Multi-area power system controller design method based on reconstruction method

Abstract

The invention discloses a multi-region power system controller design method based on a reconstruction method. The method comprises the steps of S1, constructing a power system load frequency control model under high-permeability wind power and multi-delay delay coupling; s2, introducing a reconstruction technology, and dynamically dividing the power system load frequency control model in the S1; s3, constructing a Lyapunov-Krasovskii functional containing multiple pieces of time delay information on the basis of the step S2, and accurately solving an integral term in the Lyapunov-Krasovskii functional by applying a novel integral inequality; and S4, formulating a non-fragile dissipation controller design and performance evaluation mechanism considering the disturbance term based on S3. The invention provides a non-fragile dissipative load frequency control (LFC) method for an interconnected multi-region power system under the influence of high wind power permeability (HPW) and multi-time-varying delay (MTD). According to the method, firstly, an LFC model fusing HPW and MTD is established, and stability analysis efficiency is improved by adopting a reconstruction technology based on time delay dynamic division.

Description

Technical Field

[0001] This application relates to the field of power system control technology, specifically to a design method for a multi-region power system controller based on a reconfiguration approach. Background Technology

[0002] As the global energy structure accelerates its transition to a low-carbon model, the penetration rate of renewable energy, represented by wind power, in the power system continues to rise, bringing revolutionary changes to the traditional power system operation mode. However, the output power of renewable energy is greatly affected by meteorological conditions, and energy differences in different regions increase the uncertainty of its power generation. Load frequency control (LFC) plays an indispensable role in the power system, especially in the context of a large amount of renewable energy, its importance is becoming increasingly prominent. Due to the increasing complexity and scale of power systems, upgrading traditional power systems to smart grids is imperative. Open communication networks bring many conveniences to control systems, but also increase the difficulty of system analysis and design. For example, communication delays can reduce dynamic performance and lead to system instability. Therefore, to ensure the stability of LFC schemes, latency, as an important factor of performance degradation and instability, must also be considered.

[0003] In existing technologies, methods for calculating delay margins have become key tools for handling delay problems, such as the Linear Matrix Inequality (LMI) method. This method can theoretically provide accurate stability assessments, but the stability criteria are overly conservative. For example, some improved Lyapunov-Krasovskii methods have emerged in recent years. They improve the compactness and accuracy of the standard by introducing more refined functional forms, optimizing the design of LMIs, and considering more complex system models. As with developing less conservative stability standards, computational burden is an equally important performance indicator, especially when dealing with load frequency control problems in high-dimensional regions.

[0004] Furthermore, power systems must consider not only communication delays but also various sources of uncertainty. These uncertainties may arise from external disturbances or be related to the dynamic characteristics of the system itself. Against this backdrop, nonfragile control (LFC) has gradually gained widespread attention as an effective control strategy. Its core idea is to design a controller capable of withstanding controller parameter perturbations, ensuring system stability in the face of uncertainty. This can improve system robustness and maintain flexibility when system conditions change. However, existing research often only considers specific scenarios for controller perturbations. For example, it only studies the behavior of uncertainties caused by additive disturbances, neglecting other possible forms of disturbance. While this simplifies the problem, it does not fully reflect the complex uncertainties in power systems. This means that when designing a controller, it is necessary to comprehensively consider multiple forms of perturbations and their interactions to enhance the controller's adaptability to system uncertainties. Therefore, developing robust LFC strategies resistant to cyberattacks in multi-regional power systems has become a key area of ​​focus.

[0005] Application content

[0006] The purpose of this application is to provide a design method for a multi-regional power system controller based on a reconfiguration approach, and the specific technical solution is as follows:

[0007] A design method for a multi-regional power system controller based on a reconfiguration approach includes: S1, constructing a power system load frequency control model coupled with high-penetration wind power and multiple time delays; S2, introducing reconfiguration technology to dynamically partition the power system load frequency control model in S1; S3, constructing a Lyapunov-Krasovskii functional containing multiple time delay information based on S2, and applying a novel integral inequality to accurately solve the integral terms in the Lyapunov-Krasovskii functional; S4, formulating a design and performance evaluation mechanism for a non-fragile dissipative controller considering disturbance terms based on S3.

[0008] S1 includes:

[0009] S1.1, Construct the first one with MTD The closed-loop model of the regional load frequency control system is characterized as follows:

[0010] ;

[0011] S1.2, Based on S1.1, the state-space model for multi-region load frequency control is represented as follows:

[0012] ,

[0013] in,

[0014] ,

[0015] ,

[0016] ,

[0017] ,

[0018] ,

[0019] ,

[0020] ,

[0021] ,

[0022] ;

[0023] S1.3, Based on S1.2, the time-varying delay satisfies:

[0024] .

[0025] S2 includes:

[0026] S2.1 Based on the physical properties of the power system load frequency control model, the state variables are divided into two categories using reconfiguration technology: one category consists of state variables directly affected by time delay, and the other category consists of state variables unrelated to time delay, even if:

[0027] ,

[0028] ;

[0029] S2.2, through the transition matrix Multiply, we get:

[0030] ;

[0031] S2.3. Based on model reconstruction technology, the normal system of the state-space model of multi-region load frequency control in S1.2 is characterized as follows:

[0032] ,

[0033] in,

[0034] ,

[0035] ,

[0036] ,

[0037] ,

[0038] ,

[0039] ,

[0040] ,

[0041] ,

[0042] ,

[0043] ,

[0044] ,

[0045] ,

[0046] .

[0047] S3 includes:

[0048] S3.1 When a positive definite symmetric matrix exists , , , Moreover, there exists a real symmetric matrix. , And satisfy the following linear matrix inequalities:

[0049] ,

[0050] ,

[0051] ,

[0052] ,

[0053] Then, for a given state-space model of multi-region load frequency control in S2.3, the normal system is... , It is asymptotically stable;

[0054] S3.2 To verify the asymptotic stability in S3.1, the Lyapunov-Krasovskii functional is constructed:

[0055]

[0056] ,

[0057] in,

[0058] ,

[0059] ,

[0060] ;

[0061] S3.3. Based on the V-function reasoning, the integral term of the system state derivative can be estimated by upper bound as a term about the state variable. The quadratic form function of has a corresponding matrix that satisfies the following structure:

[0062]

[0063] ,

[0064] in,

[0065] ;

[0066] S3.4, External interference Under the given conditions, the derivative of the Lyapunov-Krasovskii functional of the system ultimately satisfies:

[0067] .

[0068] S4 includes:

[0069] S4.1, the first The area control error is defined as:

[0070] ;

[0071] S4.2 To track frequency changes in a multi-regional power system, we use the following PI controller:

[0072] ;

[0073] S4.3. Combining anti-interference processing, the following input controller expression is constructed:

[0074] ;

[0075] S4.4 When dealing with the controller's disturbance term, consider both additive and multiplicative disturbances. Additive disturbances mainly describe absolute errors independent of the system state, while multiplicative perturbations characterize relative errors related to the system state, such that:

[0076] ,

[0077] ,

[0078] in, and It is a constant matrix. To meet The unknown matrix.

[0079] The beneficial effects of this application are as follows: It proposes a non-fragile dissipative load frequency control (LFC) method for interconnected multi-regional power systems under the influence of high wind power penetration (HPW) and multiple time-varying delays (MTD). This method first establishes an LFC model integrating HPW and MTD, and then employs a reconstruction technique based on time-delay dynamic partitioning to improve the efficiency of stability analysis. By constructing a Lyapunov-Krasovskii functional (LKF) containing multiple time-delay terms and using a novel integral inequality processing technique, the effects of multiple time delays are effectively characterized, and the conservatism of the stability criterion is significantly reduced, resulting in more compact stability analysis results. Furthermore, this application designs a non-fragile dissipative controller (NFDC), which can effectively cope with controller gain disturbances and system uncertainties (two types), significantly improving system robustness.

[0080] Instruction manual illustrations

[0081] Figure 1 This is a schematic diagram of the multi-region system studied in this application;

[0082] Figure 2 For the first in this application Transfer function model diagram of a regional power system;

[0083] Figure 3 The deviation variable under MTD in this application and Evolutionary diagram;

[0084] Figure 4 This is a schematic diagram of the system evolution under additive perturbations of different parameters in this application;

[0085] Figure 5 This is a schematic diagram of the system evolution under multiplicative perturbations of different parameters in this application;

[0086] Figure 6 This is a state response diagram of two regions with additive perturbation of the controller in this application;

[0087] Figure 7 This is a state response diagram of two regions with controller multiplicative perturbation in this application. Specific Implementation

[0088] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this application. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0089] like Figure 1 and 2 As shown, a design method for a multi-region power system controller based on a reconfiguration approach includes:

[0090] S1. Construct a power system load frequency control model under the coupling of high-penetration wind power and multiple time delays. Specifically:

[0091] S1.1, Construct the first one with MTD The closed-loop model of the regional load frequency control system is characterized as follows:

[0092] .

[0093] S1.2, Based on S1.1, the state-space model for multi-region load frequency control is represented as follows:

[0094] ,

[0095] in,

[0096] ,

[0097] ,

[0098] ,

[0099] ,

[0100] ,

[0101] ,

[0102] ,

[0103] ,

[0104] .

[0105] S1.3, Based on S1.2, the time-varying delay satisfies:

[0106] .

[0107] S2. Introduce reconfiguration technology to dynamically partition the power system load frequency control model in S1. Specifically:

[0108] S2.1 Based on the physical properties of the power system load frequency control model, the state variables are divided into two categories using reconfiguration technology: one category consists of state variables directly affected by time delay, and the other category consists of state variables unrelated to time delay, even if:

[0109] ,

[0110] .

[0111] S2.2, through the transition matrix Multiply, we get:

[0112] .

[0113] S2.3. Based on model reconstruction technology, the normal system of the state-space model of multi-region load frequency control in S1.2 is characterized as follows:

[0114] ,

[0115] in,

[0116] ,

[0117] ,

[0118] ,

[0119] ,

[0120] ,

[0121] ,

[0122] ,

[0123] ,

[0124] ,

[0125] ,

[0126] ,

[0127] ,

[0128] .

[0129] Proportional-integral controller design with disturbance term:

[0130] No. The area control error is defined as follows:

[0131] ,

[0132] PI controllers exhibit high reliability and stability in practical engineering applications. Therefore, to track frequency variations in a multi-regional power system, we utilize the following PI controller:

[0133] ,

[0134] However, power systems face a variety of uncertainties. Adding disturbances to the controller can reduce the system's sensitivity to external attacks or faults, thereby improving the overall system reliability. Based on this, and combined with anti-interference processing, the following input controller expression is constructed:

[0135] .

[0136] S3. Based on S2, construct a Lyapunov-Krasovskii functional containing multi-time-delay information, and apply a novel integral inequality to precisely solve the integral terms in the Lyapunov-Krasovskii functional. Specifically:

[0137] S3.1, Theorem 1, when there exists a positive definite symmetric matrix , , , Moreover, there exists a real symmetric matrix. , And satisfy the following linear matrix inequalities:

[0138] ,

[0139] ,

[0140] ,

[0141] ,

[0142] Then, for a given state-space model of multi-region load frequency control in S2.3, the normal system is... , It is asymptotically stable.

[0143] S3.2 To verify the asymptotic stability in S3.1, the Lyapunov-Krasovskii functional is constructed:

[0144]

[0145] ,

[0146] in,

[0147] ,

[0148] ,

[0149] .

[0150] S3.3. Based on the V-function reasoning, the integral term of the system state derivative can be estimated by upper bound as a term about the state variable. The quadratic form function of has a corresponding matrix that satisfies the following structure:

[0151]

[0152] ,

[0153] in,

[0154] .

[0155] S3.4, External interference Under the given conditions, the derivative of the Lyapunov-Krasovskii functional of the system ultimately satisfies:

[0156] .

[0157] in,

[0158]

[0159] ,

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175]

[0176]

[0177]

[0178]

[0179] To demonstrate system stability, LKF was chosen, as detailed below:

[0180] ,

[0181] in:

[0182]

[0183]

[0184] ,

[0185] So, The time derivative is shown below:

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192] Here, we use a modified version of the Bessel-Legend inequality to scale. The integral term. Therefore, the following inequality holds:

[0193]

[0194]

[0195] in,

[0196]

[0197] Then, based on the system formula in 2.3, the following equation is obtained:

[0198]

[0199] Finally, based on the analysis in the above formula, the following inequality holds:

[0200]

[0201] Clearly, the right side of the above inequality constitutes a statement about The quadratic polynomial. This ensures that the inequalities in S3.1 hold.

[0202] Theorem 2, if a positive definite symmetric matrix , , and There exists a real symmetric matrix. and And satisfying the following LMI, then for a given and In S2.3, the system is asymptotically stable:

[0203]

[0204]

[0205] .

[0206] in,

[0207]

[0208]

[0209]

[0210]

[0211]

[0212] .

[0213] Theorem 3, if a positive definite symmetric matrix , , and There exists a real symmetric matrix. and And satisfying the following LMI, then for a given and Asymptotically stable in S2.3:

[0214]

[0215]

[0216] .

[0217] in,

[0218] To prove stability, we construct the following augmented LKF:

[0219]

[0220] ,

[0221] in:

[0222] ,

[0223] ,

[0224] So, The time derivative is shown below:

[0225]

[0226]

[0227] ,

[0228] in:

[0229] ,

[0230] Then, according to the system formula in S2.3, the following equation is obtained:

[0231] ,

[0232] in: .

[0233] Finally, based on the analysis in the above formulas, the following inequality holds:

[0234] ,

[0235] Therefore, if any one All can be derived and The conclusion that holds true is that the system in S2.3 is strictly valid. - Dissipative.

[0236] In the above process, if and It is unknown, then There will be a nonlinear term in it, which makes it difficult to find the given... The controller parameters are defined as follows. Therefore, in this embodiment, the control gain matrix and other symbols are defined as follows:

[0237]

[0238]

[0239] and .

[0240] Next, multiply (22) by the left and right sides respectively. and We obtain LMIs (11) and (12). The output feedback controller gain matrix can be designed as follows: .

[0241] S4. Based on S3, develop a design and performance evaluation mechanism for non-fragile dissipative controllers that consider disturbance terms. Specifically:

[0242] S4.1, the first The area control error is defined as:

[0243] .

[0244] S4.2 To track frequency changes in a multi-regional power system, we use the following PI controller:

[0245] .

[0246] S4.3. Combining anti-interference processing, the following input controller expression is constructed:

[0247] .

[0248] S4.4 When dealing with the controller's disturbance term, consider both additive and multiplicative disturbances. Additive disturbances mainly describe absolute errors independent of the system state, while multiplicative perturbations characterize relative errors related to the system state, such that:

[0249] ,

[0250] ,

[0251] in, and It is a constant matrix. To meet The unknown matrix.

[0252] To make this application easier to understand, the following explanation is based on specific experiments.

[0253] Numerical examples are provided to verify the effectiveness of the stability criterion in Theorem 1, and the effectiveness of the frequency control framework for enhanced non-fragile dissipative loads in high-penetration multi-regional power systems based on the reconfiguration method. The following is a parameter list for the LFC system:

[0254]

[0255]

[0256]

[0257]

[0258] In the experiment, we conducted an in-depth analysis of the stability of the power system under different controllers, paying particular attention to the effect of time delay. Based on Theorem 1, we obtained the maximum allowable upper bound of the time delay. This ensures the stable operation of the system under various controller configurations. Furthermore, to verify the superiority of Theorem 1, we conducted a detailed comparison of these results with existing literature, and summarized the comparison results in Tables 1 and 2 for reference.

[0259] Table 1: At that time, the maximum effective upper limit comparison of a single-area LFC system

[0260]

[0261] Table 2: At that time, the maximum effective upper limit comparison of a single-area LFC system

[0262]

[0263] These tables clearly demonstrate that Theorem 1 is significantly superior to other studies in calculating delay margin. This advantage fully proves that the superiority of Theorem 1 in calculating delay margin is not only reflected in theoretical analysis but also strongly supported by experimental data.

[0264] Next, the dynamic characteristics of the dual-region system MTD were further discussed. Figure 3 The changes in deviation variables in two different regions under MTD conditions are visually displayed. The results show that Theorem 1 can more effectively control system stability, providing a theoretical basis for system design and control strategy optimization. Through comprehensive analysis of system performance under different delay conditions, experimental results verify the effectiveness and applicability of Theorem 1.

[0265] Furthermore, to visually observe the controller's response characteristics and stability performance under different perturbation conditions, we used different perturbation intensities and types to simulate the impact of external perturbations on the system. Experimental results are as follows: Figure 4 and Figure 5 As shown in the figure, when the system is subjected to external disturbances, the controller can respond quickly and effectively counteract the effects of these disturbances, causing the system state trajectory to converge rapidly to a stable state. Experimental results also demonstrate that the controller possesses good adaptability and strong performance advantages. Even under conditions of large disturbance intensity or complex disturbance types, the controller can still maintain system stability and exhibits good robustness.

[0266] Finally, based on previous single-region system experiments, this embodiment takes a two-region LFC system as the research object. Given an upper bound on the time delay, the corresponding controller gain is calculated according to Theorem 2 and Theorem 3. Based on the obtained values, the behavior of the system with additive and multiplicative disturbances in the controller is as follows: Figure 6 and 7 As shown in the figure. The results indicate that the controller has good anti-interference capability under different disturbances, and can effectively cancel these external disturbances, enabling the system state trajectory to converge quickly to a stable state.

[0267] This paper discusses the challenges of nonfragile dissipative control (LFC) in multi-region power systems, particularly in the cases of HPW and MTD. First, a time-delay-based dynamic model partitioning technique is implemented through integrated reconfiguration, significantly improving the computational efficiency of stability analysis. Then, an LKF incorporating delay terms is constructed, effectively capturing the impact of multiple delays on stability analysis. A novel integral inequality is used to handle the integral terms in the LKF, greatly reducing the conservatism of the stability criterion. Next, additive and multiplicative controller gain disturbances are carefully considered in the design of the NFDC. Finally, rigorous simulation experiments verify the superiority of the proposed stability criterion. These experiments also demonstrate the robustness and effectiveness of the proposed control method in maintaining system stability under the complex dynamics introduced by HPW and MTD.

[0268] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A design method for a multi-region power system controller based on a reconfiguration approach, characterized in that, include: S1. Construct a power system load frequency control model under the coupling of high-penetration wind power and multiple time delays; S2. Introduce reconfiguration technology to dynamically divide the power system load frequency control model in S1; S3. Based on S2, construct a Lyapunov-Krasovskii functional containing multi-delay information, and apply a novel integral inequality to precisely solve the integral terms in the Lyapunov-Krasovskii functional; S4. Based on S3, formulate a non-fragile dissipative controller design and performance evaluation mechanism that considers disturbance terms.

2. The design method for a multi-region power system controller based on the reconfiguration method as described in claim 1, characterized in that, S1 includes: S1.1, Construct the first one with MTD The closed-loop model of the regional load frequency control system is characterized as follows: ； S1.

2. Based on S1.1, the state-space model for multi-region load frequency control is characterized as follows: ， in, ， ， ， ， ， ， ， ， ； S1.

3. Based on S1.2, the time-varying delay satisfies: 。 3. The design method for a multi-region power system controller based on the reconfiguration method as described in claim 2, characterized in that, S2 includes: S2.1 Based on the physical properties of the power system load frequency control model, the state variables are divided into two categories using reconfiguration technology: one category consists of state variables directly affected by time delay, and the other category consists of state variables unrelated to time delay, even if: ， ； S2.2, through the transition matrix Multiply, we get: ； S2.

3. Based on model reconstruction technology, the normal system of the state-space model of multi-region load frequency control in S1.2 is characterized as follows: ， in, ， ， ， ， ， ， ， ， ， ， ， ， 。 4. The design method for a multi-region power system controller based on the reconfiguration method as described in claim 3, characterized in that, S3 includes: S3.1 When a positive definite symmetric matrix exists , , , Moreover, there exists a real symmetric matrix. , And satisfy the following linear matrix inequalities: ， ， ， ， Then, the normal system of the state-space model of the multi-region load frequency control in S2.3 is given... , It is asymptotically stable; S3.2 To verify the asymptotic stability in S3.1, the Lyapunov-Krasovskii functional is constructed: ， in, ， ， ； S3.

3. Based on the V-function reasoning, the integral term of the system state derivative can be estimated by upper bound as a term about the state variable. The quadratic form function of has a corresponding matrix that satisfies the following structure: ， in, ； S3.4, External interference Under the given conditions, the derivative of the Lyapunov-Krasovskii functional of the system ultimately satisfies: 。 5. The design method for a multi-region power system controller based on the reconfiguration method as described in claim 4, characterized in that, S4 includes: S4.1, the first The area control error is defined as: ； S4.2 To track frequency changes in a multi-regional power system, we use the following PI controller: ； S4.

3. Combining anti-interference processing, the following input controller expression is constructed: ， S4.4 When dealing with the controller's disturbance term, consider both additive and multiplicative disturbances. Additive disturbances mainly describe absolute errors independent of the system state, while multiplicative disturbances characterize relative errors related to the system state, such that: ， ， in, and It is a constant matrix. To meet The unknown matrix.

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