A voltage feedback battery preheating method for an integrated electric drive system
Patent Information
- Application Number
- CN202311325236.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-10-13
- Publication Date
- 2026-10-23
- Estimated Expiration
- 2043-10-13
AI Technical Summary
[0003]本发明的目的在于提供一种集成电驱系统的电压反馈电池预热方法,使得电池的工作电压控制在其极限值以内,不会损坏电池的同时,还能发挥出最大的电池加热速率以解决现有的技术缺陷和不能达到的技术要求
[0039]1、本申请通过设置电压峰谷采样模块和PI控制模块,具体的设置上限PI和下限PI,能够将电池组的电压控制在其极限电压范围内,能够保证电池组的使用寿命,并发挥出最大的电池加热能力,实现安全加热的目的。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of battery heating, specifically to a voltage feedback battery preheating method for an integrated electric drive system. Background Technology
[0002] The performance of automotive lithium-ion batteries deteriorates drastically in low-temperature environments: slow charging, easy lithium plating during high-current charging, decreased power density, significantly reduced discharge rate, and accelerated cycle life degradation. This severely restricts the promotion of pure electric vehicles in cold northern regions. Based on the current state of lithium-ion battery technology, low-temperature preheating is a feasible and effective technical solution. Compared to external heating, AC internal heating has the advantages of rapid temperature rise and no need for heating elements. However, existing technologies require changes to the circuit topology of the battery and electronic control system, which presents certain difficulties. Furthermore, to address the issue of easy lithium plating during the charging and discharging process of lithium-ion batteries in low-temperature environments, almost all strategies rely on controlling the polarization voltage. There is no good solution for controlling the battery voltage during the preheating process of an integrated electric drive system to ensure battery safety and lifespan. Therefore, proposing a voltage feedback battery preheating method for an integrated electric drive system is essential. Summary of the Invention
[0003] The purpose of this invention is to provide a voltage feedback battery preheating method for an integrated electric drive system, which controls the battery's operating voltage within its limit value, preventing battery damage while maximizing the battery heating rate, thereby overcoming existing technical defects and unmet technical requirements.
[0004] To achieve the above objectives, the present invention provides the following technical solution: a voltage feedback battery preheating method for an integrated electric drive system, comprising:
[0005] 1. Connect the preheating controller, which includes a PI control module, switching logic, voltage peak-valley sampling module, and PWM generator, to the battery pack;
[0006] 2. Input the upper limit control target value ub,max,o and the lower limit control target value ub,min,o of the battery pack into the controller;
[0007] 3. The PI control module generates a 1-zero vector proportion d0 and sends the 1-zero vector proportion d0 to the PWM generator;
[0008] IV. The PWM generator calculates the PWM physical signal based on the motor electrical angle θ in the electric drive system, and simultaneously generates a synchronous sampling signal;
[0009] 5. The PWM generator sends the PWM physical signal to the inverter in the electric drive system and sends the synchronous sampling signal to the voltage peak-valley sampling module.
[0010] 6. After receiving the sampling synchronization signal, the voltage peak and valley sampling module samples the peak voltage ub,max and valley voltage ub,min of the battery pack, then determines the switching logic based on the peak voltage ub,max and valley voltage ub,min, and finally controls the switch according to the switching logic.
[0011] 7. The switch controls the PI control module according to the switching logic;
[0012] 8. The inverter drives the stator coil of the motor according to the PWM physical signal.
[0013] Preferably, in step four, the step of the PWM generator calculating the PWM physical signal based on the motor electrical angle θ in the electric drive system is as follows:
[0014] 1) The PWM generator adds the zero vector circuit state to the effective vector circuit state and the dead zone vector circuit state. The effective vector circuit state is composed of two basic vectors, U4 and U6.
[0015] 2) The PWM generator calculates the ratio of the action times T4 and T6 of the two basic vectors based on the motor electrical angle θ;
[0016] 3) The PWM generator then expresses the dead vector action time Tx according to the proportional constant C of the total effective vector action time (T4+T6) and the dead vector action time Tx. The total effective vector action time is the sum of the action times of the two basic vectors.
[0017] 4) The PWM generator then expresses the zero vector action time T0 based on the dead vector action time Tx, the total effective vector action time, and the PWM period Ts;
[0018] 5) The PWM generator re-expresses the zero vector action time T0 based on the zero vector proportion and the PWM period Ts;
[0019] 6) Based on the representation relationships in steps 2), 3), 4) and 5), calculate the dead zone vector action time Tx, the zero vector action time T0, and the action times of the two basic vectors respectively.
[0020] Preferably, the ratio of the action times T4 and T6 of the two effective vectors in step 2) is calculated as follows:
[0021] According to the Park-Clerke coordinate transformation formula Substituting ua = T4, ub = -T6, and uc = 0 into the above equation, and setting the calculated uq = 0, we can obtain...
[0022]
[0023] Preferably, the specific method for calculating the dead zone vector action time Tx, the zero vector action time T0, and the action times of the two basic vectors in steps 2)-6) is as follows:
[0024] Based on the proportionality constant C between the total effective vector action time and the dead zone vector action time Tx, we can obtain:
[0025]
[0026] Based on the overall control period Ts, we can obtain:
[0027] T s =T x +T4+T6+T0 (3)
[0028] The overall control cycle Ts is determined by the motor control frequency H;
[0029] Furthermore, the relationship between the zero vector proportion d0, the zero vector action time T0, and the overall control period Ts is as follows:
[0030]
[0031] The values of the dead zone vector action time Tx, the zero vector action time T0, and the two basic vector action times are calculated based on the obtained relational formulas (1)-(4).
[0032] Preferably, the proportionality constant C is greater than 1.
[0033] Preferably, the zero vector action time is divided into two equal time slices and inserted after the dead zone vector action time and the effective vector action time, respectively.
[0034] Preferably, the sampling time for the peak voltage ub,max is before the end of the dead zone vector, and the sampling time for the valley voltage ub,min is before the end of the effective vector.
[0035] Preferably, the upper limit control target value ub,max,o is slightly less than the upper limit value of the battery pack voltage, and the lower limit control target value ub,min,o is slightly greater than the lower limit value of the battery pack voltage.
[0036] Preferably, the PI control module includes an upper limit PI and a lower limit PI, and the switch controls whether the zero vector percentage d0 input to the PWM generator comes from the upper limit PI or the lower limit PI according to the switching logic.
[0037] Preferably, the switching logic is as follows: first, lower limit PI control is used, and the voltage peak and valley sampling module monitors and feeds back the peak voltage in real time. If the peak voltage ub,max is close to the upper limit, then switch to upper limit PI control. After the upper limit PI control is switched, the voltage peak and valley sampling module starts to monitor and feed back the valley voltage. If the valley voltage ub,min is close to the lower limit, then switch back to lower limit PI control.
[0038] Compared with the prior art, the beneficial effects of the present invention are:
[0039] 1. This application, by setting a voltage peak-valley sampling module and a PI control module, specifically setting an upper limit PI and a lower limit PI, can control the voltage of the battery pack within its limit voltage range, ensuring the service life of the battery pack and maximizing the battery heating capacity to achieve the purpose of safe heating.
[0040] 2. By inserting the zero vector into the effective and dead zone vectors, this application can compress the action time of the non-zero vector and the dead zone vector, thereby reducing the amplitude of the discharge current and the charging current, so as to adjust the amplitude of battery voltage fluctuation and achieve the purpose of battery voltage control.
[0041] 3. This application transmits a synchronous sampling signal. Specifically, the peak voltage sampling time is set before the end of the dead zone vector, and the valley voltage sampling time is set before the end of the effective vector. This avoids voltage fluctuations during repeated charging and discharging of the battery to sample extreme voltage values, so as to accurately measure the extreme voltage points at the end of the battery pack and ensure the accuracy of this application. Attached Figure Description
[0042] Figure 1 This is a schematic diagram of the AC current control timing of the present invention;
[0043] Figure 2 This is a diagram of the preheating strategy control structure of the present invention;
[0044] Figure 3 This is a schematic diagram illustrating the synchronization principle of voltage sampling and PWM in this invention;
[0045] Figure 4 A graph showing the battery voltage and duty cycle during the heating process using a fixed duty cycle control strategy in the experimental control.
[0046] Figure 5 The graph shows the battery voltage and duty cycle during the heating process of this application in the experimental control.
[0047] Figure 6 This is a comparison table of the heating rates of this application and the fixed duty cycle control strategy in the experimental control. Detailed Implementation
[0048] The following will refer to the appendices in the embodiments of the present invention. Figure 1-6 The technical solutions in the embodiments of the present invention are clearly and completely described herein. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.
[0049] Please see Figure 1-6 Embodiments of the present invention:
[0050] Example:
[0051] A zero vector is introduced between the effective vector and the dead-zone vector. The voltage is adjusted by regulating the proportion of the zero vector throughout the control cycle. During the non-zero vector's action, the battery discharge current increases; during the zero vector's action, the battery current is zero, while the motor phase current decays rapidly; during the dead-zone vector's action, the battery current reverses to a negative value based on the phase current, charging the battery. The addition of the zero vector compresses the time of the non-zero vector and the dead zone, thus reducing the amplitude of both the discharge and charging currents. This directly adjusts the amplitude of battery voltage fluctuations, achieving the effect of voltage control.
[0052] As shown in Figure 1: Assuming the current motor rotor is positioned between the basic vectors U4 and U6, the effective vector in this application is synthesized from the two basic vectors U4 and U6. The ratio of the action times T4 and T6 of the U4 and U6 vectors is determined by the electrical angle of the current motor. The principle is to ensure that the motor output torque is zero under the action of the synthesized vector. When the rotor on the motor is stationary, there is no phase difference between the voltage vector and the current vector. Therefore, zero torque can be obtained as long as the voltage vector coincides with the d-axis is given. The d-axis is the synchronous rotating coordinate system used in the vector control of the permanent magnet synchronous motor. It rotates synchronously with the motor rotor, and the direction of the d-axis is the same as the magnetic pole of the permanent magnet of the motor stator. According to the Park-Clerke coordinate transformation formula:
[0053]
[0054] Substituting ua = T4, ub = -T6, and uc = 0 into the above formula, and setting the calculated uq = 0, the ratio of T4 to T6 can be calculated from the current electrical angle θ of the motor. The calculation formula is as follows:
[0055]
[0056] In the formula, θ represents the current electrical angle of the motor rotor, determined by the measurement value of the rotor position sensor and the number of pole pairs. To ensure the generated battery AC current is symmetrical, the proportionality constant C between the non-zero vector and the dead zone vector is calibrated experimentally. The proportionality constant C is a constant greater than 1, and is taken as 1.6, i.e.:
[0057]
[0058] like Figure 1 As shown: The zero vector's action time T0 is divided into two equal time slices, inserted after the dead zone and the non-zero vector, respectively. The overall PWM period Ts is determined by the given motor control frequency. Here, the PWM frequency is set to the commonly used motor control frequency of 10kHz, therefore:
[0059] T s =T x +T4+T6+T0=0.1ms (3)
[0060] To solve the above three equations simultaneously, given the proportion of the zero vector:
[0061]
[0062] By simultaneously obtaining the current electrical angle θ of the motor, Tx, T4, T6, and T0 can be calculated. Based on this, a 6-channel PWM wave containing the control signal d0 can be generated, and the signal output can be implemented by the PWM generator.
[0063] like Figure 2 As shown: The concrete feedback control structure of this application includes the controller and electric drive system (the controlled object consisting of a battery pack, a motor and an inverter) in the dashed box. In order to control the upper and lower limit battery voltages respectively, the PI control module is designed to consist of two PI control loops: the upper limit PI and the lower limit PI.
[0064] The input variables of the controller are the target voltage values ub,min,o and ub,max,o for controlling the upper and lower limits of the battery pack voltage. Specifically, for a single lithium-ion cell, the upper and lower limits of the battery pack voltage can be obtained by multiplying its upper and lower limit voltages by the number of series connections in the battery pack. To ensure safety, ub,min,o is set to be slightly higher than the lower limit of the battery pack voltage, and ub,max,o is set to be slightly lower than the upper limit of the battery pack voltage.
[0065] Furthermore, the 1-zero vector ratio d0 is defined as the output variable of the PI element, with a range of 0 to 1, and this value is passed to the PWM generator. Simultaneously, the PWM generator calculates the values based on the motor electrical angle θ in the electric drive system according to formulas (1)-(4), obtaining the values... Figure 1 The corresponding 6 PWM physical signals are then output to the inverter in the electric drive system, and finally act on the stator coils of the motor.
[0066] The PWM generator sends a sampling synchronization signal to the voltage peak-valley sampling module, which obtains the voltage peak value ub,max and the voltage valley value ub,min. These values are then subtracted from the target voltage values ub,min,o and ub,max,o for upper and lower limit control, respectively (ub,max-ub,max,o and ub,min-ub,min,o). This result is input to the upper and lower limit PI control modules. Simultaneously, the switching logic is determined based on the comparison results. The switch controls the PI control module according to the switching logic, selecting either upper limit PI control or lower limit PI control.
[0067] The switching between the upper limit PI and the lower limit PI is controlled by a switch connected after its output. The switch determines whether the signal input to the PWM generator at the current moment comes from the upper limit PI or the lower limit PI. The switching logic between the upper and lower limit PI is as follows: first, the lower limit PI control is used. The voltage peak-valley sampling module samples the voltage peak value ub,max. If it is close to the upper limit, it switches to upper limit PI control. The voltage peak-valley sampling module also samples the voltage valley value ub,min. If it is close to the lower limit, it switches back to lower limit PI control.
[0068] To prevent significant voltage overshoot, this application ensures that the output of the newly activated PI control loop is zero at the initial moment and at each switching moment, i.e., d0 equals 1, and the output is all zero vectors, so as to avoid excessively high or low battery terminal voltage.
[0069] The specific battery heating process is as follows: Initially, the controller is set to lower limit PI control by default. When the battery heating process is started, if the valley voltage ub,min sampled by the voltage peak-valley sampling module is lower than the lower limit target value ub,min,o, the lower limit PI controller will increase d0, causing both the battery current and polarization voltage to decrease, thereby controlling the battery pack terminal voltage above its allowable lower limit. Conversely, if the valley voltage ub,min sampled by the voltage peak-valley sampling module is higher than the lower limit target value ub,min,o, but much lower than the upper limit target value ub,max,o, the lower limit PI controller will decrease d0, causing both the battery current and polarization voltage to increase. This controls the battery pack terminal voltage to approach its lower limit voltage, ensuring high-rate heating and thus stabilizing the voltage valley at the battery pack terminal near the target voltage valley. As the battery temperature rises or when the battery SOC is high, the peak voltage ub,max sampled by the peak-valley voltage sampling module gradually increases during the voltage valley adjustment process, and may approach the upper limit voltage of the battery pack. When the peak voltage ub,max exceeds the target peak voltage ub,max,o, the PI switching logic is triggered, switching to upper limit PI control to ensure that the peak voltage of the battery pack terminal does not exceed the upper limit. During upper limit PI control, the valley voltage is monitored simultaneously. That is, as the SOC decreases, if the voltage valley is lower than the lower limit voltage, it will switch back to lower limit PI control to increase d0, decrease the current, and control the valley voltage to near the lower limit. With this control strategy, the peak and valley values of the battery pack terminal voltage can be controlled within their allowable upper and lower limits. This application sets up an alternating current in the battery pack, and the battery pack temperature Tb will gradually rise. If the battery temperature Tb is monitored to rise to a value that can start the vehicle, such as -10°C, then all the above processes will be stopped and the battery heating will end.
[0070] The PI controller incorporates an output anti-saturation strategy; specifically, this application clamps the output d0 between 0 and 1. To control overshoot, the dynamic process is adjusted to an asymptote similar to an overdamped state. To improve dynamic characteristics, the PI control period is set to the PWM period Ts. Other parameters of the PI control loop can be obtained through experimental adjustment.
[0071] During repeated charging and discharging, the battery pack's terminal voltage will inevitably fluctuate. The relationship between the battery pack's terminal voltage fluctuation pattern and the PWM wave is as follows: Figure 1As shown. During PWM switching, due to the equivalent inductance of the bus and battery, the battery terminal voltage waveform often experiences a rapid pulse disturbance. To accurately measure the extreme points of the battery pack terminal voltage, voltage sampling is performed before the effective vector and dead-time vector end to avoid this disturbance. This is why voltage peak sampling needs to be synchronized with PWM. Specifically, the voltage valley sampling time is set before the control signal of the A-phase upper transistor in the inverter switches from high to low level in each PWM cycle Ts, that is, before the effective vector ends; similarly, the voltage peak sampling time is set before the dead-time vector ends. The above advance can be calibrated experimentally. These two times are defined as sampling synchronization signals, which are transmitted from the PWM generator to the voltage peak-valley sampling module.
[0072] Experimental control:
[0073] To verify the feasibility and advantages of the above heating method, under the condition that the battery voltage does not exceed the limit, the heating rate of the constant voltage control strategy and the fixed duty cycle strategy are compared, and comparative experiments are conducted to study the beneficial effects of this method.
[0074] The specific battery was a 12-cell battery pack with upper and lower voltage limits of 30V and 50V respectively, and a state of charge (SOC) of 60%. The initial temperature and ambient temperature were both -30℃, and the timing was stopped for both sets of tests after the average battery temperature reached -10℃.
[0075] The first group of tests adopted a constant voltage control strategy: after the test, the battery was left to stand for 4 hours until the battery temperature returned to the ambient temperature before the second group of tests was carried out.
[0076] The second group of experiments adopted a fixed duty cycle strategy, with the zero vector ratio fixed at 78.4%. This value is the duty cycle of the zero vector when the battery voltage reaches the lower limit at -30℃. As the temperature rises, the battery voltage slowly increases. Therefore, as long as the PWM wave is output according to this duty cycle, it can be ensured that the battery voltage will not exceed the limit during the preheating process.
[0077] like Figure 4 As shown, under the fixed duty cycle strategy, as the battery temperature rises, the polarization voltage decreases, the minimum voltage gradually increases, and the deviation from the target value becomes further and further.
[0078] like Figure 5 It can be seen that the constant voltage control strategy can keep the minimum voltage of the battery pack around the target value of 30.5V. During the experiment, the effective vector duty cycle can be seen to gradually increase. Due to the low SOC, the battery pack voltage did not exceed the upper limit throughout the entire process.
[0079] The temperature curves and heating times corresponding to the two sets of experiments are as follows: Figure 6As shown in the figure, the heating rate of the fixed duty cycle strategy gradually decreases. This is because as the battery surface temperature rises, the temperature difference between it and the environment increases, leading to an increase in surface heat dissipation. Simultaneously, the battery's internal resistance decreases with increasing temperature, resulting in a decrease in internal heat generation. Ultimately, this manifests as a gradually decreasing heating rate. Similarly, if the constant voltage control strategy proposed in this patent is adopted, the battery voltage can be controlled within allowable limits throughout the heating process, fully utilizing the battery's self-heating capability. Therefore, as the temperature rises, the rate of increase in the battery's internal self-heating power is greater than the rate of increase in surface heat dissipation, resulting in an increasing heating rate, which ultimately effectively improves the overall heating rate.
[0080] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the scope of the invention. No reference numerals in the claims should be construed as limiting the scope of the claims.
[0081] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.
Claims
1. A method for preheating a voltage feedback battery in an integrated electric drive system, characterized in that, include:
1. Connect the preheating controller, which includes a PI control module, switching logic, voltage peak-valley sampling module, and PWM generator, to the battery pack; 2. Input the upper limit control target value ub,max,o and the lower limit control target value ub,min,o of the battery pack into the controller; 3. The PI control module generates a 1-zero vector proportion d0 and sends the 1-zero vector proportion d0 to the PWM generator; IV. The PWM generator calculates the PWM physical signal based on the motor electrical angle θ in the electric drive system, and simultaneously generates a synchronous sampling signal; 5. The PWM generator sends the PWM physical signal to the inverter in the electric drive system and sends the synchronous sampling signal to the voltage peak-valley sampling module.
6. After receiving the synchronous sampling signal, the voltage peak and valley sampling module samples the peak voltage ub,max and valley voltage ub,min of the battery pack, and then determines the switching logic based on the peak voltage ub,max and valley voltage ub,min.
7. The switch controls the PI control module according to the switching logic; 8. The inverter drives the stator coils of the motor according to the PWM physical signal; The zero vector action time is divided into two equal time slices and inserted after the dead vector action time and the effective vector action time, respectively; The PI control module includes an upper limit PI and a lower limit PI. The switch controls whether the 1-zero vector ratio d0 input to the PWM generator comes from the upper limit PI or the lower limit PI according to the switching logic. The switching logic is as follows: first, lower limit PI control is used, and the voltage peak and valley sampling module monitors and feeds back the voltage peak value in real time. If the voltage peak value ub,max is close to the upper limit control target value ub,max,o, then switch to upper limit PI control. After switching to upper limit PI control, the voltage peak and valley sampling module starts to monitor and feed back the voltage valley value. If the voltage valley value ub,min is close to the lower limit control target value ub,min,o, then switch back to lower limit PI control.
2. The voltage feedback battery preheating method for an integrated electric drive system according to claim 1, characterized in that, In step four, the step by which the PWM generator calculates the PWM physical signal based on the motor electrical angle θ in the electric drive system is as follows: 1) The PWM generator adds the zero vector circuit state to the effective vector circuit state and the dead zone vector circuit state. The effective vector circuit state is composed of two basic vectors, U4 and U6. 2) The PWM generator calculates the ratio of the action times T4 and T6 of the two basic vectors based on the motor electrical angle θ; 3) The PWM generator then expresses the dead vector duration Tx according to the proportionality constant C of the total effective vector duration and the dead vector duration Tx. The total effective vector duration is the sum of the durations of the two basic vectors. 4) The PWM generator then expresses the zero vector action time T0 based on the dead vector action time Tx, the total effective vector action time, and the PWM period Ts; 5) The PWM generator again expresses the zero vector action time T0 based on the zero vector proportion d0 and the PWM period Ts; 6) Based on the relationships in steps 2), 3), 4) and 5), calculate the dead zone vector action time Tx, the zero vector action time T0, and the action times of the two basic vectors respectively.
3. The voltage feedback battery preheating method for an integrated electric drive system according to claim 2, characterized in that, The specific method for calculating the ratio of the action times T4 and T6 of the two basic vectors in step 2) is as follows: According to the Park-Clarke coordinate transformation formula Substitute ua=T4, ub=0, uc=-T6 Substituting the above equation and setting the calculated uq=0, we can obtain... (1).
4. The voltage feedback battery preheating method for an integrated electric drive system according to claim 3, characterized in that, The specific method for calculating the dead zone vector action time Tx, the zero vector action time T0, and the action times of the two basic vectors in steps 2)-6) is as follows: Based on the proportionality constant C between the total effective vector action time and the dead zone vector action time Tx, we can obtain: (2); Based on the PWM period Ts, we can obtain: (3) The PWM period Ts is determined by the motor control frequency H; Furthermore, the relationship between the zero vector proportion d0, the zero vector action time T0, and the PWM period Ts is as follows: (4); The values of the dead zone vector action time Tx, the zero vector action time T0, and the two basic vector action times are calculated based on the obtained relational formulas (1)-(4).
5. The voltage feedback battery preheating method for an integrated electric drive system according to claim 4, characterized in that, The proportionality constant C is greater than 1.
6. The voltage feedback battery preheating method for an integrated electric drive system according to claim 1, characterized in that, The peak voltage ub,max is sampled before the dead zone vector ends, and the valley voltage ub,min is sampled before the effective vector ends.
7. The voltage feedback battery preheating method for an integrated electric drive system according to claim 6, characterized in that, The upper limit control target value ub,max,o should be slightly less than the upper limit value of the battery pack voltage, and the lower limit control target value ub,min,o should be slightly greater than the lower limit value of the battery pack voltage.
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