Equalizing the battery charges of rechargeable accumulators

Charge imbalances in high-voltage batteries, including battery cell arrays, such as lithium-ion in hybrid vehicles, tend to develop and increase over time as the batteries are charged and discharged, or even when the battery remains charged but not in use. This reduces the efficiency of the battery charging and discharging modes, and limits battery life and capacity. The article describes a method and device for performing the charge equalization operation when charging a storage battery. The elements of the charger circuit have been selected, the parameters of which are sufficient for charging with equalizing the charge of the Audi Q5 hybrid Quattro car. Calculations of the pulse mode of charging the battery of the specified car, as well as the time spent on charging with equalizing the battery charges are given. The charging time of the considered battery with the elimination of a 15% imbalance of the batteries will last up to 139 minutes (2.31 hours). The results of calculating the operating parameters of the device indicate that the device for equalizing the charge of the batteries is operable, can be implemented on a modern element base at a relatively low cost, and is capable of charging the battery in a time acceptable for the operation of the car.


Introduction
Most new electric vehicles are equipped with lithium-ion batteries.Batteries account for about 40% of the cost of electric vehicles [1].Since the voltage of individual battery cells varies from 1V to 4.5V, the cells are connected in series to increase the battery voltage level.Batteries of electric vehicles consist of elements connected in series to power electric drives of vehicles with voltage up to 400 V.At the same time, the characteristics of these elements must be strictly the same.However, it is known that no two batteries are the same, even if they are made by the same manufacturer and have the same model.Small changes in the characteristics of each cell will still take place, be it SoC (the state of charge), be it ESR (Equivalent Series Resistance), capacity or temperature characteristics.When cells are connected to each other to form a battery, changes in characteristics result in an imbalance in cell voltages.For example, if one cell has a slightly lower capacity, it will continue to discharge, and each time it is charged, it will experience a slight overvoltage.Over time, this will lead to a decrease in its capacity and service life.This phenomenon makes equalizing the charge of individual battery cells an indispensable procedure.The process of balancing voltages and SoCs between cells when they are connected and fully charged is called cell balancing.The authors of Bortecene Yildirim and others 2019 [2] investigated the following types of battery cell balancing: a. Passive balancing b.Active balancing c.Runtime balancing d.Lossless balancing Passive Balancing This is a simple form of balancing by switching a resistor between cells.Energy losses for heating balancing resistors (usually from 30 to 40 ohms) allow cells with an increased charge to be discharged.This type is acceptable when balancing requirements are low.However, as cells age, the amount of balancing required to optimize energy increases.As a result, the amount of energy lost to heat increases.It can also increase charging time when trying to reach the maximum SoC for the entire battery cell package.Active Balancing The idea here is to redistribute energy throughout the cells.Power from the cells with the highest SoC is transferred to the cells with the lowest SoC.This is the ideal approach to cell 1303 (2024) 012007 IOP Publishing doi:10.1088/1757-899X/1303/1/012007 2 balancing.However, this means that the system must be able to move energy between cells in a battery.Ideally between any two cells.Lots of wires and lots of switches means more weight, complexity and cost.Runtime Balancing Each cell is connected to a separate low power DC/DC converter, then each converter is connected in series.This then allows full control of the power given and received by each cell, depending on their capabilities.This system can provide a much higher level of reliability, but requires a significant increase in cost.Lossless Balancing This approach turns the cells on and off while charging.This means we have a lot of switches and these switches must be rated for full current.Bortecene Yildirim and others 2019 [2] showed that dissipative balancing is the simplest and most economical method, but its efficiency is low and it is not suitable for high power applications.The main disadvantage of capacitive balancing is voltage balancing, which limits the speed and accuracy of balancing.Finally, live balancing has fast and efficient balancing features and is also suitable for used batteries, but with added complexity and increased cost.Thus, each balancing method has its advantages and disadvantages, and their choice depends on the cost of the system and the application.However, capacitive balancing can be improved to improve balancing accuracy and reduce power loss.This article is devoted to the development and research of a new Device and a method for charging and equalizing the level of charge in a battery of accumulators (application for invention number 2434 dated 24.05.23,AGEPI R. Moldova), based on the principle of charging a battery of batteries by transferring energy in small portions of storage devices due to multiple connecting them in parallel to the batteries in the second stage (charging at constant voltage).In the process of research, methods of mathematical, structural and simulation modeling of instantaneous circuits of the charging device and aligning the level of battery charging were used.The calculations were performed using the Microsoft Office Excel 2007 program.The list of designations of the elements presented in Figure 1 and 2: 1a device for charging and aligning the charge level of batteries; 2high-voltage battery; B 1 , B 2 , ..., Bnaccumulators of the high-voltage battery; С 1 , С 2 , ..., Сnelectrical energy storage devices, in particular capacitors; R 1 , R 2 , ..., Rnvoltage divider resistors; S 1 , S 2 -electronic switches for switching on the battery of batteries and energy storage devices; BS 1 , BS 2 , ..., BSnelectronic switches for connecting batteries to drives; RS 1 , RS 2 , ..., RSnelectronic switches for connecting voltage divider resistors to energy storage devices; Dsensor, voltage divider; BSM -battery control unit; DC-DCpower supply for charging batteries; GNDground; Kthe point of connection of the power source to the device for charging and equalizing battery charges.The main effective electrical quantities in the device are: EB 1 , EB 2 , ..., EВn -EMF of high-voltage batteries; i Bchbattery charging current; i Bcv -is the equalizing current of accumulator charging from storage devices; i Сchstorage current charging; i Scvequalizing current of storages and voltage divider for equalization of voltage of storages; U CCis the voltage of the DC-DC power supply at the stage of charging the batteries with direct current; U CVis the voltage of the DC-DC power supply at the power stage of charging batteries at a constant voltage; U C , U C 'the voltage of the charged energy storage devices and the residual voltage after the transfer of energy to the batteries.

Battery leveling device
The proposed Device (1) for equalizing the level of charge of batteries (2) of rechargeable batteries (B 1 , B 2 , ..., Bn) when charging from a direct current source (DC-DC) operates under the control of the Battery Management System (BMS) and consists of: n energy storage devices connected in series in a circuit, which can be capacitors (C 1 , C 2 , ..., Cn); electronic switches (S 1 ) and (S 2 ) for connecting to a direct current source (DC-DC) circuits: n rechargeable batteries (B 1 , B 2 , ..., Bn) and n energy storage devices (C 1 , C 2 , ..., Cn), respectively; n series connected via electronic switches (RS 1 , RS 2 , ..., RSn) into a chain of resistors (R 1 , R 2 , ..., Rn), one output of each of the resistors (R 1 , R 2 , ..., Rn) is connected by an electrical jumper to the corresponding output of the drive energy (C 1 , C 2 , ..., Cn), in turn, one output of each of the energy storage devices (C 1 , C 2 , ..., Cn) is connected by an electrical jumper through electronic switches (BS 1 , BS 2 , ..., BSn) with the corresponding output connected in series in rechargeable battery circuit (B 1 , B 2 , ..., Bn); to the analogue input of the control unit (BMS) through a voltage divider (D) connect the input output of the drive C 1 to control the voltage of the drives.The connection diagram of the device is shown in fig. 1 where n and i are positive integers, n is greater than 1 and 1≤i≤n.

Battery equalization method
One of the most common methods for charging a lithium-ion battery is the hybrid charging approach known as CC-CV.In this approach, the battery is first charged in 2 stages: charging at constant current in the CC phase, after which the battery enters the CV phase with a given constant voltage, resulting in a continuous decrease in the charging current.The battery voltage in the CV phase is increased to the maximum safe threshold.This stage ends when either the final value of the descending current, or the target power is reached [3].In the CC charge phase, it is safe for the battery to handle higher charge currents between 0.5C and 3C.CC charging continues until the battery voltage has reached the "full" or floating voltage level, at which point, the constant voltage phase begins.
Constant voltage (CV) charge: The constant voltage (CV) threshold for Lithium cells is usually between 4.1V and 4.5V per cell.The charger Battery Management System (BMS) monitors the battery voltage during CC charging [4].For an Audi Q5 hybrid Quattro battery pack with a capacity of 5000mA/h, the nominal charge current in the first stage can be 1000-2500mA, and the boost charge current can be in the range of 2.5-5A.In this CC mode, the battery voltage is brought to the level of the end-of-charge voltage.As soon as the desired voltage is reached, charging begins in CV mode, in which the charging current is gradually reduced.When the current drops to a minimum, charging is completed and the current is turned off.The proposed technical solution is used under the control of the BMS program.The switching scheme of electronic switches in accordance with the phases of the state of the device is presented in Table .1.At the first stage of charging batteries (B 1 , B 2 , ..., Bn) from a power source (DC-DC) in constant current mode Ucc, use: -phase 1.0 of the circuit state (see Fig. 2, A) of the proposed device, is characterized by the fact that the energy storage circuit (C 1 , C 2 , ..., Cn) is connected in parallel to the battery circuit (B 1 , B 2 , ..., Bn) using electronic switches (BS 1 , BS 2 , ..., BSn) and charge the battery (B 1 , B 2 , ..., Bn) with a constant charging current i Bch , and energy storage devices (С 1 , С 2 , ..., Сn) with the charging current i Сch .Charge up to the battery charge level SoC = 80% [5].At the second stage of charging batteries (B 1 , B 2 , ..., Bn) from a power source (DC-DC) in the constant voltage mode Ucv, in order to prevent the flow of charging current through the series circuit of batteries (B 1 , B 2 , ..., Bn), they are charged by multiple parallel connection to the appropriate energy storage devices (C 1 , C 2 , ..., Cn), which, before each connection, are charged to the voltage set by the battery manufacturer: -phase 1.1 of the state of the circuit (see Fig. 2 C) of the proposed device, is characterized by the fact that for 2τ (τ is the time constant of the storage device), the voltage Ucv is applied to the chain of energy storage devices (C 1 , C 2 , ..., Cn) for additional drive charging (C 1 , C 2 , …, Cn) up to SoC = 99% of drives; -phase 1.2 of the state of the device circuit (see Fig. 2 C) is characterized by the fact that for a time of 1τ a resistor (R 1 , R 2 , ..., Cn) is connected in parallel to each storage device (C 1 , C 2 , ..., Rn) and cause the flow of an equalizing current i Scv to equalize the voltage (UC 1 , UC 2 , .., Ucn) on each drive to the voltage specified by the manufacturer, since a chain of series-connected resistors of the same resistance (R 1 , R 2 , ..., Rn) divides the source voltage (DC-DC ) for voltages specified by the battery manufacturer (B 1 , B 2 , …, Bn); -phase 1.3 of the state of the circuit of the proposed device, is designed to measure the total voltage (UC 1 , UC 2 , .., Ucn) of drives (C 1 , C 2 , ..., Cn), which is read from the sensor D and entered into the memory of the BMS device.
-phase 1.4 of the state of the circuit (see Fig. 2 D) of the proposed device, serves to charge batteries (B 1 , B 2 , ..., Bn) with an equalizing current i Bcv , which flows when the storage devices (C 1 , C 2 , ..., Cn) and batteries are connected in parallel (B 1 , B 2 , … ,Bn).The peculiarity of this charging method is that when the EMF E B of the batteries (B1, B2, ..., Bn) is equal to the voltage U C of the storage devices (C 1 , C 2 , ..., Cn), the equalizing current iBcv between these pairs will not flow, and for those batteries , for which the EMF Е В has not reached the voltage level determined by the manufacturer, the equalizing current i Bcv from the storage devices will flow and their voltage will decrease, therefore the total voltage (U C1 , U C2 , .., Ucn) of the storage devices (С 1 , С 2 , ..., Сn) is also at the end charging will go down; -phase 1.5 of the state of the circuit of the proposed device, is designed to measure the residual voltage U СV ' of storage devices (C 1 , C 2 , ..., Cn) which is read from the sensor D and entered into the memory of the BMS device.
-phase 1.6 of the circuit state is designed to compare the residual voltage U CV ' with the value stored in the memory of the BMS device.If the voltage values U СV ' = U СV are equal, the second stage of charging the batteries (B1, B2, ..., Bn) is stopped, and if the residual voltage U СV ' is less, that is, part of the storage energy is spent on charging the batteries, then go to phase 1.1 and repeat the charging process.Thus, the charging of each battery separately will be performed by current pulses of the corresponding storage device until the battery EMF is equal to the storage voltage.According to the maximum power transfer theorem, the load will receive maximum power from the source when the load resistance (Ra) is equal to the internal resistance (Rc) of the source.The BMS control unit checks U С ˂U С ' and, if the condition is met, then the cycle is repeated, if not, then the charging operation is completed with battery equalization (B1, B2, … ,Bn)

Calculation of the parameters of the charging process with battery voltage equalization
To analyze the effectiveness of the proposed device and confirm the possibility of implementing the invention, we will carry out an approximate calculation of the elements of the device and the parameters of the process of charging the Audi Q5 hybrid Quattro battery [6].
To fulfil this condition, the battery equalization device must have a storage device, in particular a capacitor with an internal resistance (Rc) equal to the internal resistance of the battery, which for the Audi Q5 hybrid Quattro battery is Ra = 20 mΩ (see Table 2).In our case, an electrolytic capacitor manufactured by Jb Capacitors Company (Table 3) with an internal resistance Rc = 19 mΩ is suitable [7].However, commercially available capacitors have a wide range of parameters: the capacitance of two identical capacitors can differ by +/-20%.Rс =19 mΩ = 0.019 Ω Therefore, in charging mode 1.1, the constant voltage from the DC-DC source will be distributed unevenly across the capacitor circuit.
To eliminate this disadvantage of capacitors, in the proposed technical solution, after charging the capacitors, they are briefly connected to the voltage divider of the DC-DC source and the voltages are equalized, since the divider is created from the same resistors (RS 1 , RS 2 , ..., RSn), the deviation of the electrical resistance of which is not more than +/-1%.For example, for a high-voltage Audi Q5 hybrid Quattro battery, a metal film resistor with a resistance of Rr = 5 Ohm was chosen with a manufacturing accuracy of +/-1% (Table 4).
For electronic switches S 1 , S The total resistance of internal resistances Rс of series-connected capacitors (C 1 , C 2 , … ,Cn) with a number nс, equal to the number of batteries n А and will be: (2) R CS = 0.019・72 = 1.368 (Ohm) Therefore, when connected to the U CV voltage, the initial charging current can be: In order to prevent the capacitors from burning out from such a current, in the proposed technical solution, the capacitor banks are charged together with the batteries at the first stage of charging at a constant current value, therefore, at the end of the first stage, the capacitors will also be charged to a voltage of Uа' (i) = 3.9 V, and some due to imbalance will be charged up to UDC = 3.85 V.For capacitors, this voltage value is 91.67% (from 4.2V), which is equivalent to a charge time of 2.5τ for capacitors [13].Therefore, at the second stage of battery charging, to charge the energy storage (capacitors), there will be enough time 3τ for the capacitor voltage to be 4.18 V (99.5% of 4.2 V) [13].The total charge of the capacitor C(i) is calculated by the formula: Let's take the EMF level at the beginning of the second stage of charging the battery Еа'' and at the end of Ea'' based on the materials of Isabelle Sourmey 2022 [11].In this case, one storage capacitor C(i) can transfer energy to the accumulator B(i) at the beginning of the second stage with Uash (i): At the end of the second stage, this capacitor can transfer energy to the battery: Charging batteries at the second stage, using the proposed technical solution, with an imbalance of +/-10%, means that individual batteries after the first stage can have a charge of about 80 -85% [12], and those that did not reach 20 -25% that is, such batteries need to be added with the help of capacitors another ΔEp = 23% of energy to charge up to E A = 65・103 J: The interval time for the capacitor for full charging is also known as transient response time τ.We can find the value from the product of the resistance and capacitance [13].Hence, τ = R ・ C (10) Where: τ = time constant, measured in seconds (s); R = resistance, measured in ohm (ohm); C = capacitance, measured in Farads (F).For capacitors (Table 3) time constant: (11) τ С = 0.019・0.027= 0.513・10 -3 (с) Charging capacitors (C 1 , C 2 , ..., Cn) to a value of 99.3% capacity, that is, up to a voltage of 4.2 V, to transfer this charge to the batteries, with an average capacitor voltage of U С = 3.93V, will require at least 3τ of time.This means that a single drive charge will require: The total time spent on multiple refuel top-up ling of the energy storage (capacitor) before transferring energy to the batteries will be: In the process of charging the capacitors, in state phase 1.1, the circuits of the device (1) after 2τ pass into the state phase 1.2 (capacitor charging with voltage equalization).This phase lasts for another 1τ , that is, one third of t' С , which is: The charging time of the capacitors for power transfer in the second stage is much less than the time required to charge the lithium-ion battery.To charge a lithium-ion battery to a level of 99%, on average, it will take t 2А = 100 minutes (6000 s).These data are accepted from Rahul Bollini 2022 [14], and from Battery University BU-409 [15].
IOP Publishing doi:10.1088/1757-899X/1303/1/01200710 After each top-up of the drive to transfer energy to the batteries, time will be spent on charging and equalizing the voltage of the batteries when the device is in phase 1.4 of the circuit state: t 2А ' = t 2А / N cycle (15) t 2А ' = 6000 / 610.4・10 3 = 9.83・10 -3 (s) Therefore, if we neglect the time spent on switching, then the total operating time of the device for charging the Audi Q5 hybrid Quattro battery from 80% to 99% of capacity, with a battery charge imbalance of 20% (see Table 2) will be: This confirms the possibility of charging the batteries from the capacitors at the second stage and performing the equalization of the battery charges.The increase in the charging time of the batteries of hybrid vehicles in the second stage of charging, caused by the equalization of the level of charge of the battery cells, does not exceed 40%.The comparison is based on Rahul Bollini 2022 [14] and Battery University BU-409 [15], where the indicated time was estimated at 100 minutes.

Calculation of the efficiency of the proposed equalization charger
Using a voltage divider across resistors to equalize the voltage of the capacitors before charging the batteries will cause energy wastage.To calculate the losses, the operation of the proposed device was simulated in relation to the Audi Q5 hybrid Quattro high-voltage battery (Table 2).The calculation of the instantaneous capacitor charging circuit at the moment of time corresponding to the charge time of the time constant 4τ С at the moment the voltage divider is turned on to equalize the voltages of the storage capacitors is performed.The charge time corresponding to the time constant 4τ С was chosen because the capacitors have already passed the time 2τ when charging together with the batteries.This circuit will make it possible to select the value of the resistances of the resistors to equalize the voltages of the capacitors.For a more compact representation of the calculation data, 72 batteries connected in series into a battery are divided into groups: nga = 9 groups, nag = 8 batteries in each group and, accordingly: ngc = 9 groups of capacitors, ncg = 8 capacitors.The rated voltage Ua = 4.2 V is taken in accordance with the battery charging voltage of the Audi Q5 hybrid Quattro battery (Table 2).The disbalance of storage capacitors capacitances is set by the coefficient of difference between the internal resistances of the group capacitors: Disb of Resrg(i).
To simplify the calculation of the internal resistance of capacitors (energy storage) Resr'(i), we express in terms of data on the values (expressed as a percentage) of voltage (Voltage) and current (Current), depending on the charge of the capacitor [13]: The equivalent resistance of the shunt resistor of the voltage divider and the internal resistance of the storage capacitor is determined by the formula:

Rеquiv'(i) = Resr' (i)・Rsh/(Resr' (i)+Rsh) (18)
The equivalent resistances of each group of series-connected resistors and capacitors are determined by the formula: The value of the nominal EMF of the capacitor as the product of the battery charging voltage determined by the manufacturer and the correction factor [11] is determined by the formula: The value of the rated charging current of the capacitor as the product of the charging current at the battery charging voltage determined by the manufacturer and the correction factor [11] is determined by the formula: The value of the charging current of capacitors with voltage equalization from a DC-DC source is determined by the formula: Electromotive force of a group of capacitors: Capacitor group charging current: The current of a group of resistors shunting capacitors: Power loss on groups of shunt resistors: Energy loss on groups of shunt resistors:

Uc'sh (i) = Ucg' (i) / nсg (33)
Voltage applied to capacitors: The calculation was made for the case of using capacitors with a typical capacitance deviation of +/-20% (parameters in Table 3), used as energy storage devices for pulsed energy transfer to batteries and divider resistors (parameters in Table 4).The resistors of the charging voltage divider U CV used to equalize the voltage of the capacitors made it possible to equalize the voltage to the limits that allow charging the batteries (see Fig. 5. and Table 7).
A new technical solution to the problem of charging a battery of batteries with the equalization of battery charges using energy storage devices is proposed.A device and a method for charging batteries connected in series are described, which excludes the flow of current through batteries that have reached the level of full charge, when charging batteries that have not reached this level.By calculating the instantaneous mode scheme at the second stage of voltage equalization and charging of storage devices with the expected spread of storage parameters, it is shown that charging lithium-ion batteries using the proposed device and the proposed method of high-voltage battery Audi Q5 hybrid Quattro allows charging lithium-ion batteries with current pulses , formed by capacitive storage devices at the second stage, at a constant value of the charging voltage close to the nominal one, preventing the flow of current through the charged batteries of the battery and without exceeding the permissible level of the charging voltage of the batteries.The charging time of the considered high-voltage battery with the elimination of 15% of the imbalance of the batteries will last up to 139 minutes (2.31 hours).To equalize the charges of the Audi Q5 hybrid Quattro high-voltage battery using capacitive storage devices in this example, additional energy costs ΣEloss' = 54.70Wth will be required, which is 4.2% of the full battery charge E AB = 1300 Wth.The expected energy loss when using a particular Audi Q5 hybrid Quattro high-voltage battery is 4.2% of a full battery charge.

Discussion
The proposed device allows you to perform individual charging of each battery at the final stage of this process using a simpler circuit compared to other methods with individual control of the voltage of each individual battery.The performed study, despite the calculations of the parameters of the device and its modes of operation, in relation to the real-life high-voltage battery Audi Q5 hybrid Quattro, requires additional studies of equalizing processes when equalizing the voltages of capacitive energy storage devices, as well as the processes of charging batteries from the energy storage devices of the proposed device.Theoretical studies of the operation of the device will require the use of special programs and a lot of time.It is advisable to carry out further studies of the proposed device experimentally on the operating model of the device in the modes of charging real batteries using modern measuring equipment at the appropriate stand.The creation of a test bench for studying the charging modes of lithium-ion batteries will not only provide new scientific results and bring the proposed technical solution to practical application, but will also allow it to be used for laboratory work in such disciplines as "Electrical and electronic equipment of vehicles", "Electric and hybrid cars".

Conclusions
The proposed device for aligning the level of battery charging during battery charging can be created on the basis of commercially available electronic components and used to equalize the charges of high-voltage batteries used in the automotive industry, as well as to accumulate energy from renewable energy sources.The use of the proposed device and the method of equalizing the level of charge of the batteries in the battery allows you to fully use the useful capacity of the batteries.Using the proposed device increases the charging time in the second stage by 40%, so the device can be used with each charge.The proposed device and method for leveling the charge level of the batteries in the battery differs in that it allows: -will increase the service life of batteries by eliminating the flow of current through fully charged batteries, that is, to prevent them from overcharging and overheating; -will reduce energy losses for heating balancing resistors, since they are turned on for a short time in the phase of capacitor voltage equalization;

Figure 1
Figure 1 Scheme of a device for equalizing the level of battery charge

Figure 2 .
Figure 2. Status diagram of the battery charger and equalizer

Figure 3 .Table 5 .
Figure 3. Audi Q5 hybrid Quattro high-voltage battery The first stage of charging ends when the battery charge reaches SoC=80%.At the first stage of charging the battery (2), its batteries (B 1 , B 2 , ... , Bn) for example lithium-cobalt oxide batteries (LiCoO 2 ) and storage devices connected to them in parallel, in this case electrolytic capacitors) (C 1 , C 2 , ... , Cn) will be charged to a voltage of U C = 3.9 V. Table 5. Parameters of electronic switches [9] SPECIFICATION TECHNICAL INFORMATION Marking: GA25N120 Manufacturer: ON Semiconductor, USA Hull: TO-3P Collector−Emitter Voltage: V CC = 1200 Vdc Collector Current I C = 25 A Maximum power dissipation: 125 W Operating temperature range:-55 to +150°C

U R1 , U R2 , … , U Rn -voltage of voltage divider resistors; U C1 , U C2 , .., U Cn -energy storage voltage;
The level of these voltages is measured using a sensor D (voltage divider);

Table 1 .
Schemes for switching on electronic switches for charging and equalizing the charge of batteries at the second stage of battery charging (2) (see Figure2) (2)ting the state of the battery charger circuit(2)Functions of the way to equalize the level of charge of the batteries (B1, B2, ..., Bn) in the battery after setting the state of the device circuit Electronic switch on

Table 6 .
Initial parameters of the energy storage voltage equalization mode

Table 7 .
Expected parameters of the energy storage voltage equalization mode