Fractional order sliding mode controller design method for improving power grid voltage stability

Abstract

The invention discloses a fractional order sliding mode controller optimization design method for improving the transient voltage stability of a power grid, and the method comprises the steps: firstly designing an additional voltage controller based on a fractional order sliding mode theory, and then carrying out the recognition of a discrete z function expression of a system through combining with a least square criterion; and finally, based on the designed transfer function of the additional voltage controller and the discrete z function, establishing a parameter optimization model of the additional voltage controller. On the basis, iterative optimization is carried out in combination with a reinforcement learning algorithm, so that a parameter self-adjustment strategy of the fractional order sliding mode controller is obtained, adaptive updating of controller parameters under different working conditions is realized, and the fractional order sliding mode controller can play a good voltage control effect under different working conditions; and the system voltage stability under variable working conditions is enhanced.

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 of a fractional-order sliding mode controller for improving transient voltage stability of a power grid. Background Art

[0002] In order to promote the 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 electricity, which has become the primary task of power development. In this context, a high proportion of renewable energy represented by wind turbines and photovoltaics is connected to the power grid. The intermittent and volatile output of renewable energy has profoundly changed the operating characteristics and behavioral characteristics of the power system, increasing the risk of system operation. Existing studies have shown that the access of a high proportion of renewable energy leads to insufficient reactive support capacity of the system to a certain extent, thereby reducing the support capacity of the grid voltage, aggravating the hollowing out of the load, and making the transient voltage stability problem prominent. Therefore, how to improve the transient voltage stability of the power grid under the access of a high proportion of renewable energy and ensure the stability domain of the system transient voltage stable operation has become one of the key issues that need to be solved for the safe and stable operation of the power system.

[0003] In order to improve the transient voltage stability of the power system, domestic and foreign scholars have conducted a lot of research. The main method is to configure a static var compensator (SVC) in the power grid, which can not only provide short-circuit capacity for the system, but also have better reactive power output characteristics. Based on this, combined with the sliding mode control theory, an additional voltage controller is designed to further improve the voltage control effect. However, the controller designed based on the sliding mode control theory is prone to overshoot and oscillation, which manifests as a high-frequency "jitter" phenomenon. In severe cases, it will cause damage to the controller components and system instability, which is not conducive to the voltage stability control of the system. Summary of the invention

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

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

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

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

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

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

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

[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 in this way:

[0013] The present invention discloses an optimization design method for a fractional-order sliding mode controller for improving transient voltage stability of a power grid. Firstly, an additional voltage controller is designed based on the fractional-order sliding mode theory, and 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 controller parameters under different working conditions, ensuring that the fractional-order sliding mode controller under different working conditions can exert a good voltage control effect, and enhancing the voltage stability of the system under variable working conditions.

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

[0015] (1) The fractional-order theory is applied to the structural design of the sliding mode controller, which overcomes the overshoot and oscillation of the traditional sliding mode controller and characterizes the high-frequency "jittering" phenomenon, greatly enhancing the performance of the sliding mode controller and helping to improve the 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 topological structure and electrical parameters of the system, which reduces the cost of controller 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 It 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 specific implementation of the present invention is described below 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 the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0024] Example

[0025] In this embodiment, Figure 2 It is a standard 10-machine 39-bus test system, which includes 10 generators and 39 buses. The wind farm is attached to bus 7, and the installed capacity of the wind farm is 1250MW. In addition, a static synchronous compensator SVC with a capacity of 100MVar is also configured at bus 7 to improve the voltage stability of the system.

[0026] In this embodiment, if Figure 1 As shown in the figure, we describe in detail a fractional-order sliding mode controller optimization design method for improving transient voltage stability of 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 static var compensator (SVC) can be expressed as;

[0029]

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

[0031] Where: 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, 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) is the output of the fractional-order sliding mode controller, and the output signal Y(t) is the input of the fractional-order sliding mode controller; θ(z) is the parameter value to be identified in the form of a system z function; z is a function operator.

[0047] S2.2. When solving the actual system, the parameter estimates obtained 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 will introduce a residual ε:

[0048]

[0049] S2.3. Parameter estimates based on the least squares criterion when the residual sum of squares J is minimized is the least squares estimate, so J can be expressed as:

[0050]

[0051] S2.4. Transforming the expression in (2.3), we can obtain:

[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. In order 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. In order to realize the real-time estimation of parameters, the recursive matrix P(k) is introduced, and the recursive expression of the parameter estimation value can be expressed as:

[0058]

[0059] Among them: λ is the forgetting factor.

[0060] S2.7, in order to achieve accurate estimation of parameters, in the iterative process, the expression in S2.6 can be used to continuously recursively reduce the value of the performance index J until Or when 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 follows:

[0062]

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

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

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

[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 is continuously reduced until the algorithm converges, thereby obtaining the optimal controller parameters.

[0067] Figure 3 The voltage deviation trajectory at bus 25 is given under the condition of disturbance 1 (generator G5 has a 20% load shedding disturbance at the 2nd second), with the three different voltage controllers, namely, the traditional sliding mode controller, the PI controller, and the fractional-order sliding mode controller proposed in this paper. It can be seen that the proposed fractional-order sliding mode controller has a better ability to suppress voltage oscillation than the traditional sliding mode controller and the PI controller, and can make the bus voltage return to a new steady state more quickly, which means that the proposed fractional-order sliding mode controller has a better voltage control capability.

[0068] Figure 4 and Figure 5The voltage fluctuations at bus 9 under the stimulation of disturbance 2 (AC line disconnection fault between bus 25 and bus 26) and disturbance 3 (AC line disconnection fault between bus 10 and bus 13) are given under three different parameter setting conditions: fixed parameters, parameters set based on the robust method, and parameters set based on the proposed method. It can be seen that the fractional-order sliding mode controller with parameters set based on the proposed method can reduce the overshoot of voltage curve fluctuations and shorten the adjustment time under different fault scenarios, which shows that the proposed parameter setting method can enable the fractional-order sliding mode controller to achieve better voltage control effect.

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

Claims

1. A fractional-order sliding mode controller design method for improving power grid voltage stability, characterized in that: The following steps are involved: (1) Design a fractional-order sliding mode controller u; (2) Estimate the discrete z function of the power system; (3) Construct a parameter optimization model for the fractional-order sliding mode controller; (4) Real-time collection of input signal U(t) and output signal Y(t) of the power system; (5) Perform Laplace transformation on the discrete z function of the power system to obtain the equivalent transfer function G(s) of the power system; (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.

2. A fractional-order sliding mode controller design method for improving grid voltage stability according to claim 1, characterized in that: The design method of the fractional-order sliding mode controller u is: (2.1) The dynamic model of static VAR compensator SVC is defined as: 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 It represents the output susceptance of SVC; (2.2), 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; (2.3) Considering that when the power system motion trajectory reaches the sliding mode surface, there exists σ=0 and Therefore, the above formula is transformed into: in, is the first-order derivative of σ; (2.4), combined with the above expressions (2.1) and (2.3), the equivalent control law of the fractional-order sliding mode controller is expressed as: (2.5), in order to make the power system trajectory reach the sliding mode surface, the reaching law of the fractional order sliding mode controller is: (2.6) 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:

3. 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: (3.1) 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 signal and input signal of the power system at time t, respectively; θ(z) is the parameter value to be identified in the form of the power system z function; z is the function operator; (3.2) When solving the actual power system, the parameter estimates are used It means that considering that there will be a certain identification error between θ and θ, the parameter estimation value can be used Replacing the true value θ will introduce a residual ε: Where k represents the number of iterations when estimating the value of the parameter to be identified in the power system; (3.3) According to the least squares criterion, the parameter estimate when the residual sum of squares J is minimized is the least squares estimate, so the residual sum of squares J is expressed as: Among them, the superscript T represents transposition; (3.4) By transforming the expression in (3.3), we can get: (3.5) Analyzing the expression in (3.4), 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, that is, we get: The parameter estimates are thus (3.6) To achieve real-time estimation of parameters, the recursive matrix P(k) is introduced, and the recursive expression of the parameter estimation value is expressed as: Among them: λ is the forgetting factor; (3.7), the recursive expression of the parameter estimate is continuously solved recursively, so that the value of the performance index J is continuously reduced until Or the number of iterations k reaches the preset maximum number of iterations, so as to obtain the final parameter estimation value, where θ set is the threshold value.

4. 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