Human-microgrid system double-time-scale optimization control method based on singular perturbation theory

Abstract

The invention aims to provide a singular perturbation theory-based dual-time-scale optimization control method for a human-micro-grid system, and belongs to the technical field of micro-grid system control. According to the method, a singular perturbation theory is adopted to decompose rapid electrical response and slow consumer motivation evolution of a micro-grid system into different time scales, and targeted optimization control strategies are respectively formulated. According to the method, the quick response capability of the micro-grid under transient disturbance is effectively improved, and meanwhile, long-term optimization under a steady-state condition is ensured, so that the stability and the operation efficiency of the system are remarkably improved. Different from a traditional control strategy, the time does not need to be divided into a plurality of time windows, and therefore the more accurate and efficient control effect is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of microgrid system control, and relates to an optimization control method for interaction between humans and microgrids, and specifically to a dual-time-scale optimization control method for a human-microgrid system based on singular perturbation theory. Background Art

[0002] As an important component of modern energy infrastructure, microgrids have become crucial due to the growing demand for clean energy and the shift to decentralized power systems. Microgrids provide higher reliability, flexibility, and efficiency by integrating distributed energy resources. The development of operating architectures and energy management systems for multi-microgrid clusters has further enhanced their potential in complex energy systems. In addition, recent advances in the planning, operation, and control of microgrids have laid the foundation for the application and promotion of a variety of control methods. However, in addition to these technological developments, human behavior also plays a vital role in shaping the future of microgrid systems.

[0003] In the prior art, for the optimization of the human-microgrid dual time scale system, the method of dividing the time window and treating the slow dynamic variables as constants is usually used to simplify the calculation. However, this method ignores the changing trend of the slow dynamic variables within the window, resulting in the controller being unable to accurately capture its dynamic characteristics, thereby reducing the control effect. In addition, treating the slow dynamic variables as constant values ​​also limits the system's real-time response to external disturbances, especially in the dual time scale, which is more likely to cause the problem of error accumulation.

[0004] Therefore, regarding the interaction between human behavior and microgrid systems, how to design control schemes to solve the dynamic balance problem between human behavior and system operation in microgrid systems in order to improve the stability and operational efficiency of the system has become the focus of researchers. Summary of the invention

[0005] In view of the problems existing in the background technology, the purpose of the present invention is to provide a dual-time-scale optimization control method for a human-microgrid system based on singular perturbation theory. This method combines the singular perturbation theory and proposes a dual-time-scale optimization framework. In the fast time scale, a control strategy is formulated to alleviate transient disturbances and ensure the dynamic stability of the system; in the slow time scale, the behavior-driven energy consumption pattern is gradually optimized to improve the long-term stability and adaptability of the system. The control method of the present invention provides a new theoretical basis for the stable operation and efficiency improvement of distributed energy systems.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] The dual-time-scale optimization control method of the human-microgrid system based on singular perturbation theory includes the following steps:

[0008] Step 1: Taking into account the electrical characteristics of the microgrid and the impact of human behavior on energy demand and load changes, the classic microgrid system and human behavior are modeled separately. Based on the complex dynamic interaction between microgrid operation and human behavior, a human-microgrid dual-time scale model combining the human behavior model and the microgrid model is constructed;

[0009] Step 2: Apply singular perturbation theory to dynamically separate the fast time scale and slow time scale of the dual time scale model;

[0010] Step 3: For the separated slow time scale system, focus on optimizing the balance between user satisfaction and energy consumption under steady-state conditions to improve the long-term adaptability and stability of the system, and design a network layer optimization controller that adapts to the slow time scale;

[0011] For the separated fast time scale system, we focus on the transient response characteristics of the system to ensure good anti-interference ability under external disturbances, achieve rapid stability of the system, and design a network layer optimization controller that adapts to the fast time scale;

[0012] Step 4: Obtain the control input of the microgrid system based on the slow dynamic subsystem optimization controller and the fast dynamic subsystem optimization controller.

[0013] Furthermore, the specific process of constructing the human-microgrid dual-time scale model in step 1 is as follows:

[0014] Build a microgrid model:

[0015]

[0016] Wherein, the subscripts d and q represent the direct axis and quadrature axis components respectively, and the superscript T represents the transpose; C f and L f They represent filter capacitor and filter inductor respectively, and together define the filter characteristics of the microgrid system; variable g represents the user load affected by user behavior, R f and R s They represent filter resistance and load resistance respectively, affecting power loss; V is load voltage, I t Produces current for the power generation unit, I L is the load current, I is the current on the transmission line, R is the resistance of the transmission line, L is the inductance of the transmission line; u is the input voltage, is the edge-node association matrix of the microgrid communication topology, ω r is the operating frequency of the system, represents the derivation;

[0017] Modeling human behavior:

[0018]

[0019] Among them, c represents the user behavior variable, B is the speed parameter of behavior change, F is the intervention intensity matrix, s is the social intervention variable, n represents the motivation variable, and w hed is the hedonic value, w bio is the biosphere value, D and E are weight parameters;

[0020] On the basis of this human behavior model, the behavioral layer and the physical layer are integrated by replacing the behavioral variable c with the load control input, thereby converting the abstract behavioral dynamics into specific physical signals and realizing the construction of the human-microgrid dual time scale model. The specific model is:

[0021]

[0022] Furthermore, the physical basis of the microgrid model is that the AC microgrid is a low-voltage island AC microgrid, consisting of N prosumers, which are interconnected through E impedance-inductive transmission lines, and the microgrid is balanced and symmetrical and its internal oscillator is synchronized.

[0023] Furthermore, the specific process of step 2 is:

[0024] The human-microgrid dual time scale model obtained in step 1 is integrated to obtain the integrated system equation:

[0025]

[0026] Where y is the partial electrical response and behavioral dynamics, z is the current on the transmission line, x represents the motivation variable, x = [n]; u is the control input, w is the value vector, H represents the influence weight of the system's values ​​on behavioral motivation, H = [DE]; P represents the system's external factors, P = [D + E]; B' y represents the effect of x on y, B' y =[0000B] T ; A yy , A yz , A zy and A zz is the intermediate process matrix;

[0027] The singular perturbation theory is applied to decouple the integrated system equations and decompose them into fast dynamic and slow dynamic subsystems, where the slow dynamic subsystem is expressed as:

[0028]

[0029] Among them, the variable x s ,y s 、z s and u s represents the slow dynamic components of x, y, z and u;

[0030] The decoupled fast dynamic subsystem is expressed as:

[0031]

[0032] Among them, the variable y f 、z f and u represent the fast dynamic components of x, y, and z.

[0033] Furthermore, the specific process of step 3 is:

[0034] Design an optimized controller for the slow dynamic subsystem obtained by decoupling. The specific process is as follows:

[0035] Constructing a slow dynamic objective function

[0036]

[0037] Among them, the subscript s represents the slow component, r represents the target value, i represents the i-th user, and θ ci represents the unit cost of user i, θ ui represents the satisfaction coefficient of user i in meeting its load demand; parameters ζ, κ, ρ, τ, φ, μ and ν are adjustable constants, ‖‖ 2 represents the square of the absolute value;

[0038] Taking the conditions of the slow system under steady state as constraints, combined with the slow system objective function Get the slow dynamic optimization problem,

[0039]

[0040] To optimize the variables, represents the optimization variable, and is the optimization variable of the state variable, is the optimization variable of the control variable;

[0041] Based on the Karush-Kuhn-Tucker (KKT) condition, the optimal solution of all relevant variables in the slow dynamic optimization problem can be obtained, and the slow dynamic subsystem optimization controller can be obtained.

[0042] Design an optimized controller for the fast dynamic subsystem obtained by decoupling. The specific process is as follows:

[0043] Constructing fast dynamic objective function

[0044]

[0045] Where, the subscript f represents the fast component, θ u ' i Reflects the effect of user load on behavior variable c if The influence of θ c ' i Indicates the adjustment current variable I tdf and I tqf The cost generated; ζ′ represents the weight of the control on the behavior during the optimization process; κ′ represents the weight of the control on the current during the optimization process; τ′ and φ′ represent the weight of the control on the voltage deviation during the optimization process; μ′ and ν′ represent the weight of the control on the control input during the optimization process;

[0046] Taking the steady-state condition of the fast system as the constraint condition, combined with the fast system objective function Get the fast dynamic optimization problem,

[0047]

[0048] The explicit form of the Lagrangian function for the fast dynamic optimization problem is as follows:

[0049]

[0050] Where λ is the Lagrange multiplier vector corresponding to the constraint,

[0051] Based on the Karush-Kuhn-Tucker (KKT) condition, the optimal solution of all relevant variables in the fast dynamic optimization problem can be obtained;

[0052] In order to maintain the stability of the microgrid system, the actual physical value needs to be input into the following formula to obtain the fast dynamic subsystem optimization controller:

[0053]

[0054] Matrix θ 1 ,θ 2 ,θ 3 ,θ 4 ....∈R N×N is a positive diagonal matrix, γ 1 ,γ 2 ,γ 3 is the coupling parameter.

[0055] Furthermore, in the fast dynamic optimization problem, each controller exchanges information with its neighboring nodes through a communication network that is consistent with the physical network topology.

[0056] Furthermore, in the steady state of the slow system, the following conditions hold:

[0057] 0=Hw-Px s

[0058]

[0059] in

[0060] In the steady state of a fast system, the following conditions hold:

[0061]

[0062] Furthermore, the coupling parameter γ 1 ,γ 2 ,γ 3 Specifically: γ 1 =I td ,γ 2 =I tq ,γ 3 =-2F T B T P T c,

[0063] The matrix P is given by the Lyapunov equation B T P+PB+Q=0 is determined, P is the symmetric positive definite matrix to be solved, and Q is the given symmetric positive definite matrix.

[0064] Furthermore, the specific process of step 4 is:

[0065] Based on the slow dynamic subsystem optimization controller and the fast dynamic subsystem optimization controller s f * The control input of the microgrid system is obtained, which is: *

[0066] s f =s f ,

[0067]

[0068] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0069] The present invention uses singular perturbation theory to decompose the fast electrical response of the microgrid system and the slower evolution of consumer motivation into different time scales, and formulates targeted optimization control strategies respectively. This method effectively improves the rapid response capability of the microgrid under transient disturbances, while ensuring long-term optimization under steady-state conditions, thereby significantly improving the stability and operating efficiency of the system. Unlike traditional control strategies, the present invention does not need to divide time into multiple time windows, thereby achieving a more accurate and efficient control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is the structural diagram of a classic low-frequency microgrid.

[0071] Figure 2 This is the connection topology diagram of ten production and sales nodes.

[0072] Figure 3 It is the dynamic curve of electrical response under normal operating conditions.

[0073] Figure 4 Dynamic curve of human behavior related parameters under normal operating conditions.

[0074] Figure 5 It is the dynamic curve of system parameters when user behavior and incentives change suddenly. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the implementation modes and the accompanying drawings.

[0076] A dual-time-scale optimization control method for a human-microgrid system based on singular perturbation theory comprises the following steps:

[0077] Step 1: A low-voltage island AC microgrid consists of N prosumers, which are interconnected through E impedance-inductive transmission lines. Figure 1 As shown in Figure 1, each prosumer can be modeled as a distributed generation unit or an equivalent distributed energy storage unit, which consists of a power source and a voltage source converter. The dynamic process of the physical layer of the microgrid is as follows:

[0078]

[0079] The subscripts d and q of the variables represent the direct axis and quadrature axis components respectively; C f and L f represent the filter capacitor and inductor, respectively, which together define the filter characteristics of the system; the variable g represents the user load, and R f and R s Represents the system and load resistance, affecting power loss; voltage V dand V q and the corresponding current I td and I tq Captures the real-time electrical status of the system; current I d and I q represents the current on the transmission line, and the resistance and inductance of the transmission line are represented by R and L respectively; the dynamic behavior of the system is controlled by the input signal u, and the matrix represents the edge-node association matrix of the microgrid communication topology, defining the information exchange structure between nodes; angular frequency ω r It describes the operating frequency of the system;

[0080] Although the dynamic characteristics of the physical layer determine the basic electrical behavior of the microgrid, the actual operation of the system is not only limited by physical factors, but also deeply affected by the complexity of human behavior patterns; in order to achieve a more comprehensive analysis, the behavioral layer must be integrated into the modeling framework to evaluate the impact of human decisions on the system's dynamic response and overall stability.

[0081] Human behavior is significantly influenced by motivation, social intervention, and personal values; motivation is driven by personal values, while social intervention further shapes behavioral choices. These factors directly affect energy consumption patterns within microgrids, as users' decisions to adjust their energy use depend not only on economic factors but also on personal values. In order to better capture these complex behavioral patterns, the present invention designs a human behavior model that integrates the dynamic interaction between motivation and intervention, can effectively describe the impact of human behavior on energy consumption, and promotes the optimization of system dynamics and stability. The human behavior model is specifically,

[0082]

[0083] Among them, variable c describes the dynamic evolution of behavior and represents the individual's response to external influences or interventions; variable n represents the motivation variable, which consists of hedonic value w hed and biosphere value w bio The intervention variable s quantifies the intensity of social intervention, while the matrix F determines the intensity of these interventions. Parameter B represents the speed of behavioral change, and parameters D and E serve as weights and time constants, respectively, to regulate the combined impact of intervention and values ​​on behavior.

[0084] Based on this human behavior model, the behavioral layer and the physical layer are integrated by replacing the behavioral variable c with the load control input g, thereby converting the abstract behavioral dynamics into specific physical signals. This conversion seamlessly integrates the user's energy decision into the load control mechanism of the microgrid, allowing the system to adaptively adjust the load according to real-time demand. The final microgrid system equation is as follows:

[0085]

[0086] Step 2: Integrate the final microgrid system equations to obtain:

[0087]

[0088] in, Representing the electrical response and behavioral dynamics, the control input vector is The system is influenced by human intrinsic values. Vector representation, x = [n] represents the motivation variable; in addition, the matrices H = [DE] and P = [D + E] describe the system's behavioral dynamics and external factors B' y =[0000B] T The relationship between A yy , A yz , A zz , A zz and G y They are all intermediate process matrices.

[0089]

[0090] In this framework, the variable n evolves at a slower time scale than the other variables, resulting in a two-time-scale system where the faster dynamics determine physical parameters such as voltage and current; traditional control methods have difficulty dealing with this difference, so specialized control strategies need to be designed for such systems.

[0091] In microgrids, fast dynamics require immediate response to changes in load and generation, while slow dynamics are driven by behavioral factors such as motivation and evolve gradually through external intervention. By applying singular perturbation theory, it is assumed that in the slow system, the fast variables have reached a steady state, while in the fast system, the slow variables remain unchanged. Therefore, the system is decomposed into fast dynamic and slow dynamic subsystems;

[0092] The decoupled slow system is expressed as follows:

[0093]

[0094] The variable x s ,y s 、z s and u s Represents the slow dynamic components of x, y, z, and u.

[0095] In the steady state of the slow system, the following conditions hold:

[0096] 0=Hw-Px s

[0097]

[0098] in

[0099] In the fast dynamic subsystem, it can be expressed as:

[0100] The variable y f 、z f and u f Represents the fast dynamic components of x, y, and z.

[0101] Independent fast dynamic equations:

[0102]

[0103] Similarly,

[0104]

[0105] In the steady state of a fast system, the following conditions hold:

[0106]

[0107] The fast dynamic state variable is expressed as Current I d and I q Through the voltage V d and V q Definition, where I d =-α 1 V d -α 2 V q and I q =-α 2 V d +α 1 V q Parameter α 1 and α 2 Respectively by and Given.

[0108] Step 3: In the system, slow dynamics capture long-term behavior and gradual changes, while fast dynamics deal with transient responses. The optimization goals of each subsystem are different: slow dynamics focus on long-term stability, efficiency, and adaptability to gradual changes, taking into account the gradual changes in demand, supply, and external factors; while fast dynamics focus on managing short-term disturbances to ensure system stability and rapid response. By coordinating these goals, the system can strike a balance between short-term response and long-term robustness, thereby improving the operating efficiency and adaptability of the microgrid.

[0109] The goal of slow dynamic optimization is to combine the performance of the physical system with user needs to develop an optimized control strategy that can balance supply and demand, improve operational efficiency, and reduce external intervention. Since user behavior is affected by factors such as economic incentives and environmental awareness, the system needs to flexibly respond to external interference and changes in consumption patterns while meeting user needs. In the process of maintaining a balance between supply and demand, optimization should also reduce energy waste, improve economic efficiency, and promote sustainable development. Through precise control strategies, the system's dependence on external intervention is minimized, thereby ensuring long-term system stability and adaptability. To achieve these goals, the following optimization objective function is designed:

[0110]

[0111] in, represents the unit cost of user i, represents the satisfaction coefficient of user i in meeting his load demand. ui The value reflects the user's higher expectation of comfort.

[0112] By minimizing the objective function, the voltage is guided to its nominal value, thus achieving accurate voltage regulation and minimizing |n is -c is |. The parameters ζ, κ, ρ, τ, φ, μ, and ν are adjustable constants, which are used to prioritize different control objectives, such as d and u q Optimize control efforts.

[0113] By using mathematical expressions describing the system steady-state conditions as constraints and combining them with predefined optimization objectives, a complete optimization problem can be constructed. In this framework, the conditions under the slow system steady state play a vital role, ensuring that the system always adheres to key physical constraints such as power balance, frequency stability, and voltage / current limits during operation. These constraints not only ensure the safety and reliability of the system, but also avoid potential instability or performance degradation in long-term operation.

[0114] Combining these constraints with the optimization goal ensures that the system not only meets the basic physical requirements but also achieves optimal operation under different operating conditions. As an optimization variable, the optimization problem for slow dynamics can be expressed as:

[0115]

[0116] Based on the Karush-Kuhn-Tucker (KKT) condition, the optimal solution of all relevant variables in the optimization problem can be derived, including the state variable and The optimal value of and control variables

[0117] According to the KKT framework, the first-order optimality condition of the optimization problem is as follows:

[0118]

[0119] Among them, λ i ' is the Lagrange multiplier vector corresponding to the constraint; in the optimization process, let the control variable It shows that the control variable has reached the optimal state. Therefore, the control variable u s Controls the corresponding state variable y s The evolution of In addition, due to the inherent dynamic characteristics of the system, the state variable x s naturally tends to its steady-state value Eventually, under this optimization framework, the system will converge to a steady-state solution and Ensure global optimal performance at different time scales.

[0120] The optimization of fast dynamics focuses on mitigating short-term disturbances and ensuring that the system can respond quickly and maintain stability under transient conditions. These disturbances may come from sudden changes in load, external environmental factors, or other unpredictable dynamic changes. Therefore, the system must be flexible enough to quickly adapt to these fluctuations. When designing a control strategy, the key is to monitor the system status in real time and adjust the control input in time to prevent instability or performance degradation caused by these disturbances. By optimizing fast dynamics, the system can quickly restore stability, thereby preventing negative impacts on long-term operating efficiency and overall stability. This design not only ensures the rapid response of the system, but also enhances the robustness of the system in complex environments, ultimately improving the dynamic response and operational reliability of the microgrid.

[0121] Let y f =yy s Represents the fast dynamic part of the system. In order to guide the system state variables to approach their optimal steady-state values ​​and minimize the impact of fast dynamics, the optimization goal is to make the fast dynamic variables as close to zero as possible. Therefore, the following optimization objective function under fast dynamics is proposed:

[0122]

[0123] Among them, the parameter θ u ' i Reflects the effect of user load on behavior variable c if The influence of θ c ' i Indicates the adjustment current variable I tdf and I tqfThe parameters ζ′, κ′, ρ′, τ′, and φ′ control the weights of the behavior, current, and voltage deviations during the optimization process, respectively. Specifically, ζ′ affects the behavior variables, ρ′ controls the social intervention, and κ′, τ′, and φ′ ensure that the current and voltage are maintained near the desired values. Finally, μ′ and ν′ adjust the control input u xf and u yf , to ensure the optimal control effect. The overall goal of this objective function is to minimize the deviation of behavior, current and voltage, while optimizing the control input to maintain the stability and performance of the system in fast dynamics.

[0124] By combining the optimization objective with the steady-state constraints of the fast dynamics, the optimization problem of the fast dynamics can be formalized. The construction of this optimization problem not only ensures the compliance of the system constraints, but also strives to achieve the predefined optimization goal.

[0125]

[0126] Among them, α 1 =(-1 / R s -α 1 ), α 2 =(ω r C f -α 2 ), α 3 =(-ω r C f -α 2 ).

[0127] set up is the Lagrange multiplier vector corresponding to the constraint. The Lagrange function is used to transform the objective function The constraints are combined into an expression that can be optimized by KKT conditions. The explicit form of the Lagrangian function of the given optimization problem of the fast dynamic subsystem is as follows:

[0128]

[0129] According to the KKT condition, the first-order optimality condition of the optimization problem is as follows:

[0130]

[0131] Given the distributed nature of the system, the control mechanism needs to ensure the realization of both local and global goals. Therefore, a distributed approach consistent with the system's communication capabilities is adopted. According to the KKT condition, assuming that each controller can exchange information with its neighboring nodes through a communication network consistent with the physical network topology, the following distributed control scheme is designed using the primal-dual dynamic mechanism to solve the given optimization problem. The specific formula is as follows:

[0132]

[0133] Matrix θ 1 ,θ 2 ,θ 3 ,θ 4 ....∈R N×N are positive diagonal matrices, and adjusting them can adjust the dynamic response of the controller. In addition, the vector γ 1 , γ 2 and γ 3 As the control input port, it facilitates the interconnection between the controller and the physical system. It should be emphasized that although the objective function is relative to and The strict non-convexity of the constraint ensures that the linearization of the constraint ensures that the given constant γ 1 , γ 2 and γ 3 In the case of is the only one.

[0134] In order to ensure that the controller can accurately respond to the dynamic fluctuations of the physical layer while maintaining system stability and performance, the control variables, external interventions, and coupling parameters γ 1 ,γ 2 ,γ 3 These parameters are used to link the physical layer to the network layer: 1 =I td ,γ 2 =I tq ,γ 3 =-2F T B T P T c

[0135] The matrix P is given by the Lyapunov equation B T P+PB+Q=0 is determined, P is the symmetric positive definite matrix to be solved, Q is the given symmetric positive definite matrix;

[0136] Step 4: Optimize controller based on slow dynamic subsystem and fast dynamic subsystem s f * The control input of the microgrid system is obtained, which is: *

[0137] s f =s f ,

[0138]

[0139] The storage function of the physical layer (the actual microgrid control system) is defined as follows:

[0140]

[0141] According to Young's inequality, we can deduce that:

[0142]

[0143] Substituting it into the physical storage function, we get:

[0144]

[0145] Similarly, the storage function of the optimized controller is:

[0146]

[0147] Its derivative is:

[0148]

[0149] The storage function of the entire closed-loop system is:

[0150] S=S p +S c

[0151] And meet:

[0152]

[0153] There exists a forward invariant set Ω, and according to the LaSalle invariance principle, any solution with initial conditions inside Ω will asymptotically converge to the maximum invariant set defined by the following conditions:

[0154]

[0155] Then, according to the corresponding conditions, it can be deduced that in this maximum invariant set, and will tend to zero. Finally, by checking the steady-state constraints, we can conclude that Depend on Therefore, it can be concluded that in steady state, the physical state variables are consistent with the corresponding optimization variables. This shows that it is feasible to realize system control by solving the optimization variables of the controller.

[0156] Example 1

[0157] In order to verify the effectiveness of the proposed controller, the present invention conducted multiple simulation experiments. The experimental setup consists of 10 interconnected classic microgrids with topological structures such as Figure 2As shown in Figure 1. The black arrows indicate the direction of current flow, and the dotted lines indicate the communication connections between microgrids. Each microgrid is connected to its neighboring nodes through transmission lines. The specific parameters of the microgrid, such as voltage, current, and load impedance, as well as the parameters related to the human behavior model are shown in Table 1. These parameters are obtained through long-term monitoring of multiple distributed energy resources and can better reflect the actual operating conditions.

[0158] Table 1

[0159]

[0160]

[0161] The parameters related to the human behavior model are as follows

[0162] D=diag(1.66,1.68,3.1,3.2,1.68,1.7,3.3,3.3,1.7,1.67)×10 -4

[0163] E=diag(2.92,2.92,1.25,1.25,2.92,2.92,1.25,1.25,2.92,2.92)×10 -4

[0164] w hed =[0.70.70.810.810.720.720.80.80.740.74] T

[0165] w bio =[0.70.70.80.80.70.80.80.70.7] T

[0166] Scenario 1: Optimization effect under normal operating conditions. In order to evaluate the effectiveness of the proposed control strategy under normal operating conditions, an initial scenario is designed where the system operates without any external disturbances or sudden fluctuations. In this scenario, it is assumed that the microgrid operates under typical load and generation patterns without transient disturbances or changes in user behavior. The purpose of this scenario is to observe how the control strategy optimizes system performance under a stable environment.

[0167] Through simulation, the dynamic change curves of the direct axis components of voltage and current in the system are obtained as follows: Figure 3 , as well as the changing trends of user behavior, social intervention intensity, and motivational variables, e.g. Figure 4As shown. The simulation results show that the control method proposed in the present invention can effectively realize the rapid dynamic regulation of voltage and current in the microgrid, ensure that the system quickly recovers stability in the short term, and maintains the voltage near the nominal value of 170V. This performance highlights the strong dynamic response capability of the strategy in dealing with transient disturbances and load changes. In addition, user behavior gradually adapts at the minimum external intervention cost and eventually converges to the steady-state value of the incentive variable, thereby verifying the effectiveness of the strategy in optimizing long-term behavioral dynamics. By dynamically adjusting external conditions, the system flexibly adjusts the intervention intensity to ensure a harmonious balance between user behavior and system stability. This adaptive mechanism not only improves the operating efficiency of the microgrid, but also shows significant potential in promoting sustainable development, indicating the wide applicability of this strategy in future distributed energy management systems.

[0168] Scenario 2: Effectiveness of the control strategy under sudden changes in user behavior and incentives. In order to rigorously evaluate the effectiveness of the proposed control strategy under complex conditions, a simulation scenario was designed. This scenario assumes that user behavior and incentive parameters suddenly change at a specific moment due to external influences. Specifically, at t=1s, the values ​​of the behavior variables change suddenly, while at t=0.5s, the values ​​of the motivation model parameters change. This simulates drastic fluctuations in user behavior and decision-making motivations caused by external interventions, economic incentives, or social pressure. The goal of this simulation scenario is to evaluate the adaptability and regulatory ability of the control strategy in dealing with sudden changes in user behavior and incentives.

[0169] This simulation provides insight into how the control strategy maintains the stability of the microgrid under rapidly changing patterns of user behavior and evaluates its dynamic response to sudden changes in behavioral variables, especially load regulation, voltage, and current. In addition, the simulation verifies the effectiveness of the control strategy in optimizing user behavior and maintaining system balance over the long term, especially when external factors significantly influence user decisions. Such evaluations are important in demonstrating the robustness and flexibility of the control strategy in managing the complex interaction between system dynamics and user behavior.

[0170] The simulation results are as follows Figure 5 , the voltage of each node V x Remains stable over time. Although at t=1s, the behavior and excitation parameters suddenly change due to external intervention, the control method of the present invention can still effectively regulate the voltage and ensure that the system quickly returns to a stable state. In addition, the current I dxThe small fluctuations in indicate that the control strategy has a strong ability to manage load changes. The changing trends of the user behavior variables c and the intervention intensity s also show that the control strategy can optimize and adjust user behavior under external influences and guide it to a steady state. These findings verify the robustness and adaptability of the proposed method in dealing with behavioral mutations, and further confirm the effectiveness of the proposed method in maintaining microgrid stability and load balance.

[0171] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A dual-time-scale optimization control method for human-microgrid system based on singular perturbation theory, characterized in that: The following steps are involved: Step 1: Taking into account the electrical characteristics of the microgrid and the impact of human behavior on energy demand and load changes, the classic microgrid system and human behavior are modeled separately. Based on the complex dynamic interaction between microgrid operation and human behavior, a human-microgrid dual-time scale model combining the human behavior model and the microgrid model is constructed; Step 2: Apply singular perturbation theory to dynamically separate the fast time scale and slow time scale of the dual time scale model; Step 3: For the separated slow time scale system, focus on optimizing the balance between user satisfaction and energy consumption under steady-state conditions to improve the long-term adaptability and stability of the system, and design a network layer optimization controller that adapts to the slow time scale; For the separated fast time scale system, we focus on the transient response characteristics of the system to ensure good anti-interference ability under external disturbances, achieve rapid stability of the system, and design a network layer optimization controller that adapts to the fast time scale; Step 4: Obtain the control input of the microgrid system based on the slow dynamic subsystem optimization controller and the fast dynamic subsystem optimization controller.

2. The dual-time-scale optimization control method for a human-microgrid system according to claim 1, characterized in that: The specific process of constructing the human-microgrid dual time scale model in step 1 is as follows: Build a microgrid model: Wherein, the subscripts d and q represent the direct axis and quadrature axis components respectively, and the superscript T represents the transpose; C f and L f represent filter capacitor and filter inductor respectively; variable g represents the user load affected by user behavior, R f and R s Represent filter resistance and load resistance respectively; V is load voltage, I t Produces current for the power generation unit, I L is the load current, I is the current on the transmission line, R is the resistance of the transmission line, L is the inductance of the transmission line; u is the input voltage, is the edge-node association matrix of the microgrid communication topology, ω r is the operating frequency of the system, represents the derivation; Modeling human behavior: Among them, c represents the user behavior variable, B is the speed parameter of behavior change, F is the intervention intensity matrix, s is the social intervention variable, n represents the motivation variable, and w hed is the hedonic value, w bio is the biosphere value, D and E are weight parameters; The human-microgrid dual time scale model is as follows:

3. The dual-time-scale optimization control method for a human-microgrid system according to claim 2, characterized in that: The physical basis of the microgrid model is that the AC microgrid is a low-voltage island AC microgrid, consisting of N prosumers, which are interconnected through E impedance-inductive transmission lines, and the microgrid is balanced and symmetrical, and the internal oscillators are synchronized.

4. The dual-time-scale optimization control method for a human-microgrid system according to claim 2, characterized in that: The specific process of step 2 is: The human-microgrid dual-time scale model obtained in step 1 is integrated to obtain the integrated system equation: Where y is the electrical response and behavior dynamics, z is the current on the transmission line, x represents the motivation variable, x = [n]; u is the control input, w is the value vector, H represents the influence weight of the system's values ​​on behavioral motivation, H = [DE]; P represents the system's external factors, P = [D + E]; B' y represents the effect of x on y, A yy , A yz , A zy and A zz is the intermediate process matrix; The singular perturbation theory is applied to decouple the integrated system equations and decompose them into fast dynamic and slow dynamic subsystems, where the slow dynamic subsystem is expressed as: Among them, the variable x s ,y s 、z s and u s represents the slow dynamic components of x, y, z and u; The decoupled fast dynamic subsystem is expressed as: Among them, the variable y f 、z f and u f Represents the fast dynamic components of x, y, and z.

5. The dual-time-scale optimization control method for a human-microgrid system according to claim 4, characterized in that: The specific process of step 3 is: Design an optimized controller for the slow dynamic subsystem obtained by decoupling. The specific process is as follows: Constructing a slow dynamic objective function Among them, the subscript s represents the slow component, r represents the target value, i represents the i-th user, and θ ci represents the unit cost of user i, θ ui represents the satisfaction coefficient of user i in meeting its load demand; parameters ζ, κ, ρ, τ, φ, μ and ν are adjustable constants, ‖‖ 2 represents the square of the absolute value; Taking the conditions of the slow system under steady state as constraints, combined with the slow system objective function Get the slow dynamic optimization problem, To optimize the variables, () * represents the optimization variable, and is the optimization variable of the state variable, is the optimization variable of the control variable; Based on the Karush-Kuhn-Tucker (KKT) condition, the optimal solution of all relevant variables in the slow dynamic optimization problem can be obtained, and the slow dynamic subsystem optimization controller can be obtained. Design an optimized controller for the fast dynamic subsystem obtained by decoupling. The specific process is as follows: Constructing fast dynamic objective function Where, the subscript f represents the fast component, θ u ' i Reflects the effect of user load on behavior variable c if The influence of θ c ' i Indicates the adjustment current variable I tdf and I tqf The cost generated; ζ′ represents the weight of the control on the behavior during the optimization process; κ′ represents the weight of the control on the current during the optimization process; τ′ and φ′ represent the weight of the control on the voltage deviation during the optimization process; μ′ and ν′ represent the weight of the control on the control input during the optimization process; Taking the steady-state condition of the fast system as the constraint condition, combined with the fast system objective function Get the fast dynamic optimization problem, The explicit form of the Lagrangian function for the fast dynamic optimization problem is as follows: Where λ is the Lagrange multiplier vector corresponding to the constraint, Based on the Karush-Kuhn-Tucker (KKT) condition, the optimal solution of all relevant variables in the fast dynamic optimization problem can be obtained; In order to maintain the stability of the microgrid system, the actual physical value needs to be input into the following formula to obtain the fast dynamic subsystem optimization controller: sf * : Matrix θ1,θ2,θ3,θ4....∈R N×N is a positive diagonal matrix, γ1,γ2,γ3 are coupling parameters.

6. The dual-time-scale optimization control method for a human-microgrid system according to claim 5, characterized in that: In the fast dynamic optimization problem, each controller exchanges information with its neighboring nodes through a communication network that is consistent with the physical network topology.

7. The dual-time-scale optimization control method for a human-microgrid system according to claim 5, characterized in that: In the steady state of the slow system, the following conditions hold: 0=Hw-Px s in In the steady state of a fast system, the following conditions hold:

8. The dual-time-scale optimization control method for a human-microgrid system according to claim 5, characterized in that: The coupling parameters γ1, γ2, and γ3 are as follows: γ1 = I td ,γ2=I tq ,γ3=-2F T B T P T c, The matrix P is given by the Lyapunov equation B T P+PB+Q=0 is determined, P is the symmetric positive definite matrix to be solved, and Q is the given symmetric positive definite matrix.

9. The dual-time-scale optimization control method for a human-microgrid system according to claim 1, characterized in that: The specific process of step 4 is: Based on the slow dynamic subsystem optimization controller and the fast dynamic subsystem optimization controller s f * The control input of the microgrid system is obtained, which is: sf=s f * ,

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