Secondary control method and system for direct-current micro-grid

Abstract

The invention provides a direct current microgrid secondary control method and system. The method comprises the following steps: establishing an inverter-based island microgrid secondary voltage and current control model; defining a voltage deviation and current sharing objective function; designing an event triggering mechanism; optimizing secondary control parameters based on a differential evolution algorithm; and verifying the stability of the micro-grid system and no Zeno behavior after the event is triggered. The method solves the technical problems that the method is easily influenced by a single-point fault, the expansibility is poor, the real-time adaptability of the system is not fully considered under the dynamically changing load and environment conditions, and the secondary voltage recovery and optimal current sharing performance of the island microgrid is poor.

Description

Technical Field

[0001] This invention relates to the field of DC microgrid operation control technology, specifically to a DC microgrid secondary control method and system. Background Technology DC microgrids have gained widespread attention in modern energy systems due to their advantages such as efficient energy transmission, convenient equipment interconnection, and adaptability to renewable energy integration. As a novel energy management system, DC microgrids face challenges in voltage stability and system coordination control while achieving efficient energy flow between distributed energy sources and loads. Especially in islanded operation mode, voltage fluctuations in DC microgrids are significant, making long-term stable operation difficult to achieve through primary control. Therefore, secondary voltage control has been proposed as an effective means to achieve voltage deviation correction and optimal current sharing performance optimization, thereby improving the operational quality and stability of DC microgrids. Traditional secondary voltage control methods are typically based on a centralized control architecture, relying on a single central controller to coordinate the entire system. However, this centralized approach is highly dependent on communication networks, susceptible to single-point failures, and has poor scalability. In practical applications, distributed control architectures are increasingly valued due to their robustness and adaptability. Distributed control methods achieve system consistency and coordinated control through local information interaction, but their performance is often limited by the design of the control algorithm and the rationality of the triggering mechanism.

[0002] In recent years, the application of intelligent optimization algorithms in the field of microgrid control has gradually emerged. Among them, genetic algorithms, as a global optimization technique, can effectively solve multi-objective optimization problems of complex systems. However, there are still many technical challenges in combining genetic algorithms with event-triggered mechanisms for secondary control of DC microgrids. These challenges include how to design an optimization objective function that adapts to the dynamic characteristics of DC microgrids, how to ensure system control accuracy while reducing communication overhead, and how to improve the robustness of the algorithm in multiple scenarios.

[0003] The existing invention patent application CN113054690A, entitled "Event-Triggered Voltage Control Method, System, and Electronic Device," describes a method that includes: acquiring the voltage prediction error of a wind turbine and determining whether the preset voltage error is greater than a preset error threshold; if the preset voltage error is less than the preset error threshold, triggering primary voltage control, which adjusts the wind turbine voltage based on a drooping reactive power control model; and if the preset voltage error is greater than the preset error threshold, triggering secondary voltage control, which adjusts the wind turbine voltage based on model predictive control, taking into account the influencing parameters in the primary voltage control. The method proposed in the aforementioned patent CN113054690A primarily focuses on wind turbine voltage control, adjusting the wind turbine voltage through primary and secondary voltage control to ensure the voltage remains within allowable limits. However, this method does not consider how to achieve optimal current sharing, which could lead to uneven current distribution among power sources in multi-microgrid systems, affecting the overall system efficiency and stability.

[0004] The existing invention patent application CN114039354A, entitled "A Fully Distributed Secondary Voltage and Energy Level Fault-Tolerant Control System for Multi-Microgrids," describes a method that achieves fully distributed secondary voltage and energy level control for multiple battery energy storage systems in an undirected communication network based on multi-microgrid secondary control, an event-triggered mechanism, and adaptive technology. For voltage control of the battery energy storage system, firstly, an adaptive coupling gain is estimated for each battery energy storage system, and a Nussbaum function is designed to handle voltage failure faults; secondly, a dynamic event-triggered mechanism is designed to avoid continuous communication between energy storage systems; finally, based on input-output feedback linearization, the secondary voltage control output voltage is provided to the droop control for adjustment. While the method proposed in the aforementioned patent CN114039354A achieves secondary voltage and energy level control for multi-microgrids, the system parameters cannot be adaptively adjusted under dynamic conditions. This means that when the system load or network topology changes, the control strategy may not be able to adapt to the new operating conditions in a timely manner, leading to a decline in control performance and failing to guarantee good voltage and current regulation effects. Existing technologies often focus on solving specific problems, such as voltage recovery or current sharing, but lack a control strategy that can simultaneously optimize voltage recovery and current sharing within a unified framework. This means that in practical applications, trade-offs may need to be made between different control objectives, preventing the achievement of optimal overall system performance. In actual microgrid operation, the system may face various complex operating conditions, such as rapid load changes and power supply switching. Existing technologies, when dealing with these complex conditions, may experience performance degradation due to limitations in control strategies or untimely parameter adjustments, failing to meet the requirements of high reliability and high stability. In summary, existing technologies suffer from several technical problems, including susceptibility to single-point failures, poor scalability, failure to adequately consider real-time adaptability of the system under dynamically changing load and environmental conditions, and poor secondary voltage recovery and optimal current sharing performance in islanded microgrids. Summary of the Invention

[0005] The technical problem to be solved by this invention is: how to solve the technical problems of existing technologies that are easily affected by single-point failures, have poor scalability, fail to fully consider the real-time adaptability of the system under dynamically changing load and environmental conditions, and have poor secondary voltage recovery and optimal current sharing performance of islanded microgrids.

[0006] The present invention solves the above-mentioned technical problems by adopting the following technical solution: A secondary control method for DC microgrids includes: S1. For inverter-based islanded microgrids, establish secondary voltage and current control models. The secondary voltage and current control models include: N The dynamic behavior of a distributed power source and load is represented by node voltage and branch current, which are used to describe the dynamic behavior of the secondary voltage and current control model. S2. Based on the secondary voltage and current control model, define the voltage deviation objective function and the current sharing objective function; S3. Design an event triggering mechanism, including: voltage event triggering mechanism and current event triggering mechanism, and obtain secondary control input under the event triggering mechanism; S4. Based on the differential evolution algorithm, optimize the secondary control parameters according to the secondary control input; S5. Verify the stability of the microgrid system after the event is triggered, and determine whether Zeno behavior exists.

[0007] This invention utilizes genetic algorithm optimization and event triggering for secondary control of DC microgrids, addressing the challenge of rapid recovery of voltage and current sharing in existing DC microgrids under load disturbances and environmental changes. The invention designs an optimization objective function adapted to the dynamic characteristics of DC microgrids, ensuring system control accuracy while reducing communication overhead and improving the robustness of the algorithm in various scenarios.

[0008] In a more specific technical solution, in S1, the electrical characteristics of the secondary voltage and current control model are expressed using the following logic: (1) In the formula, For nodes The capacitance value, For node voltage, and They are nodes The input current and output current, This represents the node load current.

[0009] According to Ohm's law, the branch current can be expressed using the following logic. : (2) In the formula, Let be the line impedance between node i and node j.

[0010] In a more specific technical solution, in S1, the secondary voltage and current control of the islanded microgrid is implemented using the following logic to design a primary control strategy: (3) In the formula, This is the voltage reference value. The nominal DC voltage. For droop gain, It is the first i indivual DG Current output; According to the transmission line resistance Express the PCC bus voltage using the following logic. With voltage reference value Relationship: (4) In equation (3) of the primary control strategy, a secondary control input is added: (5) According to equation (4), the PCC bus voltage is obtained: (6).

[0011] In a more specific technical solution, in S2, the voltage deviation objective function is defined using the following logic: (7) Restore the PCC bus voltage to its nominal value; Define the current sharing objective function using the following logic: (8) In the formula, Cost coefficient; Express the load demand balancing constraints using the following logic: (9) In the formula, Indicates the load bus j The current in.

[0012] In a more specific technical solution, based on the voltage deviation objective function, the current sharing objective function, and the load demand balancing constraint, a quadratic optimization problem with equality constraints is set up, in which the Lagrangian function is established: (10) In the formula, After solving, we get .

[0013] In a more specific technical solution, within S3, the following logic is used to design voltage event triggering mechanisms and current event triggering mechanisms: (11) (12) In the formula, This represents the time of the k-th trigger of the voltage and current corresponding to the i-th distributed power source. and exist Updated constantly and The period remains unchanged; Secondary control inputs are represented as follows under an event-triggered mechanism: (13) (14) in, For combination error, These include: (15) (16).

[0014] This invention employs an event-triggered mechanism, which reduces unnecessary control signal transmissions, lowers the system's communication burden, and optimizes the utilization efficiency of computing resources while ensuring system stability. Through the design of a secondary control layer, this invention effectively solves the problem of optimal current sharing at the tertiary layer; it not only ensures the voltage accuracy and optimal current sharing effect of the microgrid under steady state, but also rapidly restores system stability in the event of load changes or external disturbances, achieving excellent transient performance.

[0015] In a more specific technical solution, in S4, the set vector of the two parameters is... As the initial population for the differential evolution algorithm; for each individual, the fitness value is calculated according to the objective function, which includes: voltage recovery part and current sharing part: (17) (18) Express the objective function using the following logic: ,in, and The weighting coefficient between voltage recovery and optimal current sharing; The adaptive mutation operator is set using the following logic: (19) In the formula, Indicates the maximum number of iterations. This indicates the current iteration number.

[0016] Using the following logic, set the coefficient of variation F: (20) In the formula, It is calculated from equation (19), The initial coefficient of variation; Using the following logic, for each individual Perform mutation operations to generate mutated vectors. : (twenty one) In the formula, It is the coefficient of variation. , , These are different individuals randomly selected from the population; By combining adaptive crossover probability adjustment with crossover strategy, crossover operation is performed to generate test vectors. : (twenty two) In equation (22), It is the fitness of the current population. It is the maximum fitness value. and These are the minimum and maximum values ​​of the crossover probability, respectively. Determine the experimental vector using the following logic. : (twenty three) In formula (23) It is an adaptive crossover probability. It is a randomly selected index, ensuring It must inherit at least one mutated element.

[0017] This invention optimizes the secondary control parameters through a differential evolution algorithm, enabling adaptive adjustment of voltage recovery gain and current sharing gain.

[0018] In a more specific technical solution, the experimental vector is calculated. fitness value ,if Then use replace Retain individuals with better fitness; Repeat the crossover and selection operations until the upper limit of the number of iterations is reached or the error meets the requirements, and the optimal solution is obtained. , which serves as the optimal secondary control parameter.

[0019] In a more specific technical solution, in S5, the following logic is used to verify the stability of the microgrid system after the event is triggered. right ,in , Establish the following Lyapunov function: (twenty four) In the formula, Let be a positive definite matrix, where , Then the derivative of the Lyapunov function is The derivation yields: (25) Applying inequalities to equation (25), we obtain the following equation (26): (26) Based on the event trigger time, the following is obtained: , This is used to verify the stability of the event-triggered system and to determine whether Zeno behavior exists based on the time interval between adjacent triggers.

[0020] This invention effectively avoids Zeno behavior through the design of reasonable event triggering conditions.

[0021] In a more specific technical solution, the secondary control system of a DC microgrid includes: The control model building module is used to establish secondary voltage and current control models for inverter-based islanded microgrids. The secondary voltage and current control models include: N The dynamic behavior of a distributed power source and load is represented by node voltage and branch current, which are used to describe the dynamic behavior of the secondary voltage and current control model. The objective function definition module is used to define the voltage deviation objective function and the current sharing objective function based on the secondary voltage and current control model. The objective function definition module is connected to the control model construction module. The triggering mechanism setting module is used to design event triggering mechanisms, including voltage event triggering mechanisms and current event triggering mechanisms, and to obtain secondary control inputs under the event triggering mechanism. The secondary control function optimization module is used to optimize the secondary control parameters based on the differential evolution algorithm and the secondary control input. The secondary control function optimization module is connected to the trigger mechanism setting module. The microgrid verification module is used to verify the stability of the microgrid system after an event is triggered and to determine whether Zeno behavior exists. The microgrid verification module is connected to the control model construction module.

[0022] The present invention has the following advantages over the prior art: This invention utilizes genetic algorithm optimization and event triggering for secondary control of DC microgrids, addressing the challenge of rapid recovery of voltage and current sharing in existing DC microgrids under load disturbances and environmental changes. The invention designs an optimization objective function adapted to the dynamic characteristics of DC microgrids, ensuring system control accuracy while reducing communication overhead and improving the robustness of the algorithm in various scenarios.

[0023] This invention employs an event-triggered mechanism, which reduces unnecessary control signal transmissions, lowers the system's communication burden, and optimizes the utilization efficiency of computing resources while ensuring system stability. Through the design of a secondary control layer, this invention effectively solves the problem of optimal current sharing at the tertiary layer; it not only ensures the voltage accuracy and optimal current sharing effect of the microgrid under steady state, but also rapidly restores system stability in the event of load changes or external disturbances, achieving excellent transient performance.

[0024] This invention optimizes the secondary control parameters through a differential evolution algorithm, enabling adaptive adjustment of voltage recovery gain and current sharing gain.

[0025] This invention effectively avoids Zeno behavior through the design of reasonable event triggering conditions.

[0026] This invention solves the technical problems existing in the prior art, such as susceptibility to single-point failures, poor scalability, failure to fully consider the real-time adaptability of the system under dynamically changing load and environmental conditions, and poor secondary voltage recovery and optimal current sharing performance of islanded microgrids. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the basic steps of the DC microgrid secondary control method of the present invention; Figure 2 This is a block diagram of an inverter-based distributed generation unit according to Embodiment 1 of the present invention; Figure 3 This is a communication topology diagram between distributed generation units in an islanded microgrid according to Embodiment 1 of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Example 1 like Figure 1 As shown, the secondary control method for DC microgrids provided by this invention further includes the following basic steps: S1. Establish a secondary voltage and current control model for an islanded microgrid based on an inverter; like Figure 2 As shown, in this embodiment, an islanded microgrid voltage and current control model based on the inverter is established. Specifically, a model based on the inverter is established. N A DC microgrid model consisting of distributed power sources and loads can be described by its dynamic behavior using node voltages and branch currents. The system's electrical characteristics are described as follows: (1) in, For nodes The capacitance value, For node voltage, and They are nodes The input current and output current, This represents the node load current. Branch current. According to Ohm's law, it can be described as follows: (2) in, Let be the line impedance between node i and node j.

[0030] For the secondary voltage and current control of an islanded microgrid, the designed primary control strategy is described as follows: (3) in, This is the voltage reference value. The nominal DC voltage. For droop gain, It is the first i indivual DG The current output. Due to the transmission line resistance. The presence of this means the PCC bus voltage With voltage reference value The following relationships exist: (4) In the primary control, i.e., equation (3), a secondary control input is added: (5) Therefore, the PCC bus voltage, i.e., equation (4), becomes: (6) S2. Define a shared objective function for voltage deviation and current. In this embodiment, the inverter-based islanded microgrid secondary voltage and current control model defines shared objective functions for voltage deviation and current. Voltage deviation objective function: (7) That is, the PCC bus voltage is restored to its nominal value; Optimal current sharing objective function: (8) in, This is the cost factor. The load demand balancing constraint is: (9) in, Indicates the load bus j The current in the middle. Based on the objective function and equality constraints, the goal is to minimize a quadratic optimization problem with equality constraints. The Lagrangian function is established as follows: (10) in, After solving, we get .

[0031] S3. Design the event triggering mechanism; like Figure 3 As shown, in this embodiment, event triggering is designed with voltage and current event triggering mechanisms respectively, and the voltage and current event triggering mechanisms are as follows: (11) (12) in, This represents the time of the k-th trigger of the voltage and current corresponding to the i-th distributed power source. and exist Updated constantly and The input remains unchanged during this period. The secondary control input, under the event-triggered mechanism, is represented as follows: (13) (14) in, For combination error, It consists of the following two parts: (15) (16) S4. Optimize the secondary control parameters based on the differential evolution algorithm; In this embodiment, the secondary control parameters are optimized based on the differential evolution algorithm as follows; The set vector of two parameters This serves as the initial population for the differential evolution algorithm. For each individual, a fitness value is calculated based on the objective function, which includes two parts: voltage recovery and current sharing. (17) (18) The overall objective function is ,in and This is the weighting coefficient between voltage recovery and optimal current sharing.

[0032] Set the adaptive mutation operator: (19) In the formula Indicates the maximum number of iterations. This indicates the current iteration number.

[0033] The coefficient of variation F is set as follows: (20) in, This is calculated using equation (19). is the initial coefficient of variation.

[0034] Using equation (21) for each individual Perform mutation operations to generate mutation vectors : (twenty one) in, It is the coefficient of variation. , , These are different individuals randomly selected from the population.

[0035] By combining adaptive crossover probability adjustment with crossover strategy, crossover operations are performed to generate test vectors. : (twenty two) In equation (22) It is the fitness of the current population. It is the maximum fitness value. and These are the minimum and maximum values ​​of the crossover probability, respectively.

[0036] (twenty three) In formula (23) It is an adaptive crossover probability. It is a randomly selected index, ensuring It must inherit at least one mutated element.

[0037] Calculate the test vector fitness value ,if Then use replace Individuals with better fitness are retained. The crossover and selection operations are repeated until the upper limit of the number of iterations is reached or the error requirement is met, ultimately yielding the optimal solution. That is, the optimal secondary control parameters.

[0038] S5. Verify the stability of the microgrid system after the event is triggered and confirm the absence of Zeno behavior; In this embodiment, the stability of the microgrid system after the event is triggered is verified; right ,in , Establish the following Lyapunov function: (twenty four) in, Let be a positive definite matrix, where , Then the derivative of the Lyapunov function is ,further: (25) Using the inequality above, we get: (26) It can be known from the event trigger time ,thereby The event triggering system is stable, and the time interval between adjacent triggers is greater than zero, meaning there is no Zeno behavior. The microgrid's bus voltage recovers to the nominal value, and the current achieves optimal power sharing.

[0039] In summary, this invention, based on genetic algorithm optimization and event triggering, enables secondary control of DC microgrids, addressing the challenge of rapid recovery of voltage and current sharing in existing DC microgrids under load disturbances and environmental changes. The invention designs an optimization objective function adapted to the dynamic characteristics of DC microgrids, ensuring system control accuracy while reducing communication overhead and improving the robustness of the algorithm in various scenarios.

[0040] This invention employs an event-triggered mechanism, which reduces unnecessary control signal transmissions, lowers the system's communication burden, and optimizes the utilization efficiency of computing resources while ensuring system stability. Through the design of a secondary control layer, this invention effectively solves the problem of optimal current sharing at the tertiary layer; it not only ensures the voltage accuracy and optimal current sharing effect of the microgrid under steady state, but also rapidly restores system stability in the event of load changes or external disturbances, achieving excellent transient performance.

[0041] This invention optimizes the secondary control parameters through a differential evolution algorithm, enabling adaptive adjustment of voltage recovery gain and current sharing gain.

[0042] This invention effectively avoids Zeno behavior through the design of reasonable event triggering conditions.

[0043] This invention solves the technical problems existing in the prior art, such as susceptibility to single-point failures, poor scalability, failure to fully consider the real-time adaptability of the system under dynamically changing load and environmental conditions, and poor secondary voltage recovery and optimal current sharing performance of islanded microgrids.

[0044] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A secondary control method for a DC microgrid, characterized in that, The method includes: S1. For an inverter-based islanded microgrid, establish a secondary voltage and current control model, which includes: N A distributed power source and load, whose dynamic behavior is represented by node voltage and branch current, represent the dynamic behavior of the secondary voltage and current control model. S2. Based on the aforementioned secondary voltage and current control model, define the voltage deviation objective function and the current sharing objective function; S3. Design an event triggering mechanism, including a voltage event triggering mechanism and a current event triggering mechanism, and obtain secondary control input under the event triggering mechanism; S4. Based on the differential evolution algorithm, optimize the secondary control parameters according to the secondary control input; S5. Verify the stability of the microgrid system after the event is triggered, and determine whether Zeno behavior exists.

2. The secondary control method for a DC microgrid according to claim 1, characterized in that, In S1, the electrical characteristics of the secondary voltage and current control model are expressed using the following logic: （1） In the formula, For nodes The capacitance value, For node voltage, and They are nodes The input current and output current, This represents the node load current. According to Ohm's law, the branch current can be expressed using the following logic. : （2） In the formula, Let be the line impedance between node i and node j.

3. The secondary control method for a DC microgrid according to claim 1, characterized in that, In step S1, the secondary voltage and current control of the islanded microgrid are designed using the following logic, and a primary control strategy is implemented: （3） In the formula, This is the voltage reference value. The nominal DC voltage. For droop gain, It is the first i indivual DG Current output; According to the transmission line resistance Express the PCC bus voltage using the following logic. With voltage reference value Relationship: （4） In equation (3) of the primary control strategy, a secondary control input is added: （5） According to equation (4), the PCC bus voltage is obtained: （6）。 4. The secondary control method for a DC microgrid according to claim 1, characterized in that, In step S2, the voltage deviation objective function is defined using the following logic: （7） Restore the PCC bus voltage to its nominal value; The current sharing objective function is defined using the following logic: （8） In the formula, This is the cost coefficient; Express the load demand balancing constraints using the following logic: （9） In the formula, Indicates the load bus j The current in.

5. The secondary control method for a DC microgrid according to claim 4, characterized in that, Based on the voltage deviation objective function, the current sharing objective function, and the load demand balancing constraint, a quadratic optimization problem with equality constraints is set up, wherein the Lagrangian function is established: （10） In the formula, After solving, we get .

6. The secondary control method for a DC microgrid according to claim 1, characterized in that, In step S3, the voltage event triggering mechanism and the current event triggering mechanism are designed using the following logic: （11） （12） In the formula, This represents the time of the k-th trigger of the voltage and current corresponding to the i-th distributed power source. and exist Updated constantly and The period remains unchanged; Secondary control inputs are represented as follows under an event-triggered mechanism: （13） （14） in, For combination error, These include: （15） （16）。 7. The secondary control method for a DC microgrid according to claim 1, characterized in that, In S4, the set vector of the two parameters As the initial population individuals for the differential evolution algorithm; For each individual, a fitness value is calculated based on an objective function, which includes: a voltage recovery component and a current sharing component. （17） （18） The objective function can be expressed using the following logic: ,in, and The weighting coefficient between voltage recovery and optimal current sharing; The adaptive mutation operator is set using the following logic: （19） In the formula, Indicates the maximum number of iterations. This indicates the current iteration number. Using the following logic, set the coefficient of variation F: （20） In the formula, It is calculated from the above equation (19), The initial coefficient of variation; Using the following logic, for each of the individuals Perform mutation operations to generate mutated vectors. : (21) In the formula, It is the coefficient of variation. , , These are different individuals randomly selected from the population; By combining adaptive crossover probability adjustment with crossover strategy, crossover operation is performed to generate test vectors. : (22) In the above formula (22), It is the fitness of the current population. It is the maximum fitness value. and These are the minimum and maximum values ​​of the crossover probability, respectively. Determine the experimental vector using the following logic. : (23) In the above formula (23) It is an adaptive crossover probability. It is a randomly selected index, ensuring It must inherit at least one mutated element.

8. The secondary control method for a DC microgrid according to claim 7, characterized in that, Calculate the test vector fitness value ,if Then use replace Retain individuals with better fitness; Repeat the crossover and selection operations until the upper limit of the number of iterations is reached or the error meets the requirements, and the optimal solution is obtained. , which serves as the optimal secondary control parameter.

9. The secondary control method for a DC microgrid according to claim 1, characterized in that, In S5, the stability of the microgrid system after the event is triggered is verified using the following logic; right ,in , Establish the following Lyapunov function: （24） In the formula, Let be a positive definite matrix, where , Then the derivative of the Lyapunov function is The derivation yields: （25） Applying inequalities to equation (25), we obtain the following equation (26): （26） Based on the event trigger time, the following is obtained: , This is used to verify the stability of the event triggering system and to determine whether the Zeno behavior exists based on the time interval between adjacent touches.

10. A secondary control system for a DC microgrid, characterized in that, The system includes: A control model construction module is used to establish secondary voltage and current control models for inverter-based islanded microgrids. The secondary voltage and current control models include: N A distributed power source and load, whose dynamic behavior is represented by node voltage and branch current, represent the dynamic behavior of the secondary voltage and current control model. The objective function definition module is used to define the voltage deviation objective function and the current sharing objective function based on the secondary voltage and current control model. The objective function definition module is connected to the control model construction module. The triggering mechanism setting module is used to design event triggering mechanisms, including: voltage event triggering mechanism and current event triggering mechanism, under which secondary control input is obtained; The secondary control function optimization module is used to optimize the secondary control parameters based on the differential evolution algorithm and the secondary control input. The secondary control function optimization module is connected to the triggering mechanism setting module. The microgrid verification module is used to verify the stability of the microgrid system after an event is triggered and to determine whether Zeno behavior exists. The microgrid verification module is connected to the control model construction module.

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