A method and apparatus for regulating performance load frequency fault tolerance control of a multi-zone power system

Abstract

This application provides a method and apparatus for frequency-tolerant control of a specified performance load in a multi-regional power system. The method includes: establishing a system model of the multi-regional power system; obtaining specified performance indicators for frequency deviation for each control area; converting the specified performance indicators into auxiliary variables through mathematical transformation; constructing a stability function for the multi-regional power system and performing stability analysis to obtain a set of linear matrix inequalities concerning the controller gain matrix of each control area; wherein the stability function is configured to satisfy the convergence of system state variables; and the frequency deviation satisfies the specified performance indicators and the system's H under non-zero initial conditions. ∞ The norm is less than the preset performance index; by solving a system of linear matrix inequalities, the controller gain matrix of each control region is obtained to construct the fault-tolerant controller corresponding to each control region for load frequency control. This application provides a load frequency control scheme for multi-region power systems that balances robustness, fault tolerance, and dynamic quality.

Description

Technical Field

[0001] This invention relates to the field of fault-tolerant control technology, specifically to a method and apparatus for fault-tolerant control of specified performance load frequency in a multi-regional power system. Background Technology

[0002] In large-scale interconnected power systems, the integration of distributed energy resources (DERs) presents uncertainties such as external disturbances, actuator failures, and controller gain perturbations. Due to the dynamic coupling between different regions of the power system, disturbances or faults occurring in one region can rapidly propagate to the entire network, causing significant frequency fluctuations and, in severe cases, threatening the stable operation of the entire system. Therefore, designing robust and interference-resistant load frequency control strategies has become crucial for ensuring the safe and stable operation of the power grid.

[0003] To address the above problems, existing research generally employs robust control methods, such as... Sliding mode control is used to ensure the system maintains closed-loop stability under the influence of uncertainties. Based on this, fault-tolerant control (FTC) technology has received widespread attention. Its purpose is to maintain the basic operating performance of the system even when actuators or sensors fail. Fault-tolerant control mainly includes active fault-tolerant control and passive fault-tolerant control. Active fault-tolerant control relies on fault diagnosis and control system reconfiguration, while passive fault-tolerant control does not require real-time fault information; the controller itself possesses a certain degree of robustness and fault tolerance.

[0004] In recent years, to further improve the performance of multi-region coordinated control, many studies have combined robust control with intelligent optimization algorithms, such as those based on harmony search algorithms. Controllers, such as terminal sliding mode controllers based on artificial bee colony optimization, etc. While these methods perform well in terms of steady-state regulation and system stability, their designs typically do not explicitly constrain the transient dynamic performance of the system. For example, fast response indicators such as overshoot suppression, convergence speed, and transient error boundaries often cannot be strictly guaranteed.

[0005] To address this deficiency, prescribed performance control has been introduced into the control field. This method, by applying a preset time-varying boundary to the system error, ensures that the error always falls within a specified performance range throughout the dynamic process, thereby directly shaping the system's transient response behavior. Common implementation methods include backstepping control, sliding mode control, or adaptive control. However, in the presence of system uncertainties, parameter perturbations, or structural faults, traditional prescribed performance control often struggles to directly handle the complex coupling between performance boundaries and system dynamics, lacking an intuitive mapping relationship between performance parameters and controller design. This results in significant limitations in balancing robustness, fault tolerance, and dynamic performance.

[0006] In short, although the relevant robust and fault-tolerant control methods can cope with system uncertainties and faults to a certain extent, they cannot explicitly integrate transient performance indicators into the controller design. Especially in real-world scenarios such as multi-regional power systems, which are high-dimensional, strongly coupled, and prone to faults, their dynamic response capability is still insufficient. Summary of the Invention

[0007] In view of this, this application provides a load frequency fault-tolerant control method and apparatus for a multi-regional power system with specified performance, so as to directly integrate dynamic response requirements into the design of the fault-tolerant controller, and provide a load frequency control scheme for a multi-regional power system that takes into account robustness, fault tolerance and dynamic quality.

[0008] Specifically, this application is implemented through the following technical solution: According to a first aspect of the embodiments of this specification, a method for frequency-tolerant control of specified performance loads in a multi-regional power system is provided, comprising: Step S1: Establish a system model of a multi-regional power system. The system model includes system dynamic equations considering time delay, actuator hybrid fault model, and controller gain perturbation model. Step S2: For each control area of ​​the multi-regional power system, obtain the specified performance index of frequency deviation, wherein the specified performance index limits the allowable boundary of frequency deviation by a time-varying performance function; Step S3: Convert the specified performance indicators into auxiliary variables through mathematical transformation; Step S4: Based on the auxiliary variables and the system model, construct the stability function of the multi-region power system; perform stability analysis on the multi-region power system based on the stability function to obtain a set of linear matrix inequalities concerning the controller gain matrix of each control region; wherein the stability function is configured to satisfy the following conditions: The system state variables converge to zero under the influence of time delay, mixed actuator faults, and controller gain perturbations. The frequency deviation satisfies the specified performance index in both non-zero initial state and zero initial state. H of the system ∞ The norm is less than the preset performance index γ; Step S5: Solve the system of linear matrix inequalities to obtain the controller gain matrix for each control region; Step S6: Based on the controller gain matrix of each control region, construct the fault-tolerant controller corresponding to each control region for load frequency control.

[0009] According to a second aspect of the embodiments of this specification, a frequency-tolerant control device for a specified performance load in a multi-regional power system is provided, comprising: The system modeling unit is used to establish a system model of a multi-regional power system. The system model includes system dynamic equations considering time delays, actuator hybrid fault models, and controller gain perturbation models. The performance acquisition unit is used to acquire a specified performance index of frequency deviation for each control area of ​​the multi-regional power system. The specified performance index limits the allowable boundary of the frequency deviation through a time-varying performance function. The first calculation unit is used to convert the specified performance indicators into auxiliary variables through mathematical transformations; The second calculation unit is used to construct a stability function for the multi-regional power system based on the auxiliary variables and the system model, and to perform stability analysis on the multi-regional power system based on the stability function to obtain a set of linear matrix inequalities concerning the controller gain matrix of each control area; wherein the stability function is configured to satisfy the following conditions: The system state variables converge to zero under the influence of time delay, mixed actuator faults, and controller gain perturbations. The frequency deviation satisfies the specified performance index in both non-zero initial state and zero initial state. H of the system ∞ The norm is less than the preset performance index γ; The third calculation unit is used to solve the system of linear matrix inequalities to obtain the controller gain matrix for each control region. The controller design unit is used to construct the corresponding fault-tolerant controller for each control region based on the controller gain matrix of each control region, so as to perform load frequency control.

[0010] According to a third aspect of the embodiments of this specification, an electronic device is provided, including a processor; and a computer-readable storage medium storing computer program instructions that, when executed by the processor, cause the processor to perform the method described in the first aspect.

[0011] According to a fourth aspect of the embodiments of this specification, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being executed by a processor of the method described in the first aspect.

[0012] In this embodiment, by directly converting explicit transient performance indicators into stability constraints, the frequency deviation is strictly constrained to follow a preset time-varying boundary, thereby obtaining a predictable and high-performance dynamic adjustment process. Furthermore, by constructing a stability function, the system can maintain dynamic performance even when control is initiated under non-zero initial conditions, making the theoretical method closer to engineering practice. For complex scenarios involving simultaneous actuator mixed faults, controller gain perturbations, and time-varying delays, the technical solution of this embodiment can simultaneously guarantee the stability and dynamism of the system's frequency control. Attached Figure Description

[0013] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Some specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings in an exemplary and non-limiting manner. The same reference numerals in the drawings indicate the same or similar parts or components. Those skilled in the art should understand that these drawings are not necessarily drawn to scale. In the drawings: Figure 1 This is a schematic diagram of the architecture of a control area subsystem of a multi-regional power system, as illustrated in an exemplary embodiment of this application. Figure 2 This is a schematic flowchart illustrating a specified performance load frequency fault-tolerant control method for a multi-regional power system according to an exemplary embodiment of this application; Figure 3 This is a schematic diagram of the mixed fault coefficients corresponding to the three control areas shown in an exemplary embodiment of this application; Figure 4 This is a schematic diagram of the performance curves of the controller designed based on Theorem 4.1 corresponding to the three control regions shown in an exemplary embodiment of this application; Figure 5 This is a schematic diagram of the frequency deviations corresponding to the three control regions shown in an exemplary embodiment of this application; Figure 6 This is a schematic diagram of the performance curves of the controller optimized based on Theorem 4.2 for the three control regions shown in an exemplary embodiment of this application; Figure 7 This is a block diagram illustrating an electronic device according to an exemplary embodiment of this application; Figure 8 This is a block diagram illustrating a specified performance load frequency fault-tolerant control device for a multi-regional power system, as shown in an exemplary embodiment of this application. Detailed Implementation

[0014] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0015] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0016] Traditional robust or fault-tolerant control methods typically focus on ensuring asymptotic stability under faults, lacking explicit constraints and direct control over transient processes (such as overshoot, convergence speed, and steady-state accuracy). To address this, the solution in this application transforms specified transient performance indicators into constraints that can be integrated into stability analysis through mathematical transformation. Based on this, a novel Lyapunov function is constructed. This function not only includes standard terms for handling time delays and fault information but also innovatively introduces transformation error terms directly related to performance constraints, thus embedding a guarantee of dynamic performance inherently into the stability proof. Furthermore, the Lyapunov function proposed in this application explicitly considers non-zero initial states, breaking through the limitations of traditional H... ∞ The zero initial condition constraint, which is a common feature in control theory, enhances the practicality and completeness of the theory.

[0017] To overcome the coupling problem that arises in solving inequalities for the controller gain matrix, this application further employs a decoupling technique based on auxiliary variables, combined with a variable substitution method, to transform the existence condition of the controller into a set of numerically solvable linear matrix inequalities. By solving this set of inequalities, the controller gain can be directly obtained. Theoretical analysis and simulation experiments both demonstrate that the fault-tolerant controller designed in this application can ensure that the system frequency deviation always meets the preset dynamic performance boundary under conditions of actuator failure, parameter perturbation, and time delay, and achieves asymptotic stability of the closed-loop system and a specified level of interference suppression.

[0018] The multi-regional power system in this embodiment of the application consists of n It consists of interconnected control areas, and the subsystems of one control area are as follows: Figure 1As shown, the device includes a controller, speed governor, turbine, generator, etc. The connection relationships and functions of each component can be referred to by those skilled in the art, and will not be repeated in this embodiment.

[0019] The embodiments described in this specification will now be described in detail.

[0020] This application provides a method for frequency-tolerant control of specified performance loads in a multi-regional power system. Figure 2 This is a schematic flowchart illustrating a specified performance load frequency fault-tolerant control method for a multi-regional power system, as shown in an exemplary embodiment of this application. Figure 2 As shown, the load frequency fault-tolerant control method of this embodiment includes at least the following steps: Step S1: Establish a system model of a multi-regional power system. The system model includes system dynamic equations considering time delay, actuator hybrid fault model, and controller gain perturbation model.

[0021] In some embodiments, the system dynamic equations considering time delays can refer to the model shown in formula (9) below.

[0022] In some embodiments, the controller gain perturbation model may refer to the model shown in formula (8) below.

[0023] In some embodiments, the actuator hybrid fault model is described by hybrid fault coefficients, and the controller... i Corresponding mixed failure coefficient for: in, , This indicates the lower bound of the coefficient corresponding to early failures. This indicates the lower bound of the coefficient corresponding to local failure; This represents the upper bound of the coefficients under the bias amplification effect. and Both are random variables that follow a binomial distribution. , , , It is an interval constants within, , , Mixed failure coefficient The component is a bounded time-varying fault coefficient, whose value changes dynamically within a corresponding range, and the pattern of change does not need to be known in advance.

[0024] Step S2: For each control area of ​​the multi-regional power system, obtain the specified performance index of frequency deviation. The specified performance index limits the allowable boundary of the frequency deviation through a time-varying performance function.

[0025] This embodiment constrains the overshoot, convergence speed, and steady-state accuracy during the transient process using the specified performance indicators.

[0026] Step S3: Convert the specified performance index into auxiliary variables through mathematical transformation.

[0027] Step S4: Based on the auxiliary variables and the system model, construct the stability function of the multi-region power system; perform stability analysis on the multi-region power system based on the stability function to obtain a set of linear matrix inequalities concerning the controller gain matrix of each control region; wherein the stability function is configured to satisfy the following conditions: The system state variables converge to zero under the influence of time delay, mixed actuator faults, and controller gain perturbations. The frequency deviation satisfies the specified performance index in both non-zero initial state and zero initial state. H of the system ∞ The norm is less than the preset performance index γ; Step S5: Solve the system of linear matrix inequalities to obtain the controller gain matrix for each control region.

[0028] Step S6: Based on the controller gain matrix of each control region, construct the fault-tolerant controller corresponding to each control region for load frequency control.

[0029] like Figure 2 As shown in the frequency fault-tolerant control method for specified performance loads, this embodiment directly transforms explicit transient performance indicators into stability constraints to ensure that frequency deviations strictly adhere to preset time-varying boundaries, thereby achieving a predictable and high-performance dynamic adjustment process. Furthermore, by constructing a stability function, the system can maintain dynamic performance even when control is initiated under non-zero initial conditions, making the theoretical method closer to engineering practice. For complex scenarios involving simultaneous actuator mixed faults, controller gain perturbations, and time-varying delays, this embodiment can simultaneously guarantee the stability and dynamism of the system's frequency control.

[0030] In some embodiments, step S3 specifically includes: Based on the specified performance indicators, the frequency deviation is obtained. Setting Based on the aforementioned settings, the auxiliary variables are obtained. for ;in, Let be the time-varying performance function. The transformation error corresponding to the mathematical transformation process is... , and This represents the allowable boundary for frequency deviation.

[0031] The load frequency fault-tolerant control process of the embodiments of this application will now be described in detail.

[0032] To facilitate understanding of the subsequent content of this embodiment, some relevant symbol definitions and related lemmas will be introduced first.

[0033] 1) Given a square matrix Then there is ,now that This represents the sum of a matrix and its transpose.

[0034] 2) For symmetric matrices, Indicates a symmetric term. For an identity matrix of suitable dimension, then for the matrix... , Representation matrix It is a symmetric positive definite matrix. Representation matrix The expectation.

[0035] 3) This represents a diagonal matrix.

[0036] 4) For multi-regional power systems, the time delays of different control areas have corresponding upper and lower bounds. Therefore, the time delay of control area i... satisfy: .

[0037] Lemma 1: For a positive definite matrix ,satisfy positive scalar and and vector functions The following inequalities hold: Lemma 2: For a symmetric matrix The following propositions are equivalent: Lemma 3: For a symmetric matrix ,matrix and ,when Timely satisfaction Then for satisfying matrix The following inequalities hold: Lemma 4: For any matrix and scalar The following inequalities hold: Step S1: Establish the system model.

[0038] by Figure 1 The control area shown i Taking a closed-loop control system as an example, the control area i The preliminary model corresponding to the closed-loop subsystem is as follows: (1) In the above formula, These are system state variables, including the control area. i Frequency deviation, valve position deviation, and turbine output power deviation, etc. for The derivative of the operator; in the following text, any parameter containing this operator indicates a derivative operation. To output signals to the actuator, External disturbances For system output, and A , B , and C For details, please refer to formula (45) below.

[0039] In cases where actuator faults include partial and bias faults, the control area i The controller is: (2) in, The actuator is in the control area i Partial failure coefficient, The following constraints must be met: (3) In formula (3) and They represent The upper and lower bounds.

[0040] Bias fault As a boundary, and If it is a known system scalar, then the control area i The controller can also be represented as: (4) In formula (4) For mixed failure coefficients, the following constraints must be satisfied: (5) Among them, it can be based on and Calculate and Mixed failure coefficient for: (6) in, , It is a known scalar.

[0041] when At that time, the actuator experienced an early failure; when When, it indicates a serious malfunction; while when and Indicates a severe local failure; when and This corresponds to the amplification effect caused by the bias fault.

[0042] Among them, randomness changed and Follows a binomial distribution. , , , It is an interval constants within, This is the expectation operator.

[0043] Furthermore, the controller also needs to consider time delay. and gain perturbation Correspondingly, control area i The controller should be represented as: (7) In formula (7) , , Indicates proportional gain. Represents the integral gain, where , and For a known constant, Indicates the upper bound of the time delay. Represents the rate of change with time delay The upper boundary.

[0044] Substituting equation (6) into equation (7), the fault-tolerant controller can be expressed as: (8) Combining the fault-tolerant controller corresponding to formula (8) with the preliminary model of formula (1), the control area... i The closed-loop subsystem can be represented as: (9) in, , , , Here , , , , , , , and The dimensions are respectively , , , , , , , and .

[0045] Step S2: Construct the specified performance indicators for frequency deviation.

[0046] Indicates control area i The purpose of this application embodiment is to ensure that the frequency deviation tends to be zero. Based on this, this application embodiment introduces specified performance indicators into the design process of load frequency fault-tolerant control, and the specified performance indicators are: (10) in , , , . For a time-varying performance function with strictly slow decreasing characteristics, , . The degree of constraint depends on , and .

[0047] Step S3: Convert the specified performance indicators into auxiliary variables.

[0048] The performance index specified in the inequality form shown in formula (10) is difficult to apply directly to system control. This embodiment converts the above conditions into an unconstrained type. Accordingly, this embodiment sets: (11) in, It indicates that it is a strictly decreasing smooth function. It can be written as: (12) Transformation error is achieved through inverse function transformation. It can be represented as: (13) Differentiating formula (14), we get: (14) Based on formulas (12) to (14), it can be known that when Tend to hour, It tends to 0, and thus It tends towards 0. Therefore, we can obtain the auxiliary variable: (15) Step S4: Construct the stability function of the multi-regional power system.

[0049] The stability function in this embodiment is the Lyapunov function.

[0050] Theorem 1: For positive definite matrices , as well as A matrix of appropriate dimension and block matrix ,as well as right To meet the performance requirements, the Lyapunov function is as follows: (16) Based on formula (16), the following set of inequalities can be obtained: (17) in, , , , , , , , , , , , .

[0051] In formula (17), , , , , , , , , , , , , , , and controller matrix These are known set values. The weights of the auxiliary variables in control region i, The relaxation coefficient is introduced for non-zero initial conditions.

[0052] Next, we prove that when the above inequality holds, the system satisfies the stability condition, the specified performance condition, and the disturbance suppression condition. The stability condition means that the system state variables converge to zero under the influence of time delay, actuator mixed faults, and controller gain perturbations. The specified performance condition means that the frequency deviation satisfies the specified performance index under both non-zero initial states and zero initial states. The disturbance suppression condition means that the system's H... ∞ The norm is less than the preset performance index γ.

[0053] Since the specified performance parameters need to be incorporated into the controller design, the Lyapunov function can be expressed in the following form: (18) In formula (18), , , Design auxiliary variables related to specified performance, and It contains information about time delays and related faults.

[0054] To each and Taking the derivative, we get: (19) Combining formulas (14) and (15), and for Performing logarithmic operations, we have: (20) Based on the specified performance index constraints corresponding to formula (10), the following inequality can be obtained: (twenty one) Based on formula (21), it can be seen that Satisfying the typical logarithmic function The Taylor expansion condition. Therefore, for Performing a Taylor expansion, we get: (twenty two) in, , , .

[0055] Because when tend hour, Approaching 0, therefore This can be considered a distractor. According to... It can be deduced that: (twenty three) Based on formulas (22) and (23), the following inequality can be derived: (twenty four) Next Process according to We can obtain: (25) By introducing the method of free weight matrix, and combining Any matrix with appropriate dimensions All of the following conditions must be met: (26) in, .

[0056] according to The performance requirements can be obtained as follows: (27) in, , .

[0057] At the same time, based on ,exist Top Apply time integrals on both sides, when This leads to the subsequent equation: (28) Traditional robust control theory assumes This is an overly strict assumption. To extend it to non-zero initial conditions, we modify the inequality as follows: (29) in, .

[0058] Moreover, there are: (30) Given constants, there always exists such a thing: (31) Based on formulas (17) and (31), the stability function shown in formula (16) can be obtained directly.

[0059] Next, we solve the system of inequalities in formula (17).

[0060] Theorem 2: For positive definite matrices , , A matrix of appropriate dimension and scalar , and block matrix The following inequalities hold: (32) in, , , , , , , .

[0061] In formula (32), , , , , , , , , , , , , , , and controller matrix These are known settings.

[0062] Based on formula (12), when there exists a sufficiently small scalar To ensure that the following conditions are met: (33) and The upper and lower bounds can be obtained as follows: , , , , .

[0063] It is easy to see that the time-varying term on the main diagonal , and Scaling can be achieved by taking its upper bound. Conversely, for off-diagonal items... and We describe them using their upper and lower bounds: (34) in, .

[0064] Will , and Replacing them with their upper bounds and deriving formula (17) based on formula (34), we can obtain: (35) in, , , , , , .

[0065] Considering , and Since it is an unknown variable, in order to improve the robustness of the controller, this problem is solved based on Theorem 3.

[0066] Theorem 3: Auxiliary variables ensure that the system remains stable under performance constraints. If a positive definite matrix exists... , , A matrix of appropriate dimension scalar , , , , and block matrix ,as well as Performance constraints allow us to obtain the following formula: (36) in, , , , , , , , , , , , here , , , , , .

[0067] variable , and It can be rewritten as: (37) Substituting formula (37) into formula (32), and based on lemmas 2 and 3, we can obtain the corresponding result in formula (36).

[0068] Considering, as in (36) of and The existence of coupling terms complicates the design of the corresponding controller. This embodiment provides Theorem 4.1 to address the problem of coupling terms. Furthermore, disturbances in the controller can negatively impact control performance, hence Theorem 4.2 is provided.

[0069] Theorem 4.1: Design the controller as This ensures that system (9) remains stable under the specified performance constraints. For positive definite matrices... , , , A matrix of appropriate dimension and scalar , , , , , , and block matrix as well as Performance constraints then hold the following formula: (38) in, , , , , , , , , , , , , , , .

[0070] The structure of formula (36) shows that traditional decoupling methods, such as multiplying column vectors left and right or converting them into W or P problems, cannot solve the coupling terms. Therefore, this embodiment proposes a new decoupling method, namely: (39) in, If it is an auxiliary matrix with appropriate dimensions, then the controller... In formula (36), it has , The terms can be represented as: (40) in, , , , .

[0071] Using Lemma 3, the following inequality holds: (41) The proof is complete with Lemma 2 and Lemma 3.

[0072] Theorem 4.2: In giving , , , , , , , , , , , , , , and controller matrix In this case, the controller is designed as This ensures that the system remains stable under specified performance constraints. (For positive definite matrices...) , , , A matrix of appropriate dimension and scalar , , , , , , , , , and block matrix The following inequalities hold: (42) in, , , , , , , , , .

[0073] Theorem 3 Replace with The proof process is similar to that of Theorem 4.1, and will not be repeated in this embodiment.

[0074] Next, taking the load frequency control of a three-region power system as an example, we will explain that the designed fault-tolerant controller has the specified performance indicators.

[0075] The following formula (43) is for the control area in a three-region interconnected power system. The system's dynamic differential equations: (43) Control area i System state variables System output and external disturbances as follows: (44) An electric power system can be described as: (45) in, , , , , .

[0076] The controller gain matrix is ​​then... The performance index constraints specified in this embodiment apply to frequency deviation. .

[0077] Table 1 shows the simulation parameters for the three-region power system. The remaining parameters for the specified performance are selected as follows: , , , , , , , , , , , , .

[0078] Table 1 In this embodiment, the interference signal is considered as: By applying Theorem 4.1, the fault-tolerant controller that satisfies the design performance constraints can be solved as follows: .

[0079] Figure 3 The mixed failure coefficients are shown. Figure 4 A schematic diagram comparing the control performance of a traditional distributed load frequency controller with that of the controller in this embodiment is shown. The traditional distributed load frequency controller cannot stabilize the system under actuator failure.

[0080] For controllers with additive gain perturbations, ,in , , .

[0081] refer to Figure 5 The original controller designed based on Theorem 4.1 cannot meet the specified performance constraints. Therefore, according to Theorem 4.2, the controller is reconstructed as follows: , , and .

[0082] refer to Figure 6 Under additive perturbations, the reconstructed controller can meet the specified performance constraints. For example... Figure 4 and Figure 6 As shown, the fluctuation of frequency deviation is not arbitrary; it satisfies the given boundary constraints and eventually converges to zero.

[0083] Therefore, it can be seen that the fault-tolerant controller in this application embodiment achieves the goal of stability while meeting the predetermined performance.

[0084] Figure 7 This is a schematic diagram of an electronic device illustrated in this specification according to an exemplary embodiment. Please refer to... Figure 7 At the hardware level, the device includes a processor 702, an internal bus 704, a network interface 706, memory 708, a hardware acceleration device 710, and non-volatile memory 712, and may also include other hardware required for its functions. One or more embodiments of this application can be implemented in software, for example, the processor 702 reads the corresponding computer program from the non-volatile memory 712 into the memory 708 and then runs it. Of course, in addition to software implementation, one or more embodiments of this application do not exclude other implementation methods, such as logic devices or a combination of hardware and software, etc. That is to say, the execution subject of the above processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0085] Figure 8 This is a block diagram illustrating a specified performance-compliant frequency-tolerant control device for a multi-regional power system, as shown in an exemplary embodiment of this application. The specified performance-compliant frequency-tolerant control device for the multi-regional power system can be applied to, for example... Figure 7The electronic device shown implements the technical solution of this application. The multi-regional power system's specified performance compliance frequency-tolerant control device includes: a system modeling unit 810, a performance acquisition unit 820, a first calculation unit 830, a second calculation unit 840, a third calculation unit 850, and a controller design unit 860, wherein: The system modeling unit 810 is used to establish a system model of a multi-regional power system. The system model includes system dynamic equations considering time delay, actuator hybrid fault model, and controller gain perturbation model. The performance acquisition unit 820 is used to acquire a specified performance index of frequency deviation for each control area of ​​the multi-regional power system. The specified performance index limits the allowable boundary of the frequency deviation through a time-varying performance function. The first calculation unit 830 is used to convert the specified performance index into auxiliary variables through mathematical transformation; The second calculation unit 840 is used to construct a stability function for the multi-regional power system based on the auxiliary variables and the system model, and to perform stability analysis on the multi-regional power system based on the stability function to obtain a set of linear matrix inequalities concerning the controller gain matrix of each control area; wherein the stability function is configured to satisfy the following conditions: The system state variables converge to zero under the influence of time delay, mixed actuator faults, and controller gain perturbations; the frequency deviation satisfies the specified performance indicators in both non-zero initial states and zero initial states; the system's H... ∞ The norm is less than the preset performance index γ; The third calculation unit 850 is used to solve the system of linear matrix inequalities to obtain the controller gain matrix for each control region. The controller design unit 860 is used to construct a fault-tolerant controller for each control region based on the controller gain matrix of each control region, so as to perform load frequency control.

[0086] In some embodiments, the third calculation unit 850 is specifically used to obtain the frequency deviation based on the specified performance index. Setting Based on the aforementioned settings, the auxiliary variables are obtained. for ;in, Let be the time-varying performance function. The transformation error corresponding to the mathematical transformation process is... , and This represents the allowable boundary for frequency deviation.

[0087] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0088] Accordingly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any of the above embodiments.

[0089] Accordingly, embodiments of this application also provide a computer program product configured to perform the methods described in any of the above embodiments.

[0090] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer, which can take the form of a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email sending and receiving device, game console, tablet computer, wearable device, or any combination of these devices.

[0091] In a typical configuration, a computer includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0092] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0093] Computer-readable media, including both permanent and non-permanent, removable and non-removable media, can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage, quantum memory, graphene-based storage media or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0094] While this specification contains numerous specific implementation details, these should not be construed as limiting the scope of any invention or the scope of the claims, but rather are primarily intended to describe features of specific embodiments of a particular invention. Certain features described in the various embodiments herein may also be implemented in combination in a single embodiment. Conversely, various features described in a single embodiment may also be implemented separately in various embodiments or in any suitable sub-combination. Furthermore, while features may function in certain combinations as described above and even initially claimed in this way, one or more features from a claimed combination may be removed from that combination in some cases, and a claimed combination may refer to a sub-combination or a variation thereof.

[0095] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or sequentially, or requiring all illustrated operations to be performed to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0096] Thus, specific embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings are not necessarily shown in a specific order or sequence to achieve the desired result. In some implementations, multitasking and parallel processing may be advantageous.

[0097] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0098] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for frequency-tolerant control of specified performance loads in a multi-regional power system, characterized in that, Includes the following steps: Step S1: Establish a system model of a multi-regional power system. The system model includes system dynamic equations considering time delay, actuator hybrid fault model, and controller gain perturbation model. Step S2: For each control area of ​​the multi-regional power system, obtain the specified performance index of frequency deviation, wherein the specified performance index limits the allowable boundary of frequency deviation by a time-varying performance function; Step S3: Convert the specified performance indicators into auxiliary variables through mathematical transformation; Step S4: Based on the auxiliary variables and the system model, construct the stability function of the multi-region power system, perform stability analysis on the multi-region power system based on the stability function, and obtain a set of linear matrix inequalities about the controller gain matrix of each control area; The stability function is configured to satisfy the following conditions: the system state variables converge to zero under the influence of time delay, actuator mixed faults, and controller gain perturbations; the frequency deviation satisfies the specified performance index under both non-zero initial states and zero initial states; the system's H... ∞ The norm is less than the preset performance index γ; Step S5: Solve the system of linear matrix inequalities to obtain the controller gain matrix for each control region; Step S6: Based on the controller gain matrix of each control region, construct the fault-tolerant controller corresponding to each control region for load frequency control.

2. The method according to claim 1, characterized in that, The actuator hybrid fault model is described by hybrid fault coefficients, controller i Corresponding mixed failure coefficient for: ； in, , This indicates the lower bound of the coefficient corresponding to early failures. This indicates the lower bound of the coefficient corresponding to local failure. This represents the upper bound of the coefficients under the bias amplification effect. and Both are random variables that follow a binomial distribution. , , , It is an interval Changshu, within the territory , , Mixed failure coefficient The amount.

3. The method according to claim 1, characterized in that, Step S3 includes: Based on the specified performance indicators, the frequency deviation is obtained. Setting ; Based on the above settings, the auxiliary variable is obtained. for ; in, Let be the time-varying performance function. The transformation error corresponding to the mathematical transformation process is... , and This represents the allowable boundary for frequency deviation.

4. A frequency-tolerant control device for a multi-regional power system, characterized in that, The device includes: The system modeling unit is used to establish a system model of a multi-regional power system. The system model includes system dynamic equations considering time delays, actuator hybrid fault models, and controller gain perturbation models. The performance acquisition unit is used to acquire a specified performance index of frequency deviation for each control area of ​​the multi-regional power system. The specified performance index limits the allowable boundary of the frequency deviation through a time-varying performance function. The first calculation unit is used to convert the specified performance indicators into auxiliary variables through mathematical transformations; The second calculation unit is used to construct a stability function for the multi-regional power system based on the auxiliary variables and the system model, and to perform stability analysis on the multi-regional power system based on the stability function to obtain a set of linear matrix inequalities concerning the controller gain matrix of each control area; wherein the stability function is configured to satisfy the following conditions: The system state variables converge to zero under the influence of time delay, mixed actuator faults, and controller gain perturbations. The frequency deviation satisfies the specified performance index in both non-zero initial state and zero initial state. H of the system ∞ The norm is less than the preset performance index γ; The third calculation unit is used to solve the system of linear matrix inequalities to obtain the controller gain matrix for each control region. The controller design unit is used to construct the corresponding fault-tolerant controller for each control region based on the controller gain matrix of each control region, so as to perform load frequency control.

5. An electronic device, characterized in that, include: processor; as well as A computer-readable storage medium storing computer program instructions that, when executed by the processor, cause the processor to perform the method as described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which is executed by a processor according to any one of claims 1 to 3.

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