High-order differential obtaining method for reference value of three-phase LCL grid-connected converter

Abstract

The invention discloses a high-order differential acquisition method for a reference value of a three-phase LCL grid-connected converter. The method comprises the following steps: step 1, establishing a system model and a state equation based on a three-phase LCL grid-connected converter; 2, on the basis of the system model and the state equation, designing a self-adaptive backstepping control strategy of the three-phase LCL grid-connected converter according to uncertainty factors of parameter disturbance, power grid fluctuation and load change possibly occurring in the operation process; and 3, aiming at a self-adaptive backstepping control strategy of the three-phase LCL grid-connected converter, solving each order differential of a reference signal by adopting a practical finite time command filter, and ensuring the real-time performance and the stability of a control law. According to the method, the first-order to third-order differential terms of the reference signal can be accurately extracted in finite time, the time lag and instability risks caused by a traditional estimation method are effectively reduced, and the real-time response capability and control precision of the system are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of non - linear controllers for three - phase LCL grid - connected converters, and specifically relates to a method for obtaining high - order differentials of reference values of a three - phase LCL grid - connected converter. Background Technique

[0002] In modern power systems, as a conversion bridge between new - energy power generation systems and the power grid or users, the three - phase LCL grid - connected converter is responsible for converting direct current into high - quality alternating current and connecting it to the power grid, playing a crucial role in distributed generation systems. In recent years, a variety of advanced control strategies, such as adaptive control and robust control, have been proposed to improve the control performance of the converter. These control strategies have shown significant advantages in distribution networks, especially in cases where the distributed generation penetration rate is high and the load fluctuation is large, and can effectively cope with the challenges caused by disturbances and system uncertainties.

[0003] However, in practical applications, the design of non - linear controllers often relies on high - order differential terms of reference signals. The order of these differential terms is closely related to the order of the system, usually calculated based on the measured values at the current moment, and the values at future moments cannot be accurately predicted. This makes the calculation of high - order differentials of reference values, especially the acquisition of second - order and third - order differentials, more difficult and unable to ensure the boundedness of the differential results. More importantly, although some high - order differential modules can be estimated through sampled values, these estimations often introduce a certain delay, thus affecting the real - time control performance of the system. Summary of the Invention

[0004] In order to overcome the above problems existing in the prior art, the purpose of the present invention is to provide a method for obtaining high - order differentials of reference values of a three - phase LCL grid - connected converter. This method is based on the acquisition of high - order differentials of reference values using a practical finite - time command filter (PFTCF), which can accurately extract high - order differential terms such as the first - order to third - order of the reference signal within a finite time, effectively reducing the time delay and instability risks caused by traditional estimation methods, and improving the real - time response ability and control accuracy of the system. By ensuring the boundedness of high - order differential terms during the dynamic process, the method of the present invention provides reliable data support for the stable operation of non - linear controllers under complex working conditions and is applicable to power scenarios with high dynamic requirements such as distributed generation.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] A method for obtaining high - order differentials of reference values of a three - phase LCL grid - connected converter, comprising the following steps;

[0007] Step 1: Based on the three - phase LCL grid - connected converter, establish its system model and state equation;

[0008] By establishing an accurate system model and considering the circuit topology and dynamic behavior of the converter, a solid foundation is provided for the subsequent design of control strategies. This modeling process can effectively improve the system's adaptability to actual working conditions, ensure that the high-order derivatives of the reference value can be accurately reflected during dynamic changes, thereby improving the prediction accuracy and the accuracy of control response, and avoiding system instability or over-response.

[0009] Step 2: Design an adaptive backstepping control strategy for the three-phase LCL grid-connected converter;

[0010] Based on the system model and state equations, an adaptive backstepping control strategy for the three-phase LCL grid-connected converter is designed to address uncertainties such as parameter perturbations, grid fluctuations, and load changes that may occur during operation.

[0011] This strategy can dynamically adjust the control parameters according to the actual working conditions to effectively suppress the system's nonlinearity and external disturbances. Through online adaptive adjustment, the controller can continuously maintain the system stability under different operating conditions, significantly improve the robustness, reduce energy losses, lower device stress, and thus extend the service life of the equipment.

[0012] Step 3: For the adaptive backstepping control strategy of the three-phase LCL grid-connected converter, a practical finite-time command filter (PFTCF) is used to solve the high-order derivatives of the reference signal, thereby ensuring the real-time performance and stability of the control law.

[0013] After the controller design is completed, to obtain the required high-order derivatives of the reference value, a practical finite-time command filter (PFTCF) is used to solve the high-order derivatives of the reference signal, solving the problems of delay and noise existing in traditional differential methods. This method can improve the tracking speed of the control system to the changes of the reference signal, ensure the stability of the control law within a finite time, and effectively reduce the influence caused by signal estimation delay. This process significantly improves the dynamic response ability of the system and is applicable to application scenarios with high dynamic requirements such as distributed generation and power quality control.

[0014] In the said Step 1, establish the state equations of the three-phase LCL grid-connected converter:

[0015]

[0016] Among them, the system variables of the converter are as follows: X1 = [i a2 i b2 i c2 T is the current of the second filter inductor, X2 = [v ca v cb v cc T ​​is the voltage of the filtering capacitor, X3 = [i a1 i b1 i c1 T is the current of the first filtering inductor, ξ = [ξ a ξ b ξ c T are the uncertainty parameters in the distribution network, such as load fluctuations, fluctuations of distributed generation, etc.;

[0017] Definition of matrices in the state equation: inductance and resistance matrices A2, A1, B2, B1, these matrices respectively describe the inductance values and resistances of the first and second filtering inductors; capacitance matrix D, this matrix describes the distribution of capacitance between each phase; perturbation matrix φ, this matrix reflects the external perturbations in the system, including external factors such as grid voltage fluctuations, load mutations, and three-phase unbalances;

[0018] Where

[0019]

[0020] AC side system voltage: V s =[V sa V sb V sc T , s represents the AC side system, a represents phase a in the three-phase system, b represents phase b in the three-phase system, c represents phase c in the three-phase system, V sa represents the voltage of phase a of the AC side system, V sb represents the voltage of phase b of the AC side system, V sc represents the voltage of phase c of the AC side system;

[0021] Converter output voltage: U = [U a U b U c T , U a is the voltage of phase a output by the converter, U b is the voltage of phase b output by the converter, U c is the voltage of phase c output by the converter;

[0022] Current of the first filtering inductor: i a1 , i b1 , i c1 , i a1 is the current of phase a of the first filtering inductor, i b1 is the current of phase b of the first filtering inductor, i c1 is the current of phase c of the first filtering inductor; ​​​​

[0023] The current of the second filter inductor: i a2 , i b2 , i c2 , i a2 is the current of phase a of the second filter inductor, i b2 is the current of phase b of the second filter inductor, i c2 is the current of phase c of the second filter inductor;

[0024] The voltage of the filter capacitor: v ca , v cb , v cc , c represents the filter capacitor, v ca is the voltage of phase a of the filter capacitor, v cb is the voltage of phase b of the filter capacitor, v cc is the voltage of phase c of the filter capacitor;

[0025] The DC - side voltage: V DC .

[0026] Specifically, step 2 is as follows: Based on the establishment of the system model and state equation of the three - phase LCL grid - connected converter, an adaptive backstepping control strategy is adopted to design the controller. By gradually recursive means, the system error is reduced, and the unknown parameters are estimated and compensated in real time, so as to enhance the stability and control accuracy of the system under uncertainty and disturbance conditions;

[0027] Define the error variable between the reference value and the actual output:

[0028] Z1 = X1 - X 1ref

[0029]

[0030] where α1 and α2 are virtual control variables, X 1ref is the reference value

[0031] (1) Construct a Lyapunov function based on Z1 and deduce α1

[0032] Select the Lyapunov function Take the derivative of it:

[0033]

[0034] Given Z1 = X1 - X 1ref , then Substitute into it, and the derivative of Z1 can be obtained as:

[0035]

[0036] In order to make negative definite, expect (If \(K1\) is a positive definite matrix), then the virtual control quantity \(\alpha1\) can be selected such that:

[0037]

[0038] Solve to get:

[0039]

[0040] (2) Construct a Lyapunov function based on \(Z2\) and derive \(\alpha2\)

[0041] Select the Lyapunov function Take the derivative of it:

[0042]

[0043] It is known that Then Substitute into it to get the derivative of \(Z2\) as:

[0044]

[0045] In order to make negative definite, it is expected that (If \(K2\) is a positive definite matrix), then the virtual control quantity \(\alpha2\) can be selected such that:

[0046]

[0047] Solve to get:

[0048]

[0049] (3) Construct a Lyapunov function based on \(Z3\) and design the control law \(U\) k

[0050] Select the Lyapunov function Take the derivative of it:

[0051]

[0052] It is known that Then Substitute into it to get the derivative of \(Z3\) as:

[0053]

[0054] In order to make negative definite, it is expected that (If \(K3\) is a positive definite matrix), then the control rate \(U\) can be solved as k :

[0055]

[0056] The above formula fully embodies the basic structure of adaptive backstepping control through error progressive design, Lyapunov stability analysis, introduction of virtual control quantity, and final control law design; the uncertain factors existing in the system are compensated by online estimation through the introduction of an adaptation law, ultimately ensuring the stable control performance of the system under uncertain disturbances.

[0057] Specifically, step 3 is as follows: A practical finite-time command filter (PFTCF) is used to obtain the reference value X 1ref of each order of differentiation

[0058]

[0059] S(e 1,i ) = tanh(q 1,i e 1,i ), S(e 2,i ) = tanh(q 2,i e 2,i ), where q 1,i , q 2,i > 0, v 1,i , v 2,i represent the states of the filter, and λ 1,i , λ 2,i , γ 1,i , γ 2,i are positive design parameters.

[0060] where e 1,i = v 1,i - z i , e 2,i = v 2,i - z i . z i represents the input of the filter, represents the output of the filter. Substituting the reference value X 1ref for the filter input z i , the output can be obtained. Then substituting the obtained for the filter input z i , the output can be obtained. Similarly, and the nth order differentiation of the reference value can be solved.

[0061] Through the above steps, the first-order, second-order, and third-order differentiations of the reference value obtained by using the practical finite-time command filter (PFTCF), that is, Substitute it into the adaptive backstepping control law to calculate the virtual control quantity and the final actual control input, so as to achieve accurate tracking of the output current of the three-phase LCL grid-connected converter, improve the response speed and control accuracy of the system under dynamic changing working conditions, and enhance the stability and robustness of the system.

[0062] Advantages of the present invention:

[0063] Aiming at the problems in the three-phase LCL grid-connected converter that it is difficult to obtain the high-order derivative of the reference value in real time, the traditional method has a large estimation delay and affects the system response, the present invention proposes a high-performance control method. First, based on the circuit topology of the converter, its system model and state equation are established to provide support for the dynamic characteristics of the controller design. On this basis, considering the uncertain parameters and external disturbance factors that may exist in the system, a robust adaptive backstepping control strategy is designed to enhance the stable operation ability of the system under complex working conditions.

[0064] To further improve the real-time performance and accuracy of the controller during the dynamic process, the present invention introduces a practical finite-time command filter (PFTCF) to obtain the high-order derivative terms of the reference signal. Different from the traditional differential estimation method, this filter can stably output the high-order derivative values within a finite time, effectively suppressing the system fluctuation problems caused by signal delay or differential amplified noise. Through this method, the fast tracking ability of the converter system to reference changes can be enhanced, the dynamic performance and robustness during the grid connection process can be improved, and it is especially suitable for scenarios with high requirements for real-time response such as distributed generation and power quality control.

[0065] In typical distributed generation scenarios, such as wind farms or photovoltaic systems, the power generation output has strong volatility and uncertainty. When connecting to the grid, the three-phase LCL grid-connected converter needs to quickly and accurately respond to voltage disturbances, load mutations, frequency drifts, etc. to ensure the quality of the grid-connected current and the stable operation of the system. However, the traditional methods based on numerical differentiation or filter delay often cannot obtain accurate high-order differential information in real time, resulting in lagging control response, increased current distortion, and even system oscillation. The reference value differential extraction mechanism constructed by the finite-time command filter in the present invention not only improves the dynamic tracking speed, but also significantly reduces the dependence of the controller on sensor accuracy and computing resources, enhancing the feasibility of the system on a low-cost control platform. This method is particularly suitable for application scenarios that require rapid switching, real-time power control, and frequent dynamic load changes, such as microgrid grid connection, active distribution network, electric vehicle charging and discharging interface control, etc., and has good engineering practical value and popularization prospects. Description of the drawings

[0066] Figure 1 It is the circuit topology diagram of the three-phase LCL grid-connected converter system involved in the present invention. Detailed implementation manners

[0067] The present invention will be further described in detail below with reference to the accompanying drawings.

[0068] The present invention discloses a method for obtaining high-order differentials of reference values of a three-phase LCL grid-connected converter. The present invention aims to use a practical finite-time command filter (PFTCF) to calculate the differentials of each order of the reference values for a converter system with uncertain parameters and unknown external disturbances. Taking Figure 1 shown as an example, the implementation method of the present invention will be described in detail.

[0069] As Figure 1 shown, the specific detection steps are as follows:

[0070] Step1: Before starting the control design, it is first necessary to model the three-phase LCL grid-connected converter. By analyzing the circuit structure of the converter, the state equations of the system are derived using circuit analysis methods. These equations describe the dynamic characteristics of the converter, including currents, voltages, and the behavior of inductors and capacitors within the system. The accuracy of the model is the basis for the subsequent design of the control strategy.

[0071] Establish the state equations of the three-phase LCL grid-connected converter:

[0072]

[0073] Among them, the AC-side system voltage: V s =[V sa V sb V sc T , s represents the AC-side system, a represents phase a in the three-phase system, b represents phase b in the three-phase system, c represents phase c in the three-phase system, V sa represents the voltage of phase a of the AC-side system, V sb represents the voltage of phase b of the AC-side system, V sc represents the voltage of phase c of the AC-side system;

[0074] The converter output voltage: U = [U a U b U c T , U a is the voltage of phase a output by the converter, U b is the voltage of phase b output by the converter, U c is the voltage of phase c output by the converter;

[0075] The current of the first filter inductor: i a1 , i b1 , i c1 , i​​a1 The current of phase a of the first filtering inductor, i b1 The current of phase b of the first filtering inductor, i c1 The current of phase c of the first filtering inductor;

[0076] The current of the second filtering inductor: i a2 , i b2 , i c2 , i a2 The current of phase a of the second filtering inductor, i b2 The current of phase b of the second filtering inductor, i c2 The current of phase c of the second filtering inductor;

[0077] The voltage of the filtering capacitor: v ca , v cb , v cc , c represents the filtering capacitor, v ca The voltage of phase a of the filtering capacitor, v cb The voltage of phase b of the filtering capacitor, v cc The voltage of phase c of the filtering capacitor;

[0078] The DC - side voltage: V DC .

[0079] The system variables of the converter are as follows: X1 = [i a2 i b2 i c2 T is the current of the second filtering inductor, X2 = [v ca v cb v cc T is the voltage of the filtering capacitor, X3 = [i a1 i b1 i c1 T is the current of the first filtering inductor, ξ = [ξ a ξ b ξ c T is the uncertainty parameter in the distribution network, such as load fluctuation, fluctuation of distributed generation, etc.

[0080] The definitions of the matrices in the above - mentioned state equations: the inductor and resistor matrices A2, A1, B2, B1, these matrices respectively describe the inductance values and resistances of the first and second filtering inductors; the capacitor matrix D, this matrix describes the distribution of the capacitor between each phase; the perturbation matrix φ, this matrix reflects the external perturbation in the system.

[0081] Among them

[0082] ​​​​

[0083] Step 2: After establishing the system model of the three-phase LCL grid-connected converter, the next step is to design an appropriate control strategy to ensure the stability of the system. The adaptive backstepping control strategy is an effective control method that can ensure the stability of the system in the face of uncertainties and external disturbances. First, it is necessary to determine the Lyapunov function of the system to describe and analyze the stability of the system; secondly, by gradually constructing the control law and gradually eliminating the errors, the stability and robustness of the system can be ensured.

[0084] Define the error variable between the reference value and the actual output

[0085] Z1 = X1 - X 1ref

[0086]

[0087] where, α1 and α2 are virtual control variables, and X 1ref is the reference value

[0088] (1) Construct the Lyapunov function based on Z1 and derive α1

[0089] Select the Lyapunov function Take the derivative of it:

[0090]

[0091] Given Z1 = X1 - X 1ref , then Substitute into it, and the derivative of Z1 can be obtained as:

[0092]

[0093] In order to make negative definite, it is expected that (K1 is a positive definite matrix), then the virtual control variable α1 can be selected such that:

[0094]

[0095] Solve to get:

[0096]

[0097] (2) Construct the Lyapunov function based on Z2 and derive α2

[0098] Select the Lyapunov function Take the derivative of it:

[0099]

[0100] Known Then Substitute into to obtain the derivative of Z2 as follows:

[0101]

[0102] In order to make negative definite, it is expected that (K2 is a positive definite matrix), then the virtual control variable α2 can be selected such that:

[0103]

[0104] Solve to obtain:

[0105]

[0106] (3) Construct a Lyapunov function based on Z3 and design the control law U k

[0107] Select the Lyapunov function Take the derivative of it:

[0108]

[0109] Known Then Substitute into to obtain the derivative of Z3 as follows:

[0110]

[0111] In order to make negative definite, it is expected that (K3 is a positive definite matrix), then the control law U can be solved k :

[0112]

[0113] Step3: To improve the accuracy of the non - linear controller in dealing with dynamic changes, the practical finite - time command filter (PFTCF) method is used to calculate the derivatives of all orders of the reference signal. Through this method, the first - order, second - order and n - th order derivatives of the reference signal can be calculated within a finite time, thus providing more reliable dynamic information for the non - linear controller and enhancing the real - time performance, stability and control accuracy of the system.

[0114] Use the practical finite - time command filter (PFTCF) to obtain the first - order derivative 1ref of the reference value X

[0115]

[0116] S(e 1,2 ) = tanh(q 1,2 e 1,2 ),S(e 2,2 ) = tanh(q 2,2 e 2,2 ),where q 1,2 , q 2,2 > 0. v 1,2 , v 2,2 represents the state of the filter, λ 1,2 , λ 2,2 , γ 1,2 , γ 2,2 are positive design parameters.

[0117] Where e 1,2 = v 1,2 - X 1ref , e 2,2 = v 2,2 - X 1ref . X 1ref represents the input of the filter, represents the output of the filter, i.e.,

[0118] The expressions for calculating second-order differentials and higher-order differentials are the same.

Claims

1. A method for obtaining high-order differentials of reference values of a three-phase LCL grid-connected converter, characterized in that, Including the following steps; Step 1: Based on the three-phase LCL grid-connected converter, establish its system model and state equation; Step 2: Based on the system model and state equation, design an adaptive backstepping control strategy for the three-phase LCL grid-connected converter in view of the uncertain factors such as parameter perturbation, grid fluctuation and load change during the operation process; Step 3: For the adaptive backstepping control strategy of the three-phase LCL grid-connected converter, use a practical finite-time command filter (PFTCF) to solve the derivatives of each order of the reference signal to ensure the real-time performance and stability of the control law.

2. The method for obtaining the high-order differential of the reference value of a three-phase LCL grid-connected converter according to claim 1, characterized in that In the said Step 1, establish the state equation of the three-phase LCL grid-connected converter: Among them, the system variables of the converter are as follows: X1 = [i a2 i b2 i c2 T is the current of the second filter inductor, X2 = [v ca v cb v cc T is the voltage of the filter capacitor, X3 = [i a1 i b1 i c1 T is the current of the first filter inductor, ξ = [ξ a ξ b ξ c T is the uncertainty parameter in the distribution network, including the instantaneous fluctuation of the grid voltage, frequency deviation, and grid impedance;​​​​ Definition of the matrices in the state equation: Inductance and resistance matrices A2, A1, B2, B1, which respectively describe the inductance values and resistances of the first and second filter inductors; Capacitance matrix D, which describes the distribution of the capacitance between each phase; Disturbance matrix φ, which reflects the external disturbances in the system, including external factors such as grid voltage fluctuation, load mutation, and three-phase imbalance; Among them AC-side system voltage: V s = [V sa V sb V sc T , where s represents the AC-side system, a represents phase a in the three-phase system, b represents phase b in the three-phase system, c represents phase c in the three-phase system, V sa represents the voltage of phase a of the AC-side system, V sb represents the voltage of phase b of the AC-side system, V sc represents the voltage of phase c of the AC-side system;​ Converter output voltage: U = [U a U b U c T , U a is the a-phase voltage output by the converter, U b is the b-phase voltage output by the converter, U c is the c-phase voltage output by the converter;​ The current of the first filtering inductor: i a1 , i b1 , i c1 , i a1 is the current of the a-phase of the first filtering inductor, i b1 is the current of the b-phase of the first filtering inductor, i c1 is the current of the c-phase of the first filtering inductor; Second filter inductor current: i a2 , i b2 , i c2 , i a2 is the current of phase a of the second filter inductor, i b2 is the current of phase b of the second filter inductor, i c2 is the current of phase c of the second filter inductor; Filter capacitor voltage: v ca , v cb , v cc , where c represents the filter capacitor, and v ca is the phase-a voltage of the filter capacitor, v cb is the phase-b voltage of the filter capacitor, v cc is the phase-c voltage of the filter capacitor; DC-side voltage: V DC .

3. A method for obtaining a high-order differential of a reference value of a three-phase LCL grid-connected converter according to claim 1, characterized in that, The said Step 2 is specifically: Define the error variable between the reference value and the actual output: Among them, α1 and α2 are virtual control variables, and X 1ref is the reference value; (1) Construct a Lyapunov function based on Z1 and derive α1; Select the Lyapunov function Take the derivative of it: Given that Z1 = X1 - X 1ref , then Substituting into it, the derivative of Z1 can be obtained as follows: To make negative definite, it is desired that (where K1 is a positive definite matrix), and select the virtual control quantity α1 such that: Obtain: (2) Construct a Lyapunov function based on Z2 and derive α2; Select the Lyapunov function Take the derivative of it: Known Then Substitute into it, and the derivative of Z2 is obtained as: To make negative definite, it is desired that (where K2 is a positive definite matrix), select the virtual control input α2 such that: Obtain: (3) Construct the Lyapunov function based on Z3 and design the control law U k ; Select the Lyapunov function Take the derivative of it: Known Then Substitute into it, and the derivative of Z3 is obtained as: In order to make negative definite, it is expected that (where K3 is a positive definite matrix), the control law U k is obtained as follows:

4. A method for obtaining a high-order differential of a reference value of a three-phase LCL grid-connected converter according to claim 1, characterized in that The specific content of step 3 is as follows: A practical finite-time command filter (PFTCF) is used to obtain the derivatives of each order of the reference value X 1ref of S(e 1,i ) = tanh(q 1,i e 1,i ),S(e 2,i ) = tanh(q 2,i e 2,i ), where q 1,i , q 2,i > 0, v 1,i , v 2,i represents the state of the filter, λ 1,i , λ 2,i , γ 1,i , γ 2,i are positive design parameters; where e 1,i = v 1,i - z i ,e 2,i = v 2,i - z i 。z i represents the input of the filter, represents the output of the filter. Substituting the reference value X 1ref for the filter input z i , the output can be obtained Then substituting the obtained for the filter input z i , the output can be obtained Similarly, solve and the nth derivative of the reference value; Through the above steps, the first, second, and third derivatives of the reference value obtained by using the practical finite-time command filter (PFTCF), namely are substituted into the adaptive backstepping control law to calculate the virtual control quantity and the final actual control input.

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