Systems and methods for characterizing impedance of an energy storage device

1. A method for characterizing electrical impedance of an energy storage device, comprising:

(a) controlling a first switching power converter to transfer energy between a first battery and a second battery;

(b) controlling a second switching power converter to transfer energy between the second battery and a third battery;

(c) controlling the first switching power converter to generate a perturbation on electric current flowing through the first battery, the perturbation on the electric current flowing through the first battery including a sinusoidal component;

(d) determining an alternating current (AC) component of the electric current flowing through the first battery;

(e) determining an AC component of voltage across the first battery;

(f) determining a complex impedance of the first battery based at least in part on the AC component of the electric current flowing through the first battery and the AC component of the voltage across the first battery;

wherein:

the first, second, and third batteries are electrically coupled in series to form a string of batteries, and

determining the AC component of the electric current flowing through the first battery comprises determining the AC component from a difference between (a) an AC balancing current flowing to the first battery from the first switching power converter and (b) an AC current flowing between the string of batteries and circuitry external to the string of batteries.

2. The method of claim 1 , wherein steps (a) and (c) are performed simultaneously.

3. The method of claim 1 , step (c) including controlling the first switching power converter to generate the perturbation on the electric current flowing through the first battery at a plurality of frequencies, and step (f) including determining the complex impedance of the first battery at each of the plurality of frequencies.

4. The method of claim 1 , further comprising:

controlling at least one of the first switching power converter and the second switching power converter to generate a perturbation on electric current flowing through the second battery, the perturbation on the electric current flowing through the second battery including a sinusoidal component;

controlling the second switching power converter to generate a perturbation on electric current flowing through the third battery, the perturbation on the electric current flowing through the third battery including a third component;

determining an AC component of the electric current flowing through the second battery;

determining an AC component of voltage across the second battery;

determining a complex impedance of the second battery based at least in part on the AC component of the electric current flowing through the second battery and the AC component of the voltage across the second battery;

determining an AC component of the electric current flowing through the third battery;

determining an AC component of voltage across the third battery; and

determining a complex impedance of the third battery based at least in part on the AC component of the electric current flowing through the third battery and the AC component of the voltage across the third battery.

5. The method of claim 4 , further comprising:

controlling at least one of the first switching power converter and the second switching power converter to generate the perturbation on the electric current flowing through the second battery at a plurality of second frequencies;

controlling the second switching power converter to generate the perturbation on the electric current flowing through the third battery at a plurality of third frequencies;

determining the complex impedance of the second battery at each of the plurality of second frequencies; and

determining the complex impedance of the third battery at each of the plurality of third frequencies.

6. The method of claim 4 , further comprising simultaneously determining the complex impedance of the second battery and the complex impedance of the third battery.

7. A system for characterizing electrical impedance of an energy storage device, comprising:

a first switching power converter for electrically coupling to each of a first battery and a second battery, wherein:

the first switching power converter comprises a first switching device, a second switching device, and a tank circuit,

the tank circuit includes an inductor and a capacitor, and

the inductor is electrically coupled to the capacitor via the first switching device and the second switching device;

a second switching power converter for electrically coupling to each of the second battery and a third battery; and

a control subsystem, including:

a power conversion control module configured to control the first switching power converter and the second switching power converter to transfer energy between the first battery and the third battery via the second battery,

a perturbation control module configured to control the first switching power converter to generate a perturbation on electric current flowing through the first battery, the perturbation on the electric current flowing through the first battery including a sinusoidal component,

a current sensing module configured to determine an alternating current (AC) component of the electric current flowing through the first battery,

a voltage sensing module configured to determine an AC component of voltage across the first battery, and

an impedance determining module configured to determine a complex impedance of the first battery based at least in part on the AC component of the electric current flowing through the first battery and the AC component of the voltage across the first battery.

8. The system of claim 7 , the perturbation control module being further configured to control the first switching power converter to generate the perturbation on the electric current flowing through the first battery at a plurality of frequencies, and the impedance determining module being further configured to determine the complex impedance of the first battery at each of the plurality of frequencies.

9. The system of claim 8 , the power conversion control module being further configured to control the first switching power converter to control charging and discharging of the first battery.

10. The system of claim 7 , the control subsystem being at least partially implemented by a computing device including a processor and a memory, where the processor executes instructions in the form of software or firmware stored in the memory.

11. The system of claim 7 , the first switching power converter having a resonant switched-capacitor-type converter topology.

12. The system of claim 7 , wherein:

the first switching power converter is configured to transfer energy between the first battery and the second battery; and

the second switching power converter is configured to transfer energy between the second battery and the third battery.

13. The system of claim 7 , wherein:

the first battery, the second battery, and the third battery are electrically coupled in series; and

the power conversion control module is configured to control the first switching power converter and the second switching power converter to balance energy stored in each of the first battery, the second battery, and the third battery.

14. The system of claim 7 , wherein:

the first, second, and third batteries are electrically coupled in series to form a string of batteries; and

the current sensing module is further configured to determine the AC component of the electric current flowing through the first battery from a difference between (a) an AC balancing current flowing to the first battery from the first switching power converter and (b) an AC current flowing between the string of batteries and circuitry external to the string of batteries.

15. The system of claim 7 , wherein the inductor is electrically coupled between (a) a node that is common to each of the first battery and the second battery and (b) a node that is common to each of the first switching device and the second switching device.

16. The system of claim 7 , wherein:

the perturbation control module is further configured to control at least one of the first switching power converter and the second switching power converter to generate a perturbation on electric current flowing through the second battery, the perturbation on the electric current flowing through the second battery including a sinusoidal component;

the perturbation control module is further configured to control the second switching power converter to generate a perturbation on electric current flowing through the third battery, the perturbation on the electric current flowing through the third battery including a sinusoidal component;

the current sensing module is further configured to determine an AC component of the electric current flowing through the second battery;

the voltage sensing module is further configured to determine an AC component of voltage across the second battery;

the impedance determining module is further configured to determine a complex impedance of the second battery based at least in part on the AC component of the electric current flowing through the second battery and the AC component of the voltage across the second battery;

the current sensing module is further configured to determine an AC component of the electric current flowing through the third battery;

the voltage sensing module is further configured to determine an AC component of voltage across the third battery; and

the impedance determining module is further configured to determine a complex impedance of the third battery based at least in part on the AC component of the electric current flowing through the third battery and the AC component of the voltage across the third battery.

17. A system for characterizing electrical impedance of an energy storage device, comprising:

a first switching power converter for electrically coupling to each of a first battery and a second battery;

a second switching power converter for electrically coupling to each of the second battery and a third battery; and

a control subsystem, including:

a power conversion control module configured to control the first switching power converter and the second switching power converter to transfer energy between the first battery and the third battery via the second battery,

a perturbation control module configured to control the first switching power converter to generate a perturbation on electric current flowing through the first battery, the perturbation on the electric current flowing through the first battery including a sinusoidal component,

a current sensing module configured to determine an alternating current (AC) component of the electric current flowing through the first battery,

a voltage sensing module configured to determine an AC component of voltage across the first battery, and

an impedance determining module configured to determine a complex impedance of the first battery based at least in part on the AC component of the electric current flowing through the first battery and the AC component of the voltage across the first battery;

wherein:

the first switching power converter comprises a first switched capacitor stage, a second switched capacitor stage, and an inductor,

the first switched capacitor stage and the second switched capacitor stage are electrically coupled in parallel with each other, and

the inductor is electrically coupled between (a) a node that is common to each of the first battery and the second battery and (b) a node that is common to each of the first switched capacitor stage and the second switched capacitor stage.

18. The system of claim 17 , wherein the power conversion control module is further configured to cause the first switched capacitor stage and the second switched capacitor stage to switch 180 degrees out-of-phase with respect to each other.