# Patent

## Title
Capacitor-based active balancing for batteries and other power supplies

## Abstract

A system includes multiple power supplies connected in series and an active balancing circuit. The active balancing circuit includes an LC resonance circuit and multiple switches configured to selectively couple different ones of the power supplies to the LC resonance circuit. The LC resonance circuit includes a capacitor, an inductor, and an additional switch. The capacitor is configured to store energy to be transferred between two or more of the power supplies. The additional switch is configured to selectively create a resonance between the capacitor and the inductor in order to reverse a discharge current direction through the capacitor.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS AND PRIORITY CLAIM
This application claims priority under 35 U.S.C. §119(e) to the following U.S. patent applications:
U.S. Provisional Patent Application No. 61/546,439 filed on Oct. 12, 2011; and
U.S. Provisional Patent Application No. 61/546,705 filed on Oct. 13, 2011.
Both provisional patent applications are hereby incorporated by reference in their entirety.


TECHNICAL FIELD
This disclosure is generally directed to power supply balancing systems. More specifically, this disclosure is directed to capacitor-based active balancing for batteries and other power supplies.
BACKGROUND
Modern batteries often include multiple battery cells connected in series, and multiple batteries can be connected in series to form a battery module. Unfortunately, the actual output voltage provided by each individual battery cell in a battery or each battery in a battery module may vary slightly. This can be caused by any number of factors, such as manufacturing variations, temperature variations, or other internal or external factors. This can cause problems during charging and discharging of the battery cells or batteries. In some systems, voltage detection circuitry can be used to determine the output voltage of each battery cell or battery, and a voltage balancing system can be used to compensate for variations in the output voltages.
Consider battery cells connected in series, where each battery cell is designed to provide an output voltage of 3.8V. Voltage detection circuitry may determine that one of the battery cells actually has an output voltage of 3.9V. A conventional passive voltage balancing system typically includes resistors that dissipate electrical energy from battery cells or batteries having excessive output voltage. In this example, the dissipation of electrical energy causes the 3.9V output voltage to drop to the desired level of 3.8V. However, since electrical energy is dissipated using the resistors, this can result in significant energy being lost from the battery cell, which shortens the operational life of the battery.
SUMMARY
This disclosure provides capacitor-based active balancing for batteries and other power supplies.
In a first embodiment, an apparatus includes an LC resonance circuit and multiple switches configured to selectively couple different power supplies connected in series to the LC resonance circuit. The LC resonance circuit includes a capacitor, an inductor, and an additional switch. The capacitor is configured to store energy to be transferred between two or more of the power supplies. The additional switch is configured to selectively create a resonance between the capacitor and the inductor in order to reverse a discharge current direction through the capacitor.
In a second embodiment, a method includes transferring energy from at least one first power supply to a capacitor. The method also includes selectively creating a resonance between the capacitor and an inductor in order to reverse a discharge current direction through the capacitor. The method further includes transferring the energy from the capacitor to at least one second power supply. The at least one first power supply and the at least one second power supply are connected in series.
In a third embodiment, a system includes multiple power supplies connected in series and an active balancing circuit. The active balancing circuit includes an LC resonance circuit and multiple switches configured to selectively couple different ones of the power supplies to the LC resonance circuit. The LC resonance circuit includes a capacitor, an inductor, and an additional switch. The capacitor is configured to store energy to be transferred between two or more of the power supplies. The additional switch is configured to selectively create a resonance between the capacitor and the inductor in order to reverse a discharge current direction through the capacitor.
Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims.



BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of this disclosure and its features, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which:
FIG. 1 illustrates an example capacitor-based active balancing system for batteries and other power supplies in accordance with this disclosure;
FIGS. 2A and 2B illustrate example operations of the system of FIG. 1 during odd-to-odd and even-to-even power transfers in accordance with this disclosure;
FIGS. 3A through 3D illustrate example operations of the system of FIG. 1 during odd-to-even and even-to-odd power transfers in accordance with this disclosure;
FIGS. 4A and 4B illustrate example operations of the system of FIG. 1 during power transfers involving multiple discharged power supplies and multiple charged power supplies in accordance with this disclosure; and
FIG. 5 illustrates an example method for capacitor-based active balancing for batteries and other power supplies in accordance with this disclosure.



DETAILED DESCRIPTION
FIGS. 1 through 5, discussed below, and the various embodiments used to describe the principles of the present invention in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the invention. Those skilled in the art will understand that the principles of the present invention may be implemented in any suitable manner and in any type of suitably arranged device or system.
FIG. 1 illustrates an example capacitor-based active balancing system 100 for batteries and other power supplies in accordance with this disclosure. As shown in FIG. 1, the system 100 includes or is coupled to multiple power supplies 102a-102g connected in series. Each power supply 102a-102g represents any suitable source of power, such as a single battery cell. In particular embodiments, each power supply 102a-102g represents a single battery cell having a nominal voltage of 3.2V. However, each power supply 102a-102g could also represent multiple battery cells, a battery module, multiple battery modules, or other collection of battery cells. Any other types of power supplies could also be used, such as super-capacitors, fuel cells, and solar cells. Also note that any number of power supplies could be used here.
Multiple switches 104a-104h are coupled to the power supplies 102a-102g. The switches 104a-104h are opened and closed to transfer energy between selected power supplies 102a-102g via a capacitor in an inductor-capacitor (LC) resonance circuit 106. The switches 104a-104h represent any suitable switching devices, such as transistors. In particular embodiments, each of the switches 104a-104h represents two back-to-back MOSFET transistors to prevent the short-circuit of two neighboring cells by the MOSFET body diode. Any single-switch devices with no body diodes can also be used here.
The LC resonance circuit 106 transfers energy between the selected power supplies 102a-102g. In this example, the LC resonance circuit 106 includes a capacitor 108, an inductor 110, and a switch 112. As can be seen in FIG. 1, one end of the capacitor 108 is connected to a first subset of the switches 104a-104h, and another end of the capacitor 108 is connected to a second subset of the switches 104a-104h. The capacitor 108 includes any suitable capacitive structure having any suitable capacitance. The inductor 110 includes any suitable inductive structure having any suitable inductance.
The switch 112 is coupled in series with the capacitor 108 and the inductor 110. The switch 112 is used to selectively create a current path through the capacitor 108 and the inductor 110, thereby selectively controlling LC resonance in the circuit 106. The switch 112 represents any suitable switching device, such as at least one bi-directional transistor. In particular embodiments, the switch 112 represents two back-to-back MOSFET transistors.
A controller 114 controls the overall operation of the system 100. For example, the controller 114 could control the operation of the switches 104a-104h, 112 to control the charging and discharging of the power supplies 102a-102g. The controller 114 includes any suitable structure for controlling the charging and discharging of power supplies. For instance, the controller 114 could include a pulse width modulation (PWM) controller that generates control signals for the various switches, where the control signals have variable duty cycles controlled using PWM. In some embodiments, the controller 114 uses any suitable mechanism for measuring current through the capacitor 108 or other elements, such as a sense resistor coupled in series with the capacitor 108 and a high common-mode voltage precision current sensing amplifier coupled across the sense resistor.
As described in more detail below, energy can be transferred from one or more of the power supplies 102a-102g to one or more other of the power supplies 102a-102g through the capacitor 108. For example, energy can be discharged from one or more of the power supplies 102a-102g and stored in the capacitor 108, and that energy can then be transferred to one or more other of the power supplies 102a-102g. If necessary, the direction of current flow needed to discharge the capacitor 108 can be reversed using a resonance created between the capacitor 108 and the inductor 110, allowing the transfer of energy between any of the power supplies.
In this way, the system 100 provides a novel and robust active balancing architecture. Direct balancing of energy can occur between power supplies without the need for an energy buffer (such as a transformer). This leads to higher balancing efficiency, such as up to 85% efficiency or more. Moreover, this active balancing approach represents an extremely low-cost solution since it uses one switch-pair per channel (power supply) and one larger capacitor (capacitor 108) per collection of power supplies. In addition, the system 100 provides more flexibility for system-level algorithms in that it can support a wide variety of multiple-supply charging/discharging algorithms.
In the system 100 of FIG. 1, a distinction can be made between odd and even power supplies 102a-102g. Here, “odd” and “even” refer to the number assigned to the power supplies when they are numbered in series. In this example, power supplies 102a, 102c, 102e, and 102g could represent “odd” power supplies, and power supplies 102b, 102d, and 102f could represent “even” power supplies. This distinction is used since some energy transfers involve the use of the inductor 110 while other energy transfers do not. In particular, power transfers from an odd-numbered power supply to an odd-numbered power supply (“odd-to-odd” transfers) and power transfers from an even-numbered power supply to an even-numbered power supply (“even-to-even” transfers) do not involve the inductor 110. Power transfers from an odd-numbered power supply to an even-numbered power supply (“odd-to-even” transfers) and power transfers from an even-numbered power supply to an odd-numbered power supply (“even-to-odd” transfers) do involve the inductor 110.
Although FIG. 1 illustrates one example of a capacitor-based active balancing system 100 for batteries and other power supplies, various changes may be made to FIG. 1. For example, any suitable number(s), type(s), and arrangement(s) of power supplies could be used in the system 100. Also, various components in FIG. 1 could be rearranged as desired, such as by placing the switch 112 on the other side of the inductor 110. Further, additional components could be added to the system 100 according to particular needs. In addition, while specific circuit components are shown, other circuit components for performing the same or similar function(s) could be used.
FIGS. 2A and 2B illustrate example operations of the system 100 of FIG. 1 during odd-to-odd and even-to-even power transfers in accordance with this disclosure. In this particular example, a power transfer is occurring from power supply 102a to power supply 102c, making it an odd-to-off transfer. Similar operations may occur during an even-to-even transfer. The opening and closing of the switches 104a-104h here is controlled by the controller 114.
As shown in FIG. 2A, in order to transfer energy out of the power supply 102a, two switches 104a-104b are closed, while the remaining switches 104c-104h are opened. This creates a current path 202 through the power supply 102a. Also, the switch 112 is opened to disconnect the inductor 110 from the current path 202. This causes current to flow from the connected power supply 102a to the capacitor 108, charging the capacitor 108.
As shown in FIG. 2B, in order to transfer energy from the capacitor 108 to the power supply 102c, two switches 104c-104d are closed, while the remaining switches 104a-104b, 104e-104h are opened. This creates a current path 204 through the power supply 102c. Also, the switch 112 remains opened. This causes current to flow from the capacitor 108 to the connected power supply 102c, charging that power supply 102c. Note here that the currents through the capacitor 108 flow in opposite directions in FIGS. 2A and 2B (one way for charging, another way for discharging). In this implementation, complementary PWM signaling can be used to control the switches for the power supply being discharged and the power supply being charged.
FIGS. 3A through 3D illustrate example operations of the system 100 of FIG. 1 during odd-to-even and even-to-odd power transfers in accordance with this disclosure. In this particular example, a power transfer is occurring from power supply 102a to power supply 102b, making it an odd-to-even transfer. Similar operations may occur during an even-to-odd transfer. The opening and closing of the switches 104a-104h here is controlled by the controller 114.
As shown in FIG. 3A, in order to transfer energy out of the power supply 102a, two switches 104a-104b are closed, while the remaining switches 104c-104h are opened. This creates a current path 302 through the power supply 102a. Also, the switch 112 is opened to disconnect the inductor 110 from the current path 302. This causes current to flow from the connected power supply 102a to the capacitor 108, charging the capacitor 108.
As shown in FIG. 3B, all of the switches 104a-104h are opened, and the switch 112 is closed. This causes current to flow from the capacitor 108 to the inductor 110 as part of a current flow 304. This current flow 304 transfers at least some of the energy stored on the capacitor 108 to the inductor 110.
As shown in FIG. 3C, all of the switches 104a-104h remain opened, and the switch 112 remains closed. This causes current to flow from the inductor 110 to the capacitor 108 during resonance as part of a current flow 306. This current flow 306 transfers at least some of the energy stored on the inductor 110 back to the capacitor 108. The combined effect of the resonance in FIGS. 3B and 3C is to allow the capacitor 108 to be charged and discharged by currents flowing in the same direction through the capacitor 108. This effectively reverses the capacitor's discharge direction.
As shown in FIG. 3D, in order to transfer energy from the capacitor 108 to the power supply 102b, two switches 104b-104c are closed, while the remaining switches 104a, 104d-104h are opened. This creates a current path 308 through the power supply 102b. Also, the switch 112 is opened to disconnect the inductor 110 from the current path 308. This causes current to flow from the capacitor 108 to the connected power supply 102b, charging that power supply 102b. However, the discharging current flows in the same direction through the capacitor 108 as the charging current in FIG. 3A.
Note that while FIGS. 2A through 3D have dealt with the transfer of energy from a single power supply to a single power supply, transfers involving discharges from multiple power supplies and/or charges of multiple power supplies can also be performed.
FIGS. 4A and 4B illustrate example operations of the system 100 of FIG. 1 during power transfers involving multiple discharged power supplies and multiple charged power supplies in accordance with this disclosure. In this particular example, power is transferred from power supplies 102a-102c to power supplies 102d-102f. The opening and closing of the switches 104a-104h here is controlled by the controller 114.
As shown in FIG. 4A, in order to transfer energy out of the power supplies 102a-102c, the switches 104a, 104d are closed, while the remaining switches 104b-104c, 104e-104h are opened. This creates a current path 402 through the power supplies 102a-102c. Also, the switch 112 is opened to disconnect the inductor 110 from the current path 402. This causes current to flow from the connected power supplies 102a-102c to the capacitor 108, charging the capacitor 108.
Once charged, energy from the capacitor 108 can be redirected to one or multiple power supplies 102a-102g. When redirected to a single power supply, this could occur as described above (with or without the use of the inductor 110). When redirected to multiple power supplies, this could occur as shown in FIG. 4B.
As shown in FIG. 4B, in order to transfer energy from the capacitor 108 to the power supplies 102d-102f, the switches 104d and 104g are closed, while the remaining switches 104a-104c, 104e-104f, 104h are opened. This creates a current path 404 through the power supplies 102d-102f. Also, the switch 112 remains opened. This causes current to flow from the capacitor 108 to the connected power supplies 102d-102f, charging those power supplies 102d-102f. 
Note that in-rush current control can be used to control the current to the capacitor 108, as coupling multiple power supplies to the capacitor 108 could otherwise create large in-rush currents that can damage the capacitor 108. Any suitable current in-rush control can be used, such as a current feedback loop. In particular embodiments, the in-rush current can be controlled using an LM5069 in-rush current controller from TEXAS INSTRUMENTS INC.
Although FIGS. 2A through 4B illustrate examples of the operations of the system 100 of FIG. 1 during different power transfers, various changes may be made to FIGS. 2A through 4B. For example, these figures illustrate transfers between specific power supplies. Clearly, transfers between other power supplies or collections of power supplies could occur. Also, different combinations of these operations could be performed to transfer power between power supplies. For instance, power could be transferred from a single power supply to multiple power supplies or from multiple power supplies to a single power supply (with or without the use of the inductor 110). In addition, note that in the implementation shown here, power can be transferred from an odd number of power supplies to the inductor 108, and power can be transferred from the inductor 108 to an odd number of power supplies (since closing the switches around an even number of power supplies would short-circuit those supplies). However, additional switches could be used to enable power transfers to or from an even number of power supplies, although this involves use of a larger number of switches.
FIG. 5 illustrates an example method 500 for capacitor-based active balancing for batteries and other power supplies in accordance with this disclosure. As shown in FIG. 5, at least one power supply to be charged is identified at step 502, and at least one power supply to be discharged is identified at step 504. This could include, for example, the controller 114 identifying the power supply or supplies 102a-102g having the highest output voltage(s) and identifying the power supply or supplies 102a-102g having the lowest output voltage(s).
The switches associated with the at least one power supply being discharged are closed at step 506. This could include, for example, the controller 114 closing the pair of switches around the power supply or power supplies 102a-102g having the highest output voltage(s). Energy is transferred from the at least one power supply being discharged to a capacitor at step 508. This could include, for example, the power supply or power supplies 102a-102g having the highest output voltage(s) transferring at least some of their energy to the capacitor 108. The switches associated with the at least one power supply being discharged are opened at step 510. This stops the transfer of energy to the capacitor 108.
A decision is made whether the discharge current direction through the capacitor needs to be reversed at step 512. This could include, for example, the controller 114 determining whether the power transfer involves an odd-to-even or even-to-odd transfer. If so, a control switch is closed to create a resonance with the capacitor at step 514. This could include, for example, the controller 114 closing the switch 112 to create a resonance between the capacitor 108 and the inductor 110. This reverses the discharge current direction through the capacitor at step 516. This could include, for example, transferring at least some of the energy from the capacitor 108 to the inductor 110 and then back to the capacitor 108. The control switch is opened at step 518.
The switches associated with the at least one power supply being charged are closed at step 520. This could include, for example, the controller 114 closing the pair of switches around the power supply or power supplies 102a-102g having the lowest output voltage(s). Energy is transferred from the capacitor to the at least one power supply being charged at step 522. This could include, for example, the capacitor 108 transferring at least some of its stored energy to the power supply or power supplies 102a-102g having the lowest output voltage(s). The switches associated with the at least one power supply being charged are opened at step 524. This stops the transfer of energy from the capacitor 108.
In this way, the method 500 supports the direct balancing of energy between power supplies without the need for an energy buffer, which can lead to higher balancing efficiency. Moreover, this approach requires fewer components to implement compared to conventional balancing approaches, and a wide variety of algorithms can be used to select the power supplies to be charged and discharged.
Although FIG. 5 illustrates one example of a method 500 for capacitor-based active balancing for batteries and other power supplies, various changes may be made to FIG. 5. For example, while shown as a series of steps, various steps in FIG. 5 could overlap, occur in parallel, occur in a different order, or occur multiple times. As a particular example, the method 500 could be performed repeatedly for different combinations of power supplies until all of the power supplies have substantially equal output voltages.
Note that the system 100 shown above could be used in any type of system in which active balancing of power supplies is required or desired. For instance, the system 100 could be used with the power supplies in electric vehicles or hybrid electric vehicles, such as to balance lithium ion batteries or other types of batteries. Any other device or system that uses multiple power supplies could also include the system 100. Also note that any particular values (such as inductances, capacitances, resistances, and efficiencies) given above may represent exact or approximate values and are related to specific implementations of a circuit.
It may be advantageous to set forth definitions of certain words and phrases that have been used within this patent document. The term “couple” and its derivatives refer to any direct or indirect communication between components, whether or not those components are in physical contact with each other. The terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation. The term “or” is inclusive, meaning and/or. The phrase “associated with,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, have a relationship to or with, or the like.
While this disclosure has described certain embodiments and generally associated methods, alterations and permutations of these embodiments and methods will be apparent to those skilled in the art. Accordingly, the above description of example embodiments does not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure, as defined by the following claims.

## Claims

1. An apparatus comprising:
an LC resonance circuit, including
a energy transfer capacitor,
an inductor, and
a resonator switch configured to selectively connect the capacitor to the inductor as a resonator circuit;

multiple switches configured to selectively couple the capacitor to a respective one of four or more power supplies connected in series; and
a controller configured to selectively switch the multiple switches and the resonator switch to transfer energy from a selected first power supply to a selected second power supply based on:
a discharge cycle in which the selected first power supply is parallel-connected to the capacitor to transfer energy from the first power supply to the capacitor, followed selectively by either
an odd-odd/even-even charge cycle in which the capacitor is parallel-connected to the second power supply to transfer energy from the capacitor to the second power supply, or
an odd-even/even-odd charge cycle in which
the resonator switch is closed to selectively configure the capacitor and the inductor as a resonator circuit in order to reverse a discharge current direction through the capacitor, and then
the capacitor is series-connected to the second power supply to transfer energy from the capacitor to the second power supply.

2. The apparatus of claim 1,
wherein the number of series-connected power supplies is n and the number of switches is n+1; and
wherein a first end of the inductor is connected to odd-numbered switches, and a second end of the inductor is connected to even-numbered switches.

3. The apparatus of claim 1, wherein, in order to transfer the energy from the first power supply to the second power supply, the controller is configured to:
close a first pair of the multiple switches to transfer the energy from the first power supply to the capacitor;
open the first pair of the multiple switches; and
close a second pair of the multiple switches to transfer the energy from the capacitor to the second power supply.

4. The apparatus of claim 1, wherein, in order to transfer the energy from the first power supply to the second power supply, the controller is configured to:
close a first pair of the multiple switches to transfer the energy from the first power supply to the capacitor;
open the first pair of the multiple switches;
close the resonator switch to configure the resonator circuit and reverse the discharge current direction through the capacitor;
open the resonator switch; and
close a second pair of the multiple switches to transfer the energy from the capacitor to the second power supply.

5. The apparatus of claim 1, wherein, in order to transfer the energy between a first group of the power supplies and a second group of the power supplies, the controller is configured to:
close a first pair of the multiple switches to transfer the energy from the first group of power supplies to the capacitor;
open the first pair of the multiple switches; and
close a second pair of the multiple switches to transfer the energy from the capacitor to the second group of power supplies.

6. The apparatus of claim 1, wherein:
the inductor and the resonator switch are coupled in series; and
the capacitor is coupled in parallel with the inductor and the resonator switch.

7. A method of transferring energy among four or more power supplies connected in series using an energy transfer capacitor included in a selectively configurable LC resonator that includes an inductor and a resonator switch configured to selectively connect the capacitor to the inductor, comprising:
transferring energy from a selected first power supply to a selected second power supply based on:
a discharge cycle accomplished by connecting the selected first power supply in parallel with the capacitor to transfer energy from the first power supply to the capacitor, followed selectively by either
an odd-odd/even-even charge cycle accomplished by connecting the capacitor in parallel with the second power supply to transfer energy from the capacitor to the second power supply, or
an odd-even/even-odd charge cycle accomplished by
closing the resonator switch to selectively configure the capacitor and the inductor as the resonator circuit in order to reverse a discharge current direction through the capacitor, and then
connecting the capacitor in series with the second power supply to transfer energy from the capacitor to the second power supply.

8. The method of claim 7, wherein:
transferring the energy from the first power supply to the capacitor comprises using a first pair of multiple switches;
transferring the energy from the capacitor to the second power supply comprises using a second pair of the multiple switches.

9. The method of claim 8, wherein transferring the energy from the first power supply to the capacitor and transferring the energy from the capacitor to the second power supply comprise:
closing the first pair of the multiple switches to transfer the energy from the first power supply to the capacitor;
opening the first pair of the multiple switches; and
closing the second pair of the multiple switches to transfer the energy from the capacitor to the second power supply.

10. The method of claim 8, wherein transferring the energy from the first power supply to the capacitor, selectively configuring the capacitor and the inductor as a resonator circuit, and transferring the energy from the capacitor to the second power supply comprise:
closing a first pair of the multiple switches to transfer the energy from the first power supply to the capacitor;
opening the first pair of the multiple switches;
closing the resonator switch to configure the capacitor and the inductor as a resonator circuit and reverse the discharge current direction through the capacitor;
opening the resonator switch; and
closing a second pair of the multiple switches to transfer the energy from the capacitor to the second power supply.

11. The method of claim 7, wherein energy is transferred between a first group of power supplies and a second group of power supplies by:
closing a first pair of the multiple switches to transfer the energy from the first group of power supplies to the capacitor;
opening the first pair of the multiple switches; and
closing a second pair of the multiple switches to transfer the energy from the capacitor to the second group of power supplies.

12. The method of claim 11, further comprising:
using in-rush current control to control current provided to the capacitor from the first group of power supplies.

13. A system comprising:
four or more power supplies connected in series; and
an active balancing circuit comprising:
an LC resonance circuit, including
an energy transfer capacitor,
an inductor, and
a resonator switch configured to selectively connect the capacitor to the inductor as a resonator circuit;

multiple switches configured to selectively couple the capacitor to a respective one of the power supplies;
a controller configured to selectively switch the multiple switches and the resonator switch to transfer energy from a selected first power supply to a selected second power supply based on:
a discharge cycle in which the selected first power supply is parallel-connected to the capacitor to transfers energy from the first power supply to the capacitor, followed selectively by either;
an odd-odd/even-even charge cycle in which the capacitor is parallel-connected to the second power supply to transfer energy from the capacitor to the second power supply, or
an odd-even/even-odd charge cycle in which
the resonator switch is closed to selectively configure the capacitor and the inductor as a resonator circuit in order to reverse a discharge current direction through the capacitor, and then
the capacitor is series-connected to the second power supply to transfer energy from the capacitor to the second power supply.

14. The system of claim 13,
wherein the number of series-connected power supplies is n and the number of switches is n+1; and
wherein a first end of the capacitor is connected to odd-numbered switches, and a second end of the capacitor is connected to even-numbered switches.

15. The system of claim 13, wherein, in order to transfer energy from the first power supply to the second power supply, the controller is configured to:
close a first pair of the multiple switches to transfer the energy from the first power supply to the capacitor;
open the first pair of the multiple switches; and
close a second pair of the multiple switches to transfer the energy from the capacitor to the second power supply.

16. The system of claim 13, wherein, in order to transfer the energy from the first power supply to the second power supply, the controller is configured to:
close a first pair of the multiple switches to transfer the energy from the first power supply to the capacitor;
open the first pair of the multiple switches;
close the additional switch to configure the capacitor and the inductor as a resonator circuit and reverse the discharge current direction through the capacitor;
open the resonator switch; and
close a second pair of the multiple switches to transfer the energy from the capacitor to the second power supply.

17. The system of claim 13, wherein, in order to transfer the energy between a first group of the power supplies and a second group of the power supplies, the controller is configured to:
close a first pair of the multiple switches to transfer the energy from the first group of power supplies to the capacitor;
open the first pair of the multiple switches; and
close a second pair of the multiple switches to transfer the energy from the capacitor to the second group of power supplies.