Battery chargers and associated systems and methods

A method for charging a battery includes (a) applying a charging current pulse to the battery, (b) after the step of applying the charging current pulse to the battery, measuring a first voltage across the battery, (c) estimating an equilibrium voltage of the battery, (d) determining a Nernst voltage of the battery from a difference between the first voltage and the equilibrium voltage, and (e) controlling charging of the battery at least partially based on the Nernst voltage.

BACKGROUND

Batteries are used to provide electrical power in a wide variety of applications. A battery includes one or more electrochemical cells which store energy in chemical form. This stored energy is converted to electrical energy via a redox chemical reaction when an electrical load is connected to the battery. Some batteries are intended for single-use and are discarded after their stored energy is depleted. Such batteries are referred to as primary batteries. Other batteries can be recharged after their stored energy is depleted, and these batteries are referred to as secondary batteries.

One popular secondary battery is a lithium-ion battery, which includes one or more lithium-ion electrochemical cells. Each lithium-ion electrochemical cell includes an anode, a cathode, and electrolyte separating the anode and cathode. Lithium ions move through the electrolyte from the anode to the cathode during cell discharging, and lithium ions move through the electrolyte from the cathode to the anode during cell charging. Lithium-ion batteries advantageously have a high energy density, negligible memory effect, and low rate of self-discharge. However, the batteries have some significant drawbacks.

For example, lithium-ion batteries can be easily damaged by overcharging, potentially resulting in battery leakage, fire, and/or explosion. Therefore, it is critical that the batteries not be overcharged. Additionally, lithium-ion batteries can be damaged when used outside of their intended voltage range. Thus, power management circuitry must ensure that voltage of lithium-ion batteries remains within an acceptable range at all times. Furthermore, the batteries degrade over time, such as due to chemical reactions in the anodes and cathodes of constituent electrochemical cells, resulting in reduced battery capacity and increased likelihood of catastrophic battery failure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

A lithium-ion battery is conventionally charged using a constant current-constant voltage (CCCV) charging method. The CCCV charging method consists of a constant current (CC) stage followed by a constant voltage (CV) stage. Current of fixed magnitude is applied to the battery during the CC stage, and a voltage of fixed magnitude is applied to the battery during the CV stage.FIG. 1is a graph100illustrating one example of the CCCV charging method, where the vertical axis represents magnitude and the horizontal axis represents time. Graph100includes curves representing voltage102across the battery and current104into the battery. Charging begins at time to with the CC stage, and battery current104is fixed at value I1during the CC stage. The CC stage continues until time t1when battery voltage102reaches a maximum value Vmaxand the CV stage begins. Battery voltage102is fixed at Vmaxduring the CV stage. The CV stage continues until time t2when battery current104drops to a minimum threshold value12and charging ends.

Although the CCCV charging method is relatively simple to implement, it has significant shortcomings. For example, in many situations, the CCCV method will charge a battery at an unnecessarily slow rate. In particular, it is desirable that current I1during the CC stage be as large as possible to quickly charge the battery. However, too large of a value of I1will damage the battery. Additionally, the maximum permissible value of I1varies from battery-to-battery due to a number of factors, such as variations in battery manufacturing. Furthermore, the maximum permissible value of I1may change as the battery ages and as battery operating conditions change. Therefore, the value of I1is chosen so that the battery will not be overcharged under worst-case conditions, resulting in I1being lower than necessary under most conditions. Such non-optimal value of I1causes the battery to be charged at an unnecessarily slow rate under most circumstances.

Additionally, as evident fromFIG. 1, a battery spends significant time at maximum voltage Vmaxduring CCCV charging. This high voltage degrades the battery over time, and the CCCV charging method is therefore detrimental to battery longevity.

Applicant has developed battery chargers and associated systems and methods which at least partially overcome one or more of the problems discussed above with conventional charging techniques. These new battery chargers implement a pulse charging method where battery charging is controlled at least partially based on concentration stress (cstress) of the battery, where cstressis a concentration gradient of ions in the battery, e.g., a lithium ion concentration gradient in the case of a lithium-ion battery. Consequently, certain embodiments of the battery chargers are capable of optimizing battery charging for a particular battery under its current operating conditions, thereby potentially achieving faster battery charging and/or longer battery life than possible using conventional battery charging techniques.

To help understand the battery charging methods of the new battery chargers, consider graph200ofFIG. 2, which illustrates a charging current pulse applied to a lithium-ion battery. The vertical axis of graph200represents magnitude, and the horizontal axis of the graph represents time. Graph200includes respective curves representing voltage202across the battery and current204into the battery. Battery voltage202is at equilibrium value Veqnat time t1when a charging current pulse206is applied to the battery. Battery voltage202rises very quickly from time t1to t2due to ohmic over-voltage effects in the battery, and battery voltage202rises quickly from time t2to t3due to activation over-voltage effects in the battery. Battery voltage202continues to rise from time t3to t4as lithium ions are transferred from the cathode to the anode in the electrochemical cell(s) of the battery.

Charging current pulse206terminates at time t4, and battery voltage202falls very quickly from time t4to t5due to ohmic over-voltage effects in the battery, and battery voltage202falls quickly from time t5to t6due to activation over-voltage effects in the battery. Battery voltage202slowly falls during time period tNernst, which is time from time t6to t7. The battery's lithium ion concentration reaches equilibrium state at time t7, and battery voltage202is at a new equilibrium value Veqn+1at time t7. Equilibrium voltage Veqn+1is higher than equilibrium voltage Veqndue to energy delivered to the battery by charging current pulse206. It should be noted thatFIG. 2is not drawn to scale in that time period tNernstis typically very long, such as an hour or more, while the time period from time t1to time t6is much shorter.

Cstresscan be determined from battery voltage202changes due to activation over-voltage effects, i.e., battery voltage202from times t5to t6. However, significant data collection resources are required to obtain this data, and Cstresscan only be indirectly determined from activation over-voltage. Consequently, significant data collection and processing resources are required to determine Cstressfrom activation over-voltage effects.

Applicant has determined that Cstresscan instead be determined from the difference in battery voltage202between times t6and t7, referred to as VNernst. VNernstis related to Cstressas follows, where Ceqis battery ion concentration at equilibrium, R is the gas constant, T is temperature, n is number of electrons participating in the redox reaction of the battery, and F is Faraday's constant:

Ceqand n can be determined for a particular battery, and T can be measured or estimated. Accordingly, Cstresscan be determined if VNernstis known. Additionally, changes in Cstresscan determined simply from a change in VNernstassuming that T remains unchanged. T will typically not significantly vary over short time periods due to large battery thermal mass. Additionally, T can be measured during operation. Consequently, battery charging can be controlled based on Cstressby controlling charging based on VNernst.

As discussed above, time period tNernstis very long, and therefore, it would not be practical to measure battery voltage202at time t7after each charging current pulse206, because doing so would typically require waiting an hour or more after each charging current pulse for lithium ion concentration in the battery to equalize. Applicant has found, however, that battery voltage202at time t7is commonly available from battery management circuitry. For example, battery management circuitry often includes a “fuel gauge” to determine energy remaining in a battery, and the fuel gauge is typically configured to estimate battery open-circuit voltage at equilibrium, i.e., battery voltage202at time t7, when determining remaining energy. Therefore, VNernstcan be determined from (a) measured battery voltage202at time t6and (b) estimated battery open-circuit voltage at time t7, without needing to wait for battery ion concentration to equalize after each charging current pulse.

FIG. 3illustrates a battery charger300, which controls battery charging based on Cstress. Battery charger300includes power circuitry302and a controller304. Power circuitry302receives electrical power from an electrical power source306, and power circuitry302is configured to charge one or more batteries (not shown) of a battery assembly308by repeatedly applying charging current pulses to battery assembly308. In some embodiments, battery assembly308further includes additional circuitry (not shown), such as circuitry for measuring current through battery assembly308and/or circuitry for measuring voltage across battery assembly308. Electrical power source306could be either an alternating current (AC) electrical power source or a direct current (DC) electrical power source. In some embodiments, power circuitry302includes a switching power converter, such as a buck converter or a boost converter, to apply charging current pulses to battery assembly308. Alternately or additionally, power circuitry302may include a linear regulator to regulate magnitude of voltage applied to battery assembly308. In some embodiments, power circuitry302controls flow of electrical power to battery assembly308simply by opening and closing a switch electrically coupled in series or in parallel with battery assembly308. In particular embodiments, battery charger300is intended for use with one or more lithium-ion batteries, i.e., battery assembly308includes one or more lithium-ion batteries, but battery charger300could be adapted to work with other battery types without departing from the scope hereof.

Controller304is configured to control charging of the one or more batteries of battery assembly308at least partially based on Cstressof the one or more batteries, such that controller304uses Cstressas a feedback parameter. Accordingly, battery charger300operates in a closed-loop fashion. Controller304includes a processor310and a memory312. Processor310execute instructions314in the form of firmware or software stored in memory312to generate a power signal316for controlling power circuitry302, such that controller304controls charging of the one or more batteries of battery assembly308. In particular, controller304samples voltage Vbatacross battery assembly308after a charging current pulse and a subsequent short relaxation period, such as after change in Vbatdue to ohmic and activation over-voltage effects. For example, in some embodiments, controller304samples voltage Vbatat time t6inFIG. 2. In certain embodiments, controller304includes circuitry (not shown) for (a) storing a sample of voltage Vbatand (b) digitizing the stored sample, for use by processor310. Controller304also receives estimated battery open-circuit equilibrium voltage Veq, such as estimated battery voltage at time t7inFIG. 2, from a fuel gauge318. Fuel gauge318determines open-circuit equilibrium voltage Veq, Processor310then executes instructions314to determine VNernstusing EQN. 2 below or a variation thereof.
VNernst=Vbat−Veq(EQN. 2)

As discussed above with respect to EQN. 1, changes in VNernstrepresent changes in Cstressassuming battery temperature remains unchanged. Accordingly, processor310executes instructions314to control charging of the one or more batteries of battery assembly308based at least partially on VNernst, thereby controlling charging of the one or more batteries based on Cstress. For example, in some embodiments, processor310compares VNernstto one or more threshold values, and processor310varies charging rate of the one or more batteries of battery assembly308in response to VNernstcrossing the one or more threshold values. For instance, in some embodiments, processor310increases rate of charging of the one or more batteries in response to VNernstdropping below a first threshold value, and processor310decreases rate of charging of the one or more batteries in response to VNernstrising above a second threshold value. The first and second threshold values may be the same or different.

Processor310repeatedly executes the steps discussed above to repeatedly determine VNernstand control battery charging according to VNernstFor example, in some embodiments, processor310determines VNernstafter each charging current pulse, while in some other embodiments, processor310determines VNernstless frequently, such as after every N charging current pulses, where N is an integer greater than one. Several examples of possible operating methods of charger300are discussed below with respect toFIGS. 9-12. The ability to control charging according to VNernstenables battery charger308to be optimized for fast battery charging and/or for battery longevity, as discussed below. In some embodiments, controller304is further configured to control charging of the one or more batteries of battery assembly308such that battery voltage Vbatdoes not exceed a maximum permissible voltage of battery assembly308. Furthermore, in some embodiments, controller304uses ohmic and activation over-voltage along with VNernstto determine pulse shape, current magnitude, and time length of a next charging event.

In particular embodiments, power circuitry302controls charging of the one or more batteries of battery assembly308according to power signal316from controller304by varying amplitude of charging current pulses, by varying duty cycle of charging current pulses, and/or by varying frequency of charging current pulses.FIGS. 4-6illustrate several examples of battery charger300controlling charging of the one or more batteries of battery assembly308at least partially based on VNernst. Specifically,FIG. 4is a graph400of charging current pulse402magnitude verses time. Power circuitry302repeatedly generates charging current pulses402under the control of controller304. At time t1, processor310determines that VNernsthas risen above a threshold value, and in response, processor310controls power circuitry302to decrease magnitude of charging current pulses402, thereby decreasing charging rate of the one or more batteries of battery assembly308.

FIG. 5is a graph500of charging current pulse502magnitude verses time. At time t1, processor310determines that VNernsthas fallen below a threshold value, and in response, processor310controls power circuitry302to increase duty cycle of charging current pulses502, thereby increasing charging rate of the one or more batteries of battery assembly308.FIG. 6, in turn, is a graph600of charging current pulse602magnitude verses time. At time t1, processor310determines that VNernsthas fallen below a threshold value, and in response, processor310controls power circuitry302to increase frequency of charging current pulses602, thereby increasing charging rate of the one or more batteries of battery assembly308.

FIG. 7illustrates a fuel gauge700, which is one possible implementation of fuel gauge318(FIG. 3). It should be understood, however, that fuel gauge318is not limited to theFIG. 7implementation but instead could be implemented in any other manner as long as fuel gauge318is capable of providing estimated equilibrium voltage Veqto controller304. Furthermore, fuel gauge318could be replaced with another device providing equilibrium voltage Veqwithout departing from the scope hereof.

Fuel gauge700includes a resistor702, a capacitor704, and interface circuitry706. Resistor702is electrically coupled between battery assembly308and capacitor704at a node708, and interface circuitry706is electrically coupled to node708. Applicant has found that voltage Vcapacross capacitor704largely tracks equilibrium voltage of battery assembly308and is largely unaffected by load on battery assembly308. Thus, fuel gauge700outputs estimated equilibrium voltage Veqin proportion to voltage across capacitor704, i.e., voltage at node708. Interface circuitry706electrically interfaces node708with controller304. In some embodiments, interface circuitry706includes sampling circuitry for sampling voltage at node308and an analog-to-digital converter for digitizing the sampled voltage.

Resistor702and capacitor704could be replaced by, or supplemented with, other circuitry providing an integration function. Additionally, the integration achieved by resistor702and capacitor704could alternately be achieved using digital filtering techniques without departing from the scope hereof.

AlthoughFIG. 3illustrates controller304and power circuitry302being separate elements, power circuitry302and controller304could be at least partially combined without departing from the scope hereof. Additionally, controller304could be modified to further include fuel gauge318. For example, instructions314could be supplemented so that processor310executes instructions314to generate estimated equilibrium voltage Veq, such that processor310takes the place of fuel gauge318. Furthermore, processor310and memory312could be replaced with or supplemented by analog circuitry. For example, in certain alternate embodiments, processor310and memory312are replaced by an analog computer.

In some alternate embodiments, controller304is further configured to control charging of the one or more batteries of battery assembly308based on both activation over-voltage of the battery and VNernst. For example, in certain embodiments, controller304controls charging of the one or more batteries of battery assembly308according to Vfb, which is determined as follows, where Vresistivityand Vactivationare determined from battery voltage202between times t4and t6inFIG. 2:
Vfb=VNernst−Vresistivity−Vactivation(EQN. 3)

Vresistivityand Vactivationare determined from Vbat, for example, in accordance with their respective relaxation time constants, which can be determined during battery characterization. A typical time constant for Vresistivityis less than a microsecond, and a typical time constant for Vactivationis in the millisecond regime.

Controlling charging of the one or more batteries of battery assembly308based on both activation over-voltage and VNernstcan advantageously achieve tighter regulation of Cstressduring battery charging than that achievable by controlling charging based on VNernstalone. Additionally, knowledge of voltage at time t4can be used to ensure that voltage across battery assembly308does not exceed a maximum permissible voltage of battery assembly308. However, determining Cstressfrom activation over-voltage effects increases processing and data collection requirements of controller304.

Battery charger300could be co-packaged with other components. For example,FIG. 8illustrates a battery module800including battery charger300co-packaged with an instance of battery assembly308and fuel gauge318. Battery charger300is electrically coupled to battery assembly308. Details of battery charger300are not shown inFIG. 8to promote illustrative clarity.

Controller304's use of VNernstto control charging of battery assembly308can achieve significant advantages. For example, in some embodiments, controller304is configured to control charging of the one or more batteries of battery assembly308such that Cstress, as represented by VNernst, is at or slightly below a maximum permissible value of Cstressfor battery assembly308, such that controller304is optimized for fast charging. Charging the one or more batteries of battery assembly308in such manner minimizes battery charging time by maximizing rate of battery charging while preventing battery damage. CCCV charging techniques typically cannot achieve such fast charging because battery charging current must be sufficiently low to prevent battery damage under worst case conditions, as discussed above.

As another example, in some other embodiments, controller304is configured to charge the one or more batteries of battery assembly308such that Cstress, as represented by VNernst, is significantly below the maximum permissible value of Cstressfor the one or more batteries, to optimize controller304for battery longevity. Charging battery assembly308in such manner promotes battery longevity by reducing charging-induced stress in the one or more batteries of battery assembly308and by helping reduce time that the one or more batteries are exposed to high voltage. CCCV charging techniques typically cannot achieve such battery longevity because of their relatively long CV stage which subjects a battery to prolonged high voltage.

As yet another example, in particular embodiments, controller304is configured to charge the one or more batteries of battery assembly308such that Cstressrepresented by VNernst, varies during charging of the one or more batteries. For instance, in some embodiments, controller304controls charging of the one or more batteries of battery assembly308such that Cstressis relatively high at the beginning of the battery charging process and such that Cstressis reduced later in the battery charging process. Charging battery assembly308in such manner promotes both fast charging and long life of battery assembly308. In particular, concentration Cstressgradient of a battery is typically relatively low at low battery state of charge, and therefore, can be large at the beginning of the battery charging process to promote fast charging without degrading battery life. However, a battery is more susceptible to damage near the end of the battery charging process, and reducing Cstressas the battery charging process progresses reduces likelihood of battery degradation from excessive battery stress, thereby promoting battery longevity.

Discussed below with respect toFIGS. 9-12are several examples of how a battery can be charged using the new battery charging techniques developed by Applicant. Although the exemplary methods are discussed with respect to battery charger300ofFIG. 3, the examples are not limited to use with battery charger300. To the contrary, the methods could be used with other battery chargers which determine VNernst. Additionally, battery charger300is not limited to use with the following methods.

FIG. 9illustrates a method900for charging a battery. Method900begins with a step902of applying a charging current pulse to a battery. In one example of step902, power circuitry302applies a charging current pulse to battery assembly308, such as charging current pulse402,502, or602ofFIGS. 4-6, respectively. In step904, a first voltage is measured across the battery, after the step of applying the charging current pulse to the battery. In one example of step904, controller304measures voltage Vbatacross battery assembly308after the charging current pulse and a subsequent short relaxation period, such as at time t6ofFIG. 2. In step906, an equilibrium voltage of the battery is estimated. In one example of step906, fuel gauge318provides estimated equilibrium voltage Veq, i.e., estimated voltage Vbatat time t7ofFIG. 2. In step908, VNernstof the battery is determined from at least a difference between the first voltage and the equilibrium voltage. In one example of step908, processor310executes instructions314to determine VNernstfrom Vbatand Vequsing EQN. 2. In step910, charging of the battery is controlled at least partially based on VNernst. In one example of step910, processor310controls power circuitry302to control charging of battery assembly308based at least partially on VNernstby controlling at least one of magnitude, duty cycle, and frequency of charging pulses to battery assembly308. Method900optionally repeats until the battery is fully charged.

FIG. 10illustrates another method1000for charging a battery. In step1002, the battery is charged to 3.8 volts. In one example of step1002, power circuitry302applies charging current pulses to battery assembly308until battery voltage Vbatreaches 3.8 volts. In step1004, the battery is charged for 10 seconds at charging rate of 4 C. In one example of step1004, power circuitry302applies a 4 C charging current pulse to battery assembly308for 10 seconds. The term “C” in this context means a charging rate equivalent to the capacity of the battery. For example, a 3 ampere-hour battery charged with a 3 ampere current source would be charged at a 1 C rate, and the 3 ampere-hour battery charged with a 12 ampere current source would be charged at a 4 C rate.

Step1006determines if the battery has reached 4.2 volts. If yes, method1000ends, and if no, method1000continues to step1008. In one example of step1006, controller304determines whether battery voltage Vbathas reached 4.2 volts. In step1008, the battery is allowed to “rest” for one second, i.e., the battery is not charged for one second, and then VNernstis determined. In one example of step1008, power circuitry302discontinues charging of battery assembly308for one second, and controller304determines VNernstof battery assembly308. Step1010determines if VNernstis less than 60 millivolts. If yes, method1000proceeds to step1012, and if no, method1000proceeds to step1014. In one example of step1010, controller304compares VNernstto a 60 millivolt threshold. In step1012, the battery charge rate is increased by 0.25 C, and in step1014, the battery charge rate is decreased by 0.25 C. In one example of step1012, power circuitry302increases charging rate of battery assembly308by 0.25 C, and in one example of step1014, power circuitry302decreases charging rate of battery assembly308by 0.25 C. Method1000proceeds from each of steps1012and1014to step1016where the battery is charged for 10 seconds. In one example of step1016, power circuitry302charges battery assembly308for 10 seconds. Method1000returns to step1006from step1016.

Method1000maintains Cstressat an approximately constant value when charging a battery, i.e., it maintains Cstressat a value approximately corresponding to VNernstof 60 mV for the battery being charged. The value of Cstresscorresponding to VNernstfor the battery being charged can be determined from EQN. 1. Method1000could be optimized for faster charging by selecting a high value of VNernstin comparison step1010, and method1000could be optimized for long battery life by selecting a low value of VNernstin comparison step1010.

FIGS. 11 and 12respectively illustrate methods1100and1200where Cstressis maintained at a high value during early stages of battery charging and where Cstressis maintained at a low value during later stages of battery charging. In particular, Cstressis maintained at a value approximately corresponding to VNernstof 70 mV when battery voltage is less than 4.15 volts, and Cstressis maintained at a value approximately corresponding to VNernstof 40 mV when battery voltage is greater than or substantially equal to 4.15 volts, for example.

In method1100ofFIG. 11, the battery is charged at 90 percent duty cycle. Method1100begins with step1102of determining if battery voltage is less than 4.15 volts. If yes, method1100proceeds to step1104, and if no, method1100proceeds to step1114. In one example of step1102, controller304determines whether battery voltage Vbatis less than 4.15 volts. In step1104, the battery is charged for 10 seconds at a charging rate of 2 C. In one example of step1104, power circuitry302applies a 2 C charging current pulse to battery assembly308for 10 seconds. In step1106, the battery is allowed to rest for 1 second and VNernstis determined. In one example of step1106, power circuitry302discontinues charging battery assembly308for one second and controller304determines VNernstof battery assembly308.

Step1108determines if VNernstis less than 70 millivolts. If yes, method1100proceeds to step1110, and if no, method1100proceeds to step1112. In one example of step1108, controller304compares VNernstto a 70 millivolt threshold. In step1110, the battery charge rate is increased by 0.25 C, and in step1112, the battery charge rate is decreased by 0.25 C. In one example of step1110, power circuitry302increases charging rate of battery assembly308by 0.25 C, and in one example of step1112, power circuitry302decreases charging rate of battery assembly308by 0.25 C. Method1100returns from each of steps1110and1112to step1102.

In step1114, the battery is charged for 10 seconds at a charging rate of 2 C. In one example of step1114, power circuitry302applies a 2 C charging current pulse to battery assembly308for 10 seconds. In step1116, the battery is allowed to rest for 1 second and VNernstis determined. In one example of step1116, power circuitry302discontinues charging battery assembly308for one second and controller304determines VNernstof battery assembly308.

Step1118determines if VNernstis less than 40 millivolts. If yes, method1100proceeds to step1120, and if no, method1100proceeds to step1122. In one example of step1118, controller304compares VNernstto a 40 millivolt threshold. In step1120, the battery charge rate is increased by 0.25 C, and in step1122, the battery charge rate is decreased by 0.25 C. In one example of step1120, power circuitry302increases charging rate of battery assembly308by 0.25 C, and in one example of step1122, power circuitry302decreases charging rate of battery assembly308by 0.25 C. Method1100continues from each of steps1120and1122to step1124where the battery is charged for 10 seconds.

Step1126determines if battery voltage is less than 4.2 volts. If yes, method1100returns to step1116, and if no, method1100proceeds to step1128. In one example of step1126, controller304determines whether battery voltage Vbatis less than 4.2 volts. In step1128, the battery is charged at a constant voltage until battery current magnitude drops to C/20. In one example of step1128, power circuitry charges battery assembly308at 4.2 volts until battery current magnitude drops to C/20.

Method1200ofFIG. 12is like method1100ofFIG. 11, but where the battery is charged at 50 percent duty cycle. In particular, steps1104,1114, and1124of method1100are replaced with steps1204,1214, and1224, respectively, where the battery is charged for three seconds instead of for ten seconds, and steps1106and1116are replaced with steps1206and1216, respectively, where the battery is allowed to relax for three seconds instead of for one second. Method1200is otherwise like method1100.

FIG. 13is a graph1300of simulated battery capacity verses number of cycles. Curves1302and1304correspond to a battery being charged according to method1100ofFIG. 11, and curve1306corresponds to a battery being charged according to method1200ofFIG. 12. Curves1308and1310, on the other hand, correspond to a battery being charged according to a conventional CCCV method, such as the method ofFIG. 1. As evident fromFIG. 13, the batteries charged according to methods1100and1200retain significantly more capacity after cycling than the batteries charged according to the conventional CCCV method.

As discussed above, battery assembly308includes one or more batteries.FIG. 14illustrates battery assembly308being implemented by a battery assembly1408including a single battery.FIG. 15illustrates battery assembly308being implemented by a battery assembly1508including two batteries electrically coupled in series, andFIG. 16illustrates battery assembly308being implemented by a battery assembly1608including two batteries electrically coupled in parallel. Each of battery assemblies1508and1608could be modified to include additional batteries without departing from the scope hereof.FIG. 17illustrates battery assembly308being implemented by a battery assembly1708including a plurality of batteries electrically coupled in a series-parallel electrical topology. The number of batteries in battery assembly1708, as well as their specific series-parallel electrical topology, may vary without departing from the scope hereof.

In applications requiring multiple battery assemblies, a respective instance of battery charger300may be used for each battery assembly. For example,FIG. 18illustrates a battery module1800including two instances of battery charger300, where each battery charger300is electrically coupled to respective battery assembly308and a respective fuel gauge318. Although each instance of battery charger300is powered by a common electrical power source306, each battery charger300instance could alternately be powered from a respective electrical power source. Battery module1800could be modified to include additional instances of battery charger300, battery assembly308, and fuel gauge318without departing from the scope hereof. Details of battery chargers300are not shown inFIG. 18to promote illustrative clarity.

Battery chargers300are electrically coupled to electrical power source306in parallel in theFIG. 18battery module. However, battery chargers300could also be electrically coupled to an electric power source in series. For example,FIG. 19illustrates a battery module1900including two instances of battery charger300electrically coupled to electrical power source306in series. Like battery module1800, each battery charger300in battery module1900is electrically coupled to respective battery assembly308and a respective fuel gauge318. Battery module1900could be modified to include additional instances of battery charger300, battery assembly308, and fuel gauge318without departing from the scope hereof.

Combinations of Features

Features described above may be combined in various ways without departing from the scope hereof. The following examples illustrate some possible combinations:

(A1) A method for charging a battery may include (1) applying a charging current pulse to the battery, (2) after the step of applying the charging current pulse to the battery, measuring a first voltage across the battery, (3) estimating an equilibrium voltage of the battery, (4) determining a Nernst voltage of the battery from a difference between the first voltage and the equilibrium voltage, and (5) controlling charging of the battery at least partially based on the Nernst voltage.

(A2) The method denoted as (A1) may further include comparing the Nernst voltage to a first threshold value and decreasing a rate of charging of the battery in response to the Nernst voltage exceeding the first threshold value.

(A3) In the method denoted as (A2), the step of decreasing the rate of charging of the battery may include at least one of the following steps: (1) decreasing a magnitude of charging current pulses to the battery, (2) decreasing a duty cycle of charging current pulses to the battery, and (3) decreasing a frequency of charging current pulses to the battery.

(A4) Any one of the methods denoted as (A1) through (A3) may further include comparing the Nernst voltage to a second threshold value and increasing a rate of charging of the battery in response to the Nernst voltage being below the second threshold value.

(A5) In the method denoted as (A4), the step of increasing the rate of charging of the battery may include at least one of the following steps: (1) increasing a magnitude of charging current pulses to the battery, (2) increasing a duty cycle of charging current pulses to the battery, and (3) increasing a frequency of charging current pulses to the battery.

(A6) In any one of the methods denoted as (A4) and (A5), the first threshold value may be different from the second threshold value.

(A7) In any one of the methods denoted as (A4) and (A5), the first threshold value may be the same as the second threshold value.

(A8) Any one of the methods denoted as (A1) through (A7) may further include controlling charging of the battery based on an activation over-voltage of the battery.

(A9) In any one of the methods denoted as (A1) through (A8), the step of controlling charging of the battery at least partially based on the Nernst voltage may include controlling charging of the battery such that a concentration stress of the battery does not exceed a maximum permitted concentration stress of the battery.

(A10) In the method denoted as (A9), the step of controlling charging of the battery at least partially based on the Nernst voltage may further include controlling charging of the battery such that the concentration stress is substantially equal to a maximum permitted concentration stress of the battery.

(A11) In any one of the methods denoted as (A9) and (A10), the battery may include one or more lithium-ion electrochemical cells.

(A12) In the method denoted as (A11), the concentration stress may be a concentration gradient of lithium ions in the battery.

(A13) Any one of the methods denoted as (A1) through (A12) may further include controlling charging of the battery such that a voltage across the battery does not exceed a maximum permitted voltage of the battery.

(A14) In any one of the methods denoted as (A1) through (A13), the step of measuring the first voltage across the battery may include measuring the first voltage after change in voltage across the battery due to ohmic and activation over-voltage effects.

(A15) In any one of the methods denoted as (A1) through (A14), estimating the equilibrium voltage of the battery may include estimating the equilibrium voltage using a fuel gauge configured to determine energy remaining in the battery.

(B1) A battery charger may include power circuitry configured to apply charging current pulses to a battery and a controller configured to (1) cause the power circuitry to apply a first charging current pulse to the battery, (2) after the step of applying the first charging current pulse to the battery, measure a first voltage across the battery, (3) estimate an equilibrium voltage of the battery, (4) determine a Nernst voltage of the battery at least from a difference between the first voltage and the equilibrium voltage, and (5) control the power circuitry to control charging of the battery at least partially based on the Nernst voltage.

(B2) In the battery charger denoted as (B1), the controller may be further configured to compare the Nernst voltage to a first threshold value and control the power circuitry to decrease a rate of charging of the battery in response to the Nernst voltage exceeding the first threshold value.

(B3) In the battery charger denoted as (B2), the power circuitry may be configured to decrease the rate of charging of the battery by at least one of (1) decreasing a magnitude of charging current pulses to the battery, (2) decreasing a duty cycle of charging current pulses to the battery, and (3) decreasing a frequency of charging current pulses to the battery.

(B4) In any one of the battery chargers denoted as (B1) through (B3), the controller may be further configured to compare the Nernst voltage to a second threshold value and control the power circuitry to increase a rate of charging of the battery in response to the Nernst voltage being below the second threshold value.

(B5) In the battery charger denoted as (B4), the power circuitry may be configured to increase the rate of charging of the battery by at least one of (1) increasing a magnitude of charging current pulses to the battery, (2) increasing a duty cycle of charging current pulses to the battery, and (3) increasing a frequency of charging current pulses to the battery.

(B6) In any one of the battery chargers denoted as (B4) and (B5), the first threshold value may be different from the second threshold value.

(B7) In any one of the battery chargers denoted as (B4) and (B5), the first threshold value may be the same as the second threshold value.

(B8) In any one of the battery chargers denoted as (B1) through (B7), the controller may be further configured to control charging of the battery based on an activation over-voltage of the battery.

(B9) In any one of the battery chargers denoted as (B1) through (B8), the controller may be further configured to control the power circuitry such that a concentration stress of the battery does not exceed a maximum permitted concentration stress of the battery.

(B10) In the battery charger denoted as (B9), the controller may be further configured to control the power circuitry such that the concentration stress is substantially equal to a maximum permitted concentration stress of the battery.

(B11) In any one of the battery chargers denoted as (B1) through (B10), the controller may be further configured to control the power circuitry such that a voltage across the battery does not exceed a maximum permitted voltage of the battery.

(B12) In any one of the battery chargers denoted as (B1) through (B11), the controller may be further configured to measure the first voltage across the battery after change in voltage across the battery due to ohmic and activation over-voltage effects.

(C1) A battery module may include a battery and any one of the battery chargers denoted as (B1) through (B12).

(C2) In the battery module denoted as (C1), the battery may include one or more lithium-ion electrochemical cells.