Energy storage balancing system

1. An energy storage system comprising:

a high-voltage section including a high-voltage bus and a plurality of high-voltage energy storage elements electrically connected to the high-voltage bus;

a low-voltage section including a low-voltage bus and a low-voltage energy storage element, the low-voltage bus electrically connectable to a low-voltage load;

a plurality of voltage converters, each voltage converter electrically connected between one of the high-voltage energy storage elements and the low-voltage bus and operable to convert power between a high-voltage level of the high-voltage section and a low-voltage level of the low-voltage section; and

a controller coupled to the plurality of voltage converters, the controller configured to

i) determine an initial system charge state at a first sampling time, wherein the system charge state includes an element charge state corresponding to each of the high-voltage energy storage elements and low-voltage energy storage element that represents a charge level of that energy storage element and the system charge state defines a charge balance state representing relative element charge states of the high-voltage energy storage elements;

ii) calculate a plurality of potential charge balance states for a second sampling time based on the initial system charge state and a plurality of potential power transmission sets for the voltage converters, each potential charge balance state corresponding to one of the potential power transmission sets and the second sampling time being subsequent to the first sampling time;

iii) calculate a plurality of potential element charge states of the low voltage storage element at the second sampling time, each potential element charge state corresponding to one of the potential power transmission sets;

iv) select one of the potential power transmission sets by minimizing a cost function, wherein the cost function is defined using an affine transformation of the system charge state, the cost function includes a balance state component that is minimized when the charge balance state is maximally balanced, the cost function further includes a charging state component that is minimized when the element charge state of the low voltage energy storage element is at a maximum charging value, and the cost function includes at least one adjustable minimization coefficient defining a relative importance of the charging state component and the balance state component;

v) determine power converter inputs using the selected power transmission set; and

vi) adjust the power transmission level of at least one of the voltage converters using the determined power converter inputs.

2. The system of claim 1 , wherein

the power converter inputs are determined based on the plurality of potential element charge states of the low voltage energy storage element.

3. The system of claim 2 , wherein the controller is further configured to:

select a subsequent charge state of the low voltage energy storage element at the second sampling time from the at least one potential element charge state;

calculate a charging power transmission set based on the initial system charge state and the subsequent charge state;

determine a combined power transmission set by combining the charging power transmission set and the selected power transmission level set; and

determine the power converter inputs from the combined power transmission set.

4. The system of claim 3 , wherein the voltage converters permit bidirectional current flow between the high-voltage section and the low-voltage section.

5. The system of claim 1 , wherein the low voltage section further comprises a chopper element.

6. The system of claim 1 , wherein the voltage converters permit bidirectional current flow between the high-voltage section and the low-voltage section.

7. The system of claim 1 , wherein the voltage converters are unidirectional such that the voltage converters permit power to only flow from the high-voltage section to the low-voltage section.

8. The system of claim 1 , wherein the power converter inputs are determined to improve the charge balance state non-dissipatively.

9. The system of claim 1 , wherein the low-voltage energy storage element comprises a low-capacity capacitive energy storage element having a low-voltage energy storage capacity at least ten times less than a high-voltage energy storage capacity of any one of the high-voltage energy storage elements.

10. A method for balancing an energy storage unit that includes a plurality of high-voltage energy storage elements, a low-voltage section including a low-voltage bus and a low-voltage energy storage element and a plurality of voltage converters, each voltage converter electrically connected between one of the high-voltage energy storage elements and the low-voltage bus, the method comprising:

determining an initial system charge state at a first sampling time, wherein the system charge state includes an element charge state corresponding to each of the high-voltage energy storage elements and low-voltage energy storage element that represents a current charge level of that energy storage element and the system charge state defines a charge balance state representing relative element charge states of the high-voltage energy storage elements;

calculating a plurality of potential charge balance states for a second sampling time based on the initial system charge state and a plurality of potential power transmission sets for the voltage converters, each potential charge balance state corresponding to one of the potential power transmission sets and the second sampling time being subsequent to the first sampling time;

calculating a plurality of potential element charge states of the low voltage storage element at the second sampling time, each potential element charge state corresponding to one of the potential power transmission sets;

selecting one of the potential power transmission sets by minimizing a cost function, wherein the cost function is defined using an affine transformation of the system charge state, the cost function includes a balance state component that is minimized when the charge balance state is maximally balanced, the cost function further includes a charging state component that is minimized when the element charge state of the low voltage energy storage element is at a maximum charging value, and the cost function includes at least one adjustable minimization coefficient defining a relative importance of the charging state component and the balance state component;

determining power converter inputs using the selected power transmission set; and

adjusting the power transmission level of at least one of the voltage converters using the determined power converter inputs.

11. The method of claim 10 , wherein

the power converter inputs are determined based on the plurality of potential element charge states of the low voltage energy storage element.

12. The method of claim 11 , further comprising:

selecting a subsequent charge state of the low voltage energy storage element at the second sampling time from the at least one potential element charge state;

calculating a charging power transmission set based on the initial system charge state and the subsequent charge state;

determining a combined power transmission set by combining the charging power transmission set and the selected power transmission level set; and

determining the power converter inputs from the combined power transmission set.

13. The method of claim 12 , wherein the power converter inputs are determined to provide bidirectional current flow between the high-voltage section and the low-voltage section.

14. The method of claim 10 , further comprising controlling dissipation from the low voltage section using a chopper element.

15. The method of claim 10 , wherein the power converter inputs are determined to provide bidirectional current flow between the high-voltage section and the low-voltage section.

16. The method of claim 10 , wherein the power converter inputs are determined to permit power to only flow from the high-voltage section to the low-voltage section.

17. The method of claim 10 , wherein the power converter inputs are determined to improve the charge balance state non-dissipatively.

18. The method of claim 10 , wherein the low-voltage energy storage element comprises a low-capacity capacitive energy storage element having a low-voltage energy storage capacity at least ten times less than a high-voltage energy storage capacity of any one of the high-voltage energy storage elements.