A Plug-and-Play Load Frequency Control Method for Power Systems Based on Invariant Sets

Abstract

This application belongs to the field of power system load frequency control, specifically disclosing a plug-and-play power system load frequency control method based on invariant sets. The method includes: constructing a load frequency control model for a multi-region interconnected power system; predefining fixed-scale alliance subsystems within each control region, and constructing a two-layer control architecture of centralized control within the alliance and decentralized control between alliances; constructing a state feedback control law, using invariant set theory to constrain the state of the closed-loop system within an ellipsoidal invariant set using linear matrix inequalities; and using the absolute error integral of the frequency deviation and the time-weighted absolute error integral as optimization objectives, employing the Grey Wolf optimization algorithm to globally optimize the invariant set parameters and control gain, and substituting these into the state feedback control law to perform load frequency control on the system. This application can effectively improve the robustness and adaptability of power system load frequency control in plug-and-play operation scenarios with frequent unit switching.

Description

Technical Field

[0001] This application belongs to the field of power system load frequency control, and more specifically, relates to a plug-and-play power system load frequency control method based on invariant sets. Background Technology

[0002] Load Frequency Control (LFC), as a core control mechanism to ensure the balance of active power supply and demand, maintain system frequency stability and power supply reliability in multi-regional interconnected power systems, is a key support for the safe and stable operation of power systems. With the continuous integration of high proportions of renewable energy into the grid, the grid topology is becoming increasingly complex. The plug-and-play operation scenario of generator units frequently switching on and off due to planned maintenance, fault outages, and other operating conditions directly changes the system's equivalent inertia and frequency regulation capability. This can easily lead to the failure of pre-designed control strategy parameters, causing significant frequency deviations or even system instability. This places stringent industry demands on the flexibility, robustness, and adaptability of load frequency control schemes.

[0003] In existing plug-and-play design schemes for power systems, traditional proportional-integral (PI) control has limited adaptability to the nonlinear characteristics and dynamic changes in the topology of power systems. In plug-and-play scenarios, it is prone to problems such as large control overshoot, slow convergence, and even control instability. While distributed control schemes can achieve decoupling between regions and improve the frequency regulation autonomy of each control region, they generally neglect the coordination and adaptation capabilities between multiple units within the same control region. Furthermore, they are mostly designed for fixed system topologies, and unit switching can easily lead to a significant decrease in control performance, failing to meet the core requirements of plug-and-play operation. In addition, while control schemes based on invariant set theory can ensure closed-loop stability through state constraints, they do not fully integrate with the multi-unit coordinated control architecture and cannot avoid the control system dimension reconstruction problems caused by dynamic unit switching, resulting in high computational burden and insufficient adaptability.

[0004] Therefore, improving the robustness and adaptability of power system load frequency control in plug-and-play operation scenarios with frequent unit switching is an urgent problem to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this application is to provide a plug-and-play power system load frequency control method based on invariant sets, which can improve the robustness and adaptability of power system load frequency control in plug-and-play operation scenarios with frequent unit switching.

[0006] To achieve the above objectives, in a first aspect, this application provides a plug-and-play power system load frequency control method based on invariant sets, comprising the following steps: S10, Construct a load frequency control model for a multi-region interconnected power system. This model defines each control region as an independent controlled subsystem containing multiple generator sets and unknown disturbances, and establishes the state-space expression for each region. S20: Predefine a fixed-size alliance subsystem within each control area to construct a two-layer control architecture that centrally controls multiple generator sets within the alliance and maintains decentralized control between alliances. S30. Construct a state feedback control law based on the state space expression, substitute the state feedback control law into the state space expression to obtain a closed-loop system, and use linear matrix inequalities based on invariant set theory to constrain the state of the closed-loop system within an ellipsoidal invariant set to ensure the stability of the closed-loop system. S40, based on the aforementioned dual-layer control architecture, with the absolute error integral and time-weighted absolute error integral of the system frequency deviation as optimization objectives, the Grey Wolf optimization algorithm is used to globally optimize the invariant set parameters and control gain to obtain the optimal control parameters. These optimal control parameters are then substituted into the state feedback control law, which is used to control the load frequency of the system.

[0007] As a further preferred embodiment, in step S10, the state-space expression for each region is:

[0008] In the formula, For the region i The system state variables; For the region i Control input; For random perturbations; For the region i The output variable; A i The state matrix, B i For the input matrix, F i Here is the perturbation matrix. C i This is the output matrix; The state matrix A i Input matrix B i and output matrix C i The specific expression is:

[0009]

[0010] In the formula, For the region iThe generator damping coefficient; For the region i The moment of inertia of the generator; For the region i No. k The turbine time constant of the generator set; For the region i No. k The time constant of the speed controller; For the region i No. k The droop coefficient of the speed controller; For the region i No. k Taiwanese crew participation factor.

[0011] As a further preferred embodiment, in step S20, the dual-layer control architecture is configured as follows: multiple generator sets within the same alliance adopt a centralized control strategy to achieve coordinated frequency regulation of multiple units; different alliances maintain decentralized control to maintain inter-regional decoupling and coordinated operation; when a generator set is temporarily switched on or off, only the local control parameters within the corresponding alliance are updated, without modifying the control interaction logic between alliances.

[0012] As a further preferred embodiment, the state feedback control law constructed in step S30 is:

[0013] Substituting the control law into the state-space expression, we obtain the closed-loop system expression:

[0014] In the formula, The control gain matrix to be designed; This is the state matrix of the closed-loop system.

[0015] As a further preferred embodiment, in step S30, the ellipsoidal invariant set is defined as:

[0016] in, It is a positive definite symmetric matrix; Based on Lyapunov stability theory, Schur's complement lemma, and the S-Procedure, for any positive definite matrix... In any Under bounded perturbation, if and only if there exists a nonnegative constant. Sum of positive real numbers , making the matrix When the following linear matrix inequality is satisfied, the ellipsoid set The system is state invariant and has an attractive set:

[0017] in ; It is a symmetric matrix.

[0018] As a further preferred option, in step S30, when constraining the state of the closed-loop system within the ellipsoidal invariant set using linear matrix inequalities, the controller parameter design is also transformed into solving an optimization function. By using Schur's complement lemma, the optimization problem is equivalently transformed into solving a feasible solution problem using linear matrix inequalities, and the feasible interval of the invariant set parameters is derived. Within this interval, the objective function is a strictly convex function, and there exists a unique optimal solution.

[0019] As a further preferred embodiment, in step S30, the process of ensuring the stability of the closed-loop system based on invariant set theory includes: constructing a Lyapunov function. By differentiating the Lyapunov function and combining the bounded perturbation condition with the S-Procedure, the invariant set constraint is transformed into a matrix inequality. The linear matrix inequality condition is obtained through Schur's complement lemma, which makes the system state converge to the ellipsoidal invariant set, thus achieving asymptotic stability of the closed-loop system.

[0020] As a further preferred embodiment, in step S40, the optimization objective function formed by the absolute error integral of the system frequency deviation and the time-weighted absolute error integral is:

[0021] In the formula, , These are the weighting coefficients; For the region i Frequency deviation.

[0022] As a further preferred option, in step S40, the Grey Wolf optimization algorithm is used to perform global optimization of the invariant set parameters and control gain, specifically as follows: Input the load frequency control system parameters, initial control gain value, initial individuals of the invariant set parameters, population size, and maximum number of iterations; Initialize the individual positions of the gray wolf population, i.e., the invariant set parameters to be optimized; Substitute the individual gray wolf positions into the load frequency control system and calculate the optimal objective function value; Update the position of the individual gray wolves according to the iterative formula of the gray wolf optimization algorithm; Determine if the number of iterations has reached the preset maximum value. If not, continue iterating; if it has, terminate the iteration. Output the optimal invariant set parameters and the corresponding optimal control gain.

[0023] Secondly, this application provides a plug-and-play power system load frequency control system based on invariant sets, for implementing the method described in any one of the above, comprising: The model building unit is used to build a load frequency control model for a multi-region interconnected power system. The model defines each control region as an independent controlled subsystem containing multiple generator sets and unknown disturbances, and establishes the state-space expression for each region. The control architecture building unit is used to predefine a fixed-size alliance subsystem in each control area to build a two-layer control architecture that centrally controls multiple generator sets within the alliance and maintains decentralized control between alliances. The controller design unit is used to construct a state feedback control law based on the state space expression, substitute the state feedback control law into the state space expression to obtain a closed-loop system, and constrain the state of the closed-loop system within an ellipsoidal invariant set using linear matrix inequalities based on invariant set theory to ensure the stability of the closed-loop system. The parameter optimization and control unit is used to optimize the system based on the two-layer control architecture, with the absolute error integral and time-weighted absolute error integral of the system frequency deviation as the optimization objectives. The gray wolf optimization algorithm is used to globally optimize the invariant set parameters and control gain to obtain the optimal control parameters. The optimal control parameters are then substituted into the state feedback control law, and the state feedback control law is used to control the load frequency of the system.

[0024] The beneficial effects of this application are as follows: This application proposes a load frequency control scheme based on invariant set state feedback that integrates the advantages of decentralized control decoupling with the adaptability of coalition control structure. This scheme first decomposes the multi-region load frequency control system into independent controlled subsystems subject to external disturbances through inter-regional decoupling. Then, a predefined coalition structure is constructed within each control region, forming a control architecture with centralized coordination within the coalition and decentralized coordination between coalitions. Simultaneously, linear matrix inequalities are used to constrain the system state within an invariant ellipsoid set to ensure closed-loop system stability. Furthermore, a gray wolf optimizer is used to optimize the control gain to minimize frequency deviation. During dynamic unit switching, only local parameters within the corresponding coalition need to be adjusted, without large-scale reconfiguration of the control architecture. This effectively solves the problem of insufficient robustness and adaptability of power system load frequency control in scenarios with high renewable energy penetration and frequent plug-and-play operation. Attached Figure Description

[0025] Figure 1 This is a multi-regional power system model diagram considering unknown disturbances provided in the embodiments of this application; Figure 2(a) is the frequency response curve of the system in region 1 under scenario 1 provided in the embodiment of this application; Figure 2(b) shows the frequency response curve of region 3 under scenario 1 provided in the embodiment of this application; Figure 3(a) shows the frequency response curve of region 1 under scenario 2 provided in the embodiment of this application; Figure 3(b) shows the frequency response curve of region 3 under scenario 2 provided in the embodiment of this application; Figure 4(a) is the frequency response curve of the system in region 1 under scenario 3 provided in the embodiment of this application; Figure 4(b) shows the frequency response curve of region 3 under scenario 3 provided in the embodiment of this application; Figure 5(a) is the frequency response curve of the system in region 1 under scenario 4 provided in the embodiment of this application; Figure 5(b) shows the frequency response curve of region 3 under scenario 4 provided in the embodiments of this application. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0027] This application addresses the load frequency control requirements of power systems in scenarios involving high proportions of renewable energy integration and frequent plug-and-play operation of generating units. Based on invariant set theory, it integrates distributed control and coalition control architectures. Through a complete process of state feedback controller design, linear matrix inequality stability constraints, and grey wolf optimizer parameter optimization, it achieves stable frequency control and seamless plug-and-play adaptation of the power system. The specific implementation steps are as follows: Step 1: Construct a load frequency control model for a multi-regional interconnected power system Define regions in a multi-region LFC system output variables and system state variables Each control area contains k generator sets consisting of governors and non-reheat steam turbines. To address the random disturbances caused by renewable energy equipment access and user-side load fluctuations, based on the above model, a system is constructed as follows: Figure 1 The diagram shows a multi-zone load frequency control system that includes unknown disturbances.

[0028] Based on the above model, the state-space expression of the i-th region is defined as follows:

[0029] in

[0030] The specific expressions for each submatrix are shown below, where, This is the generator damping coefficient. For the generator's moment of inertia, Let be the turbine time constant of the k-th generator in region i. The time constant of the speed controller, This is the governor droop coefficient. This refers to the unit participation factor.

[0031]

[0032] Step 2: Design a load frequency control scheme based on invariant set state feedback To achieve seamless, plug-and-play operation of generating units, a fixed-size alliance subsystem is predefined within each control area, constructing a two-tiered architecture of centralized coordination within the alliance and decentralized control between alliances. This architecture involves: centralized control strategies for multiple generating units within the same alliance to achieve coordinated frequency regulation and fully exploit the unit's frequency regulation capabilities; and decentralized control between different alliances to maintain decoupling and coordinated operation between regions, ensuring a fixed number and dimensions of alliance subsystems.

[0033] Under this architecture, when a unit is temporarily switched on or off, only the local control parameters within the corresponding alliance need to be updated. There is no need to modify the control interaction logic between alliances or to carry out a large-scale reconstruction of the overall control system architecture, which provides structural support for the plug-and-play capability of the LFC system.

[0034] To ensure the actual stability of the LFC system under bounded disturbances, a load frequency control scheme based on invariant sets was designed as shown below.

[0035] 1. Constructing a state feedback control law First, based on the system model established in step 1, the state feedback control law is constructed as shown below:

[0036] In the formula, Let be the control gain matrix to be designed. Substituting the control law into the system state-space equations, we obtain the closed-loop system expression:

[0037] in, This is the state matrix of the closed-loop system.

[0038] 2. Design of control scheme based on invariant sets To ensure the closed-loop stability of the system under bounded perturbations, the following ellipsoidal invariant set is defined:

[0039] In the formula, It is a positive definite symmetric matrix.

[0040] Then, based on Lyapunov stability theory, Schur complement lemma and S-Procedure, the following control scheme design can be obtained.

[0041] For any positive definite matrix In any Under bounded perturbation, if and only if there exists a nonnegative constant. Sum of positive real numbers , making the matrix When the following linear matrix inequality is satisfied, the ellipsoid set Since the system's state remains unchanged and it has an attractive set, the designed state feedback controller can guarantee the system's closed-loop stability.

[0042] in , It is a symmetric matrix.

[0043] To prove the above control scheme, we first construct the Lyapunov function as shown below:

[0044] Differentiating equation (6) above, we get:

[0045] Assume the bounded perturbation satisfies By combining the S-Procedure to transform the invariant set constraint into a matrix inequality, and then simplifying it using Schur's complement lemma, we obtain the above condition (5). This proves that when the linear matrix inequality (5) is satisfied, for all... ,have This means that once the system state enters the ellipsoid set, it will always be constrained within the set, illustrating that the set... The invariance of.

[0046] To further illustrate the convergence properties of the Lyapunov function, solve the following differential inequality:

[0047] We can obtain:

[0048] From equation (7), it can be seen that when hour, This demonstrates that regardless of the initial values, the system state will eventually converge to the ellipsoidal invariant set, which is attractive, and the system is asymptotically stable in closed loop.

[0049] 3. Optimization of control objectives To minimize the power system frequency deviation, the controller parameter design is transformed into the following optimization function:

[0050] Using Schur's complement lemma, the optimization problem (8) can be equivalently transformed into the problem of finding the feasible solution of the LMI mentioned above. Simultaneously, the parameters are derived. The feasible interval is .in For matrix eigenvalues, and objective function It is a strictly convex function within this interval, therefore there exists a unique optimal solution.

[0051] Step 3: Design the optimal control gain tuning scheme based on the GWO algorithm For the feasible region of parameters obtained in step 2, GWO is used to perform global optimization on the invariant set parameters and control gain, with the goal of minimizing frequency deviation, to obtain the optimal control parameters.

[0052] First, we select the absolute error integral and the time-weighted absolute error integral of the system frequency deviation, and construct the following optimization objective function:

[0053] In the formula, , This is a weighting coefficient, which can be adjusted according to frequency modulation requirements.

[0054] Based on the above objective function, the following parameter optimization process is defined:

[0055] The key point of this embodiment is: (1) This scheme adopts a two-layer control architecture of decentralized decoupling between regions and alliance coordination within regions. With fixed control subsystem dimensions, only the local parameters of the corresponding alliance need to be adjusted when the unit is switched on or off, without the need for large-scale reconstruction of the control system, providing structural support for plug-and-play operation. (2) Based on the invariant ellipsoid set and linear matrix inequality constraint system state, combined with Lyapunov theory, Schur complement lemma and S-Procedure to ensure closed-loop stability, the system state is always constrained within the safe set under bounded perturbation, and has strong robustness. (3) Taking the absolute error integral of frequency deviation and the time-weighted absolute error integral as the optimization objectives, the invariant set parameters and control gain are globally optimized by the Grey Wolf Optimization Algorithm to achieve the minimization of frequency deviation and the improvement of dynamic response speed.

[0056] This embodiment conducts simulation experiments under four different control scenarios. The designed SFLFC scheme based on invariant sets is compared with the PILFC scheme and the ISMLFC scheme through MATLAB / Simulink simulation tests to verify the superiority of the method proposed in this chapter.

[0057] First, a three-region single-branch LFC power system model was built in the simulation platform, and its main simulation parameters are shown in Table 1.

[0058] Table 1 Parameters of Three-Zone Single-Branch LFC System

[0059] Select the power parameters for the three-zone tie line as follows: , , During the test, random disturbances generated by the renewable energy system and user-side loads were injected into the three areas, with amplitudes of [missing information]. ..set up Based on Algorithm 1 and the above system parameters ( The optimal parameters were calculated to be: The corresponding controller gain is: K1 = [ 14.9269, 9.25070, 10.3674, 0.9839, 51.5914] K2 = [ 20.2078, 20.5161, 9.66860, 0.4432, 91.2269] K3 = [ 8.78130, 5.64170, 7.25100, 0.5954, 41.4222).

[0060] To verify the effectiveness and advantages of the designed state feedback load frequency control method based on invariant sets, tests were conducted in the following two scenarios: Scenario 1: Area 3 is connected to the power system after 10 seconds; Scenario 2: Area 3 leaves the power system after 10 seconds.

[0061] In scenario 1, region 1 and region 2 maintain interconnected operation, while region 3 operates independently. At 10 seconds, region 3 connects to the power system, achieving interconnected and coordinated operation with regions 1 and 2. In scenario 2, the three regions initially maintain interconnected operation; at 10 seconds, region 3 disconnects from the system and switches to independent operation mode, while regions 1 and 2 maintain interconnected and coordinated operation. The performance of three different control schemes was tested in both scenarios, and the simulation results are shown in Figures 2(a), 2(b), 3(a), and 3(b).

[0062] In scenario 1, a frequency disturbance is triggered when region 3 is connected to the power system at 10 seconds. All three control schemes respond to the disturbance. Among them, the SFLFC scheme proposed in this application exhibits superior frequency deviation dynamic performance: compared to the large overshoot of the traditional PILFC scheme and the continuous frequency fluctuation of the ISMLFC scheme, the SFLFC scheme significantly reduces the frequency deviation overshoot, shortens the settling time to less than 12 seconds, and can quickly converge to near the rated frequency after the disturbance occurs, demonstrating stronger initial disturbance suppression capability.

[0063] In scenario 2, unlike scenario 1, all three regions maintain their respective frequency stability before the 10th second. Therefore, after region 3 is disconnected from the power system, the system frequency deviation under the three control schemes does not show significant changes. However, when the system is disturbed, the frequency deviation amplitude of the SFLFC scheme proposed in this application is smaller than that of the other two schemes. At the same time, after region 3 is disconnected, its own frequency hardly fluctuates, further demonstrating the superior robustness and operational stability of the scheme of this invention.

[0064] Then, to further illustrate the applicability and effectiveness of the proposed solution, a three-region, three-branch LFC power system model was rebuilt on the simulation platform, and its main simulation parameters are shown in Table 2.

[0065] Table 2 Parameters of the Three-Area Three-Branch LFC System

[0066] Select the power parameters for the three-zone tie line as follows: , , During the test, random disturbances generated by the renewable energy system and user-side loads were injected into the three areas, with amplitudes of [missing information]. ..set up Based on Algorithm 1 and the above system parameters ( The optimal parameters were calculated to be: The corresponding controller gain is: K1 = [-1.89, -0.09, -0.72, -0.82, -0.819, -0.62, 0, 0.22, -0.97] K2 = [-0.12, -0.00, -0.15, -0.26, -0.15, -0.25, 1.1, -0.2, -0.31] K3 = [-0.04, 0.03, -0.16, -0.15, -0.23, -0.2, -0.17, 1.01, -0.31].

[0067] To verify the effectiveness and advantages of the designed state feedback load frequency control method based on invariant sets, tests were conducted in the following two scenarios: Scenario 3: Area 3 is connected to the power system at 50 seconds; Scenario 4: Area 3 leaves the power system at 50 seconds.

[0068] In scenario 3, region 1 and region 2 maintain interconnected operation, while region 3 operates independently. At 50 seconds, region 3 is connected to the power system, achieving interconnected and coordinated operation with regions 1 and 2. In scenario 4, the three regions initially maintain interconnected operation; at 50 seconds, region 3 is disconnected from the system and switches to independent operation mode, while regions 1 and 2 still maintain interconnected and coordinated operation. Furthermore, unit 1 of region 1 trips offline at 40 seconds and reconnects to the grid at 90 seconds; unit 4 of region 2 trips offline at 20 seconds, and unit 7 of region 3 reconnects to the grid at 70 seconds. This operational configuration is maintained until the end of the simulation. The performance of three different control schemes was tested in both scenarios, and the results are shown in Figures 4(a), 4(b), 5(a), and 5(b).

[0069] In scenario 3, the ISMLFC scheme converges quickly after the power system experiences an initial disturbance. However, after region 3 is integrated into the power system, the frequency fluctuation duration of this scheme exceeds 40 seconds, resulting in a relatively long settling time. Furthermore, the traditional PILFC scheme significantly increases system frequency overshoot and also has a relatively long convergence time. In contrast, the SFLFC scheme of this invention significantly reduces system frequency deviation and can quickly recover stability, demonstrating strong robustness.

[0070] In Scenario 4, when the nine generating units are interconnected, the frequency deviation between ISMLFC and the traditional PILFC scheme further widens. Furthermore, even after Region 3 is disconnected from the power system, continuous frequency fluctuations persist in all regions. In contrast, the power system frequency deviation using the SFLFC scheme proposed in this application is smaller, with no long-term fluctuations. This verifies that the SFLFC scheme proposed in this application can constrain the frequency deviation to a smaller range after the generating units are disconnected or reconnected, exhibiting superior robustness.

[0071] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A plug-and-play power system load frequency control method based on invariant sets, characterized in that, Includes the following steps: S10, Construct a load frequency control model for a multi-region interconnected power system. This model defines each control region as an independent controlled subsystem containing multiple generator sets and unknown disturbances, and establishes the state-space expression for each region. S20: Predefine a fixed-size alliance subsystem within each control area to construct a two-layer control architecture that centrally controls multiple generator sets within the alliance and maintains decentralized control between alliances. S30. Construct a state feedback control law based on the state space expression, substitute the state feedback control law into the state space expression to obtain a closed-loop system, and use linear matrix inequalities based on invariant set theory to constrain the state of the closed-loop system within an ellipsoidal invariant set to ensure the stability of the closed-loop system. S40, based on the aforementioned dual-layer control architecture, with the absolute error integral and time-weighted absolute error integral of the system frequency deviation as optimization objectives, the Grey Wolf optimization algorithm is used to globally optimize the invariant set parameters and control gain to obtain the optimal control parameters. These optimal control parameters are then substituted into the state feedback control law, which is used to control the load frequency of the system.

2. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S10, the state-space expression for each region is: In the formula, For the region i The system state variables; For the region i Control input; For random perturbations; For the region i The output variable; A i The state matrix, B i For the input matrix, F i Here is the perturbation matrix. C i This is the output matrix; The state matrix A i Input matrix B i and output matrix C i The specific expression is: In the formula, For the region i The generator damping coefficient; For the region i The moment of inertia of the generator; For the region i No. k The turbine time constant of the generator set; For the region i No. k The time constant of the speed controller; For the region i No. k The droop coefficient of the speed controller; For the region i No. k Taiwanese crew participation factor.

3. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S20, the dual-layer control architecture is configured as follows: multiple generator sets within the same alliance adopt a centralized control strategy to achieve coordinated frequency regulation of multiple units; different alliances maintain decentralized control to maintain inter-regional decoupling and coordinated operation; when a generator set is temporarily switched on or off, only the local control parameters within the corresponding alliance are updated, without modifying the control interaction logic between alliances.

4. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S30, the constructed state feedback control law is: Substituting the control law into the state-space expression, we obtain the closed-loop system expression: In the formula, The control gain matrix to be designed; This is the state matrix of the closed-loop system.

5. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S30, the ellipsoidal invariant set is defined as: in, It is a positive definite symmetric matrix; Based on Lyapunov stability theory, Schur's complement lemma, and the S-Procedure, for any positive definite matrix... In any Under bounded perturbation, if and only if there exists a nonnegative constant. Sum of positive real numbers , making the matrix The ellipsoid set satisfies the following linear matrix inequality. The system is state invariant and has an attractive set: in ; It is a symmetric matrix.

6. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S30, when constraining the state of the closed-loop system within the ellipsoidal invariant set using linear matrix inequalities, the controller parameter design is transformed into solving an optimization function. By using Schur's complement lemma, the optimization problem is equivalently transformed into solving a feasible solution problem using linear matrix inequalities, and the feasible interval of the invariant set parameters is derived. Within this interval, the objective function is a strictly convex function, and there exists a unique optimal solution.

7. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S30, the process of ensuring the stability of the closed-loop system based on invariant set theory includes: constructing the Lyapunov function. By differentiating the Lyapunov function and combining the bounded perturbation condition with the S-Procedure, the invariant set constraint is transformed into a matrix inequality. The linear matrix inequality condition is obtained through Schur's complement lemma, which makes the system state converge to the ellipsoidal invariant set, thus achieving asymptotic stability of the closed-loop system.

8. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S40, the optimization objective function formed by the absolute error integral of the system frequency deviation and the time-weighted absolute error integral is: In the formula, , These are the weighting coefficients; For the region i Frequency deviation.

9. The plug-and-play power system load frequency control method based on invariant sets as described in claim 1, characterized in that, In step S40, the Grey Wolf optimization algorithm is used to globally optimize the invariant set parameters and control gain, specifically as follows: Input the load frequency control system parameters, initial control gain value, initial individuals of the invariant set parameters, population size, and maximum number of iterations; Initialize the individual positions of the gray wolf population, i.e., the invariant set parameters to be optimized; Substitute the individual gray wolf positions into the load frequency control system and calculate the optimal objective function value; Update the position of the individual gray wolves according to the iterative formula of the gray wolf optimization algorithm; Determine if the number of iterations has reached the preset maximum value. If not, continue iterating; if it has, terminate the iteration. Output the optimal invariant set parameters and the corresponding optimal control gain.

10. A plug-and-play power system load frequency control system based on invariant sets, characterized in that, For implementing the method of any one of claims 1 to 9, comprising: The model building unit is used to build a load frequency control model for a multi-region interconnected power system. The model defines each control region as an independent controlled subsystem containing multiple generator sets and unknown disturbances, and establishes the state-space expression for each region. The control architecture building unit is used to predefine a fixed-size alliance subsystem in each control area to build a two-layer control architecture that centrally controls multiple generator sets within the alliance and maintains decentralized control between alliances. The controller design unit is used to construct a state feedback control law based on the state space expression, substitute the state feedback control law into the state space expression to obtain a closed-loop system, and constrain the state of the closed-loop system within an ellipsoidal invariant set using linear matrix inequalities based on invariant set theory to ensure the stability of the closed-loop system. The parameter optimization and control unit is used to optimize the system based on the two-layer control architecture, with the absolute error integral and time-weighted absolute error integral of the system frequency deviation as the optimization objectives. The gray wolf optimization algorithm is used to globally optimize the invariant set parameters and control gain to obtain the optimal control parameters. The optimal control parameters are then substituted into the state feedback control law, and the state feedback control law is used to control the load frequency of the system.

Images