Battery Dynamic Balancing Method Based on Calculation of Cell Voltage Reference Value

Abstract

The article is devoted to solving the problem of charge equalization of multi-element batteries with rated voltage up to 1000 V, operating in dynamic modes with different charge and discharge depths. This article proposes a method of balancing the voltages of power battery elements. The essence of the proposed method is to form a reference signal equivalent to the reference voltage of the battery element for the current state of charge. The novelty of the method presented in this article, in comparison with relevant existing techniques, lies in active control over the balancing circuit proportional to real cell voltage deviation from the reference value. The proposed method can be used both for passive balancing techniques based on ballast resistors, and for circuits made on electromagnetic energy redistribution systems between galvanic cells. A number of Simulink models were developed to determine the electrical parameters of active and passive balancing circuits. Performance and accuracy study of balancing a multi-element battery in charge and discharge modes was conducted by Simulink models. It was established that, compared to classical methods, the proposed balancing method enhances the accuracy by 1.43 times and improves dynamic indices of the balancing process at any state of charge of batteries. The proposed balancing method is a perspective for energy storage systems based on multi-element batteries for power supply nodes of high-power loads with pulsed and repeated short-term operation modes.

1. Introduction

The modern development of various fields of the electric power industry is closely connected with the development of electric energy storage devices based mainly on rechargeable galvanic cells (GC) [1]. Electrochemical storage batteries have an advantage over other electric power storage devices due to having the shortest response time [2]. Rechargeable batteries’ wide range of applications includes ensuring uninterrupted power supply, balancing the balance of consumption and generation, stabilization of electricity parameters, autonomous consumer power supply, and power supply in the starting and pulse modes of electrical appliances’ operation. The ability to quickly get into operation is most relevant for ensuring uninterrupted power supply for critical customers, such as computing data centers, medical equipment, and industrial facilities [3]. The ability to quickly release the accumulated energy is crucial for powerful pulse devices. Such types of devices include laser installations and devices for processing materials by the electrophysical method [4].

The typical operating voltage range for a galvanic cell of any type comprises units of volts. The capacity of one cell does not usually exceed several tens of ampere-hours. Accordingly, the formation of a battery with high operating voltage (from tens to thousands of volts), as well as with high values of operating currents and electrical capacitance, is provided by the GC series and parallel connections [5,6,7].

The existing types of galvanic cells differ in the following parameters: operating voltage range, storage density, operating temperature range, permissible charge and discharge currents, and service life. Each galvanic cell type has its own operating characteristics. Nowadays, Li-ion batteries are the most widespread, their main difference being the cathode material. The main advantages of such batteries are long life, high charge–discharge currents, and a wide range of operating temperatures [8,9,10].

Long-term battery operation (especially in the modes with high charge and discharge currents) inevitably causes the battery’s parameters to change. Basically, the deviations affect the shape of charge and discharge curves, as well as parameters of equivalent series and parallel battery resistances, responsible for heat generation inside the GC with the current flow through and GC self-discharge [11,12,13].

The most obvious negative manifestation of GC parameters’ deviations is the voltage difference of individual elements (unbalancing) that increases during charging or discharge. This reduces the battery’s effective capacity, its life and can result in dangerous and emergency situations [14,15].

Battery imbalance effect is eliminated by passive [16,17,18,19,20] or active [21,22,23,24,25,26,27] GC voltage balancing. In both cases, the protection and balancing systems should switch off the battery from the power circuit at considerable deviations of GC electric and temperature parameters from permissible values [28,29,30,31,32]. In addition, the balancing system should provide the battery complex state monitoring (for example, monitoring of voltage and charge state of each GC) [33,34,35,36,37,38].

Among passive balancing methods to limit GC maximum voltage, resistance ballast balancing circuits are the most widely used. Various solutions of their circuit design variants are presented in publications [16,17,18,19,20,39,40,41]. Figure 1 shows a circuit sample of passive battery balancing by ballast resistors.

However, the disadvantage of such balancing keys’ control method is the elements’ unbalance during the charging process, while the balancing process itself starts with the cell voltage approaching the nominal value U_bal, i.e., towards the end of charging. Thus, the balancing speed is greatly reduced. This balancing system is suitable for low-current, low-voltage batteries, while being ineffective in high-current, high-voltage batteries [39].

Active balancing methods are considered to be the most effective. The most common active balancing systems are built on the basis of transformers, inductive or capacitive voltage converters, with energy transmission into one common storage (Figure 2a) or into one cell (Figure 2b) [22,26,42]. This provides highly efficient battery balancing without forced dissipation of excess GC charge in the form of heat on ballast resistance [43,44].

The main disadvantage of active balancing methods and technical solutions is that their operational logic is limited only by comparing GC voltages with each other. Control algorithms are aimed at comparing voltages of adjacent GCs and activating energy transfer circuits when 35 mV or greater imbalance between the elements is reached.

Such a balancing method may appear ineffective when applied to multi-element batteries since, with an increase in the number of elements, the imbalance of their individual groups significantly increases as well. In the end, it will lead to battery imbalance as a whole.

Passive and active balancing methods’ efficiency can be enhanced by mathematically processing the measured voltages on elements or cells [45]. The essence of the proposed algorithm in [45] is in forming a control pulse phase shift in accordance with the error voltage on battery cells. However, the proposed method’s disadvantages are high balancing currents and the fact that it is efficient only in the battery overcharge and overdischarge areas.

Another implementation variant of active balancing with mathematic processing of measurement signals is presented in [46]. The algorithm in [46] determines the whole battery’s average voltage, and based on voltage unbalance on individual elements, the energy between elements is transferred. The disadvantage of the proposed method is that more overcharged elements have energy transfer priority. This increases the time of voltage grading on the elements and leads to the overstatement of semiconductor switches.

This paper aims to research and develop the method of balancing battery elements’ voltages, thus eliminating the disadvantages of the existing methods. The novelty of the method presented in this article, in comparison with relevant existing techniques, lies in balancing circuit control algorithms. The essence of the method is that a reference signal is generated based on measuring the voltage values of each battery cell. Next, the balancing circuit transistor control pulse is generated in proportion to the element’s real voltage deviation from the reference value.

The authors expected that the pulse range change would make it possible to enhance the accuracy as well as dynamic indices of the balancing process throughout the whole charging process. At this, the method proposed can be used for both passive and active balancing design variants.

The proposed method and circuit solutions are designed to increase the balancing system efficiency for batteries with high operating voltages and critical values of charge/discharge currents. This is especially acute for power supply nodes of high-power loads with pulsed and repeated short-term operation modes. On the practical side, these results are intended to prototype a switched-mode power supply unit based on lithium-titanate batteries with 20 kW output power, currently being developed at Nizhny Novgorod State Technical University n.a. R.E. Alekseev.

The article is organized as follows. Section 2 presents the description and flowcharts of the proposed method for active and passive balancing systems. Simulink models to determine the electrical parameters of active and passive balancing circuits are described in Section 3. The results of the study based on simulation models are listed in Section 4. The article ends with Section 5 summarizing the proposed method’s scope and its advantage over the classical approach.

2. Materials and Methods

2.1. The Essence of Proposed Method

The proposed solution involves calculating the average battery voltage and starting balancing when the voltage of any GC exceeds the permissible deviation, which can be up to several tens of mV (Figure 3). This modification makes it possible to use a relatively primitive balancing method not only as a way to limit overcharging of the cell and equalize the voltages in the battery’s full charging zone, but also to provide balancing during the entire charging process and, if necessary, to equalize the voltage of galvanic cells in the battery disconnected from power supply.

The diagram shows charge level of five GCs of one battery in charge mode, as well as the settings at which balancing starts. The state of charge of the first, third, and fifth elements is lower than the average voltage of one battery element, so they are charged in normal mode. The charge states of the second and fourth elements exceeded the average voltage of one battery element, but the charge state of the second element did not overcome the dead zone. Thus, the balancing of the fourth element is activated while the second element continues being charged normally.

2.2. Block Diagram of Passive Balancing Electronic Nodes Using the Proposed Method

The obvious disadvantage of ballast resistors is the conversion of excess GC charge into heat and a general decrease in the power system efficiency. In this regard, the amount of ballast resistance is usually selected to be large enough to ensure the balancer operation with minimum GC discharge current:

$$R_b=\frac{U_{\mathit{cell}}}{\left(0.01\dots 0.1\right)·I_{\mathit{char}}}.$$

(1)

Minimizing the balancer current is permissible only in batteries designed for small operating currents and small capacities. An attempt to apply low-current ballast to a power battery will result in extremely low balancer efficiency, and the decrease in efficiency can only be compensated through the charger operating modes that limit charging currents when unacceptable imbalance of the battery is reached. Large current balancing in discharge mode becomes totally impossible, and the battery elements’ protection will be fully provided by the control circuit of minimum allowable charge.

Ballast circuit efficiency increase in modes with large charge/discharge currents can be achieved by relatively low-resistance ballast resistance, which is switched by a power switch controlled by a pulse width modulation-based control system (Figure 4). The method is aimed at increasing the duration of the key open state in GC ballast circuit in proportion to the magnitude of its voltage deviation from the average battery voltage:

$$R_b\left(\mathsf{\Delta }U\right)=\frac{U_{\mathit{cell}}}{\left(0.01\dots 0.1\right)I_{\mathit{char}}·\left(U_{\mathit{cell}}-U_{\mathit{ref}}\right)·k_{\mathit{gain}}},$$

(2)

where $k_{\mathit{gain}}$—the gain of the cell voltage imbalance relative to the average battery voltage. $I_{\mathit{char}}$—charging current value, A, $U_{\mathit{cell}}$—the element voltage, V and $U_{\mathit{ref}}$—the reference value of the cell voltage for the state of charge, V.

The combination of the balancing method relative to the battery voltage average value and active adjustment of switched-on state of high-current ballast circuit will allow for equalization of GC voltages at any stage of the battery charge and at any current value, including the maximum allowable.

An optional mode is voltage equalization in discharge mode, despite the fact that GC voltages’ equalization in discharge mode actually does not make any sense from the point of view of battery energy output. The subsequent cells’ discharge with the remaining increased voltage can be considered as a training cycle of a battery with the maximum discharge depth, which positively affects the alignment of galvanic cells’ voltage–discharge curves. The block diagram of passive balancing, adapting the balancing current of the element to the value of its unbalance, is shown in Figure 5.

Balancing is realized by parallel connection of a fully controlled semiconductor key together with a current-limiting resistor to the galvanic cell. If the element voltage exceeds the average voltage of all elements, the balancing is triggered, and the semiconductor switch in the pulse mode of operation discharges the element with an average current, its value proportional to the voltage imbalance value of this element relative to the average battery voltage. This method allows changing the amount of charge slowdown of individual elements in proportion to this element voltage imbalance and the average battery voltage.

2.3. Multi-Coordinate Energy Transmission Using the Proposed Method Based on Active Balancing Circuit

The proposed modification is based on transformer balancing principle, but does not employ high-voltage winding to transmit the charge of the entire battery. The use of bidirectional transistor switches and a multi-winding pulse transformer (or inductor) allows organizing the targeted energy transmission between the selected elements, as shown in Figure 6.

The diagram shows balancing system dead zones (marked in blue), the over-charge zone (red), and the under-charge zone (black) for five cells of one battery in charge/discharge mode. The state of charge of the fourth element exceeded the battery voltage average value per element U_bal, while the state of charge of the first element was lower than the battery voltage average value per U_bal element, thereby pumping excess energy from the fourth element to the first undercharged element. It should be noted that this method implies multi-coordinate energy transmission between any battery elements through a common capacitive storage device.

Figure 7 shows energy transmission mode from the recharged cells marked in red to the total capacity marked in blue.

Multi-winding inductors are an integral element of reversible circuit of a multi-channel flyback converter, which provides a directed process of battery voltage equalization. Herewith, the balancer operation is divided into two phases. In the first phase, energy is transmitted from an element with an excess charge into an intermediate capacitive storage device. In the second phase, energy is transmitted from the storage device to an element with insufficient charge. A push–pull flyback converter allows matching the magnitude of the elements’ voltages and the accumulator by controlling the amount of energy accumulated in the inductor magnetic system in the first operation cycle.

The implementation of an inductor or transformer with a large number of windings will inevitably lead to a decrease in the magnetic coupling coefficient of the windings and an increase in scattering flux. In this regard, it is preferable to perform a balancing circuit of 4 to 8 elements; following this, an additional winding is used to coordinate two separate balancing circuits.

Figure 8 shows a similar process of energy transmission, where it is transmitted to undercharged elements from a common capacitive storage device.

3. Developing Passive and Active Balancing Simulink Models

3.1. Simulink-Passive Balancing Model Using the Proposed Method

A BMS simulation model with a passive balancing type has been developed for two unbalanced lithium-titanate battery elements in order to study operating modes. One iteration of the model corresponds to 1 s of real time, while the full cycle of the model corresponds to 15,000 iterations. The power part of the simulation model is shown in Figure 9.

The power part consists of two battery cells; their rated voltage is 2.4 V, and their capacity is 40 Ah. In order to set the static imbalance, the upper element’s initial charge is 10%, and the charge of the lower one is 20%. In addition, the imbalance is created by setting the internal resistance of the battery elements: the upper element has 0.0006 ohms resistance, and the lower one has 0.0005 ohms. Balancing circuits and the main power switch is simulated by models of a field–effect transistor and a resistor with 0.8 ohms resistance (balancing current—3 A).

Using the library blocks “Voltage Measurement” and “Current Measurement”, the following parameters are measured: “Cur_Bal1” and “Cur_Bal2”, which are balancing currents of battery elements, “Uref”, which is the average voltage of one element of the entire battery, “SOC₁” and “SOC₂”, which are the state of charge of two series-connected battery elements, and “U₁” and “U₂”, which are the two battery elements’ voltages, respectively, and the parameter of SOC_Ref elements’ average state of charge is calculated as well. To simplify the simulation, the balancing process is performed relative to a given setpoint rather than calculating the average battery voltage.

The BMS control system simulation model consists of two blocks: the first block is the main power key control (Figure 10), and the second block is the balancing keys’ control (Figure 11).

Accordingly, the “Protection of overcharge” and “Protection of overdischarge” subsystems are the main element of the first block of the simulation model. These subsystems, based on the input voltage signal of the element, form a signal for the main power key conductivity to exclude emergency operation modes. The number of these protection systems corresponds to the number of battery elements; in this case, two protection systems are required for two cells. Then, the signals for the conductivity of the charging power key and the discharge power key are added through the logical operator “And” for further transmission directly to the control output of the main power key.

The input of the second block of the simulation model receives signals of the battery elements’ state of charge, as well as the average value of the state of charge of the battery per element. Based on the input data, the block generates balancing keys’ control signals. The principle of operation is to calculate the charge imbalance value of the elements relative to the average charge of the entire battery per element; following this, the imbalance value enters the input of the comparing device through a proportional regulator, while a periodic sawtooth signal is connected to the second input of the comparing device. The balancing signal is received at the input of the 4-AND logic element, with the following devices connected to its other inputs: a trigger that determines at what unbalance value the balancing circuits are actuated and at what unbalance value the balancing circuits stop operating, a block setting the start time of balancing and a block setting the limit time for the end of balancing. Thus, control pulses are formed at the output of the second block, their width proportional to the magnitude of the elements’ charge imbalance. Consequently, the operation of the balancing key is adapted to the magnitude of the elements’ charge imbalance.

The model simulating the classical balancing method differs from the one proposed in that there is no adaptation of the balancing keys to the unbalance value of the elements, and the balancing circuits are triggered according to a given setpoint (Figure 12).

The simulation results are displayed using two software oscilloscopes, “Scope”. The first oscilloscope displays the battery cells’ state of charge and the charging and discharge keys’ operating time. The second oscilloscope shows the battery cells’ state of charge and balancing currents of the elements of the classical and the proposed method models.

3.2. Active Balancing System Model with Multi-Coordinate Energy Transmission

A BMS simulation model with an active balancing type for four unbalanced lithium-ion battery elements was developed to study the operating mode of energy transmission from a given element of one battery to a given element of another battery. The power part of the simulation model is shown in Figure 13.

The model includes four battery elements, their rated voltage of 3.7 V, and their capacity of 1 Ah. The upper left element’s initial charge is 52%, and the lower right one is 48%, which simulates static battery imbalance. Balancing circuits are modeled by IGBT transistor library models, a capacitor with 100 UF capacity, and two sets of three-winding inductors; their parameters are given in

Table 1. Three-winding inductor parameters.

Parameter	Primary Winding	Secondary Winding #1	Secondary Winding #2	Magnetizing Circuit
R, Ohm	1	1	1	0.1
L, uH	100	100	100	90

.

The main objective of this model is energy transmission from a more charged element to a less charged one. The balancer control system (Figure 14) consists of a pulse generator block for controlling balancing transistors and a block for displaying simulation results.

The first block of the control system model generates a periodic sawtooth signal with 1 kHz frequency and an amplitude of 1; thereafter, the signal is sent to a comparing device, its second input connected to a constant (0.1) responsible for a given width of control pulses. At the output of the comparing device, there is a periodic sequence of rectangular pulses with a 10% fill factor, which enters the VT3 transistor control input. The VT4 transistor control input receives the output of the comparing device through an inverter. Transistors VT3 and VT4 are responsible for energy transmission from the common storage device to an undercharged battery cell. Transistors VT1 and VT2 are responsible for energy transmission from a recharged battery cell to the common storage device. These transistors’ control pulses are formed similarly, with the exception of the output voltage limitation circuit: when the common storage device voltage exceeds 10 V, the control pulse supply to transistors VT1 and VT2 is prohibited.

The main element of the second control system unit is a software oscilloscope, which displays the value of the state of charge of both the recharged element and the undercharged element, as well as the voltage on the common capacitive storage.

4. Simulation Results

4.1. Passive Balancing Method Simulation Results

The modeling result of the elements’ voltage balancing is shown in Figure 15 for the proposed method, as well as for the classical method for 0.5C charging current. The initial imbalance between the elements is set to 10% of the state of charge.

In the classical method, balancing transistors, both for the first and the second element, are triggered when the state of charge of the elements reaches 90%. Balancing transistor actuation slows down the charge, thereby changing the slope of the charging characteristic. As soon as one of the elements’ voltage reaches its maximum value, the main power charging key will open, and the battery charge will stop, the voltage imbalance being 8%. In the absence of load connection mode, balancing transistors continue operating until the imbalance is eliminated with a specified accuracy of 0.1%. Thus, balancing time under the classical method is 53 min, consisting of 15% t_zar (17 min) plus 70% t_off (36 min).

In the proposed method, balancing transistors are actuated in the middle of the charging process (the state of charge is 50%), while only the recharged element balancing transistors operate based on the element’s measured data. Balancing transistors’ operation slows down the recharged cell, while the undercharged cell charging goes on at a normal speed. When the elements’ state of charge reaches 75% value, the imbalance between them will not exceed 1%. For a more precise adjustment, balancing transistors switch to pulse mode with a gradual decrease in the fill factor until the unbalance reaches the required 0.1% accuracy. Thus, in the proposed method, the charge time is 30% t_zar to eliminate the main unbalance with 1% (37 min) accuracy; the remaining charge time of 30% t_ch (37 min) is allocated for more accurate (0.1%) elimination of the imbalance between the elements.

4.2. Active Balancing Method Simulation Results

The active balancer model is designed to determine the amount of energy that can be transmitted from a recharged cell to an undercharged one. The simulation results are shown in Figure 16.

Figure 16 shows the state of charge of the recharged SOC₁ cell and the undercharged SOC₄ cell, as well as the voltage on the total capacity, which is stabilized in the 9 to 10 V range. In 7 s, 0.028% of the charge is consumed by the first cell, and 0.02% of the charge is transmitted to the fourth. During the 36 min balancing time (the balancing time value obtained from the proposed method simulation results with a passive balancing current of 0.5C), the recharged element can be discharged by 6% of the charge, and the undercharged element can be charged by 4.32% of the charge. Consequently, the system efficiency reaches 72%.

Simulation results confirm the proposed method’s efficiency for active and passive balancing in comparison with the classical method.

5. Conclusions

The classical balancing method refers to charge levels’ stabilization of each battery element of about 90% of the state of charge with the required accuracy without measuring the voltages of the elements. Classical balancing and control systems may appear ineffective if they are used in high-power multi-element batteries operating in dynamic modes. Most active balancing systems have voltage feedback of adjacent elements or sections of elements. Due to this, such situations may appear when several sections in a multi-element battery are balanced independently of each other, which generally leaves the battery unbalanced.

The authors have suggested a balancing method of battery average voltage value which provides balancing of a multi-element battery. Simulink-models research results prove the advantages of the method proposed:

• The method allows for speeding up the time of balancing and enhances the accuracy of battery balancing;
• The method excludes the overcharge of individual GCs and provides a uniform charge of all GCs in the battery;
• The method provides for multi-coordinate energy transmission between any GCs in the battery.

This method can be applied to both passive and active balancing systems. The proposed balancing method can be widely applied in the field of building a battery up to 1000 V to ensure an uninterrupted power supply to provide power to critical clients, such as computing data centers, medical institutions, as well as industrial facilities.

Further research work will be aimed at developing and studying the balancer physical model.