FIELD OF THE INVENTION

This application is in the field of systems for managing or optimizing the charging of batteries from electrical energy sources. More specifically, this application is in the field of systems for monitoring a plurality of rechargeable batteries and an electrical energy input and optimizing the configuration of the batteries and the energy input so that the energy storage rate of the energy storage system can be maximised.

BACKGROUND TO THE INVENTION

The following discussion of the background to the invention is intended to facilitate an understanding of the present invention. However, it should be appreciated that the discussion is not an acknowledgement or admission that the material referred to was published, known or part of the common general knowledge in any jurisdiction as at the priority date of the application.

Various fitness equipment, such as treadmill, stationary bicycle, ladder climbing machine, and elliptical trainers, are operated by users who by exerting force generate electricity that can be used to charge and power various mobile devices and other electrical equipment. When this equipment displays the amount of energy stored for charging and powering mobile devices, it will encourage users to do more exercise and provide an overall more positive experience to the users.

However, due to incompatibility between the electricity generators that can be attached to fitness equipment and the charging systems of mobile devices, the efficiency of energy transfer and storage is poor. Thus it takes too long to charge mobile devices using fitness equipment for typical users to notice real benefits and rewards from their exercise time. This also limits practical uses of fitness equipment as an alternative energy source for various household devices, such as mobile phones, lightings, and fans.

A typical exercise time of a person ranges from 10 minutes to 20 minutes. During this time the amount of power generated may vary dramatically. Existing chargers focus on increasing charging currents to store the energy generated without planning charging capacity of individual batteries for later times. Without a careful planning, some batteries can switch to top-up charge stage (lower charging current), and thus the charging currents cannot be increased. The excess amount of energy generated will then be lost. Therefore, there is an urgent need for an efficient and effective system to address the aforementioned disadvantages. The present invention seeks to provide such a system for monitoring energy generation sources and configuring charging process to optimise energy storage and utilization to overcome at least in part some of the aforementioned disadvantages.

SUMMARY OF THE INVENTION

Throughout this document, unless otherwise indicated to the contrary, the terms“comprising”, “consisting of’, and the like, are to be construed as non-exhaustive, or in other words, as meaning“including, but not limited to”.

The present invention is an energy storage system for efficiently storing electrical energy from an unpredictable electrical energy source into multiple rechargeable batteries thereby maximising the combined energy storage rates of the batteries for the next short fixed duration of time by adaptively configuring the charging currents of the multiple rechargeable batteries.

In one embodiment, the electrical energy source is originated by any electricity stream from electrical generators, such as dynamos, attached to fitness equipment. Preferably, an input voltage detector electrically connected to the energy source, a number of energy storage devices electrically connected to the energy source. A charge controller electrically connected to the energy storage devices, wherein each energy storage device comprises a charging circuit and one or more batteries, the charge controller communicably coupled to the energy storage devices and the input voltage detector.

Next, the system determines the amount of input power P generated from the energy source using an input voltage and current detector and one or more parameters of the energy source.

Next, the system determines the stages of charge of the storage devices, wherein the batteries have at least 3 stages of charge including the first charge stage with the first charge rate FC, the second charge stage with the second charge rate TC, and the third charge stage with the third charge rate CO, wherein the system determines the Nf number of energy storage devices that are at the first charge rate FC, the Nt number of energy storage devices that are at the second charge rate TC, and the No number of energy storage devices that are at the third charge rate CO. For lithium ion batteries, the first charge rate can be the fast charge rate, the second charge rate can be the top-up charge rate, and the third charge rate can be 0 or disabled stage.

Next, the charge controller calculates the maximum second-stage power storage rate PT of the energy storage system, wherein PT is the energy storage rate when all of the energy storage devices are being charged at the second charge rate TC.

Next, the charge controller calculates the additional power storage rate AP = PT - P that need to be stored if PT is less than P, otherwise AP = 0. Next, the system calculates the optimal charging currents Ci of the i-th energy storage devices those that are at the first charge stage to accommodate the additional power storage rate AP if AP > 0, wherein Ci maximises the energy storage rate of the energy storage system for the next short fixed E minutes of a typical exercise time subject to at least two conditions which comprise condition 1 : Ci < FC, and condition 2: the difference between the energy storage rate PS of the energy storage system and P is minimal while satisfying condition 1.

Next, the system configures the charge currents of the energy storage devices, wherein the Nt energy storage devices are charged at TC or lower and the Nf energy storage devices are charged at the calculated optimal charging currents Ci, and Nc energy storage devices are charged at CO.

The system repeats the determining steps, the calculation steps, and the configuration step until P is less than TC, all batteries are at the third charge stage, or the input power voltage drops below a predefined value.

In one embodiment, the step of calculating the optimal charging currents Ci of the i-th storage devices maximises the energy storage rate of the energy storage system for the next E minutes subject to at least three conditions, wherein the conditions comprise: condition 1 : the Nt energy storage devices are charged at TC charge rate or lower, condition 2: Ci < FC, and condition 3: the difference between the energy storage rate PS of the energy storage system and P is minimal while satisfying condition 2.

In one embodiment, the energy storage rate PS of the energy storage system is calculated using the following equation:

where Nf is the number of energy storage devices at the first charge stage, Nt is the number of energy storage devices at the second charge stage, Vi is the voltage of the battery of the i-th energy storage device and Vt is the voltage of the batteries when they are charged at the second charge rate TC.

In one embodiment, the maximum second-stage power storage rate PT of the energy storage system is determined using the following equation:

PT = (Nf+Nt)xTCxVa

wherein Va is a predefined battery voltage, TC is the second charge rate, Nf is the number of energy storage devices at the first charge stage, and Nt is the number of energy storage devices at the second charge stage.

In one embodiment, the optimal charging currents Ci of the i-th Nf energy storage devices that are at the first charge stage are calculated using the following optimisation steps. First, calculating the average battery voltage av of the Nf energy storage devices using the following equation:

where Nf is the number of energy storage devices at the first charge stage, V _j is the battery voltage of the i-th Nf energy storage device. Next, calculating the first-charge remaining time Ti of the i-th energy storage device that can be charged at the first charge rate for Ti duration, wherein the i-th energy storage is at the first charge stage. Next, calculating the optimal charging currents Ci of the i-th energy storage devices that are at the first charge stage using at least one of the values of P, av, vi, and Ti, wherein Ci maximises the energy storage rate of the energy storage system for the next E minutes subject to one or more conditions, wherein the conditions comprise that the energy storage device being able to accommodate the additional power storage rate AP and that Ci < FC.

In one embodiment, the first-charge remaining time Ti of the i-th energy storage device is calculated as follows:

where FCTi is an estimated maximum duration of time of the i-th energy storage device, for which the i-th energy storage device can be charged at the first charge rate on average, and vi is the current battery voltage of the i-th energy storage device and vm is the minimum voltage of the i-th energy storage device, and a, b, and c are some constants.

In one embodiment, the optimal currents Ci of the i-th Nf energy storage devices that are at the first charge stage are calculated using the following optimisation steps. First, the system calculates the average battery voltage av of the Nf energy storage devices as follows:

where V _j is the battery voltage of the i-th Nf energy storage device.

Next, the system calculates the initial optimal currents Ci using the average battery voltage av:

Ci = CAxav/vi

where CA is the average current required for Nf energy storage devices to accommodate the additional power storage rate AP and vi is the current battery voltage of the i-th energy storage device that is at the first charge stage, wherein CA is calculated using the following equation:

(NtxTC + NfxCA)xVa = P

wherein Va is a predefined battery voltage;

Next, the system calculates the average excess current AEC using Ci:

wherein q(c) is a step function whose value is 0 if x < 0 and 1 if x > 0;

Next, the system updates the optimal current values Ci as follows:

Ci = FC if Ci > FC

Ci = Ci + AEC if Ci < FC

Next, the system repeats the steps of calculating the average excess current AEC, and updating the optimal current values Ci until AEC < 0.

In one embodiment, the energy storage system is a portable system that can be detached from the energy source and the fitness equipment, wherein the system continues to function as a power source for various devices.

In one embodiment, the system further comprising the step of selecting an energy storage device for discharging, wherein an energy storage device with the highest state of charge is selected for discharging.

In one embodiment, the electrical energy source is connected to at least one fitness equipment to generate electricity using a dynamo generator which converts users’ physical energy to electrical energy.

In one embodiment, the system further comprising the step of measuring the one or more parameters for the two or more energy storage devices, wherein the one or more parameters comprise at least one of a parallel resistance, a series resistance, a parallel capacitance, a phase angle, a battery temperature, a battery internal pressure, a battery internal resistance, a battery terminal voltage, and a voltage derivative with time.

BRIEF DESCRIPTION OF DRAWINGS

The present invention will now be described, by way of illustrative example only, with reference to the accompanying drawings, of which:

FIG 1 is a diagram of the wiring, controls, and devices that compose the disclosed energy storage system.

FIG. 2 is a diagram of the wiring, controls, and devices that compose the charge controller, and chargers, and discharge controller.

FIG. 3 is an overall flow of an embodiment of the charge controller processor. FIG. 4 is a flow chart of an embodiment of the charge controller processor, wherein the optimal charge currents are selected to match the input power.

FIG. 5 is a flow chart of an embodiment of the charge controller processor, wherein the optimal charge currents Ci are calculated iteratively.

DETAILED DESCRIPTION

Particular embodiments of the present invention will now be described with reference to the accompanying drawings. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of the present invention. Additionally, unless defined otherwise, all technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art to which this invention belongs.

The use of the singular forms“a”,“an”, and“the” include both singular and plural referents unless the context clearly indicates otherwise.

The use of“or”, ” means“and/or” unless stated otherwise. Furthermore, the use of terms “including” and“having” as well as other forms of those terms, such as“includes”,“included”, “has”, and“have” are not limiting.

In general, the present invention is an energy storage system for efficiently storing electrical energy from an unpredictable electrical energy source into multiple rechargeable batteries by adaptively configuring connections and charging currents of multiple rechargeable batteries to the amount of power generated from an unpredictable energy source and the states of charge of the rechargeable batteries by maximising the energy storage capacity for the next fixed duration of time.

A typical application is storing energy from fitness machines equipped with generators, where people normally perform exercise for some fixed duration of time with unpredictable varying levels of force. Scheduling charging currents of individual battery cells is essential to maximise average energy storage rate throughout the exercise time due to limited storage capacity and different states of charge of the batteries.

FIG. 1 is a diagram of the wiring, controls, and devices that compose the disclosed energy storage system 100. As shown, the energy storage system is connected to an electrical energy source 101 , such as a dynamo, that is connected to a fitness machine 102 and an AC-to-DC converter for DC voltage output. The energy storage system comprises a charge controller 103 that controls two or more energy storage devices 104 to store electrical energy from the energy source 101. Each of the energy storage devices 104 has a charger and at least one

rechargeable battery. The charging circuits are initially disabled preventing the flow of electrical energy from the energy source to the batteries. The energy storage devices are connected to a discharge controller 105 to be able to supply power to various devices 106, such as a mobile phones.

FIG.2 is a diagram of the wiring, controls, and devices that compose the charge controller 200, and energy storage devices 201 , and discharge controller 202. The charge controller 200 provides an input voltage detector 203 electrically connected to the energy source 204, a number of energy storage devices 201 electrically connected to the energy source 204 and a charge controller electrically connected to a number of energy storage devices 201 , wherein each energy storage device comprises a charging circuit 205 with a battery voltage detector 206, and one or more batteries 207. The charge controller processor 208 is communicably coupled to the energy storage devices 104, 201 and the input voltage detector 203.

FIG. 3 shows the overall flow of the energy storage system. Initially the charging circuits 205 are disabled preventing the flow of electrical energy from the energy source to the batteries.

At step 301 in FIG. 3, the charge controller 103 detects the amount of input power P generated from the energy source using the input voltage detector 203 and one or more parameters of the energy source 101 , 204, wherein the parameters include energy rating of the energy source. A dynamo with higher current rating will produce more power for the same input voltage.

Next at step 302, the charge controller determines the stages of charge of the storage devices 104, 201 , wherein the batteries have at least 3 stages of charge including the first charge stage with the first charge rate FC, the second charge stage with the second charge rate TC, and the third charge stage with the third charge rate CO, wherein it determines the Nf number of energy storage devices that are at the first charge rate FC, the Nt number of energy storage devices that are at the second charge rate TC, and the Nc number of energy storage devices that are at the third charge rate CO. Typical lithium ion batteries have the following 3 stages of charge: fast-charge stage (the first charge stage at the first charge rate FC), top-up charge stage (the second charge stage at the second charge rate TC), and zero charge stage (the third charge stage at third charge rate of 0). During the fast-charge stage, lithium ion battery cells can be charged at the maximum charge rate without damaging the batteries until the internal battery temperature reaches a certain level resulting in increased battery cell voltages.

Next at step 303, the charge controller calculates the maximum second-stage power storage rate PT of the energy storage system, wherein PT is the energy storage rate when all of the energy storage devices are being charged at the second charge rate TC. This is the maximum rate of power that can be stored in the energy storage devices using the second charge rate TC. Typical lithium ion batteries are charged at top-up charge rate when they are at top-up charge stage or to too cool down batteries during charging. This is a slow charge rate but a safe charging rate to charge a battery. Charging batteries at a rate lower than TC is slower but it will not increase the internal temperature of the batteries. Next at step 304, the charge controller calculates the additional power storage rate AP that need to be stored if PT is less than P:

AP = (P - PT)

The reason we calculate PT and AP is that if the input power P being generated is lower than PT (i.e. AP < 0), all batteries can be charged at the second charge rate or lower to avoid increasing internal temperatures of batteries, so that the batteries can be utilized during a higher input power at a later stage.

Next at step 305, if AP > 0, the charge controller calculates the optimal charging currents Ci of the i-th battery that are in the first charge stage (Nf energy storage devices) such that the energy storage system being able to accommodate the additional required power storage rate AP and maximises the energy storage rate of the energy storage system for the next E minutes. The system searches Ci values that maximises the energy storage rate of the energy storage system for the next E minutes subject to at least two conditions which comprise condition 1 : Ci < FC, and condition 2: the difference between the energy storage rate PS of the energy storage system and P is minimal while satisfying condition 1 , wherein PS is the energy storage rate of the energy storage system when some batteries at the first charge stage are configured with the optimal charge current Ci and some other batteries are configured at the second charge rate TC.

For example, a typical exercise session can last for 15 minutes. To maximise the energy storage rate during this 15 minutes, if AP is less than 0, we can charge all batteries at the second charge rate or lower (e.g., the top-up charge rate for lithium ion batteries) to avoid temperature increases until such time that AP is greater than 0. When AP becomes greater than 0, we can select some batteries to be charged at the first charge rate (e.g., fast charge rate for lithium ion batteries) to accommodate the additional power AP to be stored. This allows us to utilize more batteries at the first charge rate at a later stage when the incoming power suddenly increases allowing us to accomodate more power during remaining exercise time.

Next at step 306, the charge controller configures the charge currents of the energy storage devices wherein Nt energy storage devices are charged at TC current and Nf energy storage devices are charged at the optimal charging currents Ci, and Nc energy storage devices are charged at CO or disabled for charging.

The charge controller repeats the determining steps, the calculation steps, and the configuration step until P is less than TC, all batteries are at the third charge stage, or the input power voltage drops below a predefined value.

According to some embodiments, at the step of calculating the optimal charging currents Ci of the i-th storage devices, Ci maximises the energy storage rate of the energy storage system for the next E minutes subject to at least three conditions, wherein the conditions comprise:

condition 1 : the Nt energy storage devices are charged at the second charge rate TC or lower, condition 2: Ci < FC, and condition 3: the difference between the energy storage rate PS of the energy storage system and P is minimal while satisfying condition 2.

According to some embodiments, at the step of calculating the optimal charging currents Ci of the i-th storage devices, the energy storage rate PS of the energy storage system can be calculated using the following equation:

where Nf is the number of energy storage devices at the first charge stage, Nt is the number of energy storage devices at the second charge stage, Vi is the voltage of the battery of the i-th energy storage device and Vt is the voltage of the batteries when they are charged at the second charge rate TC.

According to some embodiments of the present invention, the maximum second-stage power storage rate PT of the energy storage system is determined using the following equation:

PT = (Nf+Nt)xTCxVa

wherein Va is a predefined battery voltage, TC is the second charge rate, Nf is the number of energy storage devices at the first charge stage, and Nt is the number of energy storage devices at the second charge stage. For lithium ion batteries, Va can the voltage used for charging the batteries at the top-up charge rate.

According to some embodiments of the present invention, the optimal charging currents Ci of the i-th Nf energy storage devices that are at the first charge stage are calculated using the following optimisation steps. First, the charge controller calculates the average battery voltage av of the Nf energy storage devices using the following equation:

where Nf is the number of energy storage devices at the first charge stage, V _j is the battery voltage of the i-th Nf energy storage device;

Next, the charge controller calculates the first-charge remaining time Ti of the i-th energy storage device that can be charged at the first charge rate for Ti duration, wherein the i-th energy storage is at the first charge stage;

Next, the charge controller calculates the optimal charging currents Ci of the i-th energy storage devices that are at the first charge stage using at least one of the values of P, av, vi, and Ti, wherein Ci maximises the energy storage rate of the energy storage system for the next E minutes subject to one or more conditions, wherein the conditions comprise that the energy storage device being able to accommodate the additional power storage rate AP and that Ci < FC. For example, using Ti, batteries with higher Ti values can be selected first to be charged at a charge current that is close to the first charge rate thereby allowing batteries with lower Ti values to be used in a later stage when the input power increases suddenly. If we utilize batteries with lower Ti values first, these batteries may be switched to the second charge stage and they cannot be used to accommodate the sudden increase of the input power from the energy source.

According to some embodiments of the present invention, the optimal currents Ci of the i-th Nf energy storage devices that are at the first charge stage are calculated using the following optimisation steps. First, the charge controller calculates the average battery voltage av of the Nf energy storage devices

where V _j is the battery voltage of the i-th Nf energy storage device;

Next, the charge controller calculates the initial optimal currents Ci using the average battery voltage av as follows:

Ci = CAxav/V _j

where CA is the average current required for Nf energy storage devices to accommodate the additional power storage rate AP and vi is the current battery voltage of the i-th energy storage device that is at the first charge stage, wherein CA is calculated using the following equation:

(NtxTC + NfxCA)xVa = P

wherein Va is a predefined battery voltage.

Next, the charge controller calculates the average excess current AEC using Ci:

wherein q(c) is a step function whose value is 0 if x < 0 and 1 if x > 0;

Next, the charge controller updates the optimal current values Ci as follows:

Ci = FC if Ci > FC

Ci = Ci + AEC if Ci < FC

The charge controller repeats the steps of calculating the average excess current AEC, and updating the optimal current values Ci until AEC < 0.

According to some embodiments of the present invention, the energy storage system is a portable system that can be detached from the energy source and the fitness equipment, wherein the system continues to function as a power source for devices, such as mobile phones. According to some embodiments of the present invention, the first-charge remaining time Ti of the i-th energy storage device is calculated as follows:

where FCTi is an estimated maximum duration of time of the i-th energy storage device, for which the i-th energy storage device can be charged at the first charge rate on average, and vi is the current battery voltage of the i-th energy storage device and vm is the minimum voltage of the i-th energy storage device, and a, b, and c are some constants. When a battery is fully discharged, the battery voltage is normally at vm. When a battery is charged at FC, the temperature of the batteries increases approximately in a square root curve, thereby increasing its voltage vi that follows approximately a square root curve. If the battery is charged at a current lower than FC, its voltage will rise slower than it is being charged at FC. The equation approximates the temperature increase rate to calculate the remaining time Ti.

According to some embodiments of the present invention, at the step of updating the optimal current values Ci during the iterative , the currents of the batteries with higher Ti values are increased first to delay the use of batteries with lower Ti values.

According to some embodiments of the present invention, the energy storage system further comprises the step of selecting an energy storage device 104, 201 for discharging when electrical equipment 106 is connected, wherein an energy storage device with the highest state of charge is selected for discharging to supply power to one or more devices 106 that are connected.

According to some embodiments of the present invention, the electrical energy source 101 , 204 is connected to at least one piece of fitness equipment 102 to generate electricity using a dynamo generator, which converts physical energy of users to electrical energy.

According to some embodiments of the present invention, the energy storage system 100 further comprises the step of measuring the one or more parameters for the two or more energy storage devices 104, 201 , wherein the one or more parameters comprise at least one of a parallel resistance, a series resistance, a parallel capacitance, a phase angle, a battery temperature, a battery internal pressure, a battery internal resistance, a battery terminal voltage, and a voltage derivative with time.

Example 1 :

Lithium ion batteries have fast-charge and top-up charge stages. During the fast-charge stage, battery cells can be charged at the maximum charge rate without damaging the batteries until the internal battery temperature reaches a certain level resulting in increased battery cell voltages. For a single cell Lithium-type battery (3.7 v) with battery capacity C of 3000mAh, it can only be charged at 3000mA current (i.e. , energy storage rate of 11.1 W) to avoid damaging the battery. A typical capacity of a 3.7v mobile phone battery is 3000mAh, that is, it can be normally charged at 1 1.1 Wh. For example, the battery voltage can rise to 4.1v for 3.7v lithium ion batteries when the internal temperature of the battery rises. The battery then needs to be charged at top-up charge stage. During the top-up charge stage, the battery cells are charged at a lower charging current of 0.2C (20% of the battery capacity) or less to cool the batteries or to top-up the battery charge levels. The top-up charge stage is used to top-up charged cells or until the batteries are cooled.

If the batteries are at different charge stages due to different charge levels and temperature, deciding which ones to charge at what voltage and current to maximise average storage rate for the remaining exercise time is a complex problem. If we charge some batteries too much forcing them into the top-up charge stage too early, the maximum energy storage rate will be greatly reduced at a later stage.

Our method carefully schedules the charge currents of individual battery cells to maintain as many batteries as we can at the fast-charge stage for the remaining exercise time to

accommodate sudden power surge during the remaining time.

Example 2:

FIG. 4 shows an embodiment of the charge controller processor that controls the charging of the energy storage devices, wherein the optimal charge currents are selected to match the input power. The input voltage 203 (the output of the energy source 101 , 204) and the battery voltages 206 of each individual battery 207 are measured during charging and the energy storage devices are initially disabled for charging. The charge controller 208 then determines the input power P of the energy source 101 , 204. If the input power is greater than a minimum requirement power value MinP, it continues, otherwise energy storage devices are disabled for charging and continue to monitor input power P. MinP can be a predetermined value or a value calculated from the capacity or charge ratings of the batteries. Next the charge controller determines the states of charge of the rechargeable batteries 207 of the energy storage devices 201. It then calculates the maximum second-stage power storage rate PT and the additional power storage rate AP required to store. If AP is greater than 0, it then calculates the optimal charging currents Ci for the batteries that are at the first charge stage; otherwise there is no need to charge any batteries at the fast charge rate, thereby setting Ci to the second charge rate TC and all batteries are charged at TC or lower to store the input power P. To calculate the optimal charging currents Ci, it first checks if AP is less than the amount NfxTF of power that Nf energy storage devices can accommodate. If AP > NfxTF, Ci are set to TF and all Nf energy storage devices are charged at TF charging current and the Nt energy storage devices are charged at TC charging current. If AP < NfxTF, the charge controller calculates Ci values that maximises the energy storage rate for the next E minutes subject to one or more conditions, wherein the conditions comprise the following conditions:

Condition

Condition where V _j is the battery voltage of the i-th Nf energy storage device. The first condition says that the left-hand side of the equation should be as close as possible to P. This ensures that the energy storage system stores most of the input power coming from the energy source. The second condition ensures that the batteries will not be charged over their limits.

Example 3:

FIG. 5 shows an embodiment of the charge controller processor, wherein the optimal charge currents Ci are calculated iteratively. In the figure, if AP < NfxTF, the charge controller calculates the optimal charging currents Ci to maximise the energy storage rate for the next E minutes. To do this, the charge controller first calculates the average voltage va of the Nf energy storage devices by summing the voltages vi of the Nf energy storage devices and dividing it by Nf: av = Sum(vi)/Nf. It then initializes Ci with the average current required to store AP: Ci =

CAxav/V _j , where CA is the average current required for the Nf energy storage devices to accommodate the additional power storage rate AP. Next, the charge controller calculates the average excess current AEC using Ci:

where q(c) is a step function whose value is 0 if x < 0 and 1 if x > 0. It then distributes AEC evenly over other batteries to reduce Ci below FC by updating the optimal current values Ci as follows:

Ci = FC if Ci > FC

Ci = Ci + AEC if Ci < FC

Example 4:

Suppose a person performs exercise in a pattern of 1 1 W for the first 10 minutes and 30W for the next 10 minutes. Let N=5 be the total number of battery cells and two batteries are at the fast-charge stage and the other three are at top-up charge stage. Also suppose all batteries have a capacity of 3000mAh. If we charge one battery at the fast-charge stage at 1 C (charging at 3A current) during the first 10 minutes, we can store electricity only at (1 + 4 ^c 0.2) ^c 3 ^c 3.7 = 20W during the next 10 minutes since the first battery would have been switched to the top-up charge stage due to its increased internal temperature. On the other hand, since Nx0.2xCx3.7 = 5x0.2x3x3.7 = 11 1W, we can charge all of the batteries at the top-up charge stage for the first 10 minutes to minimise the temperature rise of the batteries for the first 10 minutes. The system then switches to charge the first two cells at 1 C and the rest at 0.2C achieving 30W storage rate: 30W = (2 + 3x0.2)x3Ax3.7V.

During charging, the input power P (the amount of energy being generated from the energy source) and the voltages and internal temperatures of the battery cells are measured. The method then calculates the optimal charging currents for each of the battery cells in order to maximise the energy storage rate for a given fixed time (e.g., 17 minutes) for the unpredictable energy source. The system then monitors the input voltage of the electrical energy source and the voltages of the rechargeable batteries. The system adaptively reconfigures the connections and states of charge of the rechargeable batteries to the input voltage of the electrical energy source and states of charge (SOC) of the batteries to increase the energy storage rate of the system measured in watts for a next predetermined time duration.