A design method for fractional-order sliding mode controller to improve grid voltage stability

Abstract

The present invention discloses a fractional-order sliding mode controller optimization design method for improving the transient voltage stability of a power grid. First, based on the fractional-order sliding mode theory, an additional voltage controller is designed. Then, the discrete z-function expression of the system is identified in combination with the least squares criterion. Finally, a parameter optimization model of the additional voltage controller is established based on the designed transfer function of the additional voltage controller and the discrete z-function. On this basis, iterative optimization is performed in combination with a reinforcement learning algorithm to obtain a parameter self-adjustment strategy of the fractional-order sliding mode controller, thereby realizing adaptive updating of the controller parameters under different working conditions, ensuring that the fractional-order sliding mode controller can exert good voltage control effect under different working conditions, and enhancing the voltage stability of the system under variable working conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system voltage stability control, and more specifically, relates to an optimization design method for a fractional-order sliding mode controller for improving transient voltage stability of a power grid. Background Art

[0002] To promote a comprehensive green transformation of economic development, build a new power system dominated by renewable energy generation, promote the large-scale optimization of clean and renewable energy, optimize the energy structure, improve energy utilization efficiency, and accelerate the decarbonization of the power sector, becoming the primary task of power development. Against this backdrop, a high proportion of renewable energy, represented by wind turbines and photovoltaics, is connected to the grid. The intermittent and fluctuating output of renewable energy has profoundly changed the operating characteristics and behavioral traits of the power system, increasing the risks of system operation. Previous studies have shown that the integration of a high proportion of renewable energy leads to insufficient reactive power support capacity, which in turn reduces the grid's voltage support capacity, exacerbates load hollowing, and highlights transient voltage stability issues. Therefore, improving the transient voltage stability of the grid under high renewable energy integration and ensuring the stable transient voltage operation range has become a key issue that urgently needs to be addressed for the safe and stable operation of the power system.

[0003] To improve the transient voltage stability of power systems, scholars at home and abroad have conducted extensive research. The main approach is to deploy static var compensators (SVCs) in the power grid. This not only provides short-circuit capacity for the system but also improves reactive power output characteristics. Based on this, combined with sliding mode control theory, additional voltage controllers are designed to further enhance voltage control. However, controllers designed based on sliding mode control theory are prone to overshoot and oscillation, manifesting as high-frequency "chattering." In severe cases, this can damage controller components and cause system instability, hindering the system's voltage stability control. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a fractional-order sliding mode controller optimization design method for improving the transient voltage stability of the power grid. First, a new fractional-order sliding mode controller is designed using fractional-order sliding mode theory, and a robust parameter tuning method for the controller is given. The fractional-order sliding mode controller uses the increased degrees of freedom of fractional-order calculus operators to effectively reduce chattering and improve the transient voltage stability of the system. The proposed parameter tuning method can maintain the global robustness of the controller under various operating conditions.

[0005] To achieve the above-mentioned object of the invention, the present invention provides an optimization design method for a fractional-order sliding mode controller for improving transient voltage stability of a power grid, characterized by comprising the following steps:

[0006] (1) Design a fractional-order sliding mode controller u;

[0007] (2) Estimation of the power system discrete z function;

[0008] (3) Construct a parameter optimization model for the fractional-order sliding mode controller;

[0009] (4) Real-time acquisition of the input signal U(t) and output signal Y(t) of the power system;

[0010] (5) Perform Laplace transformation on the power system discrete z function to obtain the power system equivalent transfer function G(s);

[0011] (6) The input signal U(t) of the power system is used as the output of the fractional-order sliding mode controller, and the output signal Y(t) is used as the input of the fractional-order sliding mode controller. Then, the parameter optimization model of the fractional-order sliding mode controller is optimized and controlled so that its model value is continuously reduced until the algorithm converges, thereby obtaining the optimal controller parameters.

[0012] The object of the invention of the present invention is achieved like this:

[0013] The present invention discloses an optimization design method for a fractional-order sliding mode controller for improving the transient voltage stability of a power grid. The method comprises the following steps: first, based on the fractional-order sliding mode theory, an additional voltage controller is designed; then, the discrete z-function expression of the system is identified in combination with the least squares criterion; finally, a parameter optimization model of the additional voltage controller is established based on the designed transfer function of the additional voltage controller and the discrete z-function; on this basis, iterative optimization is performed in combination with a reinforcement learning algorithm to obtain a parameter self-adjustment strategy of the fractional-order sliding mode controller, thereby realizing adaptive updating of the controller parameters under different working conditions, ensuring that the fractional-order sliding mode controller can exert good voltage control effect under different working conditions, and enhancing the voltage stability of the system under variable working conditions.

[0014] At the same time, the present invention provides a fractional-order sliding mode controller optimization design method for improving the transient voltage stability of the power grid, which also has the following beneficial effects:

[0015] (1) Applying fractional order theory to the structural design of sliding mode controller overcomes the overshoot and oscillation of traditional sliding mode controller, characterizes the defect of high frequency "jittering" phenomenon, greatly enhances the performance of sliding mode controller, and helps to improve system voltage stability.

[0016] (2) A data-driven system z-function estimation method is proposed to realize the online identification of z-function parameters. Based on this, when optimizing the controller parameters, there is no need to obtain the detailed topology and electrical parameters of the system, which reduces the cost of controller tuning optimization.

[0017] (3) The reinforcement learning algorithm is introduced to solve the parameter model, which can obtain the adaptive update strategy of the controller parameters and realize the online real-time adjustment of the controller parameters, thereby improving the voltage control performance of the controller under different working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of a fractional-order sliding mode controller optimization design method for improving transient voltage stability of a power grid according to the present invention;

[0019] Figure 2 It is a 10-machine, 39-node test system;

[0020] Figure 3 is the voltage deviation trajectory at bus 25 under disturbance 1;

[0021] Figure 4 is the voltage deviation trajectory at bus 9 under disturbance 2;

[0022] Figure 5 It is the voltage deviation trajectory at bus 9 under disturbance 3. DETAILED DESCRIPTION

[0023] The following describes the specific embodiments of the present invention in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, such descriptions will be omitted here.

[0024] Example

[0025] In this embodiment, Figure 2 This is a standard 10-generator, 39-bus test system, consisting of 10 generators and 39 buses. The wind farm, with an installed capacity of 1,250 MW, is attached to bus 7. In addition, a 100 MVar static synchronous compensator (SVC) is also deployed at bus 7 to improve system voltage stability.

[0026] In this embodiment, if Figure 1 As shown in Figure 2, we describe in detail an optimization design method for a fractional-order sliding mode controller to improve transient voltage stability of the power grid, which specifically includes the following steps:

[0027] S1. Design of voltage stability controller based on fractional-order sliding mode theory;

[0028] S1.1. The dynamic model of the static var compensator (SVC) can be expressed as follows:

[0029]

[0030] f(B SVC )=(K A (V ref -V SVC )-B SVC ) / T A

[0031] Among them: K A and T A is the gain and time constant of SVC, which can be set to 25 and 0.05 respectively; V ref Indicates the reference voltage, which is 1p.u.; V SVC Indicates the real-time measured voltage of the SVC installation bus; u w is the output of the fractional-order sliding mode controller; f(B SVC ) is the intermediate variable, B SVC Indicates the output susceptance of the SVC.

[0032] S1.2. Based on the fractional-order sliding mode theory, the sliding mode surface σ of the fractional-order sliding mode controller can be designed as:

[0033] σ=D 1 -ae+Da(λ1sig(e)p 1 +λ2sig(e)q 1 )

[0034] Where, e represents the input of the fractional-order sliding mode controller; D -a (·) is the Caputo fractional derivative; α, λ1, λ2, p1 and q1 are the parameters to be optimized in the fractional-order sliding mode controller.

[0035] S1.3, Considering that when the power system trajectory reaches the sliding surface, there exists σ=0 and Therefore, the above formula can be transformed into:

[0036] D 1 -ae=-Da(λ1sig(e)p 1 +λ2sig(e)q 1 )

[0037] S1.4. Combining the above expressions (1.1) and (1.3), the equivalent control law of the fractional-order sliding mode controller can be expressed as:

[0038]

[0039] S1.5. In order to make the power system trajectory reach the sliding mode surface, the reaching law of the fractional-order sliding mode controller is expressed as:

[0040]

[0041] S1.6. According to the sliding mode control principle, the control rate can be composed of the sum of the equivalent control law and the reaching law. Therefore, the transfer function of the fractional-order sliding mode controller can be expressed as:

[0042]

[0043] S2, estimate the power system discrete z function;

[0044] S2.1. The power system model can be expressed as a z-function:

[0045] Y(t)=θ(z)U(t)

[0046] Wherein, Y(t) and U(t) are the output signal and input signal of the power system at time t, respectively. In this embodiment, U(t) serves as the output of the fractional-order sliding mode controller, and the output signal Y(t) serves as the input of the fractional-order sliding mode controller; θ(z) is the value of the parameter to be identified in the form of the system z function; and z is the function operator.

[0047] S2.2. When solving the actual system, the parameter estimates can be used Indicates that, considering θ and There will be a certain amount of identification error, so the parameter estimation value can be used Replacing the true value θ introduces a residual ε:

[0048]

[0049] S2.3. According to the least squares criterion, the parameter estimate with the minimum residual sum of squares J is the least squares estimate, so J can be expressed as:

[0050]

[0051] S2.4. Transforming the expression in (2.3) yields:

[0052]

[0053] S2.5. Analyzing the expression in (2.4), we can see that the residual sum of squares J consists of two parts. The part before the plus sign is a non-negative number, and the part after the plus sign is related to the parameter The estimated value is irrelevant. To minimize J, the part before the plus sign should be zero, which gives:

[0054]

[0055] The parameter estimates are thus

[0056]

[0057] S2.6. To achieve real-time parameter estimation, the recursive matrix P(k) is introduced. The recursive expression of the parameter estimation value can be expressed as:

[0058]

[0059] Where: λ is the forgetting factor.

[0060] S2.7. To achieve accurate estimation of parameters, during the iteration process, the expression in S2.6 can be used to continuously recursively reduce the value of the performance index J until Or the number of iterations k reaches the preset maximum number of iterations 100 times, the final parameter estimation value can be obtained, where θ set is the threshold, set to 0.05.

[0061] S3, construct the fractional order sliding mode controller parameter optimization model r as:

[0062]

[0063] Among them, ξ set is the pre-designed stability margin.

[0064] S4, real-time acquisition of the input signal U(t) and output signal Y(t) of the power system;

[0065] S5. Perform Laplace transformation on the power system discrete z function to obtain the power system equivalent transfer function G(s);

[0066] S6. The input signal U(t) of the power system is used as the output of the fractional-order sliding mode controller, and the output signal Y(t) is used as the input of the fractional-order sliding mode controller. Then, based on the reinforcement learning theory, the parameter optimization model of the fractional-order sliding mode controller is optimized and controlled so that its model value continuously decreases until the algorithm converges, thereby obtaining the optimal controller parameters.

[0067] Figure 3 The voltage deviation trajectories at bus 25 are shown for three different voltage controllers: a traditional sliding mode controller, a PI controller, and the proposed fractional-order sliding mode controller, under disturbance 1 (a 20% load shedding disturbance at generator G5 in the second second). It can be seen that the proposed fractional-order sliding mode controller has a better ability to suppress voltage oscillations than the traditional sliding mode controller and the PI controller, allowing the bus voltage to recover to a new steady state more quickly. This indicates that the proposed fractional-order sliding mode controller has better voltage control capabilities.

[0068] Figure 4 and Figure 5The voltage fluctuations at bus 9 are shown for three different parameter tuning scenarios: fixed parameters, robust parameter tuning, and the proposed parameter tuning method. These scenarios are triggered by disturbances 2 (a disconnection in the AC line between bus 25 and bus 26) and 3 (a disconnection in the AC line between bus 10 and bus 13). The proposed method can minimize overshoot and shorten the voltage curve adjustment time under different fault scenarios, demonstrating that the proposed parameter tuning method enables the fractional-order sliding mode controller to achieve better voltage control performance.

[0069] Although the above describes the illustrative specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A design method for a fractional-order sliding mode controller for improving grid voltage stability, characterized in that: The following steps are involved: (1) Design a fractional-order sliding mode controller u; (2) Estimation of the power system discrete z function; (3) Construct a parameter optimization model for the fractional-order sliding mode controller; (4) Real-time acquisition of the input signal U(t) and output signal Y(t) of the power system; (5) Perform Laplace transformation on the power system discrete z function to obtain the power system equivalent transfer function G(s); (6) The input signal U(t) of the power system is used as the output of the fractional-order sliding mode controller, and the output signal Y(t) is used as the input of the fractional-order sliding mode controller. Then, the parameter optimization model of the fractional-order sliding mode controller is optimized and controlled so that its model value is continuously reduced until the algorithm converges, thereby obtaining the optimal controller parameters. The design method of the fractional-order sliding mode controller u is as follows: 1) Define the dynamic model of static VAR compensator SVC as: f(B SVC )=(K A (V ref -V SVC )-B SVC ) / T A Among them, K A and T A is the gain and time constant of SVC; V ref Indicates the reference voltage; V SVC Indicates the measured voltage of the SVC installation bus; u w is the output of the fractional-order sliding mode controller; B SVC Indicates the output susceptance of the SVC; 2) Based on the fractional-order sliding mode theory, the sliding mode surface σ of the fractional-order sliding mode controller is designed as; Where, e represents the input of the fractional-order sliding mode controller; D -a (·) is the Caputo fractional derivative; α, λ1, λ2, p1 and q1 are the parameters to be optimized in the fractional-order sliding mode controller; 3) Considering that when the power system trajectory reaches the sliding surface, there are σ=0 and Therefore, the above formula is transformed into: in, is the first-order derivative of σ; 4) Combining the expressions of 1) and 3) above, the equivalent control law of the fractional-order sliding mode controller is expressed as: 5) In order to make the power system trajectory reach the sliding mode surface, the reaching law of the fractional-order sliding mode controller is: 6) According to the sliding mode control principle, the fractional-order sliding mode controller can be composed of the sum of the equivalent control law and the reaching law. Therefore, the transfer function of the fractional-order sliding mode controller u is expressed as:

2. The method for designing a fractional-order sliding mode controller for improving grid voltage stability according to claim 1, characterized in that: The estimation method of the power system discrete z function is: (2.1) The power system model is expressed as a z function: Y(t)=θ(z)U(t) Where Y(t) and U(t) are the output and input signals of the power system at time t, respectively; θ(z) is the value of the parameter to be identified in the form of the power system z function; z is the function operator; (2.2) When solving the actual power system, the parameter estimates are used Indicates that, considering θ and There will be a certain amount of identification error, so the parameter estimation value can be used Replacing the true value θ introduces a residual ε: Where k represents the number of iterations when estimating the value of the parameter to be identified in the power system; (2.3) According to the least squares criterion, the parameter estimate when the residual sum of squares J is the smallest is the least squares estimate, so the residual sum of squares J is expressed as: Wherein, the superscript T indicates transposition; (2.4) Transforming the expression in (2.3), we can get: (2.5) Analyzing the expression in (2.4), we can see that the residual sum of squares J consists of two parts. The part before the plus sign is a non-negative number, and the part after the plus sign is the same as the parameter The estimated value is irrelevant. To minimize J, the part before the plus sign should be zero, which gives: The parameter estimates are thus (2.6) To achieve real-time estimation of parameters, the recursive matrix P(k) is introduced. The recursive expression of the parameter estimation value is expressed as: Where: λ is the forgetting factor; (2.7) The recursive expression of the parameter estimate is continuously solved recursively, so that the value of the performance index J decreases continuously until Or the number of iterations k reaches the preset maximum number of iterations, thereby obtaining the final parameter estimate, where θ set is the threshold.

3. The method for designing a fractional-order sliding mode controller for improving grid voltage stability according to claim 1, characterized in that: The fractional-order sliding mode controller parameter optimization model r is: Among them, ξ set is the pre-designed stability margin.

Images