Traction power supply hybrid energy storage system power distribution method considering flywheel standby loss

By dividing the working condition state based on the power prediction model in the hybrid energy storage system and distributing it, the problem of flywheel standby loss is solved, and the dual effects of energy conservation and system stability are achieved.

CN119401515AActive Publication Date: 2025-02-07CHONGQING UNIV

Patent Information

Application Number
CN202411529645.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-30
Publication Date
2025-02-07
Estimated Expiration
2044-10-30

AI Technical Summary

Technical Problem

The existing hybrid energy storage system does not consider the flywheel standby loss when distributing power, resulting in the flywheel often standby for a long time at high speeds, resulting in large standby loss and wasting energy.

Method used

Based on the power prediction model of the traction power supply system, the target power sequence is predicted, and the three working conditions of the hybrid energy storage system are divided into standby, long and short working conditions, and power distribution is performed separately to reduce the flywheel standby loss.

Benefits of technology

It effectively reduces the standby loss of flywheel energy storage units, saves energy, and ensures the stable working of the traction power supply system.

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Patent Text Reader

Abstract

The invention provides a traction power supply hybrid energy storage system power distribution method considering flywheel standby loss, and the method comprises the following steps: S1, determining an initial control variable and an initial state variable of a traction power supply system, and constructing a power prediction model based on the initial control variable and the initial state variable, predicting a power sequence of the hybrid energy storage system at each moment in the future; s2, judging charging and discharging types of the hybrid energy storage system based on the power sequence of the hybrid energy storage system, wherein the charging and discharging types comprise long-time charging and discharging and short-time charging and discharging; and S3, distributing the power of an energy storage battery and a flywheel energy storage unit in the hybrid energy storage system based on the charging and discharging types.
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Description

Technical Field

[0001] The present invention relates to a power distribution method for an energy storage system, and in particular to a power distribution method for a traction power supply hybrid energy storage system taking into account flywheel standby loss. Background Art

[0002] In the traction power supply system, a hybrid energy storage system is generally used to achieve energy storage and power supply. The rationality of the hybrid energy storage power distribution is an important guarantee for meeting the system load requirements, and it is also the key to realizing the energy storage device's strengths and weaknesses.

[0003] Most of the existing hybrid energy storage power allocation strategies focus on the battery life decay as the main focus. The power allocation strategies designed with the battery SOC in mind have relatively good SOC control effects. For flywheel energy storage in hybrid energy storage systems, existing research focuses on the flywheel speed over-limit problem, and prevents the flywheel speed from over-limit by introducing the flywheel speed into the power allocation process. However, in practice, the standby loss of the flywheel energy storage unit is very high. When the flywheel standby loss is not considered during power allocation, the flywheel often stands by for a long time at a high speed, resulting in large standby losses, thereby wasting energy.

[0004] Therefore, in order to solve the above technical problems, it is urgent to propose a new technical means. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a power distribution method for a traction power supply hybrid energy storage system taking into account the flywheel standby loss. Based on the power prediction model of the traction power supply system, the target power sequence of the traction power supply system is predicted, and then the hybrid energy storage system is divided into three operating states: standby, long-time and short-time. Then, power is distributed according to the three operating states respectively, thereby effectively reducing the influence of the standby loss of the flywheel energy storage unit on the power distribution, reducing the flywheel standby energy consumption while ensuring the stable operation of the traction power supply system, and saving energy.

[0006] The present invention provides a power distribution method for a traction power supply hybrid energy storage system taking into account flywheel standby loss, comprising the following steps:

[0007] S1. Determine the initial control variables and initial state variables of the traction power supply system, and build a power prediction model based on the initial control variables and initial state variables to predict the power sequence of the hybrid energy storage system at each moment in the future;

[0008] S2. Determine the charge and discharge type of the hybrid energy storage system based on the power sequence of the hybrid energy storage system, where the charge and discharge type includes long-time charge and discharge and short-time charge and discharge;

[0009] S3. Allocate the power of the energy storage battery and the flywheel energy storage unit in the hybrid energy storage system based on the charging and discharging type.

[0010] Further, in step S1, the power prediction model is:

[0011]

[0012] Where: P T (k+1) is the output power of the traction substation at time k+1, P R (k+1) is the total power dissipated by the brake resistor at time k+1, P es (k+1) is the output power of the energy storage system at time k+1, SOC es (k+1) is the charge state of the energy storage system at time k+1, Q es.n is the rated capacity of the energy storage system, T s To set the control period, P T (k) is the output power of the traction substation at time k, P R (k) is the total power dissipated by the brake resistor at time k, P es (k) is the output power of the energy storage system at time k, SOC es (k) is the state of charge of the energy storage system at time k, P cα (k) is the converter power on the supply side at time k, P cβ (k) is the converter power on the β supply side at time k, P Rα (k) is the power dissipated by the train braking resistor on the α supply side.

[0013] Furthermore, the constraints of the power prediction model are:

[0014] At time k, the total train load P αβ When (k)≥0, the traction power supply system as a whole presents a traction energy consumption state, and the constraint condition is:

[0015]

[0016] At time k, the total train load P αβ When (k) < 0, the traction power supply system as a whole is in a regenerative braking state, and the constraint condition is:

[0017]

[0018] Where: P es.n The rated power of the energy storage system of the traction power supply system.

[0019] Furthermore, judging the charging and discharging type of the hybrid energy storage system based on the power sequence of the hybrid energy storage system specifically includes:

[0020] The power sequence is determined as: ..., P es (k-1), P es(k-2), P es (k-1), P es (k), P es (k+1), P es (k+2),…,P es (k+N);

[0021] In the power series, P es (k+1) to P es In (k+N), if there is a state where the power sequence is 0 for more than one minute, the hybrid energy storage system will enter the standby state;

[0022] Find the time point in the power sequence before and after time k that is closest to time k and passes through 0. Count the duration T between the two time points. D ;

[0023] If the duration T D If it is less than or equal to the set time threshold, the hybrid energy storage and the system are in a short-term charging and discharging state at time k; otherwise, the hybrid energy storage and the system are in a long-term charging and discharging state at time k.

[0024] Furthermore, when time k is in a short-term charging and discharging state, the power distribution of the hybrid energy storage system is as follows:

[0025] Discharge status:

[0026] P f (k) = min{P es (k),P f.n}

[0027] P ba (k) = P es (k)-P f (k);

[0028] Charging status:

[0029] P f (k) = max{P es (k),-P f.n}

[0030] P ba (k) = P es (k)-P f (k);

[0031] Where: P f (k) is the reference power of flywheel energy storage charging and discharging, P ba (k) is the reference power of battery energy storage charging and discharging, P f.n is the rated charge and discharge power of the flywheel energy storage unit.

[0032] Furthermore, when time k is in a long-term charging and discharging state, the power distribution of the hybrid energy storage system is as follows:

[0033] Discharge status:

[0034] P f (k) = min{P fw (k),P es (k),P f.n}

[0035] P ba (k) = P es (k)-P f (k)

[0036] Charging status:

[0037] P f (k) = max{-P fw (k),P es (k),-P f.n}

[0038] P ba (k) = P es (k)-P f (k);

[0039] Where: P fw (k) regulating power for the flywheel;

[0040]

[0041] Where: n f.max 、n f.min are the maximum and minimum speeds of the flywheel, P es (k) is less than 0, indicating that the hybrid energy storage system is in a charging state. es (k) is greater than 0, the hybrid energy storage system is in a discharging state, σ is the regulation coefficient and σ ≥ 0, E N (k) is an intermediate variable and T s It is the control cycle of the traction power supply system.

[0042] The beneficial effects of the present invention are as follows: Through the present invention, the target power sequence of the traction power supply system is predicted based on the power prediction model of the traction power supply system, and then the hybrid energy storage system is divided into three operating states: standby, long-time and short-time. Then, power is distributed respectively according to the three operating states, thereby effectively reducing the influence of the standby loss of the flywheel energy storage unit on the power distribution, and reducing the standby energy consumption of the flywheel while ensuring the stable operation of the traction power supply system, thereby saving energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0044] Figure 1 It is a flow chart of the present invention.

[0045] Figure 2 The present invention is a topology structure of a high-speed rail regenerative braking energy utilization system including battery and flywheel energy storage.

[0046] Figure 3 Schematic diagram of the future standby state of the energy storage system.

[0047] Figure 4 Schematic diagram of a complete discharge process of the energy storage system.

[0048] Figure 5 The result is the battery and flywheel power distribution.

[0049] Figure 6 It is the change of battery SOC and flywheel speed.

[0050] Figure 7 This is the power allocation result for the charging condition in the future standby state.

[0051] Figure 8 This is the power allocation result of the discharge condition in the future standby state.

[0052] Fig. 9 It is the power distribution result under short-time charging and discharging state.

[0053] Fig.10 Indicates whether the power distribution result of the flywheel regulating power is taken into account in the long-term charging state.

[0054] Fig.11 It is the power distribution result whether the flywheel regulating power is taken into account in the long-term discharge state. DETAILED DESCRIPTION

[0055] The present invention is further described in detail below:

[0056] The present invention provides a power distribution method for a traction power supply hybrid energy storage system taking into account flywheel standby loss, comprising the following steps:

[0057] S1. Determine the initial control variables and initial state variables of the traction power supply system, and build a power prediction model based on the initial control variables and initial state variables to predict the power sequence of the hybrid energy storage system at each moment in the future;

[0058] S2. Determine the charge and discharge type of the hybrid energy storage system based on the power sequence of the hybrid energy storage system, where the charge and discharge type includes long-time charge and discharge and short-time charge and discharge;

[0059] S3. Allocate the power of the energy storage battery and flywheel energy storage unit in the hybrid energy storage system based on the charging and discharging type. Through the above method, the target power sequence of the traction power supply system is predicted based on the power prediction model of the traction power supply system, and then the hybrid energy storage system is divided into three operating states: standby, long-time and short-time. Then, power is allocated according to the three operating states respectively, thereby effectively reducing the impact of the standby loss of the flywheel energy storage unit on the power distribution. While ensuring the stable operation of the traction power supply system, it can reduce the flywheel standby energy consumption and save energy. Among them, the traction power supply system adopts the following Figure 2 The topology of the high-speed rail regenerative braking energy utilization system shown in the figure is

[0060] In this embodiment, in step S1, the power prediction model is:

[0061]

[0062] Where: P T (k+1) is the output power of the traction substation at time k+1, P R (k+1) is the total power dissipated by the brake resistor at time k+1, P es (k+1) is the output power of the energy storage system at time k+1, SOC es (k+1) is the charge state of the energy storage system at time k+1, Q es.n is the rated capacity of the energy storage system, T s To set the control period, P T (k) is the output power of the traction substation at time k, P R (k) is the total power dissipated by the brake resistor at time k, P es (k) is the output power of the energy storage system at time k, SOC es (k) is the state of charge of the energy storage system at time k, P cα (k) is the converter power on the supply side at time k, P cβ (k) is the converter power on the β supply side at time k, P Rα (k) is the power dissipated by the train braking resistor on the α supply side.

[0063] Wherein: the constraints of the power prediction model are:

[0064] At time k, the total train load P αβ When (k)≥0, the traction power supply system as a whole presents a traction energy consumption state, and the constraint condition is:

[0065]

[0066] At time k, the total train load P αβ When (k) < 0, the traction power supply system as a whole is in a regenerative braking state, and the constraint condition is:

[0067]

[0068] Where: P es.n is the rated power of the energy storage system of the traction power supply system. Figure 3 As shown, let the current moment be k;

[0069] Judging the charging and discharging type of the hybrid energy storage system based on the power sequence of the hybrid energy storage system specifically includes:

[0070] The power sequence is determined as: ..., P es (k-1), P es (k-2), P es (k-1), P es (k), P es (k+1), P es (k+2),…,P es (k+N);

[0071] In the power series, P es (k+1) to P es In (k+N), if there is a state where the power sequence is 0 for more than one minute, the hybrid energy storage system will enter the standby state;

[0072] Find the time point in the power sequence before and after time k that is closest to time k and passes through 0. Count the duration T between the two time points. D ;like Figure 4 As shown;

[0073] If the duration T D If the time is less than or equal to the set time threshold, the hybrid energy storage and the system are in a short-term charge and discharge state at time k, otherwise, the hybrid energy storage and the system are in a long-term charge and discharge state at time k. The set time threshold is generally 2 minutes. Of course, other time thresholds can also be set according to actual working conditions.

[0074] In this embodiment, when time k is in a short-term charging and discharging state, the power distribution of the hybrid energy storage system is as follows:

[0075] Discharge status:

[0076] P f (k) = min{P es (k),P f.n}

[0077] P ba (k) = P es (k)-P f (k);

[0078] Charging status:

[0079] P f (k) = max{P es (k),-P f.n}

[0080] P ba (k) = P es (k)-P f (k);

[0081] Where: P f (k) is the reference power of flywheel energy storage charging and discharging, P ba (k) is the reference power of battery energy storage charging and discharging, P f.n is the rated charge and discharge power of the flywheel energy storage unit.

[0082] When time k is in a long-term charging and discharging state, the power distribution of the hybrid energy storage system is as follows:

[0083] Discharge status:

[0084] P f (k) = min{P fw (k),P es (k),P f.n}

[0085] P ba (k) = P es (k)-P f (k)

[0086] Charging status:

[0087] P f (k) = max{-P fw (k),P es (k),-P f.n}

[0088] P ba (k) = P es (k)-P f (k);

[0089] Where: P fw (k) regulating power for the flywheel;

[0090]

[0091] Where: n f.max 、n f.min are the maximum and minimum speeds of the flywheel, P es (k) is less than 0, indicating that the hybrid energy storage system is in a charging state. es (k) is greater than 0, the hybrid energy storage system is in a discharging state, σ is the regulation coefficient and σ ≥ 0, EN (k) is an intermediate variable and T s That is to say, through the above, the flywheel energy storage unit and the energy storage battery both work according to the above power distribution result, that is, work according to the distributed charge and discharge reference power.

[0092] The following is a further description:

[0093] In this embodiment Figure 5 The output power of the battery and flywheel using the power distribution strategy proposed by the present invention is: Figure 6 It is the change of battery SOC and flywheel speed. Figure 7-Figure 11 It is the hybrid energy storage power allocation result for the typical time period corresponding to each working condition.

[0094] In this embodiment Figure 7 and Figure 8 The power allocation results in the future standby state are shown. Figure 7 is the distribution result of the charging condition. It can be seen that Figure 7 In (a), the flywheel prioritizes the hybrid energy storage target charging power P during the period of 13:50-13:51. es , flywheel energy storage charging, speed n f When P es When it is greater than the rated charge and discharge power of the flywheel energy storage (7.5MW), the battery is supplemented with charging. In the period of 13:51-13:53, the flywheel allocated power is reduced to 0MW, the battery bears all the target power, and the flywheel enters the standby state at the current speed of 19789r / min. This is because the present invention sets the future prediction time domain of the model predictive control to 2 minutes, so the future standby condition is not predicted in the period of 13:50-13:51, and the power allocation strategy of flywheel priority charging and discharging is adopted; in the period of 13:51-13:53, it is predicted that the energy storage system will enter the standby state in the future, so the power allocation strategy of the flywheel is switched to discharge first and then charge. Figure 7 (b) The power allocation result without considering the future standby state shows that the flywheel continues to charge before entering the standby state and enters the standby state at a speed of 27745r / min. This shows that the power allocation strategy considering the future standby state proposed by the present invention reduces the standby speed of the flywheel by 28.67% during this period. Figure 8 is the distribution result of the discharge condition. It can be seen that Figure 8 In (a), during the period of 14:11-14:13, the flywheel prioritizes the total target power of the hybrid energy storage, and the battery supplements the discharge. The flywheel continues to discharge at the maximum discharge power, and its speed drops from 31826r / min to 19445r / min. At 14:13:20, the hybrid energy storage system enters the standby state, and the flywheel enters the standby condition at a speed of 19445r / min. Figure 8(b) is the power allocation result without considering the future standby state. It can be seen that the battery is allocated the target power first, and the flywheel enters the standby state at 31009r / min at 14:13:20. This shows that the power allocation strategy of the present invention considering the future standby state reduces the standby speed of the flywheel by 37.29% during this period. Table 1 is a comparison of the average speed of the flywheel when it is in standby state, indicating that the flywheel power allocation strategy of first discharging and then charging considering the future standby state of energy storage of the present invention reduces the average speed of the flywheel in the standby state by 29.35%.

[0095] In this embodiment Fig. 9 The power distribution results under short-term charging and discharging are shown. It can be seen that when the target power of the hybrid energy storage system does not exceed the rated power of the flywheel, the flywheel output power P f Equal to the target power P of the energy storage system es , the flywheel is charged and discharged first; when |P es |More than 7.5MW, the flywheel output power is maintained at 7.5MW, and the battery is charged and discharged. In the charging state, the flywheel speed continues to rise to 35341r / min; in the discharging state, the flywheel speed continues to drop to 15013r / min. This shows that in the short-term charging and discharging state, the flywheel is used for charging and discharging first, which improves the utilization rate of the flywheel and meets the performance characteristics of the flywheel as a power-type energy storage.

[0096] In this embodiment Fig.10 and Fig.11 The power distribution results under long-term charging and discharging conditions are shown whether the flywheel regulation power is taken into account. Fig.10 is the distribution result of the charging condition. It can be seen that the flywheel energy storage charging power |P f |With hybrid energy storage target power|P es | increases with the increase of | until |P f |Rated charging power is reached. As the flywheel charging speed continues to rise, the flywheel charging power slowly decreases at 16:30:50, and the speed increase rate decreases. At 16:33:10, the flywheel speed reaches the upper limit, and then stands by for 40 seconds to enter the next discharge process. Under the control of the power allocation strategy without flywheel power regulation, the flywheel continues to charge at the rated charging power, and the flywheel speed rises rapidly. At 16:32:0, the speed reaches the upper limit and enters the standby state, and the standby time is 110 seconds. Therefore, in the energy storage charging time period of 16:29-16:34, the flywheel charging amount under the control of the two strategies only differs by 1.8%, but the flywheel energy storage standby time with flywheel power regulation is shortened by 63.6%. Fig.11The distribution result of the discharge condition shows that under the power distribution strategy with flywheel regulating power, the flywheel discharge power decreases with the decrease of speed, and the speed of flywheel speed decreases slowly. At 10:25:30, the flywheel discharge power increases and the flywheel accelerates discharge. This is because of the future energy storage demand E N Influenced by the energy storage, energy storage will enter the charging state in the future, E N <0, flywheel adjustment power P fw The accelerated discharge is increased, and the flywheel speed drops to 4119r / min at 10:27:00, and the standby time is 0 seconds. Under the control of the power allocation strategy without flywheel adjustment power, the flywheel continues to discharge at the rated charging power, and the flywheel speed drops rapidly. At 10:25:50, the speed drops to 3697r / min and then enters the standby state, with a standby time of 70 seconds. Therefore, in the energy storage discharge period of 10:23-10:27, the flywheel discharge amount under the control of the two strategies differs by 2.5%, but the flywheel energy storage standby time with flywheel adjustment power control is shortened by 100%. Table 2 is a comparison of the flywheel standby time and the cumulative charge and discharge amount. It can be seen that under the regulation of the flywheel adjustment power, the cumulative charge and discharge amount of the flywheel is reduced by 3.57%, but the standby time of the flywheel energy storage in one day is shortened by 33.43%. It shows that although the introduction of flywheel adjustment power will slightly reduce the utilization rate of the flywheel, it prolongs the flywheel charge and discharge time and greatly shortens the standby time of the flywheel.

[0097] Table 3 in this embodiment shows the comparison of flywheel standby loss. It can be seen that compared with the flywheel priority power allocation strategy, the power allocation strategy proposed in the present invention reduces the flywheel standby loss by 53.29%, indicating that the present invention reduces the energy lost by the flywheel in standby state by reducing the speed and standby time when the flywheel enters the standby state.

[0098] Table 1

[0099]

[0100] Table 2

[0101]

[0102] Table 3

[0103]

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A power distribution method for a traction power supply hybrid energy storage system considering flywheel standby loss, characterized in that: The following steps are involved: S1. Determine the initial control variables and initial state variables of the traction power supply system, and build a power prediction model based on the initial control variables and initial state variables to predict the power sequence of the hybrid energy storage system at each moment in the future; S2. Determine the charge and discharge type of the hybrid energy storage system based on the power sequence of the hybrid energy storage system, where the charge and discharge type includes long-time charge and discharge and short-time charge and discharge; S3. Allocate the power of the energy storage battery and the flywheel energy storage unit in the hybrid energy storage system based on the charging and discharging type.

2. The power distribution method of the traction power supply hybrid energy storage system considering the flywheel standby loss according to claim 1 is characterized in that: In step S1, the power prediction model is: Where: P T (k+1) is the output power of the traction substation at time k+1, P R (k+1) is the total power dissipated by the brake resistor at time k+1, P es (k+1) is the output power of the energy storage system at time k+1, SOC es (k+1) is the charge state of the energy storage system at time k+1, Q es.n is the rated capacity of the energy storage system, T s To set the control period, P T (k) is the output power of the traction substation at time k, P R (k) is the total power dissipated by the brake resistor at time k, P es (k) is the output power of the energy storage system at time k, SOC es (k) is the state of charge of the energy storage system at time k, P cα (k) is the converter power on the supply side at time k, P cβ (k) is the converter power on the β supply side at time k, P Rα (k) is the power dissipated by the train braking resistor on the α supply side.

3. The power distribution method of the traction power supply hybrid energy storage system considering the flywheel standby loss according to claim 2 is characterized in that: The constraints of the power prediction model are: At time k, the total train load P αβ When (k)≥0, the traction power supply system as a whole presents a traction energy consumption state, and the constraint condition is: At time k, the total train load P αβ When (k) < 0, the traction power supply system as a whole is in a regenerative braking state, and the constraint condition is: Where: P es.n Rated power of the energy storage system for the traction power supply system.

4. The power distribution method of the traction power supply hybrid energy storage system considering the flywheel standby loss according to claim 2 is characterized in that: Judging the charging and discharging type of the hybrid energy storage system based on the power sequence of the hybrid energy storage system specifically includes: The power sequence is determined as: ..., P es (k-1), P es (k-2), P es (k-1), P es (k), P es (k+1), P es (k+2),…,P es (k+N); In the power series, P es (k+1) to P es In (k+N), if there is a state where the power sequence is 0 for more than one minute, the hybrid energy storage system will enter the standby state; Find the time point in the power sequence before and after time k that is closest to time k and passes through 0. Count the duration T between the two time points. D ; If the duration T D If it is less than or equal to the set time threshold, the hybrid energy storage and the system are in a short-term charging and discharging state at time k; otherwise, the hybrid energy storage and the system are in a long-term charging and discharging state at time k.

5. The power distribution method of the traction power supply hybrid energy storage system considering the flywheel standby loss according to claim 4 is characterized in that: When time k is in a short-term charging and discharging state, the power distribution of the hybrid energy storage system is as follows: Discharge status: P f (k)=min{P es (k),P f.n } P ba (k)=P es (k)-P f (k); Charging status: P f (k)=max{P es (k),-P f.n } P ba (k)=P es (k)-P f (k); Where: P f (k) is the reference power of flywheel energy storage charging and discharging, P ba (k) is the reference power of battery energy storage charging and discharging, P f.n is the rated charge and discharge power of the flywheel energy storage unit.

6. The power distribution method of the traction power supply hybrid energy storage system considering the flywheel standby loss according to claim 4 is characterized in that: When time k is in a long-term charging and discharging state, the power distribution of the hybrid energy storage system is as follows: Discharge status: P f (k)=min{P fw (k),P es (k),P f.n } P ba (k)=P es (k)-P f (k) Charging status: P f (k)=max{-P fw (k),P es (k),-P f.n } P ba (k)=P es (k)-P f (k); Where: P fw (k) regulating power for the flywheel; Where: n f.max 、n f.min are the maximum and minimum speeds of the flywheel, P es (k) is less than 0, indicating that the hybrid energy storage system is in a charging state. es (k) is greater than 0, the hybrid energy storage system is in a discharging state, σ is the regulation coefficient and σ ≥ 0, E N (k) is an intermediate variable and T s It is the control cycle of the traction power supply system.

Citation Information

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