Dual-Time Scale Optimal Control Method for Human-Microgrid System Based on Singular Perturbation Theory

Abstract

The object of the present invention is to provide a dual-time-scale optimal control method for a human-microgrid system based on singular perturbation theory, belonging to the technical field of microgrid system control. 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 optimal control strategies respectively. This method effectively improves the fast response ability of the microgrid under transient disturbances, while ensuring long-term optimization under steady-state conditions, thus significantly improving the stability and operation efficiency of the system. Different from traditional control strategies, the present invention does not need to divide time into multiple time windows, thus achieving a more accurate and efficient control effect.

Description

Technical Field

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

[0002] As an important part of modern energy infrastructure, microgrids have become crucial due to the increasing demand for clean energy and the shift towards decentralized power systems. Microgrids provide higher reliability, flexibility, and efficiency by integrating distributed energy sources, and the development of the operation architecture and energy management system of multi-microgrid clusters further enhances their potential in complex energy systems. In addition, the progress in the planning, operation, and control of microgrids in recent years has laid the foundation for the application and promotion of various control methods. However, in addition to these technological developments, human behavior also plays a crucial role in shaping the future of microgrid systems.

[0003] In the prior art, for the optimization of the human-microgrid two-time-scale system, the method of dividing time windows and treating slow dynamic variables as constants is usually adopted to simplify the calculation. However, this method ignores the change trend of slow dynamic variables within the window, resulting in the controller being unable to accurately capture their dynamic characteristics, thereby reducing the control effect. In addition, treating slow dynamic variables as constant values also limits the real-time response of the system to external disturbances, especially in the two-time-scale case, where the problem of error accumulation is more likely to occur.

[0004] Therefore, regarding the interaction between human behavior and the microgrid system, how to design a control scheme to solve the dynamic balance problem between human behavior and system operation in the microgrid system, so as to improve the stability and operation efficiency of the system, has become the focus of attention of researchers. Summary of the Invention

[0005] Aiming at the problems existing in the background technique, the purpose of the present invention is to provide a two-time-scale optimal control method for the human-microgrid system based on singular perturbation theory. This method combines singular perturbation theory and proposes a two-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, thereby enhancing 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 purpose, the technical solution of the present invention is as follows:

[0007] The two-time-scale optimal control method for the human-microgrid system based on singular perturbation theory includes the following steps:

[0008] Step 1: Fully consider the electrical characteristics of the microgrid and the influence mechanism of human behavior on energy demand and load changes, model the classical microgrid system and human behavior respectively, and construct a human-microgrid two-time-scale model combining the human behavior model and the microgrid model based on the complex dynamic interaction between microgrid operation and human behavior;

[0009] Step 2: Apply the singular perturbation theory to perform dynamic separation of the fast time scale and the slow time scale for the two-time-scale model;

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

[0011] For the separated fast time scale system, 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 at the same time design a network layer optimization controller adapted to the fast time scale;

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

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

[0014] Construct the microgrid model:

[0015]

[0016] where 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 the filter capacitor and filter inductor respectively, jointly defining the filtering characteristics of the microgrid system; the variable g represents the user load affected by user behavior, R f and R s represent the filter resistance and load resistance respectively, affecting the power loss; V is the load voltage, I t is the current produced by 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 incidence matrix of the microgrid communication topology, ω r is the operating frequency of the system, denotes the derivative;

[0017] Construct the human behavior model:

[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, w hed is the hedonic value, w bio is the biosphere value, and D and E are weight parameters;

[0020] Based on this human behavior model, by replacing the behavior variable c with the load control input, the integration of the behavior layer and the physical layer is realized, so as to convert the abstract behavior dynamics into specific physical signals and construct a human-microgrid double-time-scale model. The specific model is:

[0021]

[0022] Furthermore, the physical basis of the microgrid model is: the AC microgrid is a low-voltage islanded AC microgrid, composed of N prosumers, and these prosumers are interconnected through E resistive-inductive transmission lines. The microgrid is balanced and symmetric, and the internal oscillators are synchronized.

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

[0024] Integrate the human-microgrid double-time-scale model obtained in step 1 to obtain the integrated system equation,

[0025]

[0026] Among them, y is the partial 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 the behavior motivation, H = [D E]; P represents the external factors of the system, P = [D + E]; B' y represents the influence of x on y, B' y = [0000B] T ; A yy 、A yz 、A zy and A zz are intermediate process matrices;

[0027] Apply the singular perturbation theory to decouple the integrated system equation and decompose it into fast and slow dynamic subsystems. Among them, the slow dynamic subsystem is expressed as:

[0028]

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

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

[0031]

[0032] Among them, the variables 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 as follows:

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

[0035] Construct the slow dynamic objective function

[0036]

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

[0038] Using the conditions under the steady state of the slow system as the constraint conditions and combining with the slow system objective function to obtain the optimization problem of the slow dynamics,

[0039]

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

[0041] Based on the Karush-Kuhn-Tucker (KKT) conditions, the optimal solutions of all relevant variables in the optimization problem of the slow dynamics can be obtained, and thus the optimized controller of the slow dynamic subsystem can be obtained

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

[0043] Construct the fast-dynamic objective function

[0044]

[0045] where the subscript f represents the fast component, and θ u ' i reflects the influence of the user load on the behavior variable c if and θ c ' i represents the cost generated by adjusting the current variables I tdf and I tqf ; 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 weights of the control on the voltage deviation during the optimization process; μ′ and ν′ represent the weights 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 and combining it with the fast-system objective function the optimization problem of the fast dynamics is obtained.

[0047]

[0048] The explicit form of the Lagrangian function of the fast-dynamics 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) conditions, the optimal solutions of all relevant variables in the fast-dynamics optimization problem can be obtained;

[0052] To maintain the stability of the microgrid system, the actual physical values need to be input into the following formula to obtain the fast-dynamics subsystem optimization controller

[0053]

[0054] Matrices θ1, θ2, θ3, θ4....∈R N×N are positive diagonal matrices, and γ1, γ2, γ3 are coupling parameters.

[0055] Furthermore, in the fast-dynamics optimization problem, each controller exchanges information with its adjacent nodes through a communication network consistent with the physical network topology.

[0056] Furthermore, under the steady state of the slow system, the following condition holds:

[0057] 0 = Hw - Pxs

[0058]

[0059] Among them

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

[0061]

[0062] Furthermore, the coupling parameters γ1, γ2, γ3 are specifically: γ1 = I td , γ2 = I tq , γ3 = -2F T B T P T c,

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

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

[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, specifically: *

[0066] s f = s f ,

[0067]

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

[0069] The present invention uses the 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 fast response ability of the microgrid under transient disturbances, and at the same time ensures long-term optimization under steady-state conditions, thus significantly improving the stability and operation efficiency of the system. Different from traditional control strategies, the present invention does not need to divide time into multiple time windows, thus achieving a more accurate and efficient control effect. Description of the Drawings

[0070] Figure 1 It is the structure diagram of a classical low-frequency microgrid.

[0071] Figure 2 It is a 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 It is the 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 mutate. Specific implementation manners

[0075] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the implementation manners and the accompanying drawings.

[0076] A two-time-scale optimal control method for a human-microgrid system based on singular perturbation theory, comprising the following steps:

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

[0078]

[0079] Among them, the subscripts d and q of the variables respectively represent the direct-axis and quadrature-axis components; C f and L f respectively represent the filter capacitor and inductor, which jointly define the filtering characteristics of the system; the variable g represents the user load, and R f and R s respectively represent the system and load resistances, which affect the power loss; the voltages V d and V q and the corresponding currents I td and I tq capture the real-time electrical state of the system; the currents I d and I q represent the currents on the transmission line, and the resistance and inductance of the transmission line are respectively represented by R and L; the dynamic behavior of the system is controlled by the input signal u, and the matrix represents the edge-node incidence matrix of the microgrid communication topology and defines the information exchange structure between nodes; the angular frequency ω r characterizes 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 restricted by physical factors but also deeply influenced by the complexity of human behavior patterns. To achieve a more comprehensive analysis, the behavior 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 behavior choices. These factors directly affect the energy consumption patterns within the microgrid because users' decisions to adjust their energy use depend not only on economic factors but also on personal values. To better capture these complex behavior 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] where the variable c describes the dynamic evolution of behavior and represents an individual's response to external influences or interventions; the variable n represents the motivation variable, which is shaped by multiple values including the hedonic value w hed and the biosphere value w bio and these values jointly affect the individual's decision-making process; the intervention variable s quantifies the intensity of social intervention, and the matrix F determines the intensity of these interventions. The parameter B represents the speed of behavior change, and the parameters D and E respectively act as weights and time constants to regulate the combined impact of intervention and values on behavior;

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

[0085]

[0086] Step 2: Integrating the final system equations of the microgrid, we can obtain

[0087]

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

[0089]

[0090] In this framework, the evolution time scale of the variable n is slower than that of other variables, thus forming a two-time-scale system, where the faster dynamics determine physical parameters such as voltage and current; traditional control methods are difficult to handle this difference, so a dedicated control strategy needs to be designed for such systems.

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

[0092] The decoupled slow system is represented by the following equation:

[0093]

[0094] where the variable x s y s z s and u s represent the slow dynamic components of x, y, z, and u.

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

[0096] 0 = Hw - Px s

[0097]

[0098] where

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

[0100] where the variable y f z f and u f represent the fast dynamic components of x, y, and z.

[0101] Independent fast - dynamic equations:

[0102]

[0103] Similarly,

[0104]

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

[0106]

[0107] where the fast - dynamic state variables are expressed as the current I d and I q are defined through the voltages V d and V q where I d = -α1V d -α2V q and I q = -α2V d +α1V q The parameters α1 and α2 are given by and respectively.

[0108] Step 3: In the system, the slow dynamics capture the long - term behavior and gradual changes, while the fast dynamics deal with the transient response. The optimization objectives of each subsystem are different: the slow dynamics mainly focus on long - term stability, efficiency, and adaptability to gradual changes, considering the gradual changes in demand, supply, and external factors; while the fast dynamics focus on managing short - term disturbances to ensure the stability and fast response of the system. By coordinating these objectives, the system can achieve a balance between short - term response and long - term robustness, thus improving the operating efficiency and adaptability of the micro - grid.

[0109] The goal of slow - dynamics optimization is to combine the performance of the physical system with user needs, and develop an optimal control strategy that can balance supply and demand, improve operating 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 disturbances and changes in consumption patterns while meeting user needs. In maintaining the balance between supply and demand, the 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, thus ensuring long - term system stability and adaptability. To achieve these goals, the following optimization objective function is designed:

[0110]

[0111] where, represents the unit cost of user i, Represents the satisfaction coefficient of user i for meeting their load demand. A higher θ ui value reflects the user's higher expectation for comfort.

[0112] By minimizing the objective function, that is, guiding the voltage to its nominal value, precise voltage regulation is achieved and |n is -c is | is minimized. The parameters ζ, κ, ρ, τ, φ, μ, and ν are adjustable constants used to preferentially meet different control objectives, such as optimizing the control effort through u d and u q .

[0113] By taking the mathematical expressions describing the system's 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 slow system steady state play a crucial role in ensuring that the system always adheres to key physical constraints during operation, such as power balance, frequency stability, and voltage / current limits. These constraints not only guarantee the safety and reliability of the system but also avoid potential instability or performance degradation in the long run.

[0114] Combining these constraints with the optimization objectives ensures that the system not only meets the basic physical requirements but also operates optimally under different operating conditions. Let be the optimization variable. The optimization problem for slow dynamics can be expressed as:

[0115]

[0116] Based on the Karush-Kuhn-Tucker (KKT) conditions, the optimal solutions for all relevant variables in the optimization problem can be derived, including the optimal values of the state variables and , as well as the control variables

[0117] According to the KKT framework, the first-order optimality conditions for the optimization problem are as follows:

[0118]

[0119] where λ i ' is the Lagrange multiplier vector corresponding to the constraints; during the optimization process, setting the control variable indicates that the control variable has reached the optimal state. Therefore, the control variable u s controls the evolution of the corresponding state variable y s to ensure its gradual convergence to the optimal value In addition, due to the inherent dynamic characteristics of the system, the state variable x s naturally tends to its steady-state value Finally, under this optimization framework, the system will converge to a steady-state solution and ensure global optimal performance at different time scales.

[0120] Fast dynamic optimization mainly focuses on mitigating short-term disturbances, ensuring that the system can respond quickly and maintain stability under transient conditions. These disturbances may stem 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 control strategies, the key lies in real-time monitoring of the system state and timely adjustment of control inputs to prevent instability or performance degradation caused by these disturbances. By optimizing fast dynamics, the system can quickly recover stability, thus preventing negative impacts on long-term operating efficiency and overall stability. This design not only ensures the fast response of the system but also enhances its robustness in complex environments, ultimately improving the dynamic response and operational reliability of the microgrid.

[0121] Let y f = y - y s represent the fast dynamic part of the system. To guide the system state variables closer to their optimal steady-state values and minimize the impact of fast dynamics, the optimization objective is to drive the fast dynamic variables as close to zero as possible. Therefore, the following optimization objective function for fast dynamics is proposed:

[0122]

[0123] where the parameter θ u ' i reflects the influence of the user load on the behavior variable c if while θ c ' i represents the cost incurred by adjusting the current variables I tdf and I tqf ; the parameters ζ′, κ′, ρ′, τ′, and φ′ respectively control the weights for behavior, current, and voltage deviations during the optimization process. Specifically, ζ′ affects the behavior variable, ρ′ controls social intervention, while κ′, τ′, and φ′ ensure that the current and voltage are maintained near the desired values; finally, μ′ and ν′ adjust the control inputs u xf and u yf to ensure optimal control effects. The overall objective of this objective function is to minimize the deviations of behavior, current, and voltage while optimizing the control inputs to maintain the stability and performance of the system in fast dynamics.

[0124] By combining the optimization objective with the steady-state constraint conditions of fast dynamics, the optimization problem of fast dynamics can be formally expressed. The construction of this optimization problem not only ensures compliance with system constraints but also aims to achieve the predefined optimization objectives.

[0125]

[0126] where α1 = (-1 / R s - α1), α2 = (ω r C f - α2), α3 = (-ω r C f - α2).

[0127] Let be the Lagrange multiplier vector corresponding to the constraints. The Lagrange function is used to combine the objective function and the constraints into an expression that can be optimized by the KKT conditions. The explicit form of the Lagrange function for the given optimization problem of the fast dynamic subsystem is as follows:

[0128]

[0129] According to the KKT conditions, the first-order optimality conditions for the optimization problem are as follows:

[0130]

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

[0132]

[0133] Matrices θ1, θ2, θ3, θ4.... ∈ R N×N are positive diagonal matrices, and adjusting them can regulate the dynamic response of the controller. In addition, vectors γ1, γ2, and γ3 serve as control input ports to facilitate the interconnection between the controller and the physical system. It should be emphasized that although the objective function is strictly non-convex with respect to and , the linearization of the constraint conditions ensures that the optimal solution is unique given the constants γ1, γ2, and γ3.

[0134] To ensure that the controller can accurately respond to the dynamic fluctuations of the physical layer while maintaining the stability and performance of the system, specific configurations are made for the control variables, external interventions, and coupling parameters γ1, γ2, γ3, which are used to link the physical layer and the network layer: γ1 = I td , γ2 = I tq, γ3 = -2F T B T P T c

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

[0136] Step 4: Optimize the controller for the slow - dynamic subsystem and the controller for the fast - dynamic subsystem s f * Obtain the control input of the micro - grid system, specifically: *

[0137] s f = s f ,

[0138]

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

[0140]

[0141] According to the Young's inequality, it can be deduced that:

[0142]

[0143] Substitute it into the physical storage function to obtain:

[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 it satisfies:

[0152]

[0153] There exists a forward invariant set Ω. According to LaSalle's invariance principle, any solution with an initial condition within Ω will asymptotically converge to the largest invariant set defined by the following conditions:

[0154]

[0155] Subsequently, according to the corresponding conditions, it can be deduced that within this largest invariant set, and will both tend to zero. Finally, by examining the steady-state constraints, it can be concluded that is uniquely determined by . Therefore, it can be concluded that in the steady state, the physical state variables are consistent with the corresponding optimization variables. This shows that it is feasible to implement system control by solving the optimization variables of the controller in the method of the present invention.

[0156] Example 1

[0157] To verify the effectiveness of the proposed controller, the present invention conducted multiple groups of simulation experiments. The experimental setup consists of 10 interconnected classical microgrids, and the topological structure is as Figure 2 shown. The black arrows indicate the direction of current flow, and the dashed lines represent the communication connections between the microgrids. Each microgrid is connected to its neighboring nodes through transmission lines. The specific parameters of the microgrids, 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 = [0.7 0.7 0.81 0.81 0.72 0.72 0.8 0.8 0.74 0.74] T

[0165] wbio = [0.7 0.7 0.8 0.8 0.7 0.7 0.8 0.8 0.7 0.7] T

[0166] Scenario 1: Optimization effect under normal operating conditions. To evaluate the effectiveness of the proposed control strategy under normal operating conditions, an initial scenario was 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 the system performance in a stable environment.

[0167] Through simulation, the dynamic change curves of the direct-axis components of voltage and current in the system were obtained as Figure 3 , and the change trends of user behavior, social intervention intensity, and incentive variables, as Figure 4 shown. The simulation results show that the control method proposed in the present invention can effectively achieve the rapid dynamic regulation of voltage and current in the microgrid, ensure that the system quickly recovers stability in the short term, and maintain the voltage near the nominal value of 170V. This performance highlights the strong dynamic response ability of the strategy in dealing with transient disturbances and load changes. In addition, user behavior gradually adapts at the lowest external intervention cost and finally converges to the steady-state value of the incentive variable, thus verifying the effectiveness of the strategy in optimizing the long-term behavior dynamics. By dynamically adjusting the 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 the strategy in future distributed energy management systems.

[0168] Scenario 2: Effectiveness of the control strategy under sudden changes in user behavior and incentives. To strictly evaluate the effectiveness of the proposed control strategy under complex conditions, a simulation scenario was designed. This scenario assumes that due to external influences, user behavior and incentive parameters suddenly change at a specific moment. Specifically, when t = 1s, the value of the behavior variable changes abruptly, and when t = 0.5s, the value of the motivation model parameter changes. This simulates the drastic fluctuations in user behavior and decision-making motivation caused by external intervention, economic incentives, or social pressure. The goal of this simulation scenario is to evaluate the adaptability and regulation ability of the control strategy in response to sudden changes in user behavior and incentives.

[0169] Through this simulation, the control strategy can be deeply analyzed on how to maintain the stability of the microgrid under rapidly changing user behavior patterns, and its dynamic responses to sudden changes in behavioral variables, especially in terms of load regulation, voltage, and current, can be evaluated. In addition, the simulation also verifies the effectiveness of the control strategy in optimizing user behavior in the long term and maintaining system balance, especially when external factors significantly affect user decisions. Such evaluations are of great significance for 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 Figure 5 , and the voltage V of each node x remains stable over time. Although at t = 1s, due to sudden changes in behavior and incentive parameters caused by external intervention, the control method of the present invention can still effectively regulate the voltage to ensure that the system quickly returns to a stable state. In addition, the slight fluctuations in the current I dx indicate that the control strategy has strong capabilities in load change management. The changing trends of the user behavior variable 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 method of the present invention in dealing with behavioral mutations, further confirming the effectiveness of the method of the present invention in maintaining the stability and load balance of the microgrid.

[0171] The above is only a specific implementation manner of the present invention. Any feature disclosed in this specification, unless specifically described, can be replaced by other equivalent or similar-purpose alternative features; all features disclosed, or all steps in any method or process, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A dual-time scale optimal control method for a human-microgrid system based on singular perturbation theory, characterized in that It includes the following steps: Step 1: Fully consider the electrical characteristics of the microgrid and the influence mechanism of human behavior on energy demand and load changes, model the classical microgrid system and human behavior respectively, and construct a human-microgrid two-time-scale model that combines the human behavior model and the microgrid model based on the complex dynamic interaction between microgrid operation and human behavior; The specific process of constructing the human-microgrid two-time-scale model is as follows: Construct the microgrid model: where 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 the filter capacitor and filter inductor respectively; the variable g represents the user load affected by user behavior, R f and R s represent the filter resistance and load resistance respectively; V is the load voltage, I t is the current produced by 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, β is the edge-node incidence matrix of the microgrid communication topology, ω r is the operating frequency of the system, and (g) represents the derivative; Construct the human behavior model: 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, w hed is the hedonic value, w bio is the biosphere value, and D and E are weight parameters; Then the human-microgrid two-time-scale model is specifically: Step 2: Apply the singular perturbation theory to perform dynamic separation of the fast time scale and the slow time scale for the two-time-scale model. The specific process is as follows: Integrate the human-microgrid two-time-scale model obtained in Step 1 to obtain the integrated system equation, where y is the 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 = [D E]; P represents the external factors of the system, P = [D + E]; B' y represents the influence of x on y, A yy 、A yz 、A zy and A zz are intermediate process matrices; Apply the singular perturbation theory to decouple the integrated system equation and decompose it into fast dynamic and slow dynamic subsystems. Among them, the slow dynamic subsystem is expressed as: Among them, the variable x s , y s , z s and u s represent 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 represent the fast dynamic components of x, y, and z; Step 3: For the separated slow time scale system, focus on optimizing user satisfaction and energy consumption balance under steady-state conditions to improve the long-term adaptability and stability of the system. At the same time, design a network layer optimization controller adapted to the slow time scale; For the separated fast time scale system, focus on the transient response characteristics of the system to ensure good anti-interference ability under external disturbances and achieve the rapid stability of the system. At the same time, design a network layer optimization controller adapted to the fast time scale; Step 4: Obtain the control input of the microgrid system based on the optimization controllers of the slow dynamic subsystem and the fast dynamic subsystem.

2. The dual-time-scale optimal control method for the human-microgrid system according to claim 1, wherein The physical basis of the microgrid model is: The AC microgrid is a low-voltage islanded AC microgrid, composed of N prosumers, and these prosumers are interconnected through E resistive-inductive transmission lines. The microgrid is balanced and symmetric, and the internal oscillators are synchronized.

3. The dual-time-scale optimal control method for the human-microgrid system according to claim 1, wherein The specific process of Step 3 is as follows: Design an optimization controller for the decoupled slow dynamic subsystem. The specific process is as follows: Construct 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, and θ ui represents the satisfaction coefficient of user i for meeting its load demand; the parameters ζ, κ, ρ, τ, φ, μ, and ν are adjustable constants, and ‖‖ 2 represents the square of the absolute value; Taking the conditions under the slow system steady state as the constraint conditions and combining with the slow system objective function to obtain the optimization problem of the slow dynamics For optimizing variables, () * Indicates an optimizing variable, and An optimizing variable for a status variable, An optimizing variable for a control variable; Based on the Karush-Kuhn-Tucker (KKT) conditions, the optimal solutions of all relevant variables in the optimization problem of the slow dynamics can be obtained, and thus the optimal controller for the slow-dynamics subsystem can be obtained. Design an optimization controller for the decoupled fast dynamic subsystem. The specific process is as follows: Construct a fast dynamic objective function Among them, the subscript f represents the fast component, θ′ ui reflects the influence of the user load on the behavior variable c if and θ′ ci represents the cost generated by adjusting the current variables I tdf and I tqf ; 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 conditions of the fast system as the constraint conditions and combining with the fast system objective function the optimization problem of the fast dynamics is obtained The explicit form of the Lagrangian function of 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) conditions, the optimal solutions of all relevant variables in the fast dynamic optimization problem can be obtained; To maintain the stability of the microgrid system, it is necessary to input the actual physical values into the following formula to obtain the fast dynamic subsystem optimization controller s f * : Matrices θ1, θ2, θ3, θ4.... ∈ R N×N are positive diagonal matrices, and γ1, γ2, γ3 are coupling parameters.

4. The human - microgrid system dual - time - scale optimal control method according to claim 3, characterized in that, In the fast dynamic optimization problem, each controller exchanges information with its adjacent nodes through a communication network consistent with the physical network topology.

5. The human - microgrid system dual - time - scale optimal control method according to claim 3, wherein Under the steady state of the slow system, the following conditions hold: 0 = Hw - Px s Among them Under the steady state of the fast system, the following conditions hold:

6. The dual-time-scale optimal control method for the human-microgrid system according to claim 3, characterized in that The coupling parameters γ1, γ2, γ3 are specifically: γ1 = I td , γ2 = I tq , γ3 = -2F T B T P T c, where the matrix P is determined by the Lyapunov equation B T P + PB + Q = 0, where P is a symmetric positive definite matrix to be solved and Q is a given symmetric positive definite matrix.

7. The dual-time-scale optimal control method for the human-microgrid system according to claim 1, characterized in that The specific process of Step 4 is as follows: Optimized controller for slow dynamic subsystem and optimized controller for fast dynamic subsystem s f * Obtain the control input of the microgrid system, specifically: s f = s f * ,

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