Abstract: METHOD AND SYSTEM FOR CELL-BALANCING OF BATTERY PACK The present disclosure describes a system (100) for cell-balancing of a battery pack (102). The system (100) comprises a plurality of cells (104) housed within the battery pack (102). The system (100) comprises a plurality of voltage sensors (106) communicably coupled to the plurality of cells (104) and configured to measure a cell voltage value for each cell from the plurality of cells (104). The system (100) comprises a processor (108) operatively connected to the plurality of voltage sensors (106), and configured to receive the voltage value from the plurality of voltage sensors (106) and identify a voltage mismatch in the plurality of cells (104). The system (100) comprises at least one cell balancing circuit (110) operatively connected to the processor (108), and configured to minimise the voltage mismatch in the plurality of cells (104) based on a control signal generated by the processor (108). FIG. 1
DESC:METHOD AND SYSTEM FOR CELL-BALANCING OF BATTERY PACK
CROSS REFERENCE TO RELATED APPLICATIONS
The present application claims priority from Indian Provisional Patent Application No. 202521000478 filed on 02/01/2025, the entirety of which is incorporated herein by a reference.
TECHNICAL FIELD
Generally, the present disclosure relates to a diagnosis of a battery management system. Particularly, the present disclosure relates to a system and method for cell-balancing of a battery pack.
BACKGROUND
A battery pack is an assembly of multiple electrochemical cells arranged in series, parallel, or hybrid configurations to deliver required voltage and current levels for powering electrical systems. Each cell within the battery pack exhibits variations in charge retention, internal resistance, and aging characteristics, leading to voltage mismatches during charge and discharge cycles. Cell balancing is a critical process that equalizes voltages across all cells in the pack to maintain uniform charge distribution, enhance performance, extend service life, and prevent safety hazards such as overcharging or deep discharging of individual cells. Effective cell balancing ensures stable operation of high-capacity battery packs deployed in applications such as electric vehicles, renewable energy storage, and portable electronics.
Existing technologies for cell balancing employ passive cell balancing. The passive cell balancing dissipates the excess energy from cells with higher states of charge as heat, through shunt resistors connected in parallel to each cell. Further, as a cell’s voltage exceeds a certain threshold during charging, an electronic switch, such as a Metal-Oxide Field Effect Transistor (MOSFET), connects the resistor, allowing current to flow and bleed off the surplus charge until all cells reach a uniform voltage level. The above-mentioned passive cell balancing is achieved using fixed or switching shunt resistors. Furthermore, an averaging cell balancing is also employed for fixed values of voltages across each cell.
However, there are certain problems associated with the existing or above-mentioned mechanism for cell-balancing of a battery pack that arise from limited measurement accuracy, inefficient energy utilization, and slow response under dynamic operating conditions. The voltage sensors in existing arrangements provide static measurements, leading to errors during the computation of deviation voltages. The averaging-based balancing approach lacks sensitivity to localized variations in cell impedance, temperature, and state of health, resulting in limited accuracy. Over time, reliance solely on averaging fails to correct subtle but critical deviations, leading to cumulative imbalance, reduced pack efficiency, and shortened operational lifespan. Further, the passive balancing approaches waste significant energy as heat, reducing overall efficiency, while active balancing systems demand complex hardware with limited adaptability to real-time variations.
Therefore, there exists a need for a secure, interoperable, and automated alternative for cell-balancing of a battery pack.
SUMMARY
An object of the present disclosure is to provide a system for cell-balancing of a battery pack.
Another object of the present disclosure is to provide a method for cell-balancing of a battery pack.
Yet another object of the present disclosure is to provide a system and a method for providing a uniform voltage distribution across the battery pack.
In accordance with a first aspect of the present disclosure, there is provided a system for cell-balancing of a battery pack, the system comprising:
a plurality of cells housed within the battery pack and electrically connected in an array;
a plurality of voltage sensors communicably coupled to the plurality of cells, wherein the plurality of voltage sensors are configured to measure a cell voltage value for each cell from the plurality of cells;
a processor operatively connected to the plurality of voltage sensors, wherein the processor is configured to receive the voltage value from the plurality of voltage sensors and identify a voltage mismatch in the plurality of cells; and
at least one cell balancing circuit operatively connected to the processor,
wherein the at least one cell balancing circuit is configured to minimize the voltage mismatch in the plurality of cells based on a control signal generated by the processor.
The system for cell-balancing of a battery pack, as described in the present disclosure, is advantageous in terms of ensuring uniform voltage distribution across the plurality of cells, which maximizes usable capacity of the battery pack. Further, the system reduces thermal stress on individual cells by maintaining voltage within the defined threshold range, thereby extending cycle life. Furthermore, the system enhances energy efficiency by employing both the passive balancing module and the active balancing module to minimize losses. Moreover, the system improves the operational safety of the battery pack by preventing overcharging and undercharging conditions. Additionally, the system delivers consistent performance under variable load conditions through precise monitoring and control.
In accordance with another aspect of the present disclosure, there is provided a method of cell-balancing of a battery pack, the method comprising:
measuring a cell voltage value for each cell from a plurality of cells, via a plurality of voltage sensors;
computing an average cell voltage value of the plurality of cells based on the received voltage values, via the processor;
comparing the cell voltage value for each cell with the computed average cell voltage value, via the processor;
comparing the computed deviation voltage value with a threshold voltage value, via the processor; and
generating the control signal based on a voltage mismatch in the plurality of cells , via at least one cell balancing circuit.
Additional aspects, advantages, features, and objects of the present disclosure would be made apparent from the drawings and the detailed description of the illustrative embodiments constructed in conjunction with the appended claims that follow.
It will be appreciated that features of the present disclosure are susceptible to being combined in various combinations without departing from the scope of the present disclosure as defined by the appended claims.
BRIEF DESCRIPTION OF DRAWINGS
The summary above, as well as the following detailed description of illustrative embodiments, is better understood when read in conjunction with the appended drawings. For the purpose of illustrating the present disclosure, exemplary constructions of the disclosure are shown in the drawings. However, the present disclosure is not limited to specific methods and instrumentalities disclosed herein. Moreover, those in the art will understand that the drawings are not to scale. Wherever possible, like elements have been indicated by identical numbers.
Embodiments of the present disclosure will now be described, by way of example only, with reference to the following diagrams wherein:
Figure 1 illustrates a block diagram of a system for cell-balancing of a battery pack, in accordance with an embodiment of the present disclosure.
Figure 2 illustrates a flow chart of a method of cell-balancing of a battery pack, in accordance with another embodiment of the present disclosure.
In the accompanying drawings, an underlined number is employed to represent an item over which the underlined number is positioned or an item to which the underlined number is adjacent. A non-underlined number relates to an item identified by a line linking the non-underlined number to the item. When a number is non-underlined and accompanied by an associated arrow, the non-underlined number is used to identify a general item at which the arrow is pointing.
DETAILED DESCRIPTION
The following detailed description illustrates embodiments of the present disclosure and ways in which they can be implemented. Although some modes of carrying out the present disclosure have been disclosed, those skilled in the art would recognize that other embodiments for carrying out or practicing the present disclosure are also possible.
As used herein, the term “cell-balancing” refers to the procedure of equalizing the voltage levels across the plurality of cells to ensure uniform charge distribution and optimal performance. Specifically, the processor receives voltage values from a plurality of voltage sensors, computes an average cell voltage, and calculates deviation voltage values for each cell relative to the computed average. Further, the deviation voltage values are compared with a predetermined threshold voltage, and the processor generates control signals to the at least one cell balancing circuit to correct voltage mismatches. Furthermore, the cell-balancing is classified into the following types, including but not limited to passive balancing and active balancing. Moreover, the passive balancing, performed by at least one passive balancing module, dissipates excess charge from the cells with higher voltages through resistive elements, reducing the voltage difference across the battery pack. Additionally, the active balancing, performed by at least one active balancing module, transfers charge from the cells with higher voltages to cells with lower voltages using inductive or capacitive circuitry, efficiently redistributing energy within the battery pack. Ultimately, the cell-balancing process ensures voltage uniformity across series-parallel configurations of the plurality of cells, enhances battery life, prevents overcharging or deep discharge of individual cells, and maintains overall pack efficiency, providing stable and reliable operation of the battery pack.
As used herein, the terms “battery pack”, “battery”, and “battery unit” are used interchangeably and refer to an assembly of electrochemical cells organized to store and deliver electrical energy for powering electrical devices or vehicles. Specifically, the battery pack comprises the plurality of cells electrically connected in series and parallel configurations to achieve desired voltage and current ratings, with the arrangement enabling optimized energy density and load management. Further, each cell is monitored by the plurality of voltage sensors that provide real-time voltage data to the processor, that computes average cell voltage values, deviation voltages, and generates control signals for the at least one cell balancing circuit to maintain uniform cell voltage distribution. Furthermore, the battery packs are classified into types based on electrical configuration and functionality, including, but not limited to, series-connected packs for high-voltage applications, parallel-connected packs for high-current applications, and series-parallel hybrid packs that combine both to balance voltage and current requirements. Moreover, the battery pack integrates passive balancing modules and active balancing modules within the cell balancing circuit to regulate cell voltages, thereby enhancing operational safety, extending service life, and maintaining efficient energy utilization across the plurality of cells, ensuring stable performance under dynamic load conditions.
As used herein, the terms “cell”, “electrochemical cells”, and “battery cells” are used interchangeably and refer to a single electrochemical unit capable of storing and delivering electrical energy through redox reactions between the electrodes and electrolyte. Specifically, each cell produces a specific voltage and contributes to the total capacity and output of the battery pack based on the arrangement of cells in series and parallel connections. Further, the plurality of cells is monitored by voltage sensors that provide real-time voltage measurements to the processor, enabling computation of the average cell voltage, deviation voltages, and generation of control signals for the at least one cell balancing circuit to maintain uniform voltage distribution. Furthermore, the cells are classified into types based on chemistry, form factor, and performance characteristics, including, but not limited to, lithium-ion cells for high energy density and fast charge-discharge cycles, nickel-metal hydride cells for moderate energy density with high reliability, and lead-acid cells for cost-effective energy storage in stationary applications. Moreover, each cell interacts with the passive balancing module and active balancing module to dissipate excess charge or redistribute energy, maintaining voltage equilibrium, preventing overcharging or deep discharge, and optimizing the performance and lifespan of the battery pack.
As used herein, the terms “voltage sensor” and “voltmeter” are used interchangeably and refer to an electronic device designed to measure the electrical potential difference across the cells and provide accurate voltage data for monitoring and control. Specifically, the voltage sensor operates by interfacing with individual cells of a battery pack, detecting the instantaneous voltage level, and transmitting the measured values to the processor that computes the average voltage, deviation voltages, and subsequently generates the control signals for the cell balancing circuit to minimize mismatch. Further, advanced voltage sensors perform adaptive impedance matching by dynamically adjusting the reactive components to ensure precise measurements under varying load and temperature conditions, thereby maintaining measurement accuracy and system stability. Furthermore, the voltage sensors are classified into types based on measurement principle and application, including, but not limited to, resistive divider sensors for simple and cost-effective monitoring, capacitive sensors for high-frequency and low-leakage measurement, and isolated sensors employing optical or magnetic coupling for enhanced safety in the high-voltage battery packs. Moreover, the integration of such sensors in the system ensures reliable monitoring of individual cell voltages, supports effective passive and active balancing, prevents uneven charging or discharging, and contributes to extended battery life and efficient energy utilization.
As used herein, the terms “processor”, “processing module”, and “processing unit” are used interchangeably and refer to a computing unit responsible for receiving voltage values from the voltage sensors, performing analytical computations, and generating the control signals to regulate the cell balancing circuit. Specifically, the processor executes operations including, but not limited to, computation of the average cell voltage, the determination of deviation voltage for each cell, comparison of the deviation voltage with the threshold value, and initiation of balancing actions through the passive or the active modules to ensure uniform charge distribution within the battery pack. Further, the processor functions as the decision-making core of the system, enabling continuous monitoring, adaptive response, and precise coordination of balancing operations, thereby preventing overcharging, deep discharge, or excessive voltage mismatch across interconnected cells. Furthermore, the processors are classified into types based on architecture and application requirements, including, but not limited to, microcontrollers for real-time control and low-power balancing functions, digital signal processors for high-speed voltage analysis and dynamic control, and system-on-chip processors for advanced integration of computation, sensing, and communication functions within the compact platform. Moreover, the deployment of the processors ensures accurate computation, efficient balancing control, enhanced operational safety, and extended service life of the battery pack.
As used herein, the term “cell balancing circuit” refers to an electronic arrangement designed to minimize voltage mismatch across interconnected cells within a battery pack by regulating charge levels in response to control signals generated by a processor. Specifically, the cell balancing circuit functions as an interface between computational analysis and energy regulation, receiving deviation voltage data and executing corrective actions to maintain uniform voltage distribution across all the cells. Further, the cell balancing circuit incorporates balancing modules that operate either by dissipating excess charge from higher-voltage cells or by transferring charge from the higher-voltage cells to the lower-voltage cells, thereby equalizing energy levels and preventing localized stress or degradation. Furthermore, the cell balancing circuits are classified into passive and active types, with passive circuits employing resistive elements to convert excess electrical energy into heat for stable voltage alignment, and active circuits utilizing inductive, capacitive, or switched-mode topologies to transfer charge efficiently between cells for improved energy utilization. Moreover, the integration of the cell balancing circuit within the system ensures consistent voltage control, extended operational lifespan of the battery pack, enhanced energy efficiency, and improved safety under dynamic charging and discharging conditions.
As used herein, the term “control signal” refers to an electrical or logical command generated by the processor to direct the operation of the cell balancing circuit for minimizing the voltage mismatch across the cells in the battery pack. Specifically, the control signal is derived from analytical computations that include, but are not limited to, measurement of individual cell voltages, calculation of the average voltage, determination of deviation voltages, and comparison of the deviations with the predefined threshold. Furthermore, based on the outcome of the comparison, the processor issues the control signal that activates at least one of the passive balancing modules to dissipate excess charge from higher-voltage cells and the active balancing modules to transfer charge between the cells for equalization. Furthermore, the control signals are classified into types according to the form and function, including, but not limited to, digital signals for switching operations that define balancing activation states, analog signals for modulating current flow during charge transfer, and pulse-width modulated signals for precise regulation of balancing circuits in the dynamic conditions. Moreover, the implementation of the control signals ensures accurate execution of balancing strategies, stable operation of the battery pack, efficient use of stored energy, and extended service life of the entire system.
As used herein, the term “adaptive impedance matching” refers to a dynamic technique that aligns the impedance of voltage sensors with the varying internal impedance of individual cells in the battery pack to achieve accurate voltage measurement and stable operation. Specifically, the adaptive impedance matching functions by continuously adjusting reactive components such as, but not limited to, capacitors or inductors within the voltage sensors to counteract changes in the cell impedance caused by temperature variations, state of charge, or aging effects. Further, the adjustment ensures minimal signal distortion, reduced measurement error, and reliable voltage detection across all cells, which supports the precise computation of the average cell voltage, deviation voltage, and generation of the effective control signals for the cell balancing circuit. Furthermore, the adaptive impedance matching is classified into types based on the method of adjustment, including, but not limited to, analog matching that modifies component values through the variable reactive elements, digital matching that employs programmable circuits or algorithms to tune impedance characteristics, and hybrid matching that integrates both analog and digital elements for high accuracy and flexibility. Moreover, the integration of the adaptive impedance matching within the voltage sensing architecture enhances measurement precision, ensures stable feedback for the processor, improves the reliability of the passive and active balancing actions, and contributes to extended operational efficiency of the battery pack.
As used herein, the term “reactive components” refers to passive electrical elements that store and release energy in the form of electric or magnetic fields, influencing voltage and current characteristics without dissipating power as heat. Specifically, the reactive components play a critical role in the adaptive impedance matching the voltage sensors by dynamically adjusting capacitive or inductive properties to align with varying internal impedance of the cells in the battery pack, ensuring accurate measurement of voltage values under the changing load and state of charge conditions. Further, the capacitors act as the reactive components by storing energy in an electric field and providing the frequency-dependent reactance, inductors act by storing energy in the magnetic field and opposing the current changes, and certain resonant circuits combine both capacitors and inductors to achieve precise impedance control across different operating frequencies. Furthermore, the types of reactive components include, but are not limited to, fixed capacitors and inductors for the stable impedance regulation, variable capacitors and inductors for tunable adjustment in adaptive circuits, and switched reactive networks that integrate multiple discrete components to provide programmable impedance characteristics. Moreover, the incorporation of the reactive components in the voltage sensing architecture enhances measurement precision, supports processor-driven computation of the deviation voltages, improves efficiency of the control signal generation, and ensures reliable operation of passive and active balancing modules within the cell balancing circuit.
As used herein, the term “average cell voltage value” refers to a computed reference parameter representing the mean voltage across all cells in the battery pack, used as the baseline for identifying voltage mismatches. Specifically, the average cell voltage value is calculated by the processor through aggregation of the voltage data received from the voltage sensors and dividing the total voltage sum by the number of monitored cells, ensuring the precise representation of the collective state of charge. Further, the computed value serves as the comparative benchmark against which the individual cell voltages are evaluated to determine deviation voltages and assess imbalance severity. Furthermore, the types of average cell voltage value include, but are not limited to, arithmetic average derived directly from summation and division, weighted average applied in scenarios where certain cells influence pack performance more significantly due to configuration, and moving average used in the dynamic balancing strategies to account for transient fluctuations and provide stable reference values. Moreover, establishing the accurate average cell voltage value ensures reliable generation of control signals, effective engagement of the passive or active balancing modules, uniform charge distribution, and extended operational lifespan of the battery pack.
As used herein, the term “deviation voltage value” refers to the difference between the measured voltage of the individual cell and the computed average cell voltage value of the entire battery pack, serving as the indicator of imbalance. Specifically, the deviation voltage value is determined by the processor after receiving the voltage data from the voltage sensors, performing the averaging computation, and subtracting the average value from the actual voltage of each cell to quantify the extent of mismatch. Further, the deviation voltage value allows precise identification of the cells operating above or below the desired voltage level, enabling targeted balancing through activation of the passive modules for charge dissipation or the active modules for charge transfer. Furthermore, the types of deviation voltage value include, but are not limited to, positive deviation indicating a cell with a voltage higher than the average, negative deviation indicating a cell with a voltage lower than the average, and zero deviation indicating the cell operating exactly at the average voltage level. Moreover, accurate computation of deviation voltage values supports the generation of appropriate control signals, maintains uniform charge distribution across all cells, prevents localized stress conditions, and ensures stable and efficient performance of the battery pack throughout charge-discharge cycles.
As used herein, the term “threshold voltage value” refers to a predefined voltage limit used as the reference by the processor to evaluate deviation voltage values of individual cells within the battery pack. Specifically, the threshold voltage value is established based on design requirements, battery chemistry, and operational safety margins, and serves as the decision boundary for determining whether corrective balancing action is necessary. Further, during operation, the processor compares each deviation voltage value with the threshold voltage value, and only the cells exceeding the limit are subjected to the control signals that activate passive or active balancing modules to restore the voltage uniformity. Furthermore, the types of threshold voltage value include, but are not limited to, fixed threshold defined by a constant voltage level applicable to all the cells under standard conditions, dynamic threshold adjusted according to the temperature, state of charge, or aging effects to account for real-time variations, and adaptive threshold derived from predictive algorithms that optimize balancing performance under varying load cycles. Moreover, the use of the threshold voltage value ensures selective balancing intervention, prevents unnecessary energy dissipation or transfer, maintains stable voltage distribution, enhances safety, and extends the operational life of the battery pack.
As used herein, the term “passive balancing module” refers to an electronic subcircuit designed to equalize the cell voltages within the battery pack by dissipating excess charge from the cells operating at higher voltage levels. Specifically, the passive balancing module functions by receiving the control signals from the processor once deviation voltage values exceed the threshold voltage value, and activating resistive or shunt elements to discharge surplus energy from the specific cells until voltage uniformity is restored relative to the computed average cell voltage. Further, the process is straightforward and reliable, converting excess electrical energy into heat and thereby preventing overcharging of individual cells, reducing stress across the battery pack, and ensuring stable operation under varying charge-discharge cycles. Furthermore, the types of passive balancing modules include, but are not limited to, fixed resistor shunt modules that discharge excess energy at a constant rate, switched resistor modules that allow selective activation of resistive elements for controlled balancing, and hybrid modules that integrate resistors with auxiliary control circuitry to provide adaptive dissipation rates. Moreover, the integration of the passive balancing modules within the system delivers advantages of reduced circuit complexity, high reliability, predictable operation, and improved safety, ensuring consistent performance and extended lifespan of the battery pack.
As used herein, the term “active balancing module” refers to an electronic subcircuit that equalizes voltages across cells in the battery pack by transferring charge from the higher-voltage cells to the lower-voltage cells. Specifically, the active balancing module operates under the control of the processor, which generates the control signals based on deviation voltage values exceeding the threshold voltage value, directing the module to redistribute energy efficiently between the selected cells until uniform voltage levels are achieved. Further, the active balancing module employs inductive, capacitive, or switched-mode circuitry to transfer charge with minimal energy loss, maintaining total stored energy within the battery pack while correcting imbalances. Furthermore, the types of active balancing modules include, but are not limited to, inductive transfer modules that use transformers or inductors to move energy between the cells, capacitive transfer modules that utilize capacitors for temporary energy storage and redistribution, and switched-mode modules that employ high-frequency switching networks for precise control of charge flow between multiple cells. Moreover, the integration of the active balancing modules within the battery pack ensures optimized energy utilization, faster voltage equalization, reduced stress on individual cells, enhanced operational efficiency, and extended service life of the battery pack under dynamic load conditions.
In accordance with a first aspect of the present disclosure, there is provided a system for cell-balancing of a battery pack, the system comprises:
a plurality of cells housed within the battery pack and electrically connected in an array;
a plurality of voltage sensors communicably coupled to the plurality of cells, wherein the plurality of voltage sensors are configured to measure a cell voltage value for each cell from the plurality of cells;
a processor operatively connected to the plurality of voltage sensors, wherein the processor is configured to receive the voltage value from the plurality of voltage sensors and identify a voltage mismatch in the plurality of cells; and
at least one cell balancing circuit operatively connected to the processor,
wherein the at least one cell balancing circuit is configured to minimize the voltage mismatch in the plurality of cells based on a control signal generated by the processor.
Referring to figure 1, in accordance with an embodiment, there is described a system 100 for cell-balancing of a battery pack 102. The system 100 comprises a plurality of cells 104 housed within the battery pack 102 and electrically connected in an array. Further, the system 100 comprises a plurality of voltage sensors 106 communicably coupled to the plurality of cells 104, wherein the plurality of voltage sensors 106 are configured to measure a cell voltage value for each cell (104A, ........ 104N) from the plurality of cells 104. Furthermore, the system 100 comprises a processor 108 operatively connected to the plurality of voltage sensors 106, wherein the processor 108 is configured to receive the voltage value from the plurality of voltage sensors 106 and identify a voltage mismatch in the plurality of cells 104. Moreover, the system 100 comprises at least one cell balancing circuit 110 operatively connected to the processor 108. Additionally, the at least one cell balancing circuit 110 is configured to minimize the voltage mismatch in the plurality of cells 104 based on a control signal generated by the processor 108.
The system 100 operates by employing the plurality of voltage sensors 106 to continuously monitor the cell voltage value of each cell (104A, ........ 104N) from the plurality of cells 104 within the battery pack 102. Specifically, each measured cell voltage value is transmitted to the processor 108, which performs a computation to determine an average cell voltage value across the plurality of cells 104. The processor 108 further evaluates each individual cell voltage value against the computed average to identify a voltage mismatch among the cells (104A, ........ 104N). Further, a deviation voltage value for each cell (104A, ........ 104N) is obtained, which quantifies the degree of imbalance within the battery pack 102. The processor 108 compares the deviation voltage value with a defined threshold voltage value to determine whether corrective action is required. Furthermore, upon identification of the deviation exceeding the threshold voltage value, the processor 108 generates a control signal specifically configured to minimize the mismatch among the plurality of cells 104. The control signal is transmitted to at least one cell balancing circuit 110 that incorporates either a passive balancing module 112 or an active balancing module 114. Moreover, the passive balancing module 112 dissipates excess charge from a cell (104A, ........ 104N) exhibiting a higher voltage, thereby bringing the cell voltage closer to the average cell voltage. The active balancing module 114 transfers excess charge from the higher voltage cell (104A, ........ 104N) to the lower voltage cell (104A, ........ 104N), thereby redistributing energy across the plurality of cells 104. The continuous feedback mechanism maintains uniformity in charge distribution and ensures balanced operation of the battery pack 102. Consequently, enhanced reliability and efficiency of the battery pack 102 are achieved due to precise identification and correction of voltage mismatch. Uniform charge distribution across the plurality of cells 104 increases the overall usable capacity of the battery pack 102, reduces energy losses associated with imbalance, and extends operational life. Additionally, the system 100 further reduces stress on individual cells 104, thereby lowering the risk of premature degradation or failure. By integrating both the passive balancing module 112 and the active balancing module 114, the system 100 delivers flexibility in balancing strategies, ensures reduced thermal generation during balancing, and provides optimized performance in energy storage applications.
In an embodiment, the plurality of cells 104 is arranged in an electrical configuration comprising a series connection integrated with the parallel connections within the battery pack 102. Specifically, the voltage sensors 106 measure the cell voltage value of each cell (104A, ........ 104N) across the series-parallel network, and the processor 108 receives the measured values from the entire configuration. The series arrangement ensures the cumulative voltage output required for load demand, whereas the parallel arrangement stabilizes current delivery and improves redundancy. Further, the processor 108 computes the average cell voltage value across the network by aggregating the measured cell voltage values, and the deviation voltage value for each cell (104A, ........ 104N) is determined to identify mismatches that arise within the complex array. The processor 108 compares each deviation voltage value with the defined threshold voltage value and generates the control signal based on the comparison. Furthermore, the control signal is delivered to at least one cell balancing circuit 110, which executes correction within the series-parallel network. In the passive balancing module 112, excess charge is dissipated from the specific cells (104A, ........ 104N) exhibiting higher voltage levels within the configuration, thereby aligning the cells (104A, ........ 104N) closer to the average. Moreover, in the active balancing module 114, charge transfer is executed from the cells (104A, ........ 104N) at higher potential within one branch of the parallel network to cells (104A, ........ 104N) at lower potential, or across cells (104A, ........ 104N) in series, enabling uniformity across the array. The aforementioned balancing within the integrated configuration maintains voltage stability across both series and parallel paths, preventing localized overcharging or undercharging. Consequently, arranging the plurality of cells 104 in series connection integrated with parallel connections maximizes energy utilization of the battery pack 102 and increases operational safety. Further, the balanced distribution across the network reduces thermal hotspots, minimizes voltage stress across cells (104A, ........ 104N), and extends the battery packs 102 life. Additionally, the advantages include, but are not limited to, increased power density from the series arrangement, enhanced capacity from the parallel arrangement, improved reliability from redundancy across parallel cells (104A, ........ 104N), and uniform charge distribution that enables efficient discharge cycles. The system 100 thereby maintains stable performance of the battery pack 102 under variable load conditions, ensuring optimized efficiency and longevity.
In an embodiment, the plurality of voltage sensors 106 is configured to perform an adaptive impedance matching for each cell via dynamic adjustment of reactive components in the plurality of voltage sensors 106. Specifically, each voltage sensor 106 dynamically adjusts reactive components such as, but not limited to, capacitance or inductance to ensure that measurement accuracy remains stable across varying operating conditions of the cells (104A, ........ 104N). The adaptive impedance matching procedure minimizes measurement errors caused by internal resistance variations or transient fluctuations in the cell voltage value. Further, the adjusted impedance enables each voltage sensor 106 to deliver a true representation of the actual voltage of the respective cell (104A, ........ 104N), which is transmitted to the processor 108 for computation. The processor 108 utilizes the accurate values received from the plurality of voltage sensors 106 to compute an average cell voltage value across the plurality of cells 104. Furthermore, the processor 108 determines the deviation voltage value for each cell (104A, ........ 104N) by comparing the measured value with the computed average. The comparison ensures that voltage mismatches are identified with precision, without distortion from parasitic effects or sensor mismatching. Moreover, the deviation voltage value is compared against the defined threshold voltage value, and the control signal is generated to address the imbalance. The at least one cell balancing circuit 110 executes balancing functions through either the passive balancing module 112, which dissipates excess charge, or the active balancing module 114, which transfers charge between cells (104A, ........ 104N), based on the generated control signal. Consequently, the adaptive impedance matching through the plurality of voltage sensors 106 improves the accuracy of the cell voltage measurement across the battery pack 102. Further, the precise voltage sensing ensures reliable computation of the average voltage, deviation voltage, and threshold comparison, which directly improves the effectiveness of the balancing operation. Additionally, the advantages include, but are not limited to, enhanced stability of the balancing process, reduced error margins in the control signal generation, prolonged operational life of the plurality of cells 104 through uniform charge maintenance, and improved efficiency of the system 100 under diverse operating conditions. The integration of the adaptive impedance matching strengthens the robustness of voltage monitoring and enables consistent balancing performance across the entire battery pack 102.
In an embodiment, the processor 108 is configured to compute an average cell voltage value of the plurality of cells 104 based on the received voltage values. Specifically, the plurality of voltage sensors 106 measures the individual cell voltage value of each cell (104A, ........ 104N) and transmits the measured values to the processor 108. The processor 108 aggregates all received voltage values and divides the summation by the total number of cells (104A, ........ 104N) in the battery pack 102 to obtain the average cell voltage value. Further, the computed average serves as the reference voltage level representing the balanced state of the plurality of cells 104 under real-time operating conditions. The computed average cell voltage value is utilized by the processor 108 to identify voltage mismatches across the battery pack 102. Furthermore, each cell voltage value received from the plurality of voltage sensors 106 is compared against the computed average, and any variance from the reference level is quantified as the deviation voltage value. The processor 108 further analyzes the deviation voltage values across all cells (104A, ........ 104N) to assess imbalance severity and determine that intervention through the at least one cell balancing circuit 110 is necessary. Moreover, the processor 108 subsequently generates the control signal to activate either the passive balancing module 112 or the active balancing module 114, depending on the required correction method, ensuring that each cell (104A, ........ 104N) voltage value is maintained closer to the computed average. Consequently, computing the accurate average cell voltage value lies in establishing a reliable baseline for evaluating voltage mismatches within the battery pack 102. The method ensures consistent detection of undercharged or overcharged cells (104A, ........ 104N), enabling precise control over balancing operations. Additionally, the advantages include, but are not limited to, uniform distribution of voltage across the plurality of cells 104, reduced energy losses through targeted balancing, extended cycle life of the battery pack 102 due to prevention of over-stress on individual cells (104A, ........ 104N), and improved efficiency of the system 100 in maintaining operational stability under varying load conditions. The integration of the average cell voltage computation by the processor 108 ensures that the balancing process remains adaptive, consistent, and accurate for prolonged system performance.
In an embodiment, the processor 108 is configured to compare the cell voltage value for each cell with the computed average cell voltage value and compute a deviation voltage value for each cell with respect to the computed average cell voltage. Specifically, for every cell (104A, ........ 104N), the processor 108 performs a subtraction between the measured cell voltage value and the computed average cell voltage value, thereby deriving the deviation voltage value specific to the cell (104A, ........ 104N). The deviation voltage value represents the magnitude and direction of imbalance relative to the average, with a positive deviation indicating an overcharged state and a negative deviation indicating an undercharged state. Further, the computation of the deviation voltage value establishes a precise quantitative measure of the voltage mismatch across the battery pack 102. Once the deviation voltage value is determined for each cell (104A, ........ 104N), the processor 108 evaluates the set of deviations across the plurality of cells 104 to identify imbalance patterns within the battery pack 102. Furthermore, the processor 108 prepares deviation data that is further compared against the threshold voltage value in order to assess the criticality of the imbalance. Based on the aforementioned assessment, the control signal is generated and transmitted to at least one cell balancing circuit 110. The passive balancing module 112 dissipates charge from cells (104A, ........ 104N) exhibiting higher deviation voltage values. Alternatively, the active balancing module 114 redistributes charge from cells (104A, ........ 104N) at higher voltage to those at lower voltage. The aforementioned technique ensures that each deviation voltage value is progressively minimized and alignment with the average cell voltage value is achieved across the plurality of cells 104. Consequently, computing and utilizing deviation voltage values lies in the enhanced precision of detecting voltage mismatches in the battery pack 102. By quantifying the difference between each cell (104A, ........ 104N) voltage value and the computed average, the system 100 ensures targeted balancing actions that directly address specific imbalances. Moreover, the advantages include, but are not limited to, improved energy efficiency through selective intervention, reduced stress on healthy cells (104A, ........ 104N) by avoiding unnecessary balancing, increased operational safety by preventing extreme voltage deviations, and extended service life of the battery pack 102 due to consistent maintenance of uniform voltage distribution across the plurality of cells 104. The incorporation of deviation voltage computation strengthens the reliability and adaptability of the balancing strategy executed by the system 100.
In an embodiment, the processor 100 is configured to compare the computed deviation voltage value with a threshold voltage value and generate the control signal based on the comparison. Specifically, the threshold voltage value serves as a limit beyond which an imbalance within the battery pack 102 is classified as critical. For each deviation voltage value, the processor 108 executes a logical comparison to determine whether the deviation lies above or below the threshold voltage value. Further, the cells (104A, ........ 104N) exhibiting deviation values exceeding the threshold are flagged as requiring corrective balancing, while cells (104A, ........ 104N) with deviation values below the threshold are retained without adjustment to conserve energy and prevent unnecessary cycling. Based on the comparison results, the processor 108 generates the control signal that governs the operation of the at least one cell balancing circuit 110. Furthermore, the control signal identifies the specific cells (104A, ........ 104N) requiring correction and instructs the balancing circuit to apply either passive balancing through the passive balancing module 112 or active balancing through the active balancing module 114. In the passive balancing module 112, resistive elements dissipate excess energy from the cells (104A, ........ 104N) with high deviation values until alignment with the average cell voltage value is restored. Moreover, in the active balancing module 114, controlled energy transfer occurs between the higher voltage cell (104A, ........ 104N) and the lower voltage cell (104A, ........ 104N) to equalize voltage levels across the plurality of cells 104. The process continues until all deviation voltage values remain within the permissible threshold range. Consequently, comparing deviation voltage values with a threshold voltage value enhances control over the balancing process of the battery pack 102. The process further prevents unnecessary balancing of cells (104A, ........ 104N) within acceptable limits and focuses correction only on the cells (104A, ........ 104N) that threaten the stability and performance of the pack. Additionally, the advantages include, but are not limited to, reduction of energy losses due to selective balancing, minimization of thermal stress on the plurality of cells 104, improved operational safety by avoiding over-voltage or under-voltage conditions, and extension of the service life of the battery pack 102 by maintaining voltage uniformity under controlled parameters. The system 100 therefore ensures precise, efficient, and reliable balancing tailored to the actual condition of the plurality of cells 104.
In an embodiment, the at least one cell balancing circuit 110 comprises at least one passive balancing module 112, wherein the at least one passive balancing module 112 is configured to dissipate excess charge from at least one cell based on the received control signal. Specifically, the processor 108 identifies the cells (104A, ........ 104N) with deviation voltage values above the computed average cell voltage value and exceeding the threshold voltage value, and generates the control signal directed to the passive balancing module 112. Upon receiving the control signal, the passive balancing module 112 connects resistive components across the targeted cell (104A, ........ 104N), allowing excess energy to be released as heat until the voltage of the cell (104A, ........ 104N) aligns closely with the average cell voltage value. Further, the process ensures systematic discharge of only the overcharged cells (104A, ........ 104N) without affecting the remaining balanced cells (104A, ........ 104N). The process executed by the passive balancing module 112 involves repeated measurement of the cell voltage values via the plurality of voltage sensors 106, continuous evaluation of the deviation voltage values by the processor 108, and sequential activation of the resistive discharge path for the identified cells (104A, ........ 104N). Furthermore, the passive balancing module 112 operates in a controlled manner, preventing abrupt discharge that induces instability in the battery pack 102. The balancing action continues until the deviation voltage values of the overcharged cells (104A, ........ 104N) fall within the defined threshold voltage value range, thereby restoring uniformity across the plurality of cells 104. Moreover, the entire operation is regulated by the processor 108 to maintain stability of the series-parallel configuration of the battery pack 102. Consequently, incorporating the passive balancing module 112 enhances the safety and reliability of the battery pack 102 through the elimination of localized overcharging. The advantages include, but are not limited to, a simple and robust balancing mechanism, reduced complexity of circuitry compared to active balancing, improved thermal management by controlling the rate of energy dissipation, and extended cycle life of the plurality of cells 104 through prevention of the over-voltage stress. Additionally, the system 100 gains predictable and energy-efficient balancing behavior, which is particularly effective during charge cycles where excess energy must be safely released without compromising the overall performance of the battery pack 102.
In an embodiment, the at least one cell balancing circuit 110 comprises at least one active balancing module 114, wherein the at least one active balancing module 114 is configured to transfer charge from at least one cell with a higher voltage to at least one cell with a lower voltage based on the received control signal. Specifically, the processor 108 continuously monitors the cell voltage values received from the plurality of voltage sensors 106 and computes the deviation voltage values with respect to the average cell voltage. The processor 108 generates the control signal identifying cells (104A, ........ 104N) with higher voltage and cells (104A, ........ 104N) with lower voltage, which directs the active balancing module 114 to execute controlled energy transfer between the identified cells (104A, ........ 104N), thereby minimizing the voltage mismatch across the battery pack 102. Further, the procedure of active balancing involves converting the excess energy from higher voltage cells (104A, ........ 104N) into a form suitable for transfer, such as, but not limited to, through a DC-DC converter or bidirectional energy pathway, and delivering the energy to lower voltage cells (104A, ........ 104N) under the regulation of the processor 108. The active balancing module 114 continuously monitors the voltage of both source and destination cells (104A, ........ 104N), adjusting the energy transfer rate in real time to achieve alignment with the computed average cell voltage value. Furthermore, the process maintains the voltage deviation of all cells (104A, ........ 104N) within the defined threshold voltage value, ensuring uniform charge distribution across the series-parallel configuration of the battery pack 102 without dissipating energy as heat. Consequently, the active balancing module 114 enhances the energy efficiency of the battery pack 102 by redistributing charge instead of dissipating the charge, resulting in optimized utilization of stored energy. The advantages include, but are not limited to, increased overall capacity of the battery pack 102, reduced thermal losses during balancing, improved operational stability under varying load conditions, and extended lifespan of the plurality of cells 104 through prevention of overcharging and undercharging. Ultimately, the system 100 achieves precise and adaptive balancing that maintains uniform voltage across the entire battery pack 102, supporting higher performance and reliability in energy storage applications.
In an exemplary embodiment, the system 100 for cell-balancing of the battery pack 102 comprises the plurality of cells 104 connected in a series-parallel configuration, where each cell (104A, ........ 104N) is a lithium-ion cell rated at 3.7 V nominal voltage and 2.5 Ah capacity. For instance, the battery pack 102 includes 48 cells 104 connected as 12 series groups with 4 parallel cells in each group, resulting in a pack voltage of approximately 44.4 V nominal and total capacity of 10 Ah. Each cell (104A, ........ 104N) is monitored by the dedicated voltage sensor 106, which provides the real-time cell voltage value to the processor 108. The processor 108 receives values such as, but not limited to, 3.95 V, 3.90 V, 3.87 V, and 3.92 V from a subset of cells during charging and computes the average cell voltage with the equation:
V = (?_(i=1)^n¦?V(celli)?)/n
with n is the total number of cells (104A, ........ 104N). For the given subset, with values 3.95 V, 3.90 V, 3.87 V, and 3.92 V, the computed average cell voltage V equals 3.91 V. Further, the processor 108 computes the deviation voltage value for each cell using the equation ?V=V(celli)-V, with ?V representing the deviation voltage value of cell i. Based on the measured data, the deviation voltage values are +0.04 V, -0.01 V, -0.04 V, and +0.01 V, respectively. The processor 108 compares each deviation with a predefined threshold voltage value, for instance, ±0.02 V. Cells with deviation voltage values exceeding ±0.02 V are identified as requiring balancing. In the aforementioned case, the cell with +0.04 V is identified as overcharged relative to the average. The processor 108 generates the control signal instructing the at least one cell balancing circuit 110 to engage correction. If the passive balancing module 112 is selected, a resistive discharge is applied to the cell with +0.04 V until the voltage aligns with 3.91 V. Alternatively, in case the active balancing module 114 is selected, energy from the cell at 3.95 V is transferred to the cell at 3.87 V until both cells approach the average cell voltage value. The exemplary embodiment demonstrates that the system 100 ensures uniform charge distribution across the plurality of cells 104 in the battery pack 102. The process reduces voltage mismatch, increases usable pack capacity, and prevents degradation caused by sustained imbalance. The equations establish a quantifiable process for average computation, deviation calculation, and threshold-based correction. With consistent execution, the system 100 maintains the battery pack 102 at an optimized voltage distribution, enhancing efficiency, reliability, and operational life across diverse usage conditions.
In accordance with a second aspect, there is described a method of cell-balancing of a battery pack, the method comprising:
measuring a cell voltage value for each cell from a plurality of cells, via a plurality of voltage sensors;
computing an average cell voltage value of the plurality of cells based on the received voltage values, via a processor;
comparing the cell voltage value for each cell with the computed average cell voltage value, via the processor;
comparing the computed deviation voltage value with a threshold voltage value, via the processor; and
generating the control signal based on a voltage mismatch in the plurality of cells, via at least one cell balancing circuit.
Referring to figure 2, in accordance with an embodiment, there is described a method 200 of cell-balancing of a battery pack 110. At step 202, the method 200 comprises measuring a cell voltage value for each cell (104A, ........ 104N) from a plurality of cells 104, via a plurality of voltage sensors 106. At step 204, the method 200 comprises computing an average cell voltage value of the plurality of cells 104 based on the received voltage values, via a processor 108. At step 206, the method 200 comprises comparing the cell voltage value for each cell (104A, ........ 104N) with the computed average cell voltage value, via the processor 108. At step 208, the method 200 comprises comparing the computed deviation voltage value with a threshold voltage value, via the processor 108. At step 210, the method 200 comprises generating the control signal based on a voltage mismatch in the plurality of cells 104, via at least one cell balancing circuit 110.
In an embodiment, the method 200 comprises dissipating excess charge from at least one cell (104A, ........ 104N) based on the received control signal, via a passive balancing module 112.
In an embodiment, the method 200 comprises transferring charge from at least one cell (104A, ........ 104N) with a higher voltage to at least one cell (104A, ........ 104N) with a lower voltage based on the received control signal, via an active balancing module 114.
In an embodiment, the method 200 comprises measuring a cell voltage value for each cell (104A, ........ 104N) from a plurality of cells 104, via a plurality of voltage sensors 106. Further, the method 200 comprises computing an average cell voltage value of the plurality of cells 104 based on the received voltage values, via the processor 108. Furthermore, the method 200 comprises comparing the cell voltage value for each cell (104A, ........ 104N) with the computed average cell voltage value, via the processor 108. Moreover, the method 200 comprises comparing the computed deviation voltage value with a threshold voltage value, via the processor 108. Additionally, the method 200 comprises generating the control signal to minimize a voltage mismatch in the plurality of cells 104, via at least one cell balancing circuit 110. Subsequently, the method 200 comprises dissipating excess charge from at least one cell (104A, ........ 104N) based on the received control signal, via a passive balancing module 112. Alternatively, the method 200 comprises transferring charge from at least one cell (104A, ........ 104N) with a higher voltage to at least one cell (104A, ........ 104N) with a lower voltage based on the received control signal, via an active balancing module 114.
The system for cell-balancing of a battery pack, as described in the present disclosure, is advantageous in terms of ensuring uniform voltage distribution across the plurality of cells 104, which maximizes usable capacity of the battery pack 102. Further, the system 100 reduces thermal stress on individual cells 104 by maintaining voltage within the defined threshold range, thereby extending cycle life.
It would be appreciated that all the explanations and embodiments of the system 100 also apply mutatis-mutandis to the method 200.
In the description of the present disclosure, it is also to be noted that, unless otherwise explicitly specified or limited, the terms “disposed,” “mounted,” and “connected” are to be construed broadly, and may for example be fixedly connected, detachably connected, or integrally connected, either mechanically or electrically. They may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present disclosure can be understood in specific cases to those skilled in the art.
Modifications to embodiments and combinations of different embodiments of the present disclosure described in the foregoing are possible without departing from the scope of the present disclosure as defined by the accompanying claims. Expressions such as “including”, “comprising”, “incorporating”, “have”, and “is” used to describe and claim the present disclosure are intended to be construed in a non-exclusive manner, namely allowing for items, components or elements not explicitly described also to be present. Reference to the singular is also to be construed to relate to the plural where appropriate.
Although embodiments have been described with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the scope of the principles of this disclosure. More particularly, various variations and modifications are possible in the component parts and/or arrangements of the subject combination arrangement within the scope of the present disclosure, the drawings, and the appended claims. In addition to variations and modifications in the component parts and/or arrangements, alternative uses will also be apparent to those skilled in the art. ,CLAIMS:WE CLAIM:
1. A system (100) for cell-balancing of a battery pack (102), the system (100) comprising:
- a plurality of cells (104) housed within the battery pack (102) and electrically connected in an array;
- a plurality of voltage sensors (106) communicably coupled to the plurality of cells (104), wherein the plurality of voltage sensors (106) are configured to measure a cell voltage value for each cell from the plurality of cells (104);
- a processor (108) operatively connected to the plurality of voltage sensors (106), wherein the processor (108) is configured to receive the voltage value from the plurality of voltage sensors (106) and identify a voltage mismatch in the plurality of cells (104); and
- at least one cell balancing circuit (110) operatively connected to the processor (108),
wherein the at least one cell balancing circuit (110) is configured to minimize the voltage mismatch in the plurality of cells (104) based on a control signal generated by the processor (108).
2. The system (100) as claimed in claim 1, wherein the plurality of cells (104) is arranged in an electrical configuration comprising a series connection integrated with the parallel connections within the battery pack (102).
3. The system (100) as claimed in claim 1, wherein the plurality of voltage sensors (106) is configured to perform an adaptive impedance matching for each cell via dynamic adjusting of reactive components in the plurality of voltage sensors (106).
4. The system (100) as claimed in claim 1, wherein the processor (108) is configured to compute an average cell voltage value of the plurality of cells (104) based on the received voltage values.
5. The system (100) as claimed in claim 1, wherein the processor (108) is configured to compare the cell voltage value for each cell with the computed average cell voltage value and compute a deviation voltage value for each cell with respect to the computed average cell voltage.
6. The system (100) as claimed in claim 1, wherein the processor (100) is configured to compare the computed deviation voltage value with a threshold voltage value and generate the control signal based on the comparison.
7. The system (100) as claimed in claim 1, wherein the at least one cell balancing circuit (110) comprises at least one passive balancing module (112), and wherein the at least one passive balancing module (112) is configured to dissipate excess charge from at least one cell based on the received control signal.
8. The system (100) as claimed in claim 1, wherein the at least one cell balancing circuit (110) comprises at least one active balancing module (114), and wherein the at least one active balancing module (114) is configured to transfer charge from at least one cell with a higher voltage to at least one cell with a lower voltage based on the received control signal.
9. The method (200) of cell-balancing of a battery pack (110), the method (200) comprising:
- measuring a cell voltage value for each cell from a plurality of cells (104), via a plurality of voltage sensors (106);
- computing an average cell voltage value of the plurality of cells (104) based on the received voltage values, via a processor (108);
- comparing the cell voltage value for each cell with the computed average cell voltage value, via the processor (108);
- comparing the computed deviation voltage value with a threshold voltage value, via the processor (108); and
- generating the control signal based on a voltage mismatch in the plurality of cells (104), via at least one cell balancing circuit (110).
| # | Name | Date |
|---|---|---|
| 1 | 202521000478-PROVISIONAL SPECIFICATION [02-01-2025(online)].pdf | 2025-01-02 |
| 2 | 202521000478-POWER OF AUTHORITY [02-01-2025(online)].pdf | 2025-01-02 |
| 3 | 202521000478-FORM FOR SMALL ENTITY(FORM-28) [02-01-2025(online)].pdf | 2025-01-02 |
| 4 | 202521000478-FORM 1 [02-01-2025(online)].pdf | 2025-01-02 |
| 5 | 202521000478-EVIDENCE FOR REGISTRATION UNDER SSI(FORM-28) [02-01-2025(online)].pdf | 2025-01-02 |
| 6 | 202521000478-DRAWINGS [02-01-2025(online)].pdf | 2025-01-02 |
| 7 | 202521000478-DECLARATION OF INVENTORSHIP (FORM 5) [02-01-2025(online)].pdf | 2025-01-02 |
| 8 | 202521000478-FORM 3 [22-04-2025(online)].pdf | 2025-04-22 |
| 9 | 202521000478-DRAWING [01-10-2025(online)].pdf | 2025-10-01 |
| 10 | 202521000478-COMPLETE SPECIFICATION [01-10-2025(online)].pdf | 2025-10-01 |
| 11 | 202521000478-FORM-9 [02-10-2025(online)].pdf | 2025-10-02 |
| 12 | Abstract.jpg | 2025-10-14 |