Doubly-fed fan VSC-HVDC subsynchronous oscillation robust integral predefined time sliding mode control method

Abstract

The invention relates to the technical field of new energy power generation, in particular to a doubly-fed fan VSC-HVDC (Voltage Source Converter-High Voltage Direct Current) subsynchronous oscillation robust integral predefined time sliding mode control method, which comprises the following steps: S1, establishing a grid-side converter model in a doubly-fed fan; s2, establishing a phase-locked loop model in the doubly-fed fan; s3, constructing an integral sliding mode surface, and obtaining dynamic characteristics and equivalent control input of a sliding mode system; s4, designing approaching control input, and obtaining an integral predetermined time sliding mode control law; and S5, implementing an integral predetermined time sliding mode control law. Compared with a traditional PI control strategy, the robust integral predefined time sliding mode control method for the subsynchronous oscillation of the double-fed fan VSC-HVDC, provided by the invention, has the advantages that the oscillation can be converged in a shorter time, and the robustness is higher.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of new energy power generation, more particularly, to a doubly-fed wind turbine VSC-HVDC subsynchronous oscillation robust integral pre-defined time sliding mode control method. BACKGROUND

[0002] With the continuous large-scale grid connection of renewable energy in modern power systems, wind energy has been recognized as a promising and rapidly developing energy. In the mainstream of wind power generation technology, doubly-fed induction generators (DFIGs) have been widely used in large-scale wind farms due to their advantages of variable speed operation, independent regulation of active and reactive power, and relatively economical converter topology. However, doubly-fed induction generator (DFIG) wind turbine systems based on long-distance power transmission, especially voltage source converter-based high-voltage direct current transmission (VSC-HVDC) systems, have brought significant dynamic stability problems. One of the most critical problems is the occurrence of subsynchronous oscillation (SSO), which poses a great threat to system stability and safe operation of the power grid.

[0003] Subsynchronous oscillation in doubly-fed induction generator (DFIG) systems is caused by the complex electromechanical interaction between generator shaft dynamics, grid-side converter (GSC) and transmission line impedance. When such systems are connected to a weak grid or operate under low short circuit ratio (SCR) conditions, the risk of subsynchronous oscillation (SSO) is significantly amplified. In addition, the fast switching action and control dynamic characteristics of voltage source converter-based high-voltage direct current transmission (VSC-HVDC) links further complicate the electromagnetic environment, increasing the likelihood of resonance and unstable oscillation modes in the subsynchronous frequency range. If not effectively suppressed, subsynchronous oscillation can lead to increased system mechanical stress, accelerated fatigue of unit components, degraded power quality, and even complete loss of unit synchronization.

[0004] To solve the problem of subsynchronous oscillation (SSO), the commonly used controllers currently include damping controllers, model predictive controllers and additional controllers. Although these methods are effective under nominal operating conditions, many of them are highly dependent on accurate modeling of the generator and the grid. However, in practical applications, it is often not feasible to achieve accurate modeling due to the uncertainty, nonlinearity and time-varying characteristics of system parameters. In addition, when facing external large disturbances, grid parameter changes or measurement noise, the performance of traditional linear controllers will decrease, thereby limiting their effectiveness in highly dynamic and uncertain environments.

[0005] Against this backdrop, sliding mode control has attracted widespread attention due to its strong robustness to model uncertainties and external disturbances. Sliding mode control ensures that the system state reaches and remains on a predefined sliding surface, thus exhibiting fast response and strong disturbance rejection capabilities. However, traditional sliding mode control has several drawbacks, such as chattering and limited control accuracy near the equilibrium point. To overcome these limitations, researchers have proposed finite-time and fixed-time sliding mode control methods. Among them, predefined-time sliding mode control guarantees that the system trajectory converges within a user-defined finite time, and this convergence time is independent of the initial state.

[0006] To address the impact of model uncertainty and external disturbances on the controller's ability to suppress subsynchronous oscillations, and to overcome the problem that current control methods cannot converge oscillations within a user-defined finite time, this invention proposes a robust integral predefined time sliding mode control method for subsynchronous oscillations in doubly fed wind turbine VSC-HVDC. Summary of the Invention

[0007] This invention addresses the impact of model uncertainty and external disturbances on the controller's ability to suppress subsynchronous oscillations. Furthermore, to overcome the current control method's inability to converge oscillations within a user-defined finite time, it aims to provide a robust integral predefined time sliding mode control method for doubly fed wind turbine VSC-HVDC subsynchronous oscillations that solves the aforementioned problems.

[0008] A robust integral predefined time sliding mode control method for subsynchronous oscillation of a doubly fed wind turbine (VSC-HVDC) includes the following steps:

[0009] S1. Establish the grid-side converter model in the doubly fed wind turbine;

[0010] S2, Establish the phase-locked loop model in the doubly fed wind turbine;

[0011] S3, construct the integral sliding surface to obtain the dynamic characteristics and equivalent control input of the sliding system;

[0012] S4, design the approximation control input to obtain the integral predetermined time sliding mode control law;

[0013] S5, implements the integral predetermined time sliding mode control law.

[0014] Furthermore, in step S1, the dynamic characteristics of the grid-side converter are characterized by the following mathematical model:

[0015]

[0016] Where, ω g L, R represent the angular frequency of the power grid, the inductance of the grid-side filter, and its resistance, respectively. gd and V gqThe dq-axis components represent the grid voltage; while u gd and u gq This corresponds to the dq-axis component of the grid-side converter output voltage; i gd and i gq This represents the dq-axis component of the grid current injected from the grid-side converter.

[0017] By accurately constructing the control model of the outer power loop and inner current loop of the grid-side converter, and introducing an additional damping controller, the dq-axis current of the converter is dynamically adjusted, thereby suppressing the subsynchronous oscillation.

[0018] Furthermore, in step S2, the control model corresponding to the phase-locked loop is as follows:

[0019]

[0020] Where θ represents the output phase angle of the phase-locked loop; K i and K p These represent the integral gain and proportional gain in a phase-locked loop control system, respectively.

[0021] Under normal operating conditions, U q Set to zero; when the system is in steady state, the phase angle of the phase-locked loop output is θ = ωt; when U q When disturbed by the subsynchronous oscillation voltage component, the phase-locked loop will output a phase angle θ that includes the subsynchronous oscillation component.

[0022] To ensure phase synchronization with the power grid, this method employs a phase-locked loop (PLL) to monitor and track the voltage phase angle at the point of common coupling. Simultaneously, the PLL provides the necessary phase angle for the Parker transformation in the grid-side converter control loop of the doubly-fed induction generator (DFIG). This PLL operates based on the vector-oriented control principle, achieving system synchronization by orienting the grid voltage vector along the q-axis.

[0023] Furthermore, in step S3, before constructing the integral sliding mode, define the relationship with i gd and i gq The relevant tracking error is defined as:

[0024] e1 = i gd -i gdref e2=i gq -i gqref (4)

[0025] Among them, i gdref and i gqref For current component i gd and i gq Reference signal.

[0026] Furthermore, in step S3, for tracking i ds, the integral sliding surface is constructed as follows:

[0027]

[0028] where T c is a predefined time, s1 is the integral sliding surface, k1 and k2 are positive numbers, and sign(.) δ = | | δ .

[0029] When the stator d-axis current error e1 converges to the integral sliding surface ISS, the system dynamics satisfy the following expression:

[0030]

[0031] Then, according to equations (5) and (6), the dynamic equation of the integral sliding surface ISS is:

[0032]

[0033] Correspondingly, the dynamic characteristics of the sliding mode system are described as:

[0034]

[0035] Combining equations (4) and (8), the equivalent control input U eq_gd is designed as follows:

[0036]

[0037] where T c is a predefined time, γ, k1, and k2 are positive numbers, and e1 is the stator d-axis current error.

[0038] Further, in step S4, to ensure that the error e1 can effectively reach the integral sliding surface and remain on the sliding surface, the approaching control input U r_gd is designed as follows:

[0039]

[0040] where k3 and k4 are greater than 0.

[0041] Based on equations (9) and (10), the integral predetermined time sliding mode control law for tracking i ds is:

[0042]

[0043] The integral sliding surface ISS as defined in equation (5) and the integral predetermined time sliding mode control

[0044] As shown in the IPT SMC control law, the sliding surface is constructed based on the integral sliding surface ISS framework, and the integral predetermined time sliding mode control IPTSMC is a continuous control law. The implementation of this continuous control law helps to significantly weaken the chattering phenomenon inherent in the traditional sliding mode control method.

[0045] Further, in step S3, for tracking i qs The integral sliding surface is constructed as follows:

[0046]

[0047] Where: T c is a predefined time, s2 is the integral sliding surface, k5 and k6 are positive numbers, and sign(.) δ = |. | δ sign(.);

[0048] When the stator q-axis current error e2 converges to the integral sliding surface, the system dynamics satisfy the following expression:

[0049]

[0050] Then, according to equations (12) and (13), the dynamic equation of the integral sliding surface is:

[0051]

[0052] Correspondingly, the dynamic characteristics of the sliding mode system are described as:

[0053]

[0054] By combining equations (4) and (15), the equivalent control input U eq_gq is designed as follows:

[0055]

[0056] Where: T c is a predefined time, γ, k5, and k6 are positive numbers, and e2 is the stator q-axis current error.

[0057] Further, in step S4, to ensure that the error e2 can effectively reach the integral sliding surface and remain on the sliding surface, the approaching control input U r_gq is designed as follows:

[0058]

[0059] Where k7 and k8 are greater than 0.

[0060] Finally, based on equations (16) and (17), for tracking i qsThe integral pre-defined time sliding mode control law is:

[0061]

[0062] Compared with the prior art, the present application has the beneficial effects that:

[0063] The double-fed wind turbine VSC-HVDC subsynchronous oscillation robust integral pre-defined time sliding mode control method provided by the present application can make the oscillation converge in a shorter time and has stronger robustness compared with the traditional PI control strategy. BRIEF DESCRIPTION OF DRAWINGS

[0064] The accompanying drawings are included to provide a further understanding of the present application and are incorporated in and constitute a part of the specification, illustrate embodiments of the present application and are used to explain the present application, but do not constitute a limitation on the present application. In the drawings:

[0065] Figure 1 is a structural schematic diagram of the double-fed wind turbine accessing the VSC-HVDC system in the present application. DETAILED DESCRIPTION

[0066] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0067] Embodiment:

[0068] Figure 1 The system model of the double-fed wind turbine accessing the VSC-HVDC is provided. The double-fed wind turbine VSC-HVDC subsynchronous oscillation robust integral pre-defined time sliding mode control method in the present embodiment includes the following steps:

[0069] S1, a grid-side converter model in the double-fed wind turbine is established.

[0070] The present method focuses on the core role of the grid-side converter (GSC) in the double-fed induction generator (DFIG) in suppressing the subsynchronous oscillation (SSO). Therefore, the focus of modeling is on the dynamic characteristics and control architecture of the grid-side converter. The technical principle is as follows: by accurately constructing the control model of the power outer ring and the current inner ring of the grid-side converter, and introducing an additional damping controller (SDC), the dq-axis current of the converter is dynamically adjusted, so as to realize the suppression of the subsynchronous oscillation.

[0071] The dynamic characteristics of the grid-side converter are characterized by the following mathematical model:

[0072]

[0073] where ω g , L, R represent the angular frequency of the grid, the inductance and resistance of the grid-side filter, respectively, V gd and V gq represent the dq-axis components of the grid voltage; and u gd and u gq correspond to the dq-axis components of the grid-side converter output voltage; i gd and i gq represent the dq-axis components of the grid current injected from the grid-side converter.

[0074] S2, establish a phase-locked loop model in the doubly-fed wind turbine.

[0075] To ensure synchronization with the grid phase, the method uses a phase-locked loop (PLL) to monitor and track the voltage phase angle of the point of common coupling. At the same time, the phase-locked loop provides the required phase angle for the Park transformation in the grid-side converter control loop of the doubly-fed induction generator. The phase-locked loop works based on the principle of vector-oriented control, and the system is synchronized by orienting the grid voltage vector to the q-axis.

[0076] The control model corresponding to the phase-locked loop is as follows:

[0077]

[0078] where θ represents the output phase angle of the phase-locked loop; K i and K p represent the integral gain and proportional gain in the phase-locked loop control system, respectively;

[0079] Under normal operating conditions, U q is set to zero, and U q is the q-axis component of the grid voltage; when the system is in steady state, the phase angle output by the phase-locked loop is θ = ωt; when U q is disturbed by a subsynchronous oscillation voltage component, it will cause the phase-locked loop to output a phase angle θ containing a subsynchronous oscillation component.

[0080] S3, construct an integral sliding surface to obtain the dynamic characteristics and equivalent control input of the sliding mode system.

[0081] S4, design the approaching control input to obtain the integral predetermined time sliding mode control law.

[0082] The primary goal of the grid-side converter GSC control is to ensure that the current components i gd and i gq can accurately track their respective reference signals i gdref and i gqref , so the tracking error related to i gd and i gq is defined as follows:

[0083] e1 = i gd - i gdref e2 = i gq - i gqref (4)

[0084] For tracking i ds , the integral pre-defined time sliding mode control (IPTSMC) design procedure is as follows:

[0085] The integral sliding surface s1 is constructed as follows:

[0086]

[0087] where T c is a pre-defined time, s1 is the integral sliding surface, k1 and k2 are positive numbers, and sign(.) = |. |. δ δ

[0088] When the stator d-axis current error e1 converges to the integral sliding surface ISS, the system dynamics satisfy the following expression:

[0089]

[0090] Then, according to equations (5) and (6), the dynamic equation of the integral sliding surface ISS is:

[0091]

[0092] Correspondingly, the dynamic characteristics of the sliding mode system are described as:

[0093]

[0094] Combining equations (4) and (8), the equivalent control input U eq_gd is designed as follows:

[0095]

[0096] where T c is a pre-defined time, γ, k1, and k2 are positive numbers, and e1 is the stator d-axis current error.

[0097] Subsequently, the approaching control input U r_gd is designed to ensure that the error e1 can effectively reach the integral sliding surface ISS and remain on the sliding surface. Accordingly, U r_gd is designed as follows:

[0098]

[0099] where k3 and k4 are greater than 0. ​​

[0100] Based on equations (9) and (10), the integral pre-defined time sliding mode control IPTSMC is designed as follows:

[0101]

[0102] The integral sliding surface ISS defined as equation (5) and the integral pre-defined time sliding mode control IPTSMC given by equation (11)

[0103] The sliding surface is constructed based on the integral sliding surface ISS framework, and the integral pre-defined time sliding mode control IPTSMC is a continuous control law. The implementation of this continuous control law helps to significantly weaken the chattering phenomenon inherent in the traditional sliding mode control method.

[0104] The control input U gq is designed as follows: gd The design process of U qs is similar to that of U

[0105] The integral pre-defined time sliding mode control IPTSMC design process for tracking i c is as follows:

[0106] The integral sliding surface is constructed as follows:

[0107]

[0108] Where: T δ is a predefined time, s2 is the integral sliding surface, k5 and k6 are positive numbers, and sign(.) δ = |. | ; eq_gq sign(.);

[0109] When the stator q-axis current error e2 converges to the integral sliding surface, the system dynamics satisfy the following expression:

[0110]

[0111] Then, according to equations (12) and (13), the dynamic equation of the integral sliding surface is:

[0112]

[0113] Correspondingly, the dynamic characteristics of the sliding mode system are described as:

[0114]

[0115] By combining equations (4) and (15), the equivalent control input U eq_gq is designed as follows:

[0116]

[0117] Where: T cfor a predefined time, and k5 and k6 are positive numbers, and e2 is the stator q-axis current error.

[0118] To ensure that the error e2 can effectively reach the integral sliding mode surface and remain in the sliding mode surface, the approaching control input U r_gq The design is as follows:

[0119]

[0120] wherein k7 and k8 are greater than 0.

[0121] Finally, based on formula (16) and (17), the integral predefined time sliding mode control IPTSMC is designed as follows:

[0122]

[0123] S5, the integral predefined time sliding mode control law is implemented, and the above IPTSMC is applied to the double-fed wind turbine connected to the VSC-HVDC system.

[0124] The specific data of the double-fed wind turbine used in the application are as follows: rated power 1.5 MW, rated voltage 575 V, rated frequency 60 Hz, stator resistance 0.023 pu, stator leakage inductance 0.18 pu, rotor resistance 0.016 pu, rotor leakage inductance 0.16 pu, mutual inductance 2.9 pu, DC bus voltage 1200 V, DC bus capacitance 10000 mu F. The IPTSMC controller parameters are as follows: k1=2, k2=2, k3=2, k4=2, k5=2, k6=2, k7=2, k8=2, and gamma=0.404; the PI controller parameters are as follows: K p =0.83, and K i =5. Under the condition of wind speed change: the wind speed is initially 12 m / s, and drops to 7 m / s at t=2 s and lasts for 0.5 s. Under this working condition, the oscillations of active power, reactive power and DC bus voltage under the IPTSMC control of integral predefined time sliding mode control converge at about t=8 s, 6 s and 7 s respectively, while the oscillations of active power, reactive power and DC bus voltage under the traditional PI control converge at about t=10 s, 8 s and 10 s respectively. It can be seen that, compared with the traditional PI control strategy, the IPTSMC control strategy of integral predefined time sliding mode control can make the oscillations converge in a shorter time and has stronger robustness.

[0125] Finally, it should be noted that the above only describes the preferred embodiments of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art will appreciate that the technical solutions described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalent ones. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A doubly-fed wind turbine VSC-HVDC subsynchronous oscillation robust integral pre-defined time sliding mode control method, characterized in that, The method comprises the following steps: S1, establishing a model of a grid-side converter in a doubly-fed wind turbine; S2, establishing a model of a phase-locked loop in the doubly-fed wind turbine; S3, constructing an integral sliding mode surface to obtain dynamic characteristics and equivalent control input of a sliding mode system; S4, designing an approaching control input to obtain an integral pre-defined time sliding mode control law; S5, implementing the integral pre-defined time sliding mode control law.

2. The method according to claim 1, wherein, in step S1, dynamic characteristics of the grid-side converter are represented by the following mathematical model: where ω g , L, R represent the angular frequency of the grid, the inductance and its resistance of the grid-side filter, respectively, V gd and V gq represent the dq-axis components of the grid voltage; while u gd and u gq correspond to the dq-axis components of the grid-side converter output voltage; i gd and i gq represent the dq-axis components of the grid current injected from the grid-side converter.

3. The method according to claim 2, wherein, in step S2, a control model corresponding to the phase-locked loop is as follows: wherein θ represents the output phase angle of the phase-locked loop; K i and K p Kipand Kprespectively represent the integral gain and the proportional gain in the phase-locked loop control system; Under normal operating conditions, U q is set to zero; when the system is in steady state, the phase angle output by the phase-locked loop is θ = ωt; when U q is disturbed by a subsynchronous oscillation voltage component, it will result in the phase-locked loop outputting a phase angle θ containing a subsynchronous oscillation component.

4. The method according to claim 3, wherein, In step S3, before constructing the integral sliding surface, define the tracking error related to i gd and i gq is defined as: e1 = i gd - i gdref e2 = i gq - i gqref (4) where i gdref and i gqref are the reference signals for the current components i gd and i gq .

5. The method according to claim 4, wherein, In step S3, the tracking i ds The integral sliding surface is constructed as follows: where T c is a predefined time, s1 is an integral sliding surface, k1 and k2 are positive numbers, sign(.) δ = | | δ sign(.). when the stator d-axis current error e1 converges to the integral sliding mode surface ISS, the system dynamics satisfy the following expression: Then, according to the expressions (5) and (6), the dynamic equation of the integral sliding mode surface ISS is: Correspondingly, the dynamic characteristics of the sliding mode system are described as: Combining equations (4) and (8), the equivalent control input U eq_gd The design is as follows: where T c is a predefined time, γ, k1, and k2 are positive numbers, and e1 is a stator d-axis current error.

6. The method according to claim 5, wherein, In step S4, in order to ensure that the error el can effectively reach the integral sliding mode surface and remain on the sliding mode surface, the approaching control input U r_gd The design is as follows: wherein k3 and k4 are greater than 0. Based on equations (9) and (10), the integral scheduled time- sliding mode control law is: ds , the integral scheduled time- sliding mode control law is:

7. The method according to claim 6, wherein, In step S3, the tracking i qs The integral sliding surface is constructed as follows: where: T c is a predefined time, s2is an integral sliding surface, k5and k6are positive numbers, sign(.) δ = | | δ sign(.) when the stator q-axis current error e2 converges to the integral sliding mode surface, the system dynamics satisfy the following expression: Then, according to the expressions (12) and (13), the dynamic equation of the integral sliding mode surface is: Correspondingly, the dynamic characteristics of the sliding mode system are described as: By combining equations (4) and (15), the equivalent control input U eq_gq The design is as follows: where T c is a predefined time, γ, k5, and k6 are positive numbers, and e2 is the stator q-axis current error.

8. The method according to claim 7, wherein, In step S4, to ensure that the error e2 can effectively reach the integral sliding mode surface and remain on the sliding mode surface, the approaching control input U r_gq The design is as follows: wherein k7 and k8 are greater than 0. Finally, based on equations (16) and (17), the integral scheduled time- sliding mode control law is given as: qs , the integral scheduled time-sliding mode control law is given as:

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