein the method may comprise: selecting a number of intermediate switched- capacitor cells; and forming each series of switched-capacitor cells by:connecting a first output node (B1) of each of the intermediate switched- capacitor cells to a first input node (A1 ) of a subsequent switched-capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of each of the intermediate switched-capacitor cells to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched-capacitor cells; and connecting a second cell node (BO) of each of the intermediate switched-capacitor cells to a first cell node (AO) of the subsequently switched- capacitor cell in that series of switched-capacitor cells.

[0035] Other features and advantages of the present application will become apparent from the following detailed description taken together with the accompanying drawings. It should be understood, however, that the detailed description and the specific examples, while indicating preferred embodiments of the application, are given by way of illustration only, since various changes and modifications within the spirit and scope of the application will become apparent to those skilled in the art from this detailed description.BRIEF DESCRIPTION OF THE DRAWINGS

[0036] For a better understanding of the various embodiments described herein, and to show more clearly how these various embodiments may be carried into effect, reference will be made, by way of example, to the accompanying drawings which show at least one example embodiment, and which are now described. The drawings are not intended to limit the scope of the teachings described herein.

[0037] FIG. 1 shows a schematic diagram of an example embodiment of a bidirectional and scalable multilevel converter, in accordance with the teachings provided herein.

[0038] FIG. 2A shows a schematic circuit diagram of an example switched- capacitor cell of the bidirectional and scalable multilevel converter of FIG. 1.

[0039] FIG. 2B shows a schematic circuit diagram of an example unidirectional bipolar switch of the bidirectional and scalable multilevel converter of FIG. 1.

[0040] FIG. 2C shows a schematic circuit diagram of an example bidirectional bipolar switch of the bidirectional and scalable multilevel converter of FIG. 1.

[0041] FIG. 3 shows a schematic circuit diagram of an example embodiment of the bidirectional and scalable multilevel converter of FIG. 1 that includes two switched-capacitor cells.

[0042] FIG. 4A shows a schematic diagram of charging levels of capacitors of the bidirectional and scalable multilevel converter of FIG. 1 using a first control mode, in accordance with the teachings provided herein.

[0043] FIG. 4B shows a schematic diagram of charging levels of capacitors of the bidirectional and scalable multilevel converter of FIG. 1 using a second control mode, in accordance with the teachings provided herein.

[0044] FIG. 5A shows an example graph of the modulating signal and carrier signals that can be used to generate switch control signals for the bidirectional and scalable multilevel converter of FIG. 3 in an example implementation of the first control mode of FIG. 4A, in accordance with the teachings provided herein.

[0045] FIG. 5B shows an example graph of the modulating signal, carrier signal and switch control signals for the bidirectional and scalable multilevel converter of FIG. 3 in another example implementation of the first control mode of FIG. 4A, in accordance with the teachings provided herein.

[0046] FIGS. 5C and 5D show example voltage and current waveforms measured for the example embodiment of the bidirectional and scalable multilevel converter of FIG. 3 and using the switch control signals of FIG. 5B.

[0047] FIG. 6A shows an example graph of the modulating signal and carrier signals that can be used to generate switch control signals for the bidirectional and scalable multilevel converter of FIG. 3 in an example implementation of the second control mode of FIG. 4B, in accordance with the teachings provided herein.

[0048] FIG. 6B shows an example graph of the modulating signal, carrier signal and switch control signals for the bidirectional and scalable multilevel converter of FIG. 3 in another example implementation of the second control mode of FIG. 4B, in accordance with the teachings provided herein.

[0049] FIGS. 6C and 6D show example voltage and current waveforms measured for the example embodiment of the bidirectional and scalable multilevel converter of FIG. 3 and using the switch control signals of FIG. 6B.

[0050] FIG. 7 shows a schematic circuit diagram of an example embodiment of the bidirectional and scalable multilevel converter of FIG. 1 that includes three switched-capacitor cells.

[0051] FIGS. 8A and 8B show example voltage and current waveforms measured for the example embodiment of the bidirectional and scalable multilevel converter of FIG. 7 and using an example implementation of the first control mode of FIG. 4A to control the switches of the converter.

[0052] FIGS. 9A and 9B show example voltage and current waveforms measured for the example embodiment of the bidirectional and scalable multilevel converter of FIG. 7 and using an example implementation of the second control mode of FIG. 4B to control the switches of the converter.

[0053] FIG. 10 shows example efficiency and voltage total harmonic distortions (THD) curves measured for various embodiments and control modes of the bidirectional and scalable multilevel converter of FIG. 1.

[0054] FIG. 11 shows a schematic diagram of another example embodiment of a bidirectional and scalable multilevel converter, in accordance with the teachings provided herein.

[0055] Further aspects and features of the example embodiments described herein will appear from the following description taken together with the accompanying drawings.DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] The headings and Abstract of the Disclosure provided herein are for convenience only and do not interpret the scope or meaning of the embodiments.

[0057] Various embodiments in accordance with the teachings herein will be described below to provide an example of at least one embodiment of the claimed subject matter. No embodiment described herein limits any claimed subject matter. The claimed subject matter is not limited to devices, systems or methods having all of the features of any one of the devices, systems or methods described below or to features common to multiple or all of the devices, systems or methods described herein. It is possible that there may be a device, system or method described herein that is not an embodiment of any claimed subject matter. Any subject matter that is described herein that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim or dedicate to the public any such subject matter by its disclosure in this document.

[0058] Furthermore, it will be appreciated that for simplicity and clarity of illustration, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements. In addition, numerous specific details are set forth in order to provide a thorough understanding of the embodiments described herein. However, it will be understood by those of ordinary skill in the art that the embodiments described herein may be practiced without these specific details. In other instances, well- known methods, procedures and components have not been described in detail so as not to obscure the embodiments described herein. Also, the description is not to be considered as limiting the scope of the embodiments described herein.

[0059] It should also be noted that the terms “coupled” or “coupling” as used herein can have several different meanings depending on the context in which these terms are used. For example, the terms coupled or coupling can have a mechanical or electrical connotation. For example, as used herein, the termscoupled or coupling can indicate that two elements or devices can be directly connected to one another or connected to one another through one or more intermediate elements or devices via an electrical signal, electrical connection, or a mechanical element, depending on the particular context.

[0060] Unless the context requires otherwise, throughout the specification and claims which follow, the word “comprise” and variations thereof, such as, “comprises” and “comprising” are to be construed in an open, inclusive sense, that is, as “including, but not limited to”.

[0061] It should also be noted that, as used herein, the wording “and / or” is intended to represent an inclusive-or. That is, “X and / or Y” is intended to mean X or Y or both, for example. As a further example, “X, Y, and / or Z” is intended to mean X or Y or Z or any operable combination thereof. Accordingly, the term “any combination thereof” is meant to cover any operable combination of the elements which precede the phrase. For example, the phrase “A, B, C, D or any combination thereof” includes A; B; C; D; A and B; A and C; A and D; B and C; B and D; C and D; A, B and C; A, B and D; A, C and D; B, C and D as well as A, B, C and D assuming that all such combinations are operable (i.e., they can be used together in practice in a working embodiment).

[0062] It should be noted that terms of degree such as "substantially", "about" and "approximately" as used herein mean a reasonable amount of deviation of the modified term such that the end result is not significantly changed. These terms of degree may also be construed as including a deviation of the modified term, such as by ±1 %, ±2%, ±5% or ±10%, for example, if this deviation does not negate the meaning of the term it modifies.

[0063] Furthermore, the recitation of numerical ranges by endpoints herein includes all numbers and fractions subsumed within that range (e.g., 1 to 5 includes 1 , 1.5, 2, 2.75, 3, 3.90, 4, and 5). It is also to be understood that all numbers and fractions thereof are presumed to be modified by the term "about" which means a variation of up to a certain amount of the number to which reference is being made if the end result is not significantly changed, such as ±1 %, ±2%, ±5%, or ±10%, for example.

[0064] Reference throughout this specification to “one embodiment”, “an embodiment”, “at least one embodiment” or “some embodiments” means that one or more particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, unless otherwise specified to be not combinable or to be alternative options.

[0065] As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. It should also be noted that the term “or” is generally employed in its broadest sense, that is, as meaning “and / or” unless the content clearly dictates otherwise.

[0066] In addition, at least a portion of the example embodiments of the systems, devices or methods described in accordance with the teachings herein may be implemented as a combination of hardware or software. For example, a portion of the embodiments described herein may be implemented, at least in part, by using hardware that includes logic gates and / or integrated circuits. As another example, a portion of the embodiments described herein may be implemented, at least in part, by using one or more computer programs, executing on one or more programmable devices comprising at least one processing element, and at least one data storage element (including volatile and non-volatile memory). These devices may also have at least one input device (e.g., a keyboard, a mouse, a touchscreen, other input elements or any operable combination thereof) and at least one output device (e.g., a display screen, a printer, a wireless radio, other output elements or any operable combination thereof) depending on the type of device. For example, a portion of the embodiments described herein may be implemented, at least in part, by using an application executing on a mobile device.

[0067] It should also be noted that some elements that are used to implement at least part of the embodiments described herein may be implemented via software that is written in a high-level procedural language such as object-oriented programming. The program code may be written in, for example, JAVA, PYTHON, C, C++, Javascript, or in any other suitableprogramming language and may comprise modules or classes, as is known to those skilled in object-oriented programming. Alternatively, or in addition thereto, some of these elements implemented via software may be written in assembly language, machine language, or firmware as needed. For example, some of these elements may be implemented by programming a field- programmable gate array (FPGA) and / or a programmable logic device (PLD).

[0068] At least some of the software programs used to implement at least one of the embodiments described herein may be stored on a storage media or a device that is readable by a general or special purpose programmable device. The software program code, when read by the programmable device, configures the programmable device to operate in a new, specific and predefined manner in order to perform at least one of the methods described herein.

[0069] Furthermore, at least some of the programs associated with the systems and methods of the embodiments described herein may be capable of being distributed in a computer program product comprising a computer readable medium that bears computer usable instructions, such as program code, for one or more processors. The program code may be preinstalled and embedded during manufacture and / or may be later installed as an update for an already deployed computing system. The medium may be provided in various forms, including non-transitory forms such as, but not limited to, one or more diskettes, compact disks, DVD, tapes, chips, and magnetic, optical and electronic storage. In alternative embodiments, the medium may be transitory in nature such as, but not limited to, wire-line transmissions, satellite transmissions, internet transmissions (e.g., downloads), media, digital and analog signals, and the like. The computer usable instructions may also be in various formats, including compiled and non-compiled code.

[0070] Accordingly, any device described herein that executes software instructions may include or otherwise have access to computer readable media such as storage media, computer storage media, or data storage devices (removable and / or non-removable) such as, for example, magnetic disks,optical disks, or tape. Computer storage media may include volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information, such as computer readable instructions, data structures, program modules, or other data. Examples of computer storage media include RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information, and which can be accessed by an application, module, or both. Any such computer storage media may be part of the device or accessible or connectable thereto.

[0071] The disclosed bidirectional and scalable multilevel converter embodiments described herein may provide a modular and scalable structure. For example, the disclosed bidirectional and scalable multilevel converter may include one or more switched-capacitor cells. In some embodiments, the converter includes multiple switched-capacitor cells and at least two or more of the multiple switched-capacitor cells may be identical or substantially similar.

[0072] The converter may be easily scalable by selecting the number of switched-capacitor cells. For example, the number of switched-capacitor cells may be selected based on the converter design requirements, e.g., based on the desired maximum voltage gain and / or number of voltage levels. Higher number of switched-capacitor cells may be used for higher maximum voltage gain and / or higher number of voltage levels. Lower number of switched- capacitor cells may be used for lower control complexity and / or lower cost. The modularity of the converter including two or more identical switched-capacitor cells may also enable easier replacement / repair. The switched-capacitor cells may not include any inductors and provide high efficiencies (e.g., >97%) and high power densities.

[0073] The disclosed bidirectional and scalable multilevel converter embodiments can provide bidirectional DC-AC power transfer. For example, at least one of the converters described herein can provide power transferbetween any suitable DC system, grid, network, source or load and any suitable AC system, grid, network, source or load. At least one of the embodiments of the disclosed bidirectional and scalable multilevel converters described herein may be used in applications such as grid-connected renewable energy systems, vehicle-to-grid (V2G) systems and battery energy storage systems (BESS) where bi-directional power transfer capability is required. Furthermore, at least one of the embodiments of the disclosed bidirectional and scalable multilevel converters described herein may be used as a DC-AC converter for voltage and / or frequency control, supplying single or three-phase loads in railway systems, HVAC systems, photovoltaic systems, and single-stage small wind energy systems.

[0074] The disclosed bidirectional and scalable multilevel converter may include multiple control modes in various embodiments. The multiple control modes can enable different number of output voltage levels and / or maximum voltage gains for a given number of switched-capacitor cells by controlling the switching devices of the switched-capacitor cells of the converter. This can provide greater operational flexibility when the converter is in use. For example, a first control mode of a converter having two switched-capacitor cells may provide a maximum voltage gain of 1 and five output voltage levels. A second control mode for the same converter may provide a maximum voltage gain of 1 .5 and four output voltage levels. As another example, a first control mode of an converter having three switched-capacitor cells may provide a maximum voltage gain of 1 .5 and seven output voltage levels. A second control mode for the same converter may provide a maximum voltage gain of 3.5 and eight output voltage levels.

[0075] Other converters may use multiple stages to compensate for low maximum voltage gains, for example, using a first DC-DC boost-type converter stage to raise the input DC voltage for a second DC-AC converter stage. However, the additional circuit components for the multiple stages of conventional converters can increase the cost, weight, and / or volume of the converter. In contrast, the disclosed bidirectional and scalable multilevelconverter embodiments described herein can be implemented to reduce the number of required circuit components. For example, a converter having two switched-capacitor cells may include four capacitors and six to eight switching devices (based on the switching device implementation used for the first and second bipolar switches of the converter). As another example, a converter having three switched-capacitor cells may include six capacitors and ten to fourteen switching devices (based on the switching device implementation used for the first and second bipolar switches of the converter).

[0076] In at least one embodiment, the disclosed bidirectional and scalable multilevel converter described herein may have a symmetrical topology that can enable easier control compared with asymmetrical common-grounded topologies. In at least one embodiment, the disclosed converter described herein may include a grounded DC-side midpoint structure that generates low levels of leakage current.

[0077] In at least one embodiment, the disclosed bidirectional and scalable multilevel converter may not require any inductors (except for filtering the AC output voltage). This can enable reduction in weight, volume, and / or cost of the converter.

[0078] It should be noted that the term converter is used herein to refer generally to all power processors, which may work as an inverter or a rectifier. By virtue of being bidirectional, the converters described herein can function as an inverter or rectifier, depending on the direction of the power flow.

[0079] Referring first to FIG. 1 , shown therein is a schematic diagram of an example embodiment of a bidirectional and scalable multilevel converter 100. Converter 100 may include a cell topology 110, a control system 120, a filter 130, a DC input connector 140 and an AC output connector 150.

[0080] DC input connector 140 may be connected to any suitable DC system, grid, network, source and / or load including, but not limited to, output DC network of a renewable energy generation system, DC loads (e.g., electric vehicles, data centers, LED lighting), energy storage devices (e.g., batteries) etc. AC output connector 150 may be connected to any suitable AC system,grid, network, source, and / or load, including, but not limited to, AC utility grids, AC auxiliary loads in rail vehicles (to feed auxiliary services of locomotives and coaches, for example, passenger information systems, low power sockets), etc.

[0081] Cell topology 110 may include any suitable number of switched- capacitor cells 160. The number of switched-capacitor cells 160 for converter 100 may be selected based on desired maximum voltage gain and / or number of output voltage levels. For example, cell topology 110 may include 1 to 4 switched-capacitor cells based on the maximum voltage gain and / or number of output voltage levels requirements. In other examples, cell topology may include greater than 4 switched-capacitor cells. A larger number of switched- capacitor cells may provide larger voltage gains and / or larger number of output voltage levels. A larger number of switched-capacitor cells may increase the cost and / or control complexity of converter 100.

[0082] Referring now to FIG. 2A, shown therein a schematic circuit diagram of an example switched-capacitor cell 160. Switched-capacitor cell 160 may include a first capacitor 235, a second capacitor 240, a first unipolar, bidirectional switch 245, and a second unipolar bidirectional switch 250. First capacitor 235 may be connected between a first input node 205 and a first cell node 210. Second capacitor 240 may be connected between first cell node 210 and a second input node 215. First unipolar bidirectional switch 245 may be connected between first input node 205 and a second cell node 225. Second unipolar bidirectional switch 250 may be connected between second cell node 225 and second input node 215. Unipolar bidirectional switches 245 and 250 may be implemented using any suitable switches that provide unipolar voltage polarity applied across the switch and support a bidirectional current through the switch. In some embodiments, unipolar bidirectional switches 245 and / or 250 may be implemented using semiconductor switching devices (e.g., IGBTs, MOSFETs, etc.). Switched-capacitor cell 160, operating as a single cell, can operate as a half-bridge converter.

[0083] Bipolar switches 255 and 260 may connect switched-capacitor cell 160 to other switched-capacitor cells. Bipolar switch 255 may be connectedbetween first input node 205 and a first output node 220. Bipolar switch 260 may be connected between second input node 215 and a second output node 230.

[0084] Bipolar switches 255 and 260 may be unidirectional or bidirectional switches. In some embodiments, bipolar switches 255 and / or 260 may be implemented using semiconductor switching devices (e.g., diodes, IGBTs, MOSFETs, etc.). Any suitable configuration of the semiconductor switching devices may be used to implement bipolar switches 255 and 260. For example, FIG. 2B shows an example unidirectional bipolar switch 255a and FIG. 2C shows an example bidirectional bipolar switch 255b. In other examples, bipolar switch 255 and / or 260 may be implemented using a suitable monolithic switching device. This may provide an advantage by reducing the total number of switches to be controlled during converter operation.

[0085] In some embodiments, bipolar switches 255 and 260 may be used to connect a first switched-capacitor cell 160a to a second switched-capacitor cell 160b. Referring now to FIG. 3, shown therein is a schematic circuit diagram of an example cell topology 110a that includes a first switched-capacitor cell 160a connected to a second switched-capacitor cell 160b.

[0086] First switched-capacitor cell 160a may include a first capacitor 235a, a second capacitor 240a, a first unipolar bidirectional switch 245a, and a second unipolar bidirectional switch 250a. Second switched-capacitor cell 160b may include a first capacitor 235b, a second capacitor 240b, a first unipolar bidirectional switch 245b, and a second unipolar bidirectional switch 250b.

[0087] First output node 220a of first switched-capacitor cell 160a may be connected to first input node 205b of second switched-capacitor cell 160b. Second output node 230a of first switched-capacitor cell 160a may be connected to second input node 215b of second switched-capacitor cell 160b. Second cell node 225a of first switched-capacitor cell 160a may be connected to first cell node 210b of second switched-capacitor cell 160b.

[0088] Bipolar switch 255 may be connected between first input node 205a and first output node 220a of first switched-capacitor cell 160a. Bipolar switch 260 may be connected between second input node 215a and second output node 230a of first switched-capacitor cell 160a.

[0089] A DC input voltage 305 (Vdc) may be connected between first input node 205a and second input node 215a of first switched-capacitor cell 160a. An unfiltered AC output voltage may be provided between second cell node 225b of second switched-capacitor cell 160b and first cell node 210a of first switched-capacitor cell 160a. In some embodiments, first cell node 210a may be connected to electrical ground to provide a path for leakage currents.

[0090] A control system (e.g., control system 120 shown in FIG. 1) may be configured to control switching of unipolar bidirectional switches 245a, 250a, 245b, 250b and bipolar switches 255, 260 to control a voltage gain and a number of voltage levels of the unfiltered AC output voltage. In some embodiments, the control system may control the switching based on a first control mode or a second control mode. First capacitor 235a and second capacitor 240a may correspond to an input capacitor topology with a dc-side mid-point connection, and each of first capacitor 235a and second capacitor 240a may be charged to a voltage of VdC / 2.

[0091] In the first control mode, the control system may control the switching to charge first capacitor 235b and second capacitor 240b of second switched- capacitor cell 160b to the same voltage of VdC / 2. In the second control mode, the control system may control the switching to charge each capacitor 235b and 240b of second switched-capacitor cell 160b using both capacitors 235a and 240a of first switched-capacitor cell 160a associated in series. In the second control mode, each capacitor 235b and 240b of second switched- capacitor cell 160b may be charged to voltage of VdC.

[0092] The control modes may be similarly implemented for converters having cell topologies including more than two switched-capacitor cells. Referring now to FIGS. 4A and 4B, shown therein are schematic diagrams of charging levels of capacitors of converter 100 having cell topologies includingn number of switched-capacitor cells. FIG. 4A shows the capacitor charging levels using the first control mode and FIG. 4B shows the capacitor charging levels using the second control mode.

[0093] As shown in FIG. 4A, using the first control mode, capacitors 235 and 240 of each switched-capacitor cell 160a-160n may be charged to the same voltage of VdC / 2. As shown in FIG. 4B, using the second control mode, capacitors 235a and 240a of first switched-capacitor cell 160a may be associated in series to charge each capacitor 235b and 240b of second switched-capacitor cell 160b to a voltage of VdC. Similarly, capacitors 235b and 240b of second switched-capacitor cell 160b may be associated in series to charge each capacitor 235c and 240c of third switched-capacitor cell 160c to a voltage of 2VdC. For a converter 100 having n number of switched-capacitor cells 160, the capacitors 235n and 240n of the nthswitched-capacitor cell may be charged to a voltage of (2n'2)VdC.

[0094] Referring now to FIGS. 1 and 3, cell topology 110a may provide an unfiltered AC output voltage (Vinv) having a maximum of five output voltage levels when control system 120 controls the switches of cell topology 110a using the first control mode. Table I provides a summary of Vinvlevels, the corresponding topological states A5-F5, and states of switches 255 (Si), 245b (S2), 250b (S3), 260 (S4), 245a (S5), and 250a (Se) of cell topology 110a using the first control mode. In the first control mode, peak output voltage of cell topology 110a can be Vdc providing a maximum voltage gain of 1 .TABLE I - Output voltage, corresponding topological states and switch states of cell topology 110a using the first control mode.

[0095] Any suitable method may be used to control the timing of change in topological states and switch states to generate the AC output voltage. In some embodiments, control system 120 may use pulse width modulation (PWM) of one or more carrier signals to generate corresponding switch control signals for switches 255 (Si), 245b (S2), 250b (S3), 260 (S4), 245a (S5), and 250a (S6).

[0096] Reference is now made to FIGS. 5A and 5B. FIG. 5A shows example graphs of the carrier and modulating signals that can be used to generate switch control signals for cell topology 110a in an example implementation of the first control mode. FIG. 5B shows example graphs of the modulating signal, carrier signal and switch control signals for cell topology 110a in another example implementation of the first control mode. In the first control mode, the AC output voltage may have five voltage levels that correspond to four regions l-IV. FIG. 5A shows a modulating signal 505 (M sin(cot), where M corresponds to maximum voltage gain of 1) and four carrier signals 510a-510d corresponding to the four regions l-IV.

[0097] In some embodiments, a single carrier signal may be used to generate the switch control signals. This may reduce complexity of control system 120. FIG. 5B shows a modulating signal 515 and a single carrier 520 that may be used to generate switch control signal 525a (v5) and complementary switch control signal 525b (i^). Table II provides a summary of the regions l-IV, the corresponding topological states and switch control signals provided to switches 255 (Si), 245b (S2), 250b (S3), 260 (S4), 245a (S5), and 250a (Se). As summarized in Table II, in each region, a switch may be always On, always Off, or switched between On and Off states based on switch control signal 525a (v5) or 525b (v^).TABLE II - Switch control signal applied to the switches of cell topology 110a for each region l-IV using the first control mode.„ T. States M sin cot Switch state e^' Involved Interval Si S2 S3 S4 S-- Sg

[0098] Reference is now made to FIGS. 3, 5C and 5D. FIGS. 5C and 5D show example voltage and current waveforms measured for a converter 100 (FIG. 1 ) including cell topology 110a and using the first control mode to control the switches. Table III summarizes the design specifications used during the measurements. For the illustrated example, the measurements were conducted for a control system 120 (FIG. 1 ) including a microcontroller STM32F303RE (NUCLEO-F303RE board) and the filter 130 including an LCL filter having an inductor 197C10 (1 mH / 10A) and a capacitor B32656T7394K000 (0.39pF / 500V). In other example embodiments, any other suitable implementation of control system 120 and / or filter 130 may be used (e.g., other microcontrollers, other inductors and / or capacitors, other types of filters etc.).TABLE III - Design specifications.Symbol Description ValueVdc DC input voltage 400 VVoOutput voltage (RMS) 220 VPoOutput power 1 kW fsSwitching frequency 42 kHz foOutput voltage frequency 60 Hz

[0099] FIG. 5C shows example graphs of unfiltered output voltage 530 (Vjnv) of cell topology 110a, filtered AC output voltage 535 (Vo) of converter 100 and AC output current 540 (i0) of converter 100. FIG. 5D shows example graphs of voltages 545a (Vci), 545b (Vc2), 545c (Vcs), and 545d (Vc4) across capacitors 235b (Ci), 240b (C2), 235a (C3), and 240a (C4) respectively of cell topology 110a. The voltages 545a, 545b, 545c, and 545d are measured with reference to ground voltage levels 550a, 550b, 550c, and 550d respectively. In the first control mode, voltages across each capacitor 235b (Ci), 240b (C2), 235a (C3), and 240a (C4) is equal (-200V). The voltages 545b (Vc2) and 545d (Vc4) appear negative because the node voltages were measured with respect to the midpoint 210 (Ao) of each switched-capacitor cell 160.

[0100] Referring back to FIGS. 1 and 3, cell topology 110a may provide an unfiltered AC output voltage (Vjnv) having four output voltage levels whencontrol system 120 controls the switches of cell topology 110a using the second control mode. Table IV provides a summary ofnvlevels, the corresponding topological states A4-D4, and states of switches 255 (Si ), 245b (S2), 250b (S3), 260 (S4), 245a (S5), and 250a (Se) of cell topology 110a using the second control mode. In the second control mode, peak output voltage of cell topology 110a can be 1 ,5VdCproviding a maximum voltage gain of 1 .5.TABLE IV - Output voltage, corresponding topological states and switch states of cell topology 110a using the second control mode. v T . Switch state J • luie C' C' C' C' C' C'

[0101] Reference is now made to FIGS. 6A and 6B. FIG. 6A shows example graphs of the carrier and modulating signals that can be used to generate switch control signals for cell topology 110a in an example implementation of the second control mode. FIG. 6B shows example graphs of the modulating signal, carrier signal and switch control signals for cell topology 110a in another example implementation of the second control mode. In the second control mode, the AC output voltage may have four voltage levels that correspond to three regions l-lll. FIG. 6A shows a modulating signal 605 (M sin(wt), where M corresponds to maximum voltage gain of 1.5) and three carrier signals 610a- 610c corresponding to the three regions l-lll.

[0102] In some embodiments, a single carrier signal may be used to generate the switch control signals. This may reduce complexity of control system 120. FIG. 6B shows a modulating signal 615 and a single carrier 620 that may be used to generate switch control signal 625a (vg) and complementary switch control signal 625b (v ). Table V provides a summary of the regions l-lll, the corresponding topological states and switch control signals provided to switches 255 (Si), 245b (S2), 250b (S3), 260 (S4), 245a (S5), and 250a (Se). As summarized in Table V, in each region, a switch may be alwaysOn, always Off, or switched between On and Off states based on switch control signal 625a (vg) or 625b (v^).TABLE V - Switch control signal applied to the switches of cell topology 110a for each region l-lll using the second control mode.RT. States M sin mt Switch state e^' Involved Interval Si S2 S3 S4 Ss SeI A4-B4 [0.5, 1.5] v 1 0 0 v

[0103] Reference is now made to FIGS. 3, 6C and 6D. FIGS. 6C and 6D show example voltage and current waveforms measured for a converter 100 (FIG. 1) including cell topology 110a and using the second control mode to control the switches. Table VI summarizes the design specifications used during the measurements. For the illustrated example, the measurements were conducted for a control system 120 (FIG. 1) including a microcontroller STM32F303RE (NUCLEO-F303RE board) and the filter 130 including an LCL filter having an inductor 197C10 (1 mH / 10A) and a capacitor B32656T7394K000 (0.39pF / 500V). In other examples, any other suitable implementation of control system 120 and / or filter 130 may be used (e.g., other microcontrollers, other inductors and / or capacitors, other types of filters etc.).TABLE VI - Design specifications.Vdc DC input voltage 250 VVoOutput voltage (RMS) 220 VPoOutput power 1 kW fsSwitching frequency 42 kHz foOutput voltage frequency 60 Hz

[0104] FIG. 6C shows example graphs of unfiltered output voltage 630 (Vnv) of cell topology 110a, filtered AC output voltage 635 (Vo) of converter 100 and AC output current 640 (i0) of converter 100. FIG. 6D shows example graphs of voltages 645a (Vci), 645b (Vc2), 645c (Vcs), and 645d (Vc4) across capacitors 235b (Ci), 240b (C2), 235a (C3), and 240a (C4) respectively of cell topology 110a. The voltages 645a, 645b, 645c, and 645d are measured with referenceto ground voltage levels 650a, 650b, 650c, and 650d respectively. In the second control mode, voltages across capacitors 235b (Ci) and 240b (C2) of second switched-capacitor cell 160b are -250V, which is twice that of the voltages across capacitors 235a (C3), and 240a (C4) of first switched-capacitor cell 160a. The voltages 645b (Vc2) and 645d (Vc4) appear as negative because the node voltages were measured with respect to the midpoint 210 (Ao) of each switched-capacitor cell 160.

[0105] In some embodiments, the bidirectional and scalable multilevel converter may include a series of switched-capacitor cells. The series of switched-capacitor cells may include a first switched-capacitor cell, one or more intermediate switched-capacitor cells and a terminal switched-capacitor cell. Referring now to FIG. 7, shown therein is a schematic circuit diagram of an example cell topology 110b that includes a first switched-capacitor cell, a single intermediate switched-capacitor cell and a terminal switched-capacitor cell. As shown in FIG. 7, cell topology 110b includes three switched-capacitor cells 160a, 160b and 160c.

[0106] Each switched-capacitor cell may include a first capacitor 235, a second capacitor 240, a first unipolar bidirectional switch 245, a second unipolar bidirectional switch 250, a first bipolar switch 255, and a second bipolar switch 260. For example, first switched-capacitor cell 160a may include a first capacitor 235a, a second capacitor 240a, a first unipolar bidirectional switch 245a, a second unipolar bidirectional switch 250a, a first bipolar switch 255a, and a second bipolar switch 260a. Second switched-capacitor cell 160b may include a first capacitor 235b, a second capacitor 240b, a first unipolar bidirectional switch 245b, a second unipolar bidirectional switch 250b, a first bipolar switch 255b, and a second bipolar switch 260b. Third switched- capacitor cell 160c may include a first capacitor 235c, a second capacitor 240c, a first unipolar bidirectional switch 245c, and a second unipolar bidirectional switch 250c. The first bipolar switch and the second bipolar switch may not be required for a terminal switched-capacitor cell (e.g., third switched-capacitor cell 160c) because there is no next cell (e.g., no subsequent cell) in the seriesto be connected to the third switched-capacitor cell. In the illustrated example, third switched-capacitor cell 160c does not include a first bipolar switch and a second bipolar switch. This may reduce the total number of circuit components. In other examples, third switched-capacitor cell 160c may include a first bipolar switch and a second bipolar switch that are unused. This may improve modularity of the converter because all the switched-capacitor cells used in the converter have identical components.

[0107] First output node 220 of the first switched-capacitor cell and each of the intermediate switched-capacitor cells may be connected to first input node 205 of a next or subsequently switched-capacitor cell in the series. For example, first output node 220a of first switched-capacitor cell 160a may be connected to first input node 205b of second switched-capacitor cell 160b. First output node 220b of second switched-capacitor cell 160b may be connected to first input node 205c of third switched-capacitor cell 160c.

[0108] Second output node 230 of the first switched-capacitor cell and each of the intermediate switched-capacitor cells may be connected to second input node 215 of a next or subsequently switched-capacitor cell in the series. For example, second output node 230a of first switched-capacitor cell 160a may be connected to second input node 215b of second switched-capacitor cell 160b. Second output node 230b of second switched-capacitor cell 160b may be connected to second input node 215c of third switched-capacitor cell 160c.

[0109] Second cell node 225 of the first switched-capacitor cell and each of the intermediate switched-capacitor cells may be connected to first cell node 210 of a next or subsequently switched-capacitor cell in the series. For example, second cell node 225a of first switched-capacitor cell 160a may be connected to first cell node 210b of second switched-capacitor cell 160b. Second cell node 225b of second switched-capacitor cell 160b may be connected to first cell node 210c of third switched-capacitor cell 160c.

[0110] First bipolar switch 255 of the first switched-capacitor cell and each of the intermediate switched-capacitor cells may be connected between first input node 205 and first output node 220 of that switched-capacitor cell. Forexample, first bipolar switch 255a may be connected between first input node 205a and first output node 220a of first switched-capacitor cell 160a. First bipolar switch 255b may be connected between first input node 205b and first output node 220b of second switched-capacitor cell 160b.

[0111] Second bipolar switch 260 of the first switched-capacitor cell and each of the intermediate switched-capacitor cells may be connected between second input node 215 and second output node 230 of that switched-capacitor cell. For example, second bipolar switch 260a may be connected between second input node 215a and second output node 230a of first switched- capacitor cell 160a. Second bipolar switch 260b may be connected between second input node 215b and second output node 230b of second switched- capacitor cell 160b.

[0112] In the illustrated example, third switched-capacitor cell 160c does not include a first bipolar switch and a second bipolar switch. In embodiments where switched-capacitor cell 160c includes a first bipolar switch and a second bipolar switch, the first bipolar switch may be connected between first input node 205c and a first output node of third switched-capacitor cell 160c. The second bipolar switch may be connected between second input node 215c and a second output node of third switched-capacitor cell 160c.

[0113] A DC input voltage 705 (Vdc) may be connected between first input node 205a and second input node 215a of first switched-capacitor cell 160a. An unfiltered AC output voltage may be provided between second cell node 225c of third switched-capacitor cell 160c and first cell node 210a of first switched-capacitor cell 160a. In some embodiments, first cell node 210a may be connected to electrical ground to provide a path for leakage currents.

[0114] A control system (e.g., control system 120 shown in FIG. 1) may be configured to control switching of unipolar bidirectional switches 245a, 250a, 245b, 250b, 245c, 250c and bipolar switches 255a, 255b, 260a, and 260b to control a voltage gain and a number of voltage levels of the unfiltered AC output voltage. In some embodiments, the control system may control the switching based on a first control mode or a second control mode.

[0115] In the first control mode, the control system may control the switching to charge first capacitors 235 and second capacitors 240 of each switched- capacitor cell 160 to the same voltage of VdC / 2. Cell topology 110b may provide an unfiltered AC output voltage (Vjnv) having seven output voltage levels when control system 120 controls the switches of cell topology 110b using the first control mode. Table VII provides a summary ofnvlevels, the corresponding topological states A7-H7, and states of switches 255a (Si), 255b (S2), 245c (S3), 250c (S4), 260b (S5), 260a (Se), 245b (S7), 250b (S8), 245a (S9), and 250a (S10) of cell topology 110b using the first control mode. In the first control mode, peak output voltage of cell topology 110b can be 1 ,5Vdc providing a maximum voltage gain of 1.5.TABLE VII - Output voltage, corresponding topological states and switch states of cell topology 110b using the first control mode.

[0116] Any suitable method may be used to control the timing of change in topological states and switch states to generate the AC output voltage. In some embodiments, control system 120 may use pulse width modulation (PWM) of one or more carrier signals to generate corresponding switch control signals for switches 255a (Si), 255b (S2), 245c (S3), 250c (S4), 260b (S5), 260a (Se), 245b (S7), 250b (S8), 245a (S9), and 250a (S10).

[0117] Reference is now made to FIGS. 7, 8A and 8B. FIGS. 8A and 8B show example voltage and current waveforms measured for a converter 100 (FIG. 1 ) including cell topology 110b and using the first control mode to control the switches. Table VIII summarizes the design specifications used during the measurements. For the illustrated example, the measurements were conducted for a control system 120 (FIG. 1 ) including a microcontroller STM32F303RE(NUCLEO-F303RE board) and the filter 130 including an LCL filter having an inductor 197C10 (1 mH / 10A) and a capacitor B32656T7394K000 (0.39pF / 500V). In other example embodiments, any other suitable implementation of control system 120 and / or filter 130 may be used (e.g., other microcontrollers, other inductors and / or capacitors, other types of filters etc.).TABLE VIII - Design specifications.Symbol Description ValueVdc DC input voltage 250 VVoOutput voltage (RMS) 220 VPoOutput power 1 kW fsSwitching frequency 42 kHz foOutput voltage frequency 60 Hz

[0118] FIG. 8A shows example graphs of unfiltered output voltage 805 (Vinv) of cell topology 110b, filtered AC output voltage 810 (Vo) of converter 100 and AC output current 815 (i0) of converter 100. FIG. 8B shows example graphs of voltages 820a (Vci), 820b (Vcs), and 820c (Vcs) across capacitors 235c (Ci), 235b (C3), and 235a (C5) respectively of cell topology 110b. The voltages 820a, 820b, and 820c are measured with reference to ground voltage levels 825a, 825b, and 825c respectively. In the first control mode, voltages across each capacitor 235c (Ci), 235b (C3), and 235a (C5) is equal at 0.5VDC (-125V).

[0119] In the second control mode, the control system may control the switching to charge capacitors 235b and 240b of second switched-capacitor cell 160b to Vdcusing both capacitors 235a and 240a of first switched-capacitor cell 160a associated in series. Further, capacitors 235c and 240c of third switched-capacitor cell 160c to 2VdCusing both capacitors 235b and 240b of second switched-capacitor cell 160b associated in series.

[0120] In the second control mode, cell topology 1 10b may provide an unfiltered AC output voltage (Vjnv) having eight output voltage levels when control system 120 controls the switches of cell topology 110b using the second control mode. Table IX provides a summary of Vinv levels, the corresponding topological states A8-H8, and states of switches 255a (Si), 255b (S2), 245c (S3), 250c (S4), 260b (S5), 260a (Se), 245b (S7), 250b (S8), 245a (S9), and 250a(Sw) of cell topology 110b using the second control mode. In the second control mode, peak output voltage of cell topology 110a can be 3.5VdCproviding a maximum voltage gain of 3.5.TABLE IX - Output voltage, corresponding topological states and switch states of cell topology 110b using the second control mode.

[0121] Reference is now made to FIGS. 7, 9A and 9B. FIGS. 9A and 9B show example voltage and current waveforms measured for an converter 100 (FIG. 1) including cell topology 110b and using the second control mode to control the switches. T able X summarizes the design specifications used during the measurements. For the illustrated example, the measurements were conducted for a control system 120 (FIG. 1) including a microcontroller STM32F303RE (NUCLEO-F303RE board) and the filter 130 including an LCL filter having an inductor 197C10 (1 mH / 10A) and a capacitor B32656T7394K000 (0.39pF / 500V). In other example embodiments, any other suitable implementation of control system 120 and / or filter 130 may be used (e.g., other microcontrollers, other inductors and / or capacitors, other types of filters etc.).TABLE X - Design specifications.Symbol Description ValueVdc DC input voltage 100 VVoOutput voltage (RMS) 220 VPoOutput power 1 kW fsSwitching frequency 42 kHz foOutput voltage frequency 60 Hz

[0122] FIG. 9A shows example graphs of unfiltered output voltage 905 (Vjnv) of cell topology 110b, filtered AC output voltage 910 (Vo) of converter 100 andAC output current 915 (i0) of converter 100. FIG. 9B shows example graphs of voltages 920a (Vci), 920b (Vcs), and 920c (Vcs) across capacitors 235c (Ci), 235b (C3), and 235a (C5) respectively of cell topology 110b. In the second control mode, voltage across capacitor 235a (C5) of first switched-capacitor cell 160a is 0.5VDC (~50V). The voltage across capacitor 235b (C3) of second switched-capacitor cell 160b is VDC (-100V), i.e., twice the voltage across capacitor 235a (C5) of first switched-capacitor cell 160a. The voltage across capacitor 235c (Ci) of third switched-capacitor cell 160c is 2VDC (-200V), i.e., twice the voltage across capacitor 235b (C3) of second switched-capacitor cell 160b.

[0123] Referring now to FIG. 10, shown therein are example efficiency and voltage total harmonic distortions (THD) curves measured by a power analyzer (Yokogawa WT 1800) for various cell topologies and control modes of converter 100. FIG. 10 shows the example efficiency and voltage total harmonic distortions (THD) curves corresponding to 4-level (cell topology 110a, second control mode), 5-level (cell topology 110a, first control mode), 7-level (cell topology 110b, first control mode), and 8-level (cell topology 110b, second control mode) operations of converter 100. For the illustrated example, the peak efficiencies corresponding to the 4L, 5L, 7L and 8L operations are 97.015%, 97.058%, 97.777%, and 96.757% respectively. In the illustrated example, the largest voltage TH Ds of the unfiltered AC output voltage correspond to the rated power throughput and are 12.991 %, 12.893%, 8.552%, and 5.844%, for the 4L, 5L, 7L and 8L operations respectively.

[0124] Table XI provides a comparative analysis for various cell topologies and control modes of converter 100, including 4-level (cell topology 110a, second control mode), 5-level (cell topology 110a, first control mode), 7-level (cell topology 110b, first control mode), and 8-level (cell topology 110b, second control mode) operations of the converter. The maximum voltage stress, the total standing voltage (TSV), and the total capacitors’ voltage (TCV) are analyzed per unit in order to provide a fairer comparison because the maximumvoltage gains and the voltage ranges are not the same for each cell topology / control mode operation of the converter.TABLE XI - Comparative analysis for various cell topologies and control modes of the bidirectional and scalable multilevel converter.

[0125] Referring back to FIG. 1 , filter 130 may be used to filter the AC output voltage of cell topology 110. Converter 100 may provide filtered AC output voltage at AC output connector 150. In some embodiments, converter 100 may not include filter 130. Converter 100 may provide an unfiltered AC output voltage that can be filtered by an external filter.

[0126] Any suitable filter may be used for implementing filter 130. In some embodiments, a LCL filter may be used. The size of the filter components can be a function of the number of levels of the unfiltered voltage. The size of the filter components may be based on the following equations:where AVinv is the converter voltage ripple and defined as the difference between the two voltage levels that the output voltage swings between in a region, and 21 / 1 is the converter current ripple and defined as the current swing in that region. Parameters Lf, Cf, fs, and f0denote the inductance of the two inductors, the capacitance of the capacitor, the switching frequency, and the output voltage fundamental frequency respectively. For a given peak value, l / op , of the fundamental voltage, 211 / / can be calculated based on the number of unfiltered voltage levels, m, using the following equation:

[0127] For example, for a bipolar (two-level) output voltage, ni_ = 2 and AVinv equals 2V0Pk. As another example, for a unipolar (three-level) output voltage, IV / nv is equal to V0Pk corresponding to ni. = 3. Similarly, for a 4-, 5-, 7-, and 8- level output voltage, AVinv is equal to 2 / 3, 1 / 2, 1 / 3, and 2 / 7 times Vopk, respectively, in accordance with equation (3). Increasing the number of voltage levels can reduce AVinv in accordance with equation (3) and thereby reduce size of the required filter components in accordance with equations (1) and (2). For example, changing from 3 voltage levels to 5 voltage levels can result in a filter that is 25% less expensive and approximately 60% lighter and smaller.

[0128] Referring now to FIG. 11 , shown therein is a schematic diagram of an example embodiment of a multi-phase bidirectional and scalable multilevel converter 1100. Converter 1100 can provide bidirectional DC-AC power transfer between any suitable DC system, grid, network, source or load; and any suitable multi-phase AC system, grid, network, source or load. In the illustrated example embodiment, converter 1100 is configured for three-phase AC operation. In other examples, converter 1100 may be configured for operation with any suitable number of phases.

[0129] In the illustrated example embodiment, converter 1100 includes a first phase of the topology 110c, a second phase of the topology 110d, a third phase of the topology 110e, a control system 1120, a DC input connector 1140 and a three-phase AC output connector 1150 (that includes connectors 1150a- 1150c for the three phases).

[0130] DC input connector 1140 may be connected to any suitable DC system, grid, network, source and / or load. In the illustrated example, the same DC input voltage may be connected to each of phase of the topology 110c- 110e. If the same DC input voltage is connected to each phase of the topology 110c-110e, the first capacitor 235 of each phase is in parallel with the first capacitor 235 of the other phases. Optionally, a single first capacitor 235 may be used that is shared by all the phases. This can reduce the total number ofcomponents of converter 1100. Similarly, if the same DC input voltage is connected to each phase of the topology 110c- 110e, the second capacitor 240 of each phase is in parallel with the second capacitor 240 of the other phases. Optionally, a single second capacitor 240 may be used that is shared by all the phases. This can reduce the total number of components of converter 1100. In other examples, different DC input voltages may be connected to each of cell topologies 110c-110e. AC output connector 1150 may be connected to any suitable three-phase AC system, grid, network, source, and / or load.

[0131] Each cell topology 110c-110e may provide one phase of the three- phase AC voltage. Each cell topology 110c-110e can provide a corresponding phase output voltage between second cell node 225 of the terminal switched- capacitor cell and first cell node 210 of the first switched-capacitor cell of that cell topology 110. In some embodiments, converter 1100 can provide a three- phase, three-wire output voltage connection at connectors 1150a-1150c. For example, a three-phase AC load may be connected to second cell node 225 of the terminal switched-capacitor cell of each cell topology 110c-110e, but without any direct connection of the three-phase AC load to first cell node 210 of the first switched-capacitor cell of each cell topology 110c-110e.

[0132] Cell topologies 110c-110e may include any suitable number of switched-capacitor cells 160. The number of switched-capacitor cells 160 for converter 1100 may be selected based on desired maximum voltage gain and / or number of output voltage levels, as described herein with reference to converter 100. For an output voltage defined between second cell node 225 and first cell node 210 of any given phase of the topology 110c-110e, the voltage gain and number of output voltage levels can be the same as described herein with reference to converter 100. For a multi-phase output voltage (e.g., line voltage / phase-to-phase voltage), the voltage gain and number of output voltage levels can be based on the individual values of the voltage gain and number of output voltage levels for each phase of the topology 110c-110e and the relationship between the phases.

[0133] Control system 1120 may be configured to control switching of the switches of cell topologies 110c-110e to control a voltage gain and a number of voltage levels of the AC output voltage. For example, control system 1120 may control the switching based on a first control mode or a second control mode as described herein. Control system 1120 may be further configured to control a timing of the switching signals to cell topologies 110c-110e to control a phase shift between the three phases. In some embodiments, converter 1100 may include a separate control system 120 to control switching for each cell topology 110c-110e. Control system 1120 may provide control signals to each control system 120 to control the voltage gain and voltage levels of each phase of the multi-phase AC voltage.

[0134] In some embodiments, converter 1100 may include one or more filters 130 (not shown in FIG. 11). For example, each phase of the three-phase AC voltage may have a separate filter 130 and converter 1100 may provide filtered AC output voltage at AC output connector 1150. In other embodiments, converter 1100 may not include any filter 130. Converter 1100 may provide an unfiltered AC output voltage that can be filtered by an external filter.

[0135] While the applicant's teachings described herein are in conjunction with various embodiments for illustrative purposes, it is not intended that the applicant's teachings be limited to such embodiments as the embodiments described herein are intended to be examples. On the contrary, the applicant's teachings described and illustrated herein encompass various alternatives, modifications, and equivalents, without departing from the embodiments described herein, the general scope of which is defined in the appended claims.

Claims

CLAIMS:1 . A switched-capacitor cell for use in a bidirectional and scalable multilevel converter, the switched-capacitor cell comprising: a first capacitor (Ca) connected between a first input node (A1) and a first cell node (AO); a second capacitor (Cb) connected between the first cell node (AO) and a second input node (A2); a first unipolar bidirectional switch (Sc) connected between the first input node (A1 ) and a second cell node (BO); a second unipolar bidirectional switch (Sd) connected between the second cell node (BO) and the second input node (A2); a first bipolar switch (Sa) connected between the first input node (A1) and a first output node (B1 ) of the first switched-capacitor cell; and a second bipolar switch (Sb) connected between the second input node (A2) and a second output node (B2) of the first switched-capacitor cell.

2. A bidirectional and scalable multilevel converter comprising: a first switched-capacitor cell and a second switched capacitor cell that are both defined according to claim 1 wherein: a first output node (B1 ) of the first switched-capacitor cell is connected to a first input node (A1) of the second switched- capacitor cell; a second output node (B2) of the first switched-capacitor cell is connected to a second input node (A2) of the second switched- capacitor cell; and a second cell node (BO) of the first switched-capacitor cell is connected to a first cell node (AO) of the second switched- capacitor cell; and a control system configured to control switching of (i) a first unipolar bidirectional switch (Sc) and a second unipolar bidirectional switch (Sd) of each switched-capacitor cell, (ii) a first bipolar switch (Sa), and (iii) asecond bipolar switch (Sb) to control a voltage gain and a number of voltage levels of an AC output voltage, wherein: an AC output for providing the AC output voltage is provided between a second cell node (BO) of the second switched- capacitor cell and a first cell node (AO) of the first switched- capacitor cell; and a voltage gain of the converter is defined with reference to a DC input voltage connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell.

3. The bidirectional and scalable multilevel converter of claim 2, wherein the control system is configured to control the switching based on a first control mode, wherein a first capacitor and a second capacitor of each switched- capacitor cell are charged to a voltage of 0.5 times the DC input voltage, the AC output voltage of the first control mode having a maximum of five voltage levels and a maximum voltage gain of 1 .

4. The bidirectional and scalable multilevel converter of claim 1 or claim 2, wherein the control system is configured to control the switching based on a second control mode, wherein: the first capacitor and the second capacitor of the first switched- capacitor cell are charged to a voltage of 0.5 times the DC input voltage; and the first capacitor and the second capacitor of the second switched- capacitor cell are charged to a voltage equal to the DC input voltage, the AC output voltage of the second control mode having a maximum of four voltage levels and a maximum voltage gain of 1 .5.

5. The bidirectional and scalable multilevel converter of any one of claims 2 to 4, wherein one or more of (i) the first unipolar bidirectional switch (Sc) and the second unipolar bidirectional switch (Sd) of each switched-capacitor cell, (ii) the first bipolar switch (Sa), and (iii) the second bipolar switch (Sb) include semiconductor switching devices.

6. The bidirectional and scalable multilevel converter of any one of claims 2 to 5, wherein the DC input voltage is provided by a renewable energy source, an energy storage device, a DC link from a front-end converter, or a DC microgrid.

7. The bidirectional and scalable multilevel converter of any one of claims 2 to 6, wherein the AC output is connected to an electric utility grid or an AC load.

8. The bidirectional and scalable multilevel converter of claim 7 further comprising a filter connecting the AC output to the electric utility grid or the AC load.

9. The bidirectional and scalable multilevel converter of claim 8, wherein the filter is a LCL filter.

10. A bidirectional and scalable multilevel converter comprising: a series of switched-capacitor cells including a first switched-capacitor cell, one or more intermediate switched-capacitor cells and a terminal switched- capacitor cell, each switched-capacitor cell being defined according to claim 1 ; and the series of switched-capacitor cells is formed by: connecting a first output node (B1) of the first switched-capacitor cell and each of the intermediate switched-capacitor cells to a first input node (A1 ) of a subsequent switched-capacitor cell in the series of switched-capacitor cells; connecting a second output node (B2) of the first switched- capacitor cell and each of the intermediate switched-capacitor cells to a second input node (A2) of the subsequent switched- capacitor cell in the series of switched-capacitor cells; and connecting a second cell node (BO) of the first switched-capacitor cell and each of the intermediate switched-capacitor cells to a first cell node (AO) of the subsequent switched-capacitor cell in the series of switched-capacitor cells; anda control system that is coupled to the series of switched-capacitor cells and is configured to control switching of a first unipolar bidirectional switch (Sc), a second unipolar bidirectional switch (Sd), a first bipolar switch (Sa), and a second bipolar switch (Sb) of each switched-capacitor cell to control a voltage gain and a number of voltage levels of an AC output voltage, wherein: an AC output for providing the AC output voltage is provided between the second cell node (BO) of the terminal switched- capacitor cell and the first cell node (AO) of the first switched- capacitor cell; and a voltage gain of the convertor is defined with reference to a DC input voltage connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell.11 . The bidirectional and scalable multilevel converter of claim 10, wherein the series of switched-capacitor cells includes a single intermediate switched- capacitor cell, and the control system is configured to control the switching based on a first control mode, wherein a first capacitor and a second capacitor of each switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage, the AC output voltage of the first control mode having a maximum of seven voltage levels and a maximum voltage gain of 1 .5.

12. The bidirectional and scalable multilevel converter of claim 10, wherein the series of switched-capacitor cells includes a single intermediate switched- capacitor cell, and the control system is configured to control the switching based on a second control mode, wherein: a first capacitor and a second capacitor of the first switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage; a first capacitor and a second capacitor of the single intermediate switched-capacitor cell are charged to a voltage equal to the DC input voltage; and a first capacitor and a second capacitor of the terminal switched- capacitor cell are charged to a voltage equal to twice the DC inputvoltage, and the AC output voltage during the second control mode has a maximum of eight voltage levels and a maximum voltage gain of 3.5.

13. The bidirectional and scalable multilevel converter of any one of claims 10 to 12, wherein one or more of (i) the first unipolar bidirectional switch (Sc), (ii) the second unipolar bidirectional switch (Sd), (iii) the first bipolar switch (Sa), and (iv) the second bipolar switch (Sb) of each switched-capacitor cell include semiconductor switching devices.

14. The bidirectional and scalable multilevel converter of any one of claims 10 to 13, wherein the DC input voltage is provided by a renewable energy source, an energy storage device, a DC link from a front-end converter, or a DC microgrid.

15. The bidirectional and scalable multilevel converter of any one of claims 10 to 14, wherein the AC output voltage is connected to an electric utility grid or an AC load.

16. The bidirectional and scalable multilevel converter of claim 15 further comprising a filter connecting the AC output of the converter to the electric utility grid or the AC load.

17. The bidirectional and scalable multilevel converter of claim 16, wherein the filter is a LCL filter.

18. A method of controlling a voltage gain and a number of voltage levels of an AC output voltage of a bidirectional and scalable multilevel converter comprising a control system and a series of switched-capacitor cells including a first switched-capacitor cell and a terminal switched-capacitor cell, that are each defined according to claim 1 , wherein the method comprises: connecting the series of switched-capacitor cells formed by: connecting a first output node (B1) of the first switched-capacitor cell to a first input node (A1) of a subsequent switched-capacitor cell in the series of switched-capacitor cells;connecting a second output node (B2) of the first switched- capacitor cell to a second input node (A2) of the subsequent switched-capacitor cell in the series of switched-capacitor cells; and connecting a second cell node (BO) of the first switched-capacitor cell to a first cell node (AO) of the subsequently switched- capacitor cell in the series of switched-capacitor cells; and selecting a control mode of operation for the control system to control switching of the first unipolar bidirectional switch (Sc), the second unipolar bidirectional switch (Sd), the first bipolar switch (Sa), and the second bipolar switch (Sb) of each switched-capacitor cell, wherein: an AC output for providing an AC output voltage is between the second cell node (BO) of the terminal switched-capacitor cell and the first cell node (AO) of the first switched-capacitor cell; and the voltage gain is defined with reference to a DC input voltage connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell.

19. The method of claim 18, wherein the series of switched-capacitor cells further includes one or more intermediate switched-capacitor cells that are each defined according to claim 1 , wherein the method further comprises: selecting a number of the intermediate switched-capacitor cells; and connecting the series of switched-capacitor cells formed by: connecting a first output node (B1) of each of the intermediate switched-capacitor cells to a first input node (A1 ) of a subsequent switched-capacitor cell in the series of switched-capacitor cells; connecting a second output node (B2) of each of the intermediate switched-capacitor cells to a second input node (A2) of the subsequent switched-capacitor cell in the series of switched- capacitor cells; andconnecting a second cell node (BO) of each of the intermediate switched-capacitor cells to a first cell node (AO) of the subsequently switched-capacitor cell in the series of switched- capacitor cells.

20. The method of claim 19, wherein the series of switched-capacitor cells includes two or more intermediate switched-capacitor cells, and the method comprises controlling the switching based on a first control mode, wherein a first capacitor and a second capacitor of each switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage, and the AC output voltage during the first control mode has a maximum number of voltage levels greater than seven and there is a maximum voltage gain greater than 1 .5.21 . The method of claim 19, wherein the series of switched-capacitor cells includes two or more intermediate switched-capacitor cells, and the method comprises controlling the switching based on a second control mode, wherein: a first capacitor and a second capacitor of the first switched-capacitor cell are charged to a voltage of 0.5 times the DC input voltage; a first capacitor and a second capacitor of each intermediate switched- capacitor cell and the terminal switched-capacitor cell are charged to a voltage equal to twice the voltage of the first capacitor and a second capacitor of corresponding previous switched-capacitor cell, and the AC output voltage of the second control mode has a maximum number of voltage levels greater than eight and a maximum voltage gain that is greater than 3.5.

22. The method of any one of claims 18 to 21 , wherein the method comprises obtaining the DC input voltage from a renewable energy source, an energy storage device, a DC link from a front-end converter, or a DC microgrid.

23. The method of any one of claims 18 to 22, wherein the method comprises coupling the AC output to an electric utility grid or an AC load.

24. The method of claim 23, wherein the method comprises connecting a filter between the AC output of the converter and the electric utility grid or the AC load.

25. A multi-phase bidirectional and scalable multilevel converter comprising: multiple series of switched-capacitor cells, each series of switched- capacitor cells including a first switched-capacitor cell and a terminal switched- capacitor cell that are defined according to claim 1 , each series of switched- capacitor cells being formed by: connecting a first output node (B1) of the first switched-capacitor cell to a first input node (A1) of a subsequent switched-capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of the first switched-capacitor cell to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched- capacitor cells; and connecting a second cell node (BO) of the first switched-capacitor cell to a first cell node (AO) of the subsequent switched-capacitor cell in that series of switched-capacitor cells; and a control system that is coupled to the multiple series of switched- capacitor cells, the control system being configured to control switching of the first unipolar bidirectional switch (Sc), the second unipolar bidirectional switch (Sd), the first bipolar switch (Sa), and the second bipolar switch (Sb) of each switched-capacitor cell to control a voltage gain and a number of voltage levels of a multi-phase AC output voltage, wherein each phase of the multi-phase AC output voltage is provided by the second cell node (BO) of the terminal switched-capacitor cell of a corresponding series of switched-capacitor cells; and wherein the voltage gain is defined with reference to a DC input voltage that is connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell of each series of switched-capacitor cells.

26. The multi-phase bidirectional and scalable multilevel converter of claim 25, wherein:each series of switched-capacitor cells includes one or more intermediate switched-capacitor cells that are defined according to claim 1 , and each series of switched-capacitor cells being formed by: connecting a first output node (B1) of each of the intermediate switched-capacitor cells to a first input node (A1) of a subsequent switched-capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of each of the intermediate switched-capacitor cells to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched-capacitor cells; and connecting a second cell node (BO) of each of the intermediate switched-capacitor cells to a first cell node (AO) of the subsequent switched-capacitor cell in that series of switched-capacitor cells.

27. A method of controlling a voltage gain and a number of voltage levels of a multi-phase AC output voltage of a multi-phase bidirectional and scalable multilevel converter comprising a control system and multiple series of switched-capacitor cells, each series of switched-capacitor cells including a first switched-capacitor cell and a terminal switched-capacitor cell that are each defined according to claim 1 , wherein the method comprises: forming each series of switched-capacitor cells by: connecting a first output node (B1) of the first switched-capacitor cell to a first input node (A1) of a subsequent switched-capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of the first switched- capacitor cell to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched-capacitor cells; and connecting a second cell node (BO) of the first switched-capacitor cell to a first cell node (AO) of the subsequently switched- capacitor cell in that series of switched-capacitor cells; and selecting a control mode of operation for configuring the control system to control switching of the first unipolar bidirectional switch (Sc), the secondunipolar bidirectional switch (Sd), the first bipolar switch (Sa), and the second bipolar switch (Sb) of each switched-capacitor cell, wherein each phase of the multi-phase AC output voltage is provided by the second cell node (BO) of the terminal switched-capacitorcell of a corresponding series of switched-capacitor cells; and wherein the voltage gain is defined with reference to a DC input voltage that is connected between the first input node (A1) and the second input node (A2) of the first switched-capacitor cell of each series of switched-capacitor cells.

28. The method of claim 27, wherein each series of switched-capacitor cells further includes one or more intermediate switched-capacitor cells that are each defined according to claim 1 , wherein the method comprises: selecting a number of intermediate switched-capacitor cells; and forming each series of switched-capacitor cells by: connecting a first output node (B1) of each of the intermediate switched-capacitor cells to a first input node (A1 ) of a subsequent switched-capacitor cell in that series of switched-capacitor cells; connecting a second output node (B2) of each of the intermediate switched-capacitor cells to a second input node (A2) of the subsequent switched-capacitor cell in that series of switched- capacitor cells; and connecting a second cell node (BO) of each of the intermediate switched-capacitor cells to a first cell node (AO) of the subsequently switched-capacitor cell in that series of switched- capacitor cells.

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