Predefined finite-time control method and system for islanded microgrid

Abstract

The application provides a predefined finite time control method and system for an island micro-grid, and the method comprises the following steps: establishing a large signal model of a distributed power generation unit (DG) based on an inverter; obtaining a second-order feedback system of a single distributed power generation unit (DG) through input-output feedback linearization; designing a disturbance observer for estimating nonlinear uncertain items of the feedback system; designing a distributed virtual controller based on predefined finite time; and constructing an overall Lyapunov function to verify that all signals are bounded in the distributed power generation units (DG) realized by all designed backstepping control strategies, and the synchronization error converges to a predefined finite time function within a predefined finite time. The application solves the technical problems that the inertia of the DG is small, the IMG is affected by uncertain and intermittent environmental changes, the transient performance index is poor, and the secondary voltage control effect of the IMG is restricted.

Description

Technical Field

[0001] This invention relates to the field of AC microgrid control, and more specifically to a predefined finite-time control method and system for islanded microgrids. Background Technology

[0002] AC microgrids are small power systems that integrate distributed generation units (DGs), energy storage devices, and loads, typically operating in grid-connected or islanded modes. Islanded AC microgrids (IMGs) require appropriate control strategies to maintain voltage and frequency stability and effectively manage power. In recent years, hierarchical control strategies have become the mainstream approach for regulating voltage, frequency, and power sharing. The goal of primary control is to maintain a balance between the IMG's output power and load demand. However, primary control can cause frequency and voltage deviations from reference values, thus secondary control is introduced to eliminate these deviations. There are three categories of secondary control: centralized control, decentralized control, and distributed control. Compared to centralized and decentralized control, distributed secondary control is implemented through sparse communication networks, where each DG's controller only exchanges information with its neighbors, thereby reducing communication dependencies and improving controller reliability. Therefore, distributed control is widely used in secondary control strategies.

[0003] To address the secondary control problem of IMG (Inverter-Based Microgrid) systems, some studies have proposed distributed cooperative secondary control to achieve system stability. For example, the existing invention patent application CN118630824A, entitled "A Secondary Voltage Control Method for Islanded Microgrids Based on Disturbance Observer," includes: establishing a large-signal state-space model of the secondary voltage control of an inverter-based islanded microgrid; linearizing its feedback to obtain the voltage control input under nonlinear disturbance conditions; designing a nonlinear disturbance observer and providing an estimate of the voltage control input; and calculating... t In the first time island microgrid i The deviation between the estimated values ​​of each distributed generation unit and the actual nonlinear disturbance is used to obtain the disturbance estimation error. This disturbance estimation error is then substituted into the large-signal model to construct a model for the case of nonlinear disturbances. t Time-isolated microgrids i The voltage control input of the first distributed generation unit; calculate the voltage control input of the first distributed generation unit. i The deviation of the distributed generation unit from the output voltage value received from its neighboring distributed generation units is obtained as follows: i Distributed generation units in t Voltage deviation at time t and its derivative; using the t... i The voltage deviation and its derivative of each distributed generation unit at time t are constructed. t Time-isolated microgridsi The sliding mode surface of the distributed generation unit is used; an auxiliary control input is calculated using a sliding mode surface based on the exponential reaching law to control the first distributed generation unit in the islanded microgrid. i The output voltage of each distributed generation unit follows a voltage reference value to ensure microgrid stability; the islanded microgrid at time t is constructed. i The Lyapunov function of a closed-loop system model of a distributed generation unit (IMG) is derived, and the system convergence is proven. However, convergence and stability are two important but distinct metrics. Therefore, convergence is also an important performance indicator for IMGs, and good convergence performance ensures that IMGs can achieve voltage following quickly and accurately. Recently, some finite-time control methods for IMGs have been proposed to achieve fast system convergence. For example, the existing invention patent application document CN113972687A, entitled "A Secondary Control Method for Islanded Microgrids Based on Switching Topology," includes the following steps: Step S1, using a mobile emergency generator as a distributed generator for islanded microgrid scheduling; Step S2, designing a fixed-time distributed secondary control method to compensate for frequency and voltage errors caused by primary control, thereby accurately distributing active power; Step S3, designing a distributed finite-time controller to adjust the voltage and frequency of all distributed generators to a fixed reference level. However, these control strategies need to meet the conditions of finite-time stability analysis. This requirement makes control design and implementation more difficult. On the other hand, in IMG, most loads, such as motors, need to operate at rated frequency and voltage, while DG has low inertia and is susceptible to environmental changes. Therefore, the system often needs to ensure good transient performance indicators.

[0004] To address the aforementioned issues, some existing solutions have investigated the adaptive quadratic control problem of IMG under predefined performance during DoS (Denial of Service) attacks. To achieve the predefined performance, constrained tracking error behavior is typically transformed into equivalent unconstrained tracking error behavior, which increases the complexity of stability proofs and controller design. Furthermore, if the parameters of the selected error transformation function are inappropriate, singular value problems can arise, leading to improper design of the distributed quadratic controller of the DG within the IMG, thereby causing instability of the entire IMG.

[0005] In summary, existing technologies suffer from technical problems such as the small inertia of the DG causing the IMG to be affected by uncertain and intermittent environmental changes, as well as poor transient performance indicators, which restrict the control effect of the IMG secondary voltage. Summary of the Invention

[0006] The technical problem to be solved by this invention is: how to solve the problem in the prior art that the small inertia of the DG causes the IMG to be affected by uncertain and intermittent environmental changes, and the poor transient performance index restricts the control effect of the IMG secondary voltage.

[0007] This invention solves the above-mentioned technical problems by employing the following technical solution: a predefined finite-time control method for islanded microgrids, comprising:

[0008] S1. Establish the first inverter-based... k Large-signal model of a distributed generation unit (DG);

[0009] S2, the first in the IMG of the islanded AC microgrid k The large-signal model of a distributed generation unit (DG) is used to perform input-output feedback linearization to obtain the relationship between voltage control input and voltage control output. Through input-output feedback linearization, the second-order feedback system of a single distributed generation unit (DG) is obtained.

[0010] S3. Design and use a perturbation observer (DO) to estimate the current nonlinear uncertainty.

[0011] S4. Select the Lyapunov function and applicable parameters, and set the disturbance observer for the current nonlinear uncertainty term for the second-order feedback system.

[0012] S5. Find the first... in the IMG of the isolated AC microgrid. k The synchronization error between the state variables of the linearized system of a distributed generation unit (DG) and the state variables of the system received from the neighboring distributed generation unit (DG).

[0013] S6. Set a predefined finite-time function, wherein if the smooth function satisfies the preset conditions, the smooth function is used as the predefined finite-time function;

[0014] S7. Based on a predefined finite-time function, and using Lyapunov theory and a backstepping control strategy, design a distributed virtual controller.

[0015] S8. Construct the overall Lyapunov function to verify whether all signals in the distributed generation unit (DG) implemented by the backstepping control strategy are bounded, and verify whether the synchronization error is within a predefined finite time and whether it converges to the function within a predefined finite time.

[0016] This invention provides secondary control of an islanded AC microgrid (IMG) based on a predefined finite-time function. The aim is to constrain the synchronization error between distributed generation units (DGs) within a predefined finite-time function when the IMG is in islanded operation mode. This reduces the impact of uncertainties and intermittent environmental changes on the IMG due to the small inertia of the DGs, achieving finite-time convergence of the synchronization error between DGs. This ensures rapid system stability of the islanded AC microgrid IMG and also guarantees good transient performance indicators, ultimately improving the effectiveness of the IMG's secondary voltage control and achieving consistent control of the IMG.

[0017] In a more specific technical solution, in S1, during the secondary voltage control process of the islanded AC microgrid IMG, the following logic is used to establish the inverter-based first... k Large-signal model of a distributed generation unit (DG):

[0018] (1)

[0019] In equation (1), k Indicates the serial number of the distributed generation unit (DG). t Indicates time;

[0020]

[0021] for t The isolated microgrid of moments in IMG k The state vector of a distributed generation unit (DG). for t The isolated microgrid of moments in IMG k The derivative of the state vector of a distributed generation unit (DG). , , They represent t The isolated microgrid of moments in IMG k The three state matrices of the large-signal model of a distributed generation unit (DG) include: , and Different linear and nonlinear relationships, express t The isolated microgrid of moments in IMG k Voltage control input of each distributed generation unit (DG) express t The isolated microgrid of moments in IMG k Nonlinear disturbances experienced by each distributed generation unit (DG) expresst The isolated microgrid of moments in IMG k Voltage control output of each distributed generation unit (DG) for t In the IMG section of the time-isolated microgrid, the first... k Output voltage of each distributed generation unit (DG); d and q They represent d - q In transformation d shaft and q axis, l Representative line Lind, o Represents the output. express t In the IMG section of the time-isolated microgrid, the first... k The angle of the reference coordinate system of each distributed generation unit (DG) relative to the common reference coordinate system. express t In the IMG section of the time-isolated microgrid, the first... k The active power of each distributed generation unit (DG) express t In the IMG section of the time-isolated microgrid, the first... k The reactive power of each distributed generation unit (DG) express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The deviation component of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The deviation component of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The deviation component of the shaft's output current. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The deviation component of the shaft's output current. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d Shaft line current components, express t In the IMG section of the time-isolated microgrid, the first... kDistributed generation unit (DG) q Shaft line current components, express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The components of the shaft's output voltage. This represents the common angular velocity of the isolated AC microgrid IMG. , They represent t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d, q Shaft bus voltage component.

[0022] In a more specific technical solution, in S2, the voltage control input is expressed using the following logic. Voltage control output The relationship between them:

[0023] (2)

[0024] In equation (2),

[0025] , for The second derivative, express Along Lie derivative in the direction,

[0026] And it satisfies:

[0027] , express Along The Lie derivative in the direction, and This indicates the first [unit / item] in the isolated AC microgrid IMG. kNonlinear uncertainties in a distributed generation unit (DG); express:

[0028] Along The Lie derivative in the direction, and

[0029] This indicates the first [unit / item] in the isolated AC microgrid IMG. k Linear deterministic terms in a distributed generation unit (DG).

[0030] This invention considers the presence of parameter disturbances, unmodeled dynamics, and various uncertainties in the system of each distributed generation unit (DG) in an islanded AC microgrid (IMG) after modeling. It designs a corresponding disturbance observer to accurately estimate the nonlinear uncertainties contained in the system of each DG.

[0031] In a more specific technical solution, in S3, a nonlinear uncertainty term is defined. satisfy: ,in For preset unknown constants;

[0032] Design a perturbation observer (DO) using the following logic to estimate the current nonlinear uncertainty. :

[0033] (4)

[0034] In equation (4), express t In the IMG section of the time-isolated microgrid, the first... k The expression for a second-order feedback system by a distributed generation unit (DG) is given by equation (3). The estimated value, for t In the IMG section of the time-isolated microgrid, the first... k The expression for a second-order feedback system by a distributed generation unit (DG) is given by equation (3). The estimated value;

[0035] express The estimation error, and there is , These are the design parameters for the disturbance observer DO.

[0036] In a more specific technical solution, in S4, according to equation (4) of the nonlinear uncertainty term, t In the IMG of isolated microgrids at any given moment, the first... k Estimated value of DG per distributed generation unit and tIn the IMG section of the time-isolated microgrid, the first... k The actual nonlinear uncertainty of a distributed generation unit (DG) deviation Choose the Lyapunov function:

[0037] Based on the second-order feedback system, equation (4), and deviation and the Lyapunov function, regarding the Lyapunov function with respect to time t By taking the derivative and processing the results, we obtain the boundedness criterion inequality, and thus deduce the Lyapunov function. Bounded, Bounded:

[0038] ;

[0039] Select applicable parameters By using a perturbation observer, the nonlinear uncertainty term is adjusted. Estimation accuracy.

[0040] In a more specific technical solution, in S5, the synchronization error is represented by the following logic;

[0041] (9)

[0042] In equation (9), l Indicating an isolated AC microgrid in IMG and the first k The serial number of the distributed generation unit (DG) that communicates with the distributed generation unit (DG). For communication networks and the first k A collection of distributed generation units (DGs) that communicate with each other. For the first k The distributed generation unit DG and the first l Communication connectivity of each distributed generation unit (DG); This is the reference voltage value for the isolated AC microgrid IMG. The first in the IMG of isolated AC microgrids k Distributed generation unit (DG) and voltage reference value Communication connectivity; It is the output of the command filter, and its derivative satisfies ,in As a preset constant, express time and The value, , They represent , Synchronization error, Indicates the firstk The virtual controller required for designing a distributed generation unit (DG) Indicates the first k Among the neighbors of the distributed generation unit (DG), the first... l The output voltage value of a distributed generation unit (DG).

[0043] In a more specific technical solution, in S6, a predefined finite-time function is selected according to the following logic:

[0044] (10)

[0045] In equation (10), , Indicated by e The base of the natural logarithm;

[0046] Indicates the first k The stabilization time of a DG Indicates time t With the k The deviation between the settling times of each DG Indicates the first k A predefined finite-time function of a DG, , These are represented as the initial and final values ​​of a predefined finite-time function.

[0047] This invention relates to predefined finite-time secondary voltage control of isolated microgrids (IMGs). It is a system design for independently operating isolated AC microgrids (IMGs) using a predefined finite-time controller. This reduces the impact of uncertainties and intermittent environmental changes on the IMG caused by the low inertia of distributed generation units (DGs), achieving the goal of predefined-time convergence of local synchronization errors. Furthermore, it ensures that the synchronization error is constrained within a predefined finite-time function, thereby guaranteeing rapid system stability and consistent IMG control. Compared to traditional distributed controllers, this method ensures better transient performance indicators and ultimately improves the effectiveness of IMG secondary voltage control, demonstrating significant engineering application value.

[0048] In a more specific technical solution, within S7, the following logic is used to construct the barrier Lyapunov function. ;

[0049] Based on the second-order feedback system and equation (9), the barrier Lyapunov function... Regarding time t Taking the derivative, we get:

[0050] (12)

[0051] In equation (12), , ;

[0052] express The derivative, Indicates inclusion The expression, express The derivative of the synchronization error, express The derivative, express The derivative, express The derivative, express The second derivative;

[0053] Introducing a distributed virtual controller Scaling equation (12) to:

[0054] (13)

[0055] In equation (13), The control parameters that need to be designed for the distributed virtual controller, and satisfy:

[0056] .

[0057] The distributed backstepping control strategy based on predefined finite time adopted in this invention restores the voltage amplitude of all distributed generation units (DGs) to the voltage reference value, while ensuring that the islanded AC microgrid (IMG) system achieves predefined finite time stability and that the islanded AC microgrid (IMG) system has good transient performance indicators.

[0058] In more specific technical solutions, for the islanded AC microgrid IMG... k Each distributed generation unit (DG) constructs a distributed virtual controller. Substituting the distributed virtual controller into equation (13), we obtain inequality (15):

[0059] (15)

[0060] Choosing Lyapunov functions :

[0061] (16)

[0062] Combining the second-order feedback system and equation (16), the Lyapunov function is... Regarding timet Differentiating, we get equation (17):

[0063] (17)

[0064] In equation (17), This represents the control parameters of the virtual controller. express The derivative, Indicates the output of the command filter The derivative, Lyapunov function representing the barrier The derivative;

[0065] By combining inequalities (15) and (17) and simplifying, we get:

[0066] (18)

[0067] Using the following logic, t The island of communication microgrids in a moment IMG k The actual controller of a distributed generation unit (DG) Designed as follows:

[0068] (19)

[0069] In equation (19), This represents the control parameters of the actual controller. Indicating an isolated AC microgrid, IMG's first... k The actual controller of a distributed generation unit (DG) The control parameters, and satisfy ;

[0070] Substituting equation (19) into inequality (18), we obtain the following inequality (20):

[0071] (20)

[0072] This represents the control constant of the actual controller. This represents the control constant of the virtual controller.

[0073] In more specific technical solutions, the islanded microgrid secondary control system based on a predefined finite time includes:

[0074] The large-signal model building module is used to establish the first inverter-based model. k A large signal model of DG;

[0075] The feedback linearization module is used to linearize the first line in the IMG. kA large-signal model of a DG is used to perform input-output feedback linearization to obtain the voltage control input. Voltage control output The relationship between them is obtained through feedback linearization, resulting in a second-order feedback system for a single DG. The feedback linearization module is connected to the large-signal model construction module.

[0076] The uncertainty estimation module is used to design the perturbation observer (DO) and estimate the current nonlinear uncertainty. The uncertainty estimation module is connected to the feedback linearization module;

[0077] The perturbation observer design module is used to select the Lyapunov function and applicable parameters. For a second-order feedback system, design the current nonlinear uncertainty term. The perturbation observer is designed and connected to the uncertainty estimation module.

[0078] The synchronization error calculation module is used to calculate the synchronization error in the IMG. k The synchronization error between the state variables of the linearized DG system and the state variables of the received neighboring DG system is calculated by the synchronization error calculation module, which is connected to the disturbance observer design module.

[0079] The finite-time function setting module is used to set predefined finite-time functions, including smooth functions. Satisfying the preset conditions, the smooth function As a predefined finite-time function;

[0080] The controller design module is used to design a controller based on a predefined finite-time function, employing Lyapunov theory and a backstepping control strategy. The controller design module is connected to the finite-time function setting module.

[0081] The signal boundedness and convergence verification module is used to construct the overall Lyapunov function, verify that all signals in the DG implemented by the backstepping control strategy are bounded, and verify that the synchronization error converges to a predefined finite-time function within a finite time. The signal boundedness and convergence verification module is connected to the controller design module.

[0082] The present invention has the following advantages over the prior art:

[0083] This invention provides secondary control of an islanded AC microgrid (IMG) based on a predefined finite-time function. The aim is to constrain the synchronization error between distributed generation units (DGs) within a predefined finite-time function when the IMG is in islanded operation mode. This reduces the impact of uncertainties and intermittent environmental changes on the IMG due to the small inertia of the DGs, achieving finite-time convergence of the synchronization error between DGs. This ensures rapid system stability of the islanded AC microgrid IMG and also guarantees good transient performance indicators, ultimately improving the effectiveness of the IMG's secondary voltage control and achieving consistent control of the IMG.

[0084] This invention considers the presence of parameter disturbances, unmodeled dynamics, and various uncertainties in the system of each distributed generation unit (DG) in an islanded AC microgrid (IMG) after modeling. It designs a corresponding disturbance observer to accurately estimate the nonlinear uncertainties contained in the system of each DG.

[0085] This invention relates to predefined finite-time secondary voltage control of isolated microgrids (IMGs). It is a system design for independently operating isolated AC microgrids (IMGs) using a predefined finite-time controller. This reduces the impact of uncertainties and intermittent environmental changes on the IMG caused by the low inertia of distributed generation units (DGs), achieving the goal of predefined-time convergence of local synchronization errors. Furthermore, it ensures that the synchronization error is constrained within a predefined finite-time function, thereby guaranteeing rapid system stability and consistent IMG control. Compared to traditional distributed controllers, this method ensures better transient performance indicators and ultimately improves the effectiveness of IMG secondary voltage control, demonstrating significant engineering application value.

[0086] The distributed backstepping control strategy based on predefined finite time adopted in this invention restores the voltage amplitude of all distributed generation units (DGs) to the voltage reference value, while ensuring that the islanded AC microgrid (IMG) system achieves predefined finite time stability and that the islanded AC microgrid (IMG) system has good transient performance indicators.

[0087] This invention solves the technical problems in the prior art where the small inertia of the DG leads to the IMG being affected by uncertain and intermittent environmental changes, and the poor transient performance indicators restrict the control effect of the IMG secondary voltage. Attached Figure Description

[0088] Figure 1 This is a schematic diagram of the basic steps of the predefined finite-time control method for islanded microgrids of the present invention;

[0089] Figure 2 This is a block diagram of an inverter-based distributed generation unit according to Embodiment 1 of the present invention;

[0090] Figure 3 This is a communication topology diagram between distributed generation units in an islanded microgrid according to Embodiment 1 of the present invention. Detailed Implementation

[0091] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] Example 1

[0093] like Figure 1 As shown, the predefined finite-time control method for islanded microgrids provided by this invention includes the following basic steps:

[0094] S1. Establish the first inverter-based... k Large-signal model of a distributed generation unit (DG);

[0095] like Figure 2 As shown, in this embodiment, during the secondary voltage control process of the islanded AC microgrid IMG, the following logic is used to establish the inverter-based first... k Large-signal model of a distributed generation unit (DG):

[0096] (1)

[0097] In equation (1), k Indicates the serial number of the distributed generation unit (DG). t Indicates time;

[0098]

[0099] for t In the IMG section of the time-isolated microgrid, the first... k The state vector of a distributed generation unit (DG). for t In the IMG section of the time-isolated microgrid, the first... k The derivative of the state vector of a distributed generation unit (DG). , , They represent t In the IMG section of the time-isolated microgrid, the first... kThe three state matrices of a distributed generation unit (DG) large-signal model include, but are not limited to: , and Different linear or nonlinear relationships, express t In the IMG section of the time-isolated microgrid, the first... k Voltage control input of each distributed generation unit (DG)

[0100] express t In the IMG section of the time-isolated microgrid, the first... k Nonlinear disturbances experienced by each distributed generation unit (DG) express t In the IMG section of the time-isolated microgrid, the first... k Voltage control output of each distributed generation unit (DG) for t In the IMG section of the time-isolated microgrid, the first... k The output voltage of each distributed generation unit (DG) d and q They represent d - q In transformation d shaft and q axis, l Representative line Lind, o Represents the output. express t In the IMG section of the time-isolated microgrid, the first... k The angle of the reference coordinate system of each distributed generation unit (DG) relative to the common reference coordinate system. express t In the IMG section of the time-isolated microgrid, the first... k The active power of each distributed generation unit (DG) express t In the IMG section of the time-isolated microgrid, the first... k The reactive power of each distributed generation unit (DG) express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The deviation component of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The deviation component of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... kDistributed generation unit (DG) d The deviation component of the shaft's output current. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The deviation component of the shaft's output current. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d Shaft line current components, express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q Shaft line current components, express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The components of the shaft's output voltage. This represents the common angular velocity of the isolated AC microgrid IMG. , They represent t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d, q Shaft bus voltage component.

[0101] S2, the first in the IMG of the islanded AC microgrid k The large-signal model of a distributed generation unit (DG) is used to perform input-output feedback linearization to obtain the relationship between voltage control input and voltage control output. Through input-output feedback linearization, the second-order feedback system of a single distributed generation unit (DG) is obtained. Specifically, the relationship between voltage control input and voltage control output is expressed by the following equation (2):

[0102] (2)

[0103] In equation (2),

[0104] , for The second derivative, express Along Lie derivative in the direction,

[0105] And it satisfies:

[0106] , express Along The Lie derivative in the direction, and This indicates the first [unit / item] in the isolated AC microgrid IMG. k Nonlinear uncertainties in a distributed generation unit (DG) system; express:

[0107] Along The Lie derivative in the direction, and

[0108] It represents the first in the islanded AC microgrid IMG. k The linear determination term in each distributed generation unit (DG). In this embodiment, the linear determination term in each distributed generation unit (DG) is... and Abbreviated as and In the following expression, time will be omitted unless it causes ambiguity. t .

[0109] S3. Design and use a perturbation observer (DO) to estimate the current nonlinear uncertainty. ;

[0110] In this embodiment, after input-output feedback linearization in S2, a second-order feedback system for a single distributed generation unit (DG) is obtained. A disturbance observer (DO) is designed to estimate the nonlinear uncertainty. ;

[0111] Equation (2) is transformed into a second-order feedback system, as shown in equation (3):

[0112] (3)

[0113] In equation (3), Indicates control output. and These represent nonlinear uncertain terms and linear deterministic terms, respectively. and All indicate The first derivative, express The second derivative, Right now , Right now ;

[0114] In this embodiment, since equation (3) contains a nonlinear uncertainty term... This can be viewed as a nonlinear perturbation term, and it is assumed that it satisfies... ,in It is an unknown constant. Design a perturbation observer (DO) to estimate this nonlinear uncertainty. See equation (4):

[0115] (4)

[0116] In equation (4), express t In the IMG section of the time-isolated microgrid, the first... k The expression for a second-order feedback system by a distributed generation unit (DG) is given by equation (3). The estimated value, for t Moment in IMG k In equation (3) representing a second-order feedback system, the DG represents the system. The estimated value, express The estimation error, and there is , These are the design parameters for DO.

[0117] S4. Select the Lyapunov function and applicable parameters. r DO For a second-order feedback system, set the disturbance observer for the current nonlinear uncertainty term;

[0118] In this embodiment, according to equation (4) of the nonlinear uncertainty term t In the IMG section of the time-isolated microgrid, the first... k Estimated value of DG per distributed generation unit With equation (3) t In the IMG section of the time-isolated microgrid, the first... k The actual nonlinear uncertainty of a distributed generation unit (DG) deviation :

[0119] (5)

[0120] express t Moment in IMG k Estimated value of DG per distributed generation unit With equation (3) t Moment in IMG k The actual nonlinear uncertainty term of DG deviation, Right now , Represents nonlinear uncertainty terms The first derivative;

[0121] Therefore, according to formula (5), the Lyapunov function is selected. for:

[0122] (6)

[0123] express t Time of the first k Among the DG The square of .

[0124] Therefore, according to equations (3) to (6), for the Lyapunov function Regarding time t Taking the derivative, it is expressed as

[0125] (7)

[0126] express t Time of the first k In each distributed generation unit (DG) The derivative, express t Time of the first k In each distributed generation unit (DG) The derivative, express t Time of the first k In each distributed generation unit (DG) The derivative of .

[0127] From (7), we obtain the boundedness criterion inequality (8):

[0128] (8)

[0129] Deducing Lyapunov functions Bounded, Bounded, that is If you select the applicable parameters The nonlinear uncertainty term can be guaranteed by equation (4) of the designed perturbation observer. Estimation accuracy.

[0130] S5. Find the first... in the IMG of the isolated AC microgrid. k The synchronization error between the state variables of the linearized system of a distributed generation unit (DG) and the state variables of the system received from the neighboring distributed generation unit (DG).

[0131] In this embodiment, the first element in the islanded AC microgrid IMG is expressed as... k After linearization, the state variables of the second-order feedback system represented by equation (3) are the synchronization error between the received state variables of the neighboring distributed generation units (DG) system.

[0132] like Figure 3 The diagram shows the connectivity of the communication network. Equation (9) is used to represent the synchronization error between the state variables of the second-order feedback system (Equation (3)) after the linearization of the k-th DG in the IMG and the received state variables of the neighboring DG system.

[0133] (9)

[0134] In equation (9), l Indicates that in IMG and the first k The sequence number of the DG used for communication. For communication networks and the first k A set of DGs that communicate with each other. M , For the first k The DG and the first l The communication connectivity of a DG, when w kl When =1, it means that the first element in the IMG is... k The DG can be with the first l Each DG communicates when , indicating the first in IMG k The DG cannot be with the first l Each DG communicates; This is the reference voltage value for the IMG. Indicates the first in IMG k DG and voltage reference value The communication connectivity, when At that time, it indicates the first in IMG k Each DG can obtain a reference voltage value. ,when , indicating the first in IMG k The DG cannot obtain a reference voltage value. ; It is the output of the command filter, and its derivative satisfies ,in It is a sufficiently large constant. express time and The value, , They represent , Synchronization error, Indicates the first k The virtual controller required for designing a distributed generation unit (DG) Indicates the first k Among the neighbors of the distributed generation unit (DG), the first... l The output voltage value of a distributed generation unit (DG).

[0135] S6. Set a predefined finite-time function, wherein if the smooth function satisfies the preset conditions, the smooth function is used as the predefined finite-time function;

[0136] In this embodiment, for the design of subsequent control algorithms, the concept of a predefined finite-time function is given below:

[0137] Specifically, if the smooth function A function that satisfies the following preconditions is called a predefined finite-time function:

[0138] 1) ;

[0139] 2) ;

[0140] 3) ;

[0141] 4) For all .in Represents any small constant. Settlement time.

[0142] in, Represented as a smooth function The derivative, This represents the smooth function value corresponding to the settling time;

[0143] Based on the above concepts, a predefined finite-time function can be selected as follows:

[0144] (10)

[0145] In equation (10), , and The initial and final values ​​of a predefined finite-time function are defined. Furthermore, Indicated by eThe base of the natural logarithm is approximately equal to the base of an exponential function with a base of 2.71828.

[0146] Indicates the first k The stabilization time of a DG Indicates time t With the k The deviation between the settling times of each DG Indicates the first k A predefined finite-time function of a DG.

[0147] S7. Based on a predefined finite-time function, and using Lyapunov theory and a backstepping control strategy, design a distributed virtual controller.

[0148] In this embodiment, the controller is designed using Lyapunov theory and a backstepping control strategy, constructing a barrier Lyapunov function. As shown in equation (11):

[0149] (11)

[0150] In equation (11), and it satisfies .also, It is the natural logarithm.

[0151] Based on equations (3) and (9), the barrier Lyapunov function Differentiate with respect to time t Taking the derivative, we get

[0152] (12)

[0153] In equation (12), , .

[0154] express The derivative, Indicates inclusion The expression, express The derivative of the synchronization error, express The derivative, express The derivative, express The derivative, express The second derivative;

[0155] Furthermore, a distributed virtual controller is introduced. Equation (12) can be scaled down to:

[0156] (13)

[0157] In equation (13), The control parameters that need to be designed for the virtual controller, and which satisfy... Therefore, for the isolated AC microgrid IMG, the first... k Each distributed generation unit (DG) constructs a distributed virtual controller. :

[0158] (14)

[0159] In equation (14), For virtual controllers The control parameters, Control parameters for both virtual controllers.

[0160] Furthermore, substituting equation (14) representing the distributed virtual controller into equation (13) yields:

[0161] (15)

[0162] In this embodiment, the Lyapunov function is selected. As shown in equation (16):

[0163] (16)

[0164] Combining equations (3) and (16), for Regarding time t Taking the derivative, we get:

[0165] (17)

[0166] This represents the control parameters of the virtual controller. express The derivative, Indicates the output of the command filter The derivative, Lyapunov function representing the barrier The derivative;

[0167] Therefore, combining the aforementioned inequality (15), equation (17) can be further simplified:

[0168] (18)

[0169] So, t Moment IMG k The actual controller of a DG Designed as follows:

[0170] (19)

[0171] In equation (19), This represents the control parameters of the actual controller. Indicating an isolated AC microgrid, IMG's first... k The actual controller of a distributed generation unit (DG) The control parameters, This also indicates that IMG's... k The actual controller of a DG The control parameters, and satisfy Furthermore, substituting equation (19) into inequality (18), we have:

[0172] (20)

[0173] This represents the control constant of the actual controller. These are the control constants of the virtual controller;

[0174] S8. Construct the overall Lyapunov function to verify whether all signals in the distributed generation unit (DG) implemented by the backstepping control strategy are bounded, and verify whether the synchronization error is within a predefined finite time and whether it converges to a function within a predefined finite time.

[0175] In this embodiment, based on the steps discussed above, the following demonstrates... t All signals of a second-order feedback system with any DG closed loop in IMG at time IMG are bounded, and it is also proven that... t Synchronization error of any DG in the IMG at time step and It asymptotically converges to zero, and t Synchronization error of any DG in the IMG at time step It remains within a predefined finite-time function.

[0176] In this embodiment, to prove t All signals in a second-order feedback system of any DG closed loop at time IMG are bounded. (Definition) t The global Lyapunov function of the time-matter IMG as follows:

[0177] (twenty one)

[0178] In equation (21), M Let represent the set of all DGs in IMG. Combining inequality (20), for Regarding time t Taking the derivative, we get:

[0179] (twenty two)

[0180] Furthermore, regarding inequality (22) with respect to time... t Integrating, we get:

[0181] (twenty three)

[0182] In equation (23), The initial time applied to the IMG secondary control strategy.

[0183] It is a constant.

[0184] Represents the integral variable. This represents the control parameters of the virtual controller;

[0185] Therefore, for the first in IMG k For each DG, the following inequality holds:

[0186] Therefore, we can obtain:

[0187]

[0188] That is, for t Moment in IMG k Synchronization error of each DG It remains within the predefined constraints. Furthermore, it is clear that... t Moment in IMG k Equation (14) representing the distributed virtual controller of each DG is bounded, which means that It is also bounded. This can be verified according to equation (19). t Moment in IMG k The actual control input of each DG It is bounded. Therefore, t It is proved that all signals of a second-order feedback system with any DG closed loop in IMG at time IMG remain bounded.

[0189] In this embodiment, to prove t Synchronization error of any DG in the IMG at time step and It asymptotically converges to zero, and t Synchronization error of any DG in the IMG at time step It remains within a predefined finite-time function. According to equation (23), we can obtain...

[0190] (twenty four)

[0191] Furthermore, we can obtain:

[0192] (25)

[0193] (26)

[0194] Therefore, the following equation holds.

[0195] (27)

[0196] Right now, t Moment in IMG k Synchronization error of each DG and It asymptotically converges to zero, and t Synchronization error of any DG in the IMG at time step By keeping it within a predefined finite-time function, the proof is complete.

[0197] In summary, this invention utilizes predefined finite-time secondary control of an islanded AC microgrid IMG to constrain the synchronization error between distributed generation units (DGs) within a designed predefined finite-time function when the IMG is in islanded operation mode. This reduces the impact of uncertainties and intermittent environmental changes on the islanded AC microgrid IMG caused by the small inertia of the DGs, achieving the goal of finite-time convergence of the synchronization error between DGs. This ensures the rapid stabilization of the islanded AC microgrid IMG system and also guarantees good transient performance indicators, ultimately improving the effectiveness of the IMG's secondary voltage control and achieving consistent control of the IMG.

[0198] This invention considers the presence of parameter disturbances, unmodeled dynamics, and various uncertainties in the system of each distributed generation unit (DG) in an islanded AC microgrid (IMG) after modeling. It designs a corresponding disturbance observer to accurately estimate the nonlinear uncertainties contained in the system of each DG.

[0199] This invention relates to predefined finite-time secondary voltage control of isolated microgrids (IMGs). It is a system design for independently operating isolated AC microgrids (IMGs) using a predefined finite-time controller. This reduces the impact of uncertainties and intermittent environmental changes on the IMG caused by the low inertia of distributed generation units (DGs), achieving the goal of predefined-time convergence of local synchronization errors. Furthermore, it ensures that the synchronization error is constrained within a predefined finite-time function, thereby guaranteeing rapid system stability and consistent IMG control. Compared to traditional distributed controllers, this method ensures better transient performance indicators and ultimately improves the effectiveness of IMG secondary voltage control, demonstrating significant engineering application value.

[0200] The distributed backstepping control strategy based on predefined finite time adopted in this invention restores the voltage amplitude of all distributed generation units (DGs) to the voltage reference value, while ensuring that the islanded AC microgrid (IMG) system achieves predefined finite time stability and that the islanded AC microgrid (IMG) system has good transient performance indicators.

[0201] This invention solves the technical problems in the prior art where the small inertia of the DG leads to the IMG being affected by uncertain and intermittent environmental changes, and the poor transient performance indicators restrict the control effect of the IMG secondary voltage.

[0202] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A pre-defined finite-time control method for islanded microgrid, characterized in that, The method comprises: S1, establishing a large-signal model of the inverter-based first k distributed generation unit DG; S2, the first in the islanded AC microgrid IMG k The large-signal model of a distributed generation unit (DG) is used to perform input-output feedback linearization to obtain the relationship between voltage control input and voltage control output. Through the input-output feedback linearization, the second-order feedback system of a single distributed generation unit (DG) is obtained. S3, a disturbance observer (DO) is designed and used to estimate a current nonlinear uncertain term; S4, a Lyapunov function and applicable parameters are selected, and the disturbance observer of the current nonlinear uncertain term is set for the second-order feedback system; S5, obtaining the state variable of the linearized system of the first distributed generation unit DG in the island alternating current micro-grid IMG and the synchronization error of receiving the state variable of the neighbor distributed generation unit DG system; k ​ S6, a predefined finite time function is set, wherein if a smooth function meets a preset condition, the smooth function is taken as the predefined finite time function; S7, according to the predefined finite time function, a distributed virtual controller is designed based on a predefined finite time by using Lyapunov theory and a backstepping control strategy; S8, an overall Lyapunov function is constructed, and it is verified whether all signals in a distributed generation unit (DG) realized by the backstepping control strategy are bounded, and whether the synchronization error is converged to a function of the predefined finite time within the predefined finite time.

2. The pre-defined finite-time control method for island-oriented microgrid according to claim 1, wherein, In the S1, in the secondary voltage control process of the islanded alternating current microgrid IMG, the following logic is used to establish a large signal model of the first k distributed power generation unit DG based on the inverter: （1） In the formula (1), k denotes the serial number of the distributed power generation unit DG, t denotes time; for t The isolated AC microgrid IMG at time 1 k The state vector of each of the distributed generation units (DGs). for t The isolated AC microgrid IMG at time 1 k The derivative of the state vector of each of the distributed generation units (DGs). , , They represent t The isolated AC microgrid IMG at time 1 k The three state matrices of the large-signal model of the distributed generation unit (DG) include: , and Different linear and nonlinear relationships, express t The isolated AC microgrid IMG at time 1 k The voltage control input of the distributed generation unit (DG). express t The isolated AC microgrid IMG at time 1 k The nonlinear disturbances experienced by each of the distributed generation units (DGs) express t The isolated AC microgrid IMG at time 1 k The voltage control output of the distributed generation unit (DG). for t The isolated AC microgrid IMG at the specified time point k The output voltage of the distributed generation unit (DG) is as follows; d and q They represent d - q In transformation d shaft and q axis, l Representative line Lind, o Represents the output. express t In the IMG section of the time-isolated microgrid, the first... k The angle of the reference coordinate system of each distributed generation unit (DG) relative to the common reference coordinate system. express t In the IMG section of the time-isolated microgrid, the first... k The active power of each distributed generation unit (DG) express t In the IMG section of the time-isolated microgrid, the first... k The reactive power of each distributed generation unit (DG) express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The deviation component of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The deviation component of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The deviation component of the shaft's output current. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The deviation component of the shaft's output current. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d Shaft line current components, express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q Shaft line current components, express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d The components of the shaft's output voltage. express t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) q The components of the shaft's output voltage. This represents the common angular velocity of the isolated AC microgrid IMG. , They represent t In the IMG section of the time-isolated microgrid, the first... k Distributed generation unit (DG) d, q axis bus voltage component.

3. The pre-defined finite-time control method for island-oriented microgrid according to claim 1, wherein, In the S2, the relationship between the voltage control input and the voltage control output is expressed by the following logic: ​​ （2） In formula (2), , is the second derivative of denotes the Lie derivative along the direction and meet: ， denotes along the Lie derivative in the direction of , denotes a non-linear uncertain term in the jth distributed generation unit DG in the islanded alternating current microgrid IMG; k denotes denotes: Lie derivatives along directions, and , represents a linear determinant in a k-th distributed generation unit DG in the islanded alternating current microgrid IMG. k , represents a linear determinant in a k-th distributed generation unit DG in the islanded alternating current microgrid IMG.

4. The pre-defined finite-time control method for islanded microgrid according to claim 1, wherein, In the S3, set nonlinear uncertain term Satisfies: Wherein Is a preset unknown constant; The disturbance observer DO is designed to estimate the current nonlinear uncertainty term using the following logic : （4） In equation (4), express t The isolated AC microgrid IMG at the specified time point k In the expression representing the second-order feedback system of the distributed generation unit DG, The estimated value, for t The isolated AC microgrid IMG at the specified time point k In the expression representing the second-order feedback system of the distributed generation unit DG, The estimated value; represents an estimation error of , is a design parameter of the disturbance observer DO.

5. The pre-defined finite-time control method for islanded microgrid according to claim 1, wherein, In the S4, according to the nonlinear uncertain term in formula (4), t In the island alternating current micro-grid IMG at the moment, the estimated value of the first k Distributed power generation unit DG And t In the island alternating current micro-grid IMG at the moment, the deviation of the actual nonlinear uncertain term of the first k Distributed power generation unit DG , select the Lyapunov function:​ According to the second order feedback system, formula (4), the deviation and the Lyapunov function, the derivative of the Lyapunov function with respect to time t is taken, a boundedness judgment inequality is obtained, and it is concluded that the Lyapunov function is bounded, is bounded: ； selecting the applicable parameters , adjusting the non-linear uncertainty term estimation accuracy using the disturbance observer.

6. The pre-defined finite-time control method for islanded microgrid of claim 1, wherein, In S5, the synchronization error is represented by using the following logic: (9) In formula (9), l represents the serial number of the distributed power generation unit DG in communication with the first k distributed power generation unit DG in the islanded alternating current micro-grid IMG, is a set of the distributed power generation units DG in communication with the first k distributed power generation unit DG in the communication network, is the communication connectivity of the first k distributed power generation unit DG with the first l distributed power generation unit DG, is the reference voltage value of the islanded alternating current micro-grid IMG, represents the communication connectivity of the first k distributed power generation unit DG with the voltage reference value in the islanded alternating current micro-grid IMG, is the output of the command filter, the derivative of which satisfies wherein is a preset constant, represents the value of at the moment and , , respectively represent the synchronization error of , , represents a virtual controller designed for the first k distributed power generation unit DG, represents the output voltage value of the first k distributed power generation unit DG in the first l distributed power generation unit DG neighbor.

7. The pre-defined finite-time control method for islanded microgrid of claim 1, wherein, In S6, According to the following logic, the predefined finite time function is selected: （10） In equation (10), , Indicates e The base of the natural logarithm; denotes the settling time of the k denotes the time instant t denotes the deviation between the time instant k and the settling time of the k denotes a predefined finite time function of the , denotes the initial and final values of the predefined finite time function.​​ 8. The pre-defined finite-time control method for island-oriented microgrid of claim 1, wherein, In the S7, the following logic is used to construct the barrier Lyapunov function ; According to the second order feedback system, formula (9), the barrier Lyapunov function With respect to time t Taking the derivative, we get: （12） In formula (12), , ; denotes the derivative of denotes the expression comprising denotes the derivative of denotes the derivative of denotes the derivative of denotes the derivative of denotes the second derivative of ​​​​​​​ Introducing a distributed virtual controller reducing the equation (12) to （13） In formula (13), is a control parameter required for the design of the distributed virtual controller, and satisfies: 。 9. The method of pre-defined finite-time control for islanded microgrid according to claim 8, wherein, For the islanded AC microgrid IMG, the first k Each of the distributed generation units (DG) constructs a distributed virtual controller. Substituting the distributed virtual controller into equation (13), we obtain inequality (15): （15） A Lyapunov function is chosen : （16） In conjunction with the second order feedback system, the formula (16), the Lyapunov function With respect to time t Derivation, get formula (17): （17） in formula (17), denotes a control parameter of the virtual controller, denotes a derivative of denotes a derivative of the output of the command filter denotes a derivative of the barrier Lyapunov function denotes a derivative of the barrier Lyapunov function denotes a derivative of the barrier Lyapunov function By combining the inequality (15) and the formula (17), the following formula (19) is obtained: （18） With the following logic, the islanded AC microgrid IMG at the time instant t is t the actual controller of the DG unit DG k is designed as:​ （19） In formula (19), represents the control parameter of the actual controller, represents the control parameter of the actual controller of the islanded alternating current micro-grid IMG, and satisfies k represents the control parameter of the actual controller of the islanded alternating current micro-grid IMG, and satisfies ;​ The formula (19) is substituted into the inequality (18) to obtain the following inequality (20): （20） represents a control constant of the actual controller, is a control constant of the virtual controller.

10. A predefined finite-time control system for islanded microgrid, characterized in that, The system comprises: The large-signal model building module is used to establish the first inverter-based model. k Large-signal model of a distributed generation unit (DG); The feedback linearization module is used to linearize the first line of the isolated AC microgrid IMG. k The large-signal model of a distributed generation unit (DG) is used to perform input-output feedback linearization to obtain the relationship between voltage control input and voltage control output. Through the input-output feedback linearization, the second-order feedback system of a single DG is obtained. The feedback linearization module is connected to the large-signal model construction module. An uncertain term estimation module is used to design and use a disturbance observer (DO) to estimate a current nonlinear uncertain term, and the uncertain term estimation module is connected with the feedback linearization module; A disturbance observer design module is used to select a Lyapunov function and applicable parameters, and set the disturbance observer of the current nonlinear uncertain term for the second-order feedback system, and the disturbance observer design module is connected with the uncertain term estimation module; The synchronization error calculation module is used to calculate the synchronization error in the isolated AC microgrid IMG, specifically the first... k The synchronization error between the state variables of the linearized distributed generation unit (DG) system and the state variables of the received neighboring DG system is calculated by the synchronization error calculation module, which is connected to the disturbance observer design module. A finite time function setting module is used to set a predefined finite time function, wherein if a smooth function meets a preset condition, the smooth function is taken as the predefined finite time function; A controller design module is used to design a distributed virtual controller based on a predefined finite time by using Lyapunov theory and a backstepping control strategy according to the predefined finite time function, and the controller design module is connected with the finite time function setting module; A signal boundedness and convergence verification module is used to construct an overall Lyapunov function, verify whether all signals in a distributed generation unit (DG) realized by the backstepping control strategy are bounded, and verify whether the synchronization error is converged to a function of the predefined finite time within the predefined finite time, and the signal boundedness and convergence verification module is connected with the controller design module.

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