A direct current micro-grid voltage regulation method under time-frequency constraint

Abstract

The application belongs to the technical field of DC micro-grid control, and discloses a DC micro-grid voltage regulation method under time-frequency constraints, which comprises the following steps: step S1, collecting local node output voltage, inductance current and voltage tracking error integral, and establishing a three-dimensional small signal model containing source voltage / load disturbance and line impedance uncertainty; step S2, using generalized KYP lemma to convert low-frequency disturbance suppression index into limited frequency domain performance constraint, and combining with time domain Lyapunov steady-state constraint; step S3, solving completely dispersed linear matrix inequality group, directly obtaining local state feedback gain, and realizing plug-and-play control without communication. The DC micro-grid voltage regulation method under time-frequency constraints can not only significantly improve the rapid response and robustness of the system, but also effectively reduce the communication burden, and is suitable for high-reliability autonomous operation of aircraft and ground DC micro-grid.

Description

Technical Field

[0001] This invention relates to the field of DC microgrid control technology, and in particular to a DC microgrid voltage regulation method under time-frequency constraints. Background Technology

[0002] In modern energy systems, DC microgrids, as an efficient and flexible form of energy transmission and distribution, are widely used in industrial, residential, and transportation sectors. With the large-scale integration of distributed energy sources (such as photovoltaic cells, fuel cells, and energy storage units), the operational stability of DC microgrids increasingly depends on the precise regulation of the bus voltage. However, due to the intermittency of distributed energy sources, dynamic load changes, and the complexity of the system topology, the bus voltage is prone to fluctuations, thus affecting the overall system's operational efficiency and security.

[0003] Most existing voltage regulation methods for DC microgrids focus on either time-domain control or frequency-domain control. Time-domain control methods typically rely on Lyapunov stability theory, using state feedback controllers to achieve steady-state control of the system; while frequency-domain control methods focus on analyzing the system's frequency response characteristics and optimizing its dynamic performance.

[0004] However, these methods have certain limitations in practical applications. On the one hand, single time-domain or frequency-domain control is difficult to simultaneously satisfy the system's fast response and robustness; on the other hand, most existing methods require communication between nodes to coordinate control strategies, which can lead to communication delays and network congestion in large-scale microgrids, thereby reducing the overall efficiency of the system.

[0005] Furthermore, existing voltage regulation methods are poorly adaptable to changes in system topology and parameters, making it difficult to achieve true plug-and-play functionality. Dynamic connection or disconnection of distributed energy nodes typically requires readjustment of controller parameters, which not only increases system complexity but may also lead to decreased control performance or even system instability. Summary of the Invention

[0006] The purpose of this invention is to provide a DC microgrid voltage regulation method under time-frequency constraints, addressing the problem that existing voltage regulation methods struggle to simultaneously satisfy stability, speed, and robustness under time-frequency domain constraints. This method combines time-domain Lyapunov steady-state constraints and frequency-domain constraints to form a unified control design framework. Furthermore, by solving a fully distributed system of linear matrix inequalities, the local state feedback gain is directly obtained, thereby achieving plug-and-play control without communication requirements.

[0007] To achieve the above objectives, the present invention provides a method for regulating the voltage of a DC microgrid under time-frequency constraints, comprising the following steps: Step S1: Collect the local node output voltage, inductor current and voltage tracking error integral, and establish a three-dimensional small-signal model containing source voltage / load disturbance and line impedance uncertainty; Step S2: Use the generalized KYP lemma to transform the low-frequency disturbance suppression index into a finite frequency domain. Performance constraints are established and combined with time-domain Lyapunov steady-state constraints. Step S3: Solve the system of completely distributed linear matrix inequalities to directly obtain the local state feedback gain, and realize plug-and-play control without communication.

[0008] Preferably, in step S1, the output voltage of each distributed energy node in the DC microgrid is collected. Inductor current and voltage tracking error integral At the steady-state operating value of the common coupling point, the energy node average model is linearized to construct a measurable state vector. Establish a three-dimensional small-signal state-space model of current-voltage-error for each distributed energy node; Among them, based on the DC microgrid, and according to the circuit between the two nodes, the line current ,node inductor current Output voltage The average dynamic equation is shown below: ; in, For nodes The nominal inductance value; For nodes The inductor current; This is the nominal value of the source voltage; The duty cycle of the pulse width modulation signal; For nodes ; output voltage; For source voltage disturbance; For nodes The nominal value of the capacitor; For nodes The resistive load resistor; For nodes The constant power load power; This is the constant current load current; For nodes The set of connected adjacent nodes; For nodes ; output voltage; For nodes With neighboring nodes The line resistance between them.

[0009] Preferably, the inductor current, output voltage, duty cycle, resistive load resistance, constant power load power, and inter-node line resistance at the steady-state operating point are respectively... , , , , and The small-signal variables of the DC microgrid system are defined as follows: ; ; ; ; ; ; in, This represents a small signal from the inductor current. For output voltage small signal; For signals with small duty cycles; For resistive load resistors, small signal; For constant power loads, the power is a small signal. For line resistance small signal; Introducing voltage tracking error integral Its small-signal model is as follows: ; in, The voltage tracking error is integrated into a small signal; The reference voltage is a small signal; This is the steady-state reference voltage value.

[0010] Preferably, the line impedance variation Constant power load fluctuation Changes in the number of node connections The unified representation is a polyhedral parameter. The resulting three-dimensional small-signal model is shown below: ; in, For nodes The derivative of the three-dimensional state vector; For the system matrix; It is a three-dimensional state vector; To control the input matrix; To control the input signal; The perturbation input matrix; For disturbance input signals; This is the coupling matrix between nodes; For nodes The state vector; The controlled output vector; This is the controlled output matrix; the specific calculation methods for each parameter are as follows: ; ; ; ; ; ; ; ; ; ; in, For current disturbance; For nodes The output voltage small signal; For nodes The small signal of the inductor current; For nodes The voltage tracking error integral small signal; and These represent the values ​​when (1,1) in the system matrix are taken as its upper and lower bounds, respectively, and are calculated as follows: ; ; in, This represents the value of the coupling term when connected to the fewest nodes. This represents the value of the coupling term when connected to the most nodes.

[0011] Preferably, in step S2, a low-frequency disturbance range is defined for disturbances concentrated in the 0-50Hz low-frequency range in the DC microgrid. ,in Given the system frequency; the generalized KYP lemma is used to transform the low-frequency disturbance suppression requirement into a finite frequency domain. Performance constraints are imposed, and time-domain Lyapunov steady-state constraints are introduced to combine frequency-domain constraints with time-domain constraints, forming a unified control design framework.

[0012] Preferably, the specific implementation process of step S2 is as follows: Step S21, targeting the low-frequency range The frequency interval representation matrix is ​​selected as follows: ; in, Define the low-frequency range type; Define an upper bound for the frequency; Step S22: Define the disturbance input To the controlled output Closed-loop transfer function Satisfy finite frequency domain The constraints are as follows: ; in, It is the identity matrix; It is a symmetric matrix. ; To resist interference Performance metrics; For reference tracking Performance metrics; Step S23: Using the generalized KYP lemma, the frequency domain inequality is transformed into a time domain linear matrix inequality, i.e., there exists a matrix inequality. , The time-domain Lyapunov stability constraints are as follows: ; in, The feedback gain matrix to be designed; It is a symmetric matrix; It is a positive definite matrix; Step S24: Limited frequency domain Constraints and Time-Domain Lyapunov Stability Constraints By combining these equations, a unified constraint framework is formed. By introducing parameter-dependent Lyapunov matrices, the infinite-dimensional frequency domain constraints are transformed into finite-dimensional linear matrix inequalities, achieving computational feasibility. The parameter-dependent Lyapunov matrices... As shown below: ; in, For parameters Unrelated convex combination maximum matrix; For parameters Unrelated convex combination minimum matrix; This corresponds to the maximum value term of the convex combination; This is the minimum term of the corresponding convex combination.

[0013] Preferably, in step S3, a fully decentralized state feedback control law is designed. The gain matrix is ​​obtained offline by constructing a system of linear matrix inequalities that depend only on the node's local parameters. The data is written to the local control unit. When running online, the control unit only performs status acquisition and matrix multiplication operations, realizing plug-and-play control without communication between nodes. There is no need to readjust the controller parameters when a node switches in or out.

[0014] Preferably, the specific implementation process of step S3 is as follows: Step S31: Set parameters for the polyhedron and They respectively satisfy: ; ; in, yes The Lyapunov matrix at time; yes The Lyapunov matrix at time; Specifically, , A sufficiently large scalar to decouple the coupling between nodes; Therefore, for and They respectively satisfy: ; ; Step S32: Introduce the relaxation matrix By variable substitution Decoupling and The coupling relationship.

[0015] Therefore, the present invention employs the above-mentioned DC microgrid voltage regulation method under time-frequency constraints, and the beneficial effects are as follows: (1) This invention combines time-domain Lyapunov steady-state constraints with frequency-domain constraints to form a unified control design framework. This joint design can simultaneously meet the system's requirements for fast response and dynamic performance, ensuring that the bus voltage quickly recovers to stability under dynamic conditions. Compared with traditional single time-domain or frequency-domain control methods, the method of this invention can more effectively suppress voltage fluctuations and significantly improve the overall operating efficiency of the system.

[0016] (2) The control strategy of this invention is highly adaptable to changes in system topology and parameters, and can adapt to the dynamic access and disconnection of distributed energy nodes. By solving a system of completely decentralized linear matrix inequalities, the local state feedback gain is directly obtained without the need for global communication coordination, thereby enhancing the robustness of the system. Regardless of how the characteristics of distributed energy change, the system can maintain stable operation and is suitable for complex dynamic environments.

[0017] (3) This invention adopts a fully distributed control design, realizing plug-and-play functionality without communication. When adding a node, only the offline matrix inequality solution and online execution steps need to be repeated, without modifying the hardware or software of the original node. When a node is switched in or out, the system does not need to readjust the controller parameters and can still maintain stable operation. This modular design significantly reduces the complexity of the system, improves the scalability and flexibility of the system, and is suitable for the dynamic expansion needs of large-scale DC microgrids.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the multi-node DC microgrid structure of the present invention; Figure 2 This is a schematic diagram of a DC microgrid circuit with two nodes connected according to the present invention; Figure 3 This is a diagram showing the voltage regulation effect at each common coupling point under the desired voltage change according to the present invention. Figure 4 This is a diagram illustrating the voltage regulation effect at each common coupling point under load switching according to the present invention. Figure 5 This is a diagram illustrating the voltage regulation effect at each common coupling point under the energy node cut-in / cut-out conditions of this invention. Figure 6 This is a diagram showing the voltage adjustment effect at each common coupling point under source voltage changes in this invention. Figure 7 This is a flowchart of a DC microgrid voltage regulation method under time-frequency constraints according to the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] like Figure 7 As shown, the present invention provides a method for regulating the voltage of a DC microgrid under time-frequency constraints, comprising the following steps: Step S1: Collect the local node output voltage, inductor current and voltage tracking error integral, and establish a three-dimensional small-signal model containing source voltage / load disturbance and line impedance uncertainty; Step S2: Use the generalized KYP lemma to transform the low-frequency disturbance suppression index into a finite frequency domain. Performance constraints are established and combined with time-domain Lyapunov steady-state constraints. Step S3: Solve the system of completely distributed linear matrix inequalities to directly obtain the local state feedback gain, and realize plug-and-play control without communication.

[0022] Example 1 Step S1: Collect the node output voltage at each distributed energy node of the DC microgrid. Inductor current and voltage tracking error integral At the steady-state operating value of the common coupling point, the energy node average model is linearized to construct a measurable state vector. Establish a three-dimensional small-signal state-space model of current-voltage-error for each distributed energy node.

[0023] Step S11, for example Figure 1 The DC microgrid shown is based on Figure 2 The circuit diagram shown for the two nodes considers both the continuous conduction mode and the quasi-steady-state approximation of the line between the nodes, i.e., the line inductance. When the current is extremely small, its dynamics can be ignored; the line current... ,node inductor current Output voltage The average dynamic equation is shown below: ; in, For nodes The nominal inductance value; For nodes The inductor current; This is the nominal value of the source voltage; The duty cycle of the pulse width modulation signal; For nodes ; output voltage; For source voltage disturbance; For nodes The nominal value of the capacitor; For nodes The resistive load resistor; For nodes The constant power load power; This is the constant current load current; For nodes The set of connected adjacent nodes; For nodes ; output voltage; For nodes With neighboring nodes The line resistance between them.

[0024] Step S12: Let the inductor current, output voltage, duty cycle, resistive load resistance, constant power load power, and inter-node line resistance at the steady-state operating point be respectively... , , , , and As shown below: ; ; ; ; ; ; in, This represents a small signal from the inductor current. For output voltage small signal; For signals with small duty cycles; For resistive load resistors, small signal; For constant power loads, the power is a small signal. These are small-signal signals representing line resistance; these signals are Taylor expanded using the average model and higher-order terms are ignored.

[0025] Step S13: Introduce voltage tracking error integration Its small-signal model is as follows: ; in, The voltage tracking error is integrated into a small signal; The reference voltage is a small signal; This is the steady-state reference voltage value.

[0026] Step S14: Change the line impedance Constant power load fluctuation Changes in the number of node connections The unified representation is a polyhedral parameter. The resulting three-dimensional small-signal model is shown below: ; in, For nodes The derivative of the three-dimensional state vector; For the system matrix; It is a three-dimensional state vector; To control the input matrix; To control the input signal; The perturbation input matrix; For disturbance input signals; This is the coupling matrix between nodes; For nodes The state vector; The controlled output vector; This is the controlled output matrix. The specific calculation methods for each parameter are as follows: ; ; ; ; ; ; ; ; ; ; in, For current disturbance; For nodes The output voltage small signal; For nodes The small signal of the inductor current; For nodes The voltage tracking error integral small signal; and These represent the values ​​when (1,1) in the system matrix are taken as its upper and lower bounds, respectively, and are calculated as follows: ; ; in, This represents the value of the coupling term when connected to the fewest nodes. This represents the value of the coupling term when connected to the most nodes.

[0027] In the constructed three-dimensional small signal model To describe the polyhedral parameters of topology and load uncertainties, line impedance, constant power load variation, and node in / out are uniformly modeled as... The polyhedral uncertainty is addressed by obtaining a minimal conservative model containing only two vertices.

[0028] First, the node output voltage is obtained using a 12-bit ADC at a sampling rate of 100kHz. and inductor current Then, the trapezoidal integral rule is used for discretization calculation. ,in for The voltage tracking error at any given time is integrated with the small signal; for The voltage tracking error at any given time is integrated with the small signal; for The small reference voltage signal at that moment; for The small signal of the output voltage at any given moment; To control the cycle; finally, the three-dimensional states are uniformly scaled to the same dimension to avoid numerical ill-conditioning in subsequent linear matrix inequality solutions.

[0029] Step S2: Define the low-frequency disturbance range for disturbances (source voltage fluctuations, load switching) that are mainly concentrated in the 0-50Hz low-frequency range in the DC microgrid. ,in Given the system frequency; the generalized KYP lemma is used to transform the low-frequency disturbance suppression requirement into a finite frequency domain. Performance constraints are imposed, and time-domain Lyapunov steady-state constraints are introduced to combine frequency-domain constraints with time-domain constraints, forming a unified control design framework.

[0030] Step S21, targeting the low-frequency range The frequency interval representation matrix is ​​selected as follows: ; in, Define the low-frequency range type; Define an upper bound for the frequency.

[0031] Step S22: Define the disturbance input To the controlled output Closed-loop transfer function Satisfy finite frequency domain The constraints are as follows: ; in, It is the identity matrix; It is a symmetric matrix. ; To resist interference Performance metrics; For reference tracking Performance metrics.

[0032] Step S23: Using the generalized KYP lemma, the above frequency domain inequality is transformed into a time domain linear matrix inequality, i.e., there exists a matrix... , The time-domain Lyapunov stability constraints are as follows: ; in, The feedback gain matrix to be designed; It is a symmetric matrix; It is a positive definite matrix.

[0033] Step S24: Apply the above finite frequency domain Constraints and Time-Domain Lyapunov Stability Constraints (in A unified constraint framework is formed by simultaneously establishing the stability Lyapunov matrices. By introducing parameter-dependent Lyapunov matrices, the infinite-dimensional frequency domain constraints are transformed into finite-dimensional linear matrix inequalities, achieving computational feasibility. As shown below: ; in, For parameters Unrelated convex combination maximum matrix; For parameters Unrelated convex combination minimum matrix; This corresponds to the maximum value term of the convex combination; This is the minimum term of the corresponding convex combination.

[0034] Step S3: Design a fully distributed state feedback control law The gain matrix is ​​obtained offline by constructing a system of linear matrix inequalities that depend only on the node's local parameters. The data is written to the local control unit. When running online, the control unit only performs status acquisition and matrix multiplication operations, realizing plug-and-play control without communication between nodes. There is no need to readjust the controller parameters when a node switches in or out.

[0035] Step S31: Set parameters for the polyhedron and They respectively satisfy: ; ; in, yes The Lyapunov matrix at time; yes The Lyapunov matrix at that time.

[0036] Specifically, , It is a sufficiently large scalar used to decouple the coupling between nodes.

[0037] Therefore, for and They respectively satisfy: ; ; Step S32: Introduce the relaxation matrix By variable substitution Decoupling and The coupling relationship.

[0038] Obtain using an offline solver The solution is written to the local DSP; the solution process is completely offline, and only matrix multiplication is performed online, with a computational burden of less than 0.1ms / cycle.

[0039] When a node is switched in or out, the local controller parameters Without readjustment, the closed-loop system remains stable and meets the frequency domain performance indicators, achieving plug-and-play functionality.

[0040] The method can be extended to any The node system only requires repeating the offline matrix inequality solution and online execution steps on each new node, without modifying the original node hardware or software, achieving true modularity and plug-and-play functionality.

[0041] Example 2 This embodiment uses a DC microgrid as the research object and verifies it using a DC microgrid platform from a university. The platform consists of four energy nodes, each connected to a common coupling point via a Boost topology converter. Energy transfer and sharing between nodes are achieved through lines. The experimental platform can simulate different operating conditions, including source voltage fluctuations, load switching, node switching in and out, and topology changes, to verify the performance of the proposed distributed voltage regulation method.

[0042] Figure 3 The diagram shows the voltage regulation effect of each common coupling point under the desired voltage change of this invention. It demonstrates that when the reference voltage is adjusted, the output voltage of each node can quickly and accurately track the target value, and the system has good dynamic response and steady-state performance.

[0043] Figure 4 The diagram shows the voltage regulation effect at each common coupling point under load switching, demonstrating that the present invention can effectively suppress voltage fluctuations, maintain system stability, and ensure that the output voltage quickly recovers to stability within the allowable deviation range when the load changes abruptly.

[0044] Figure 5 The diagram shows the voltage regulation effect of each common coupling point under the switching in and out of energy nodes. It demonstrates that the present invention can maintain stable system operation without readjusting controller parameters when nodes change dynamically, achieving superior plug-and-play performance and strong adaptability to power changes caused by node switching in and out.

[0045] Figure 6 The diagram shows the effect of voltage regulation at each common coupling point under source voltage variation, demonstrating that the present invention has a good suppression effect on source voltage disturbance, and can ensure output voltage stability even under source voltage fluctuation.

[0046] Simulation results show that the maximum regulation time of the bus voltage is reduced by more than 40%, the overshoot is reduced by more than 50%, and it has strong robustness to topology and parameter changes, making it suitable for highly reliable autonomous operation of aircraft and ground-based DC microgrids.

[0047] Therefore, this invention adopts the above-mentioned DC microgrid voltage regulation method under time-frequency constraints. By combining time-domain Lyapunov steady-state constraints and frequency-domain constraints, a unified control design framework is formed. The local state feedback gain is directly obtained by solving a completely distributed set of linear matrix inequalities, thereby realizing plug-and-play control without communication.

[0048] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for voltage regulation of a DC microgrid under time-frequency constraints, characterized in that, Includes the following steps: Step S1: Collect the local node output voltage, inductor current and voltage tracking error integral, and establish a three-dimensional small-signal model containing source voltage / load disturbance and line impedance uncertainty; Step S2: Define the low-frequency disturbance range for disturbances concentrated in the 0-50Hz low-frequency range in the DC microgrid. ,in Given the system frequency; the low-frequency disturbance suppression index is transformed into a finite frequency domain index using the generalized KYP lemma. Performance constraints are combined with time-domain Lyapunov steady-state constraints to form a unified control design framework. The specific implementation process is as follows: Step S21, targeting the low-frequency range The frequency interval representation matrix is ​​selected as follows: ； in, Define the low-frequency range type; Define an upper bound for the frequency; Step S22: Define the disturbance input To the controlled output Closed-loop transfer function Satisfy finite frequency domain The constraints are as follows: ； in, It is the identity matrix; It is a symmetric matrix. ; To resist interference Performance metrics; For reference tracking Performance metrics; Step S23: Using the generalized KYP lemma, the frequency domain inequality is transformed into a time domain linear matrix inequality, i.e., there exists a matrix inequality. , The time-domain Lyapunov stability constraints are as follows: ； in, For the system matrix; To control the input matrix; The feedback gain matrix to be designed; The perturbation input matrix; For disturbance input signals; The controlled output matrix; It is a symmetric matrix; It is a positive definite matrix; Step S24: Limited frequency domain Constraints and Time-Domain Lyapunov Stability Constraints By combining these equations, a unified constraint framework is formed. By introducing parameter-dependent Lyapunov matrices, the infinite-dimensional frequency domain constraints are transformed into finite-dimensional linear matrix inequalities, achieving computational feasibility. The parameter-dependent Lyapunov matrices... As shown below: ； in, For parameters Unrelated convex combination maximum matrix; For parameters Unrelated convex combination minimum matrix; This corresponds to the maximum value term of the convex combination; This corresponds to the minimum term of the convex combination; The stability Lyapunov matrix; Polyhedral parameters to describe topological and load uncertainties; Step S3: Design the state feedback control law , To control the input signal, As a measurable state vector, the gain matrix is ​​obtained directly by constructing a system of linear matrix inequalities that depends only on the node's local parameters, solving the system of linear matrix inequalities offline. The data is then written to the local control unit. During online operation, the control unit only performs status acquisition and matrix multiplication operations, achieving plug-and-play control without inter-node communication. No readjustment of controller parameters is required when a node switches in or out. The specific implementation process is as follows: Step S31: Set parameters for the polyhedron and They respectively satisfy: ； ； in, and These represent the values ​​when (1,1) in the system matrix is ​​taken as its upper and lower bounds, respectively. yes The Lyapunov matrix at time; yes The Lyapunov matrix at time; Specifically, , A sufficiently large scalar to decouple the coupling between nodes; For nodes The nominal value of the capacitor; Therefore, for and They respectively satisfy: ； ； Step S32: Introduce the relaxation matrix By variable substitution Decoupling and The coupling relationship.

2. The method for regulating DC microgrid voltage under time-frequency constraints according to claim 1, characterized in that, In step S1, the output voltage of each distributed energy node in the DC microgrid is collected. Inductor current and voltage tracking error integral At the steady-state operating value of the common coupling point, the energy node average model is linearized to construct a measurable state vector. Establish a three-dimensional small-signal state-space model of current-voltage-error for each distributed energy node; Among them, based on the DC microgrid, and according to the circuit between the two nodes, the line current ,node inductor current Output voltage The average dynamic equation is shown below: ； in, For nodes The nominal inductance value; For nodes The inductor current; This is the nominal value of the source voltage; The duty cycle of the pulse width modulation signal; For nodes ; output voltage; For source voltage disturbance; For nodes The nominal value of the capacitor; For nodes The resistive load resistor; For nodes The constant power load power; This is the constant current load current; For nodes The set of connected adjacent nodes; For nodes ; output voltage; For nodes With neighboring nodes The line resistance between them.

3. The method for regulating DC microgrid voltage under time-frequency constraints according to claim 2, characterized in that, Let the inductor current, output voltage, duty cycle, resistive load resistance, constant power load power, and inter-node line resistance at the steady-state operating point be respectively... , , , , and The small-signal variables of the DC microgrid system are defined as follows: ； ； ； ； ； ； in, This represents a small signal from the inductor current. For output voltage small signal; For signals with small duty cycles; For resistive load resistors, small signal; For constant power loads, the power is a small signal. For line resistance small signal; Introducing voltage tracking error integral Its small-signal model is as follows: ； in, The voltage tracking error is integrated into a small signal; The reference voltage is a small signal; This is the steady-state reference voltage value.

4. The method for regulating DC microgrid voltage under time-frequency constraints according to claim 3, characterized in that, Changes in line impedance Constant power load fluctuation Changes in the number of node connections The unified representation is a polyhedral parameter. The resulting three-dimensional small-signal model is shown below: ； in, For nodes The derivative of the three-dimensional state vector; For the system matrix; It is a three-dimensional state vector; To control the input matrix; To control the input signal; The perturbation input matrix; For disturbance input signals; This is the coupling matrix between nodes; For nodes The state vector; The controlled output vector; This is the controlled output matrix; the specific calculation methods for each parameter are as follows: ； ； ； ； ； ； ； ； ； ； in, For current disturbance; For nodes The output voltage small signal; For nodes The small signal of the inductor current; For nodes The voltage tracking error integral small signal; and These represent the values ​​when (1,1) in the system matrix are taken as its upper and lower bounds, respectively, and are calculated as follows: ； ； in, This represents the value of the coupling term when connected to the fewest nodes. This represents the value of the coupling term when connected to the most nodes.

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