Energy collaborative control strategy of distributed energy storage system
Patent Information
- Application Number
- CN202311598034.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-27
- Publication Date
- 2026-09-04
- Estimated Expiration
- 2043-11-27
AI Technical Summary
同时下垂控制作为直流微电网中常用的协调控制方法,由于自身固有的局限性无法同时兼顾功率精确分配和母线电压跌落,因此需要根据储能单元的容量和SOC调节其输出电流,实现输出电流按储能单元的容量成比例精确分配、SOC均衡和母线电压维持在参考值附近的控制目标
[0025] Compared to existing technologies, this invention and its preferred embodiments mainly include a consistency control module, a current sharing control module, a voltage compensation control module, a SOC equalization control module, and a voltage and current dual closed-loop control module. Through the consistency control module, each energy storage unit only needs to exchange information with adjacent nodes to obtain the average value of the energy storage system's SOC and state variables. Through the current sharing control module and the voltage compensation control module, the output current of the energy storage units is accurately distributed proportionally to their capacity, while effectively avoiding deviations in the bus voltage and maintaining it near the reference value. Through the SOC equalization control module, a SOC equalization factor is constructed and multiplied by the current inner loop reference value, causing the output current to dynamically change with the SOC, further achieving SOC equalization, and ultimately realizing coordinated energy control.
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Figure CN117526372B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of DC microgrid energy storage system technology, and in particular to an energy coordination control strategy for distributed energy storage systems. Background Technology
[0002] With global economic development and the large-scale use of new energy sources, research on microgrids has attracted widespread attention. Compared with AC microgrids, DC microgrids have advantages such as simplified structure, fewer energy conversion stages, and no need to consider reactive power and harmonics. Due to the uncertainty of renewable energy output and the volatility of load demand, distributed energy storage systems are needed to maintain stable bus voltage, thereby improving system stability. Since the charging and discharging power and capacity of a single energy storage unit are relatively small, multiple energy storage units need to be connected in parallel to form a distributed energy storage system. When multiple energy storage units are operating in parallel, coordinated management of each unit is required to ensure the balance of state-of-charge (SOC) of each energy storage unit, avoid overcharging and over-discharging, and improve the overall utilization efficiency and service life of the energy storage system. At the same time, droop control, as a commonly used coordinated control method in DC microgrids, cannot simultaneously take into account precise power distribution and bus voltage sag due to its inherent limitations. Therefore, it is necessary to adjust the output current according to the capacity and SOC of the energy storage unit to achieve the control objectives of precise distribution of output current proportional to the capacity of the energy storage unit, SOC balance, and maintaining the bus voltage near the reference value. Summary of the Invention
[0003] In view of the defects and shortcomings of existing technologies, the purpose of this invention is to provide an energy collaborative control strategy for distributed energy storage systems.
[0004] The present invention specifically adopts the following technical solution:
[0005] Firstly, an energy collaborative control strategy for a distributed energy storage system is provided, characterized by the following steps:
[0006] 1) Assume multiple energy storage units are connected to corresponding converters, and the line impedance r is... linei Connected in parallel to the DC bus, they jointly supply power to the load r load Power supply, at the beginning of each sampling period, the state of charge (SOC) of the energy storage unit is... i Output voltage u oi Output current i oi Inductor current i Li Samples were taken separately;
[0007] 2) Obtain the State of Charge (SOC) of each energy storage unit in the energy storage system. i and state variable x iThe global information is then used to obtain the average state of charge (SOC) of the energy storage system using a dynamic consensus algorithm. avg and the average value of the state variable x avg ;
[0008] 3) The output current i oi Divide by the maximum rated current i of the energy storage unit max Divide by the energy storage unit capacity factor c i The intermediate coefficient β is obtained. i Then subtract the intermediate coefficient β from the coefficient 1. i Obtain the flow equalization factor γ i ;
[0009] 4) Adjust the flow equalization factor γ i Multiply by the output voltage u oi Obtain the state variable x i The average value x of the state variable is obtained using the dynamic consensus algorithm. avg Then use the average value of the state variable x avg Divide by the flow equalization factor γ i Obtain the equilibrium voltage u ai Then use the reference voltage u ref Subtract the balance voltage u ai The voltage compensation amount Δu is obtained after passing through an integrator. i ;
[0010] 5) The voltage compensation amount Δu obtained from the voltage compensation control module i Apply to reference voltage u ref Above, subtract the output voltage u oi Then it passes through the voltage outer loop PI controller G V (s) Obtain the reference current I of the inner current loop. i Then I i With SOC equilibrium factor k i Multiply and then subtract the inductor current i Li The result is then processed by the inner current loop PI controller G. I (s), to obtain the driving voltage u zi Then drive voltage u zi The PWM modulation signal is obtained by comparing it with a triangular carrier wave.
[0011] Furthermore, the SOC balancing factor k i的 The specific calculation process is as follows:
[0012] The State of Charge (SOC) of the local energy storage unit i The nth power minus the average state of charge (SOC) of the energy storage system avgThe result of raising the product to the power of n is multiplied by the SOC equilibrium coefficient λ to obtain the intermediate coefficient z. Then, the intermediate coefficient z is taken as the arcsine function arcsin, and then multiplied by... Finally, add the coefficient 1 to obtain the SOC equilibrium factor k. i SOC equilibrium factor k i The expression is:
[0013]
[0014] Furthermore, in step 5), the SOC equilibrium coefficient λ ranges from 0.1 to 0.8.
[0015] An energy coordination control system for a distributed energy storage system includes:
[0016] The system comprises a consistency control module, a current sharing control module, a voltage compensation control module, a SOC equalization control module, and a voltage and current dual closed-loop control module. Through the consistency control module, each energy storage unit only needs to exchange information with adjacent nodes to obtain the average value of the energy storage system's SOC and state variables. The current sharing and voltage compensation control modules ensure that the output current of each energy storage unit is precisely distributed proportionally to its capacity, while effectively avoiding deviations in the bus voltage and maintaining it near the reference value. The SOC equalization control module constructs a SOC equalization factor and multiplies it by the current inner loop reference value, causing the output current to dynamically change with the SOC, further achieving SOC equalization and ultimately realizing coordinated energy control.
[0017] Furthermore, assuming multiple energy storage units are connected to corresponding converters, and the line impedance r... linei Connected in parallel to the DC bus, they jointly supply power to the load r load Power supply, at the beginning of each sampling period, the state of charge (SOC) of the energy storage unit is... i Output voltage u oi Output current i oi Inductor current i Li Samples were taken separately;
[0018] In the consistency control module, each energy storage unit only needs to exchange information with its adjacent energy storage units, and can obtain the state of charge (SOC) of each energy storage unit in the energy storage system without the need for a central controller. i and state variable x i The global information is then used to obtain the average state of charge (SOC) of the energy storage system using a dynamic consensus algorithm. avg and the average value of the state variable x avg ;
[0019] In the current sharing control module, the output current i oi Divide by the maximum rated current i of the energy storage unitmax Then divide by the energy storage unit capacity factor c. i The intermediate coefficient β is obtained. i Then subtract the intermediate coefficient β from the coefficient 1. i Obtain the flow equalization factor γ i ;
[0020] In the voltage compensation control module, the current sharing factor γ is... i Multiply by the output voltage u oi Obtain the state variable x i Then, the average value x of the state variable is obtained using the dynamic consensus algorithm. avg Then use the average value of the state variable x avg Divide by the flow equalization factor γ i Obtain the equilibrium voltage u ai Then use the reference voltage u ref Subtract the balance voltage u ai The voltage compensation amount Δu is obtained after passing through an integrator. i ;
[0021] In the SOC equalization control module and the voltage-current dual closed-loop control module, the voltage compensation amount Δu obtained from the voltage compensation control module is... i Apply to reference voltage u ref Above, then subtract the output voltage u oi Then it passes through the voltage outer loop PI controller G V (s) Obtain the reference current I of the inner current loop. i Then I i With SOC equilibrium factor k i Multiply and then subtract the inductor current i Li The result is then processed by the inner current loop PI controller G. I (s), to obtain the driving voltage u zi Then the driving voltage u zi The PWM modulation signal is obtained by comparing it with a triangular carrier wave.
[0022] Furthermore, the SOC equilibrium factor k i The specific calculation process is as follows:
[0023] The State of Charge (SOC) of the local energy storage unit i The nth power minus the average state of charge (SOC) of the energy storage system obtained by the consistency control module avg The result of the nth power is multiplied by the SOC equilibrium coefficient λ to obtain the intermediate coefficient z. Then, the intermediate coefficient z is taken as the arcsine function arcsin, and then multiplied by... Adding a coefficient of 1, we obtain the SOC equilibrium factor k. i SOC equilibrium factor k i The expression is:
[0024]
[0025] Compared to existing technologies, this invention and its preferred embodiments mainly include a consistency control module, a current sharing control module, a voltage compensation control module, a SOC equalization control module, and a voltage and current dual closed-loop control module. Through the consistency control module, each energy storage unit only needs to exchange information with adjacent nodes to obtain the average value of the energy storage system's SOC and state variables. Through the current sharing control module and the voltage compensation control module, the output current of the energy storage units is accurately distributed proportionally to their capacity, while effectively avoiding deviations in the bus voltage and maintaining it near the reference value. Through the SOC equalization control module, a SOC equalization factor is constructed and multiplied by the current inner loop reference value, causing the output current to dynamically change with the SOC, further achieving SOC equalization, and ultimately realizing coordinated energy control. Attached Figure Description
[0026] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:
[0027] Figure 1 This is the main circuit diagram of the distributed energy storage system in an embodiment of the present invention;
[0028] Figure 2 This is a control block diagram of the energy coordination control strategy of the distributed energy storage system in an embodiment of the present invention;
[0029] Figure 3 This is a waveform diagram of the SOC of the energy storage unit in an embodiment of the present invention;
[0030] Figure 4 This is a waveform diagram of the DC-side output current of the energy storage unit in an embodiment of the present invention;
[0031] Figure 5 This is a waveform diagram of the bus voltage of the energy storage system in an embodiment of the present invention. Detailed Implementation
[0032] In the following, specific embodiments of this application will be described in detail with reference to the accompanying drawings. Based on these detailed descriptions, those skilled in the art will be able to clearly understand and implement this application. Without departing from the principles of this application, features from various embodiments can be combined to obtain new implementations, or certain features from some embodiments can be substituted to obtain other preferred implementations.
[0033] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0034] To make the features and advantages of this patent more apparent and understandable, specific embodiments are provided below for detailed explanation:
[0035] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0036] Figure 1 This is the main circuit diagram of the distributed energy storage system provided as an analysis example in this embodiment. The energy storage system consists of two energy storage units connected in parallel via a DC-DC converter. The line impedance r of the two energy storage units is... line1 and r line2 The values are 0.4Ω and 0.5Ω respectively, r load U is the load resistance. bus This is the bus voltage. ESU1 is the first energy storage unit, u o1 i is the DC-side output voltage of the first energy storage unit. o1 This is the DC output current of the first energy storage unit; ESU2 is the second energy storage unit, u o2 i is the DC-side output voltage of the second energy storage unit. o2 This is the DC output current for the second energy storage unit.
[0037] Figure 2 The control block diagram of the energy collaborative control strategy for the distributed energy storage system of the DC microgrid provided in this embodiment includes the following steps:
[0038] The two energy storage units are connected via corresponding converters and the line impedance r.linei Connected in parallel to the DC bus, they jointly supply power to the load r load Power supply, at the beginning of each sampling period, the state of charge (SOC) of the energy storage unit is... i Output voltage u oi Output current i oi Inductor current i Li Samples were taken separately;
[0039] In the consistency control module, each energy storage unit only needs to exchange information with its neighboring energy storage units, and can obtain the State of Charge (SOC) of each energy storage unit in the energy storage system without the need for a central controller. i and state variable x i The global information is then used to obtain the average state of charge (SOC) of the energy storage system using a dynamic consensus algorithm. avg and the average value of the state variable x avg ;
[0040] In the current sharing control module, the output current i oi Divide by the maximum rated current i of the energy storage unit max Then divide by the energy storage unit capacity factor c. i The intermediate coefficient β is obtained. i Then subtract the intermediate coefficient β from the coefficient 1. i Obtain the flow equalization factor γ i ;
[0041] In the voltage compensation control module, the current sharing factor γ is... i Multiply by the output voltage u oi Obtain the state variable x i Then, the average value x of the state variable is obtained using the dynamic consensus algorithm. avg Then use the average value of the state variable x avg Divide by the flow equalization factor γ i Obtain the equilibrium voltage u ai Then use the reference voltage u ref Subtract the balance voltage u ai The voltage compensation amount Δu is obtained after passing through an integrator. i ;
[0042] In the SOC equalization control module and the voltage-current dual closed-loop control module, the voltage compensation amount Δu obtained from the voltage compensation control module is... i Apply to reference voltage u ref Above, then subtract the output voltage u oi Then it passes through the voltage outer loop PI controller G V (s) Obtain the reference current I of the inner current loop. i Then I i With SOC equilibrium factor k i Multiply and then subtract the inductor current iLi The result is then processed by the inner current loop PI controller G. I (s), to obtain the driving voltage u zi Then the driving voltage u zi The PWM modulation signal is obtained by comparing it with a triangular carrier wave, where the SOC equalization factor k i The specific calculation process is as follows:
[0043] The State of Charge (SOC) of the local energy storage unit i The nth power minus the average state of charge (SOC) of the energy storage system obtained from the consistency control module avg The result of the nth power is multiplied by the SOC equilibrium coefficient λ to obtain the intermediate coefficient z. Then, the intermediate coefficient z is taken as the arcsine function arcsin, and then multiplied by... Adding a coefficient of 1, we obtain the SOC equilibrium factor k. i SOC equilibrium factor k i The expression is:
[0044]
[0045] Figure 3 The diagram shows the SOC waveform of the energy storage unit. The distributed energy storage system is operating in discharge mode, with initial SOC1 and SOC2 at 90% and 87%, respectively. Before system SOC equalization, SOC1 is higher than the system's average state of charge (SOC). avg Its SOC equalization factor k1 > 1, and it preferentially discharges and i o2 >0, and SOC1 drops rapidly; at this time, the second energy storage unit has not yet started discharging and i o1 =0, its SOC2 remains unchanged, and finally SOC equilibrium is achieved at 1.03 seconds, after which SOC1 and SOC2 decrease at the same rate.
[0046] Figure 4 The diagram shows the DC-side output current waveform of the energy storage unit. Since the capacity ratio of the two energy storage units is 3:2, their capacity coefficients are selected as c1 = 3 and c2 = 2, respectively. In discharge mode, the state of charge (SOC) of the two energy storage units is balanced after 1.03 seconds. Due to the capacity coefficients c1 and c2, the current is relatively stable. i With the presence of these two energy storage units, the output currents are 12A and 8A respectively, which satisfies the principle that the output current is precisely distributed proportionally to its capacity.
[0047] Figure 5 This is a waveform diagram of the bus voltage of the energy storage system. Due to the presence of the voltage compensation control module, the bus voltage u can be guaranteed after the system stabilizes. bus Maintained near the reference value of 400V; during the initial stage of discharge, the bus voltage u busThe voltage did not reach around 400V, but the system SOC achieved equilibrium in 1.03 seconds, and the bus voltage u... bus It reached around 400V and remained around the reference value of 400V.
[0048] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.
[0049] The system and method provided in this embodiment can be stored in a computer-readable storage medium in the form of code, implemented as a computer program, and the basic parameter information required for calculation can be input through computer hardware, and the calculation results can be output.
[0050] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0051] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0052] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0053] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.
[0055] This patent is not limited to the above-described preferred embodiments. Anyone can derive other forms of energy coordination control strategies for distributed energy storage systems based on the inspiration of this patent. All equivalent changes and modifications made within the scope of this patent application shall fall within the scope of this patent.
Claims
1. A method for coordinated energy control of a distributed energy storage system, characterized in that, Includes the following steps: 1) Assume multiple energy storage units are connected to corresponding converters, and the line impedance r is... linei Connected in parallel to the DC bus, they jointly supply power to the load r load Power supply, at the beginning of each sampling period, the state of charge (SOC) of the energy storage unit is... i Output voltage u oi Output current i oi Inductor current i Li Samples were taken separately; 2) Obtain the State of Charge (SOC) of each energy storage unit in the energy storage system. i and state variable x i The global information is then used to obtain the average state of charge (SOC) of the energy storage system using a dynamic consensus algorithm. avg and the average value of the state variable x avg ; 3) Output current i oi Divide by the maximum rated current i of the energy storage unit max Divide by the energy storage unit capacity factor c i The intermediate coefficient β is obtained. i Then subtract the intermediate coefficient β from the coefficient 1. i Obtain the flow equalization factor γ i ; 4) Adjust the flow equalization factor γ i Multiply by the output voltage u oi Obtain the state variable x i The average value of the state variable x is obtained using the dynamic consensus algorithm. avg Then use the average value of the state variable x avg Divide by the flow equalization factor γ i Obtain the equilibrium voltage u ai Then use the reference voltage u ref Subtract the balance voltage u ai The voltage compensation amount Δu is obtained after passing through an integrator. i ; 5) The voltage compensation amount Δu obtained from the voltage compensation control module i Apply to reference voltage u ref Above, subtract the output voltage u oi Then it passes through the voltage outer loop PI controller G V (s) Obtain the inner current loop reference current I i Then I i With SOC equilibrium factor k i Multiply and then subtract the inductor current i Li The obtained result is processed by the inner current loop PI controller G. I (s), to obtain the driving voltage u zi Then drive voltage u zi The PWM modulation signal is obtained by comparing it with a triangular carrier wave. The SOC equilibrium factor k i The specific calculation process is as follows: The State of Charge (SOC) of the local energy storage unit i The nth power minus the average state of charge (SOC) of the energy storage system avg The result of the nth power is multiplied by the SOC equilibrium coefficient λ to obtain the intermediate coefficient z. Then, the intermediate coefficient z is taken as the arcsine function arcsin, and then multiplied by... Finally, add the coefficient 1 to obtain the SOC equilibrium factor k. i SOC equilibrium factor k i The expression is: 。 2. The energy collaborative control method for a distributed energy storage system according to claim 1, characterized in that: In step 5), the SOC equilibrium coefficient λ has a range of 0.1 < λ < 0.
8.
3. An energy collaborative control system for a distributed energy storage system, characterized in that, include: Consistency control module, current sharing control module, voltage compensation control module, SOC equalization control module, and voltage and current dual closed-loop control module; Through the consistency control module, each energy storage unit only needs to exchange information with its neighboring nodes to obtain the average value of the energy storage system's SOC and state variables; through the current sharing control module and voltage compensation control module, the output current of the energy storage unit is accurately distributed proportionally to its capacity, while effectively avoiding deviations in the bus voltage and keeping the bus voltage near the reference value; through the SOC equalization control module, an SOC equalization factor is constructed and multiplied by the current inner loop reference value, so that the output current changes dynamically with the SOC, ultimately achieving coordinated energy control. Assume multiple energy storage units are connected through corresponding converters, and the line impedance r... linei Connected in parallel to the DC bus, they jointly supply power to the load r load Power supply, at the beginning of each sampling period, the state of charge (SOC) of the energy storage unit is... i Output voltage u oi Output current i oi Inductor current i Li Samples were taken separately; In the consistency control module, each energy storage unit only needs to exchange information with its adjacent energy storage units, and can obtain the state of charge (SOC) of each energy storage unit in the energy storage system without the need for a central controller. i and state variable x i The global information is then used to obtain the average state of charge (SOC) of the energy storage system using a dynamic consensus algorithm. avg and the average value of the state variable x avg ; In the current sharing control module, the output current i oi Divide by the maximum rated current i of the energy storage unit max Then divide by the energy storage unit capacity factor c. i The intermediate coefficient β is obtained. i Then subtract the intermediate coefficient β from the coefficient 1. i Obtain the flow equalization factor γ i ; In the voltage compensation control module, the current sharing factor γ is... i Multiply by the output voltage u oi Obtain the state variable x i Then, the average value of the state variable x is obtained using the dynamic consensus algorithm. avg Then use the average value of the state variable x avg Divide by the flow equalization factor γ i Obtain the equilibrium voltage u ai Then use the reference voltage u ref Subtract the balance voltage u ai The voltage compensation amount Δu is obtained after passing through an integrator. i ; In the SOC equalization control module and the voltage-current dual closed-loop control module, the voltage compensation amount Δu obtained from the voltage compensation control module is... i Apply to reference voltage u ref Above, then subtract the output voltage u oi Then it passes through the voltage outer loop PI controller G V (s) Obtain the reference current I of the inner current loop. i Then I i With SOC equilibrium factor k i Multiply and then subtract the inductor current i Li The result is then processed by the inner current loop PI controller G. I (s), to obtain the driving voltage u zi Then the driving voltage u zi The PWM modulation signal is obtained by comparing it with a triangular carrier wave. SOC equilibrium factor k i The specific calculation process is as follows: The State of Charge (SOC) of the local energy storage unit i The nth power minus the average state of charge (SOC) of the energy storage system obtained by the consistency control module avg The result of the nth power is multiplied by the SOC equilibrium coefficient λ to obtain the intermediate coefficient z. Then, the intermediate coefficient z is taken as the arcsine function arcsin, and then multiplied by... Adding a coefficient of 1, we obtain the SOC equilibrium factor k. i SOC equilibrium factor k i The expression is: 。
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