Transient stability analysis method based on doubly-fed fan and electronic equipment
By constructing a full-order model and reducing it to a second-order slow subsystem, and analyzing the stability parameters, the stability problem of the doubly fed wind turbine during transient processes was solved, and the transient stability of the system was improved.
Patent Information
- Application Number
- CN202510951509.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-10
- Publication Date
- 2025-10-10
AI Technical Summary
Doubly-fed wind turbines are prone to rotor current loss of control and phase-locked loop loss of synchronism during transient processes such as grid voltage drops and frequency fluctuations, leading to instability in the new energy power system.
A full-order model based on a doubly fed wind turbine is constructed, considering the phase-locked loop dynamics and current loop control. The model is reduced to a second-order slow subsystem model through the singular perturbation method. The stability boundary under stability parameters is analyzed, and the Lyapunov second method is used for stability analysis.
The transient stability of the doubly fed wind turbine system is enhanced and the stability characteristics during disturbances are improved.
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of transient stability analysis based on doubly-fed wind turbines, and particularly relates to a transient stability analysis method based on a doubly-fed wind turbine and an electronic device. BACKGROUND
[0002] With the development of the wind power market, doubly-fed induction generators (DFIG) are widely used due to their low cost and high efficiency. However, the doubly-fed wind turbine is prone to rotor current out-of-control, phase-locked loop (PLL) step-out and other phenomena during transient processes such as grid voltage drop and frequency fluctuation, resulting in instability of the new energy power system. Therefore, how to improve the transient stability characteristics of the doubly-fed wind turbine in the face of disturbances is a technical problem that needs to be solved at present. SUMMARY
[0003] The present disclosure provides a transient stability analysis method based on a doubly-fed wind turbine, an electronic device, an apparatus and a storage medium to at least solve the above technical problems existing in the prior art.
[0004] According to a first aspect of the present application, a transient stability analysis method based on a doubly-fed wind turbine is provided, the doubly-fed wind turbine comprising a doubly-fed induction generator, a back-to-back converter and a control circuit, the doubly-fed induction generator and the back-to-back converter being connected to the control circuit; the back-to-back converter comprises a rotor-side converter and a grid-side converter, and the stator side of the doubly-fed induction generator is coupled to an inverter and then connected in parallel to a power grid; the method comprises:
[0005] constructing a full-order model of the doubly-fed wind turbine based on the control circuit, the rotor-side converter and a state equation of a target phase-locked loop of the doubly-fed wind turbine;
[0006] performing order reduction on the full-order model of the doubly-fed wind turbine to obtain a second-order slow subsystem model;
[0007] analyzing the second-order slow subsystem model to determine the stability boundary of the doubly-fed wind turbine under different stability parameters.
[0008] In an implementation manner, the full-order model of the doubly-fed wind turbine is constructed based on the control circuit, the rotor-side converter and the state equation of the phase-locked loop, comprising:
[0009] determining a state equation of a rotor current loop based on the control circuit and the rotor-side converter of the doubly-fed wind turbine;
[0010] determining first voltage and flux phasors of the doubly-fed wind turbine in the dq axis based on the control circuit of the doubly-fed wind turbine;
[0011] determining a target stator voltage based on the first voltage, the magnetic flux phasor, and the grid voltage;
[0012] Transform the state equation of the phase-locked loop to the dq axis of the control circuit to obtain the target phase-locked loop state equation;
[0013] Based on the state equation of the rotor current loop, the target stator voltage equation and the target phase-locked loop state equation, the full-order model of the doubly fed wind turbine is obtained.
[0014] In one embodiment, the first voltage includes a first stator voltage and a first rotor voltage, and the magnetic flux phasor includes a stator flux phasor and a rotor flux phasor. The state equation of the rotor current loop is determined based on the control circuit and the rotor-side converter of the doubly fed wind turbine, including:
[0015] Ignoring rotor resistance transformation of the first voltage, a second voltage is obtained; the second voltage includes a second stator voltage and a second rotor voltage;
[0016] Determine the feedback electromotive force in the control circuit based on the three-phase balanced fault on the grid side;
[0017] Based on the control circuit of the doubly-fed wind turbine, determine the rotor voltage control quantity;
[0018] Considering the dynamic response of the phase-locked loop, determining the conversion relationship between the control circuit dq rotating coordinate system of the doubly fed wind turbine and the phase-locked loop dq rotating coordinate system;
[0019] The state equation of the rotor current loop is obtained based on the first voltage, magnetic flux phasor, second voltage, feedback electromotive force, rotor voltage control variable and the conversion relationship between the control circuit dq rotating coordinate system and the phase-locked loop dq rotating coordinate system.
[0020] In one embodiment, the full-order model of the doubly-fed wind turbine is subjected to order reduction processing to obtain a second-order slow subsystem model, including:
[0021] Based on the preset condition of rotor transient inductance, the state equation of the rotor current loop is transformed by using the singular perturbation method to obtain the transformation equation;
[0022] Solving the transformation equation to obtain a first rotor current;
[0023] The first rotor current is transformed based on a constant reference current and a linearly varying angle difference to obtain a second rotor current; the angle difference is a phase-locked loop output frequency angle and an actual rotor angle in the dq axis of the control circuit; the second rotor current is integrated to obtain an integrated rotor current;
[0024] Based on the preset conditions of rotor transient inductance, target stator voltage, differential equation of target stator voltage, integrated rotor current and target phase-locked loop state equation, a second-order slow subsystem model is obtained.
[0025] In one possible implementation, analyzing the second-order slow subsystem model to determine the stability boundary of the doubly-fed wind turbine under different stability parameters includes:
[0026] Lyapunov's second method is used to transform the second-order slow subsystem model to obtain a standard model;
[0027] Construct an energy function based on the angle difference;
[0028] Determining stability parameters of the second-order slow subsystem model based on the positive definiteness of the energy function;
[0029] Determine the stability boundary of the doubly fed wind turbine under different stability parameters.
[0030] In one embodiment, the stability parameters include current reference, phase-locked loop controller, grid voltage, line inductance and phase-locked loop control parameters; the phase-locked loop control parameters include proportional and integral coefficients of the PI controller in the phase-locked loop.
[0031] In one embodiment, the energy function is
[0032]
[0033] in, is the energy function, M is the inertia term, K is the stiffness term, δ is the angle difference, is the first derivative of the angle difference δ.
[0034] In one embodiment, the full-order model is
[0035]
[0036] Where σ is the magnetic flux leakage coefficient, k p 、k i are the proportional and integral coefficients of the PI controller in vector control respectively; is the control quantity of the rotor current reference value; U s 、U r are the stator voltage and rotor voltage of the doubly fed wind turbine respectively; I s , I r are the stator current and rotor current phasors respectively; j represents the unit vector of the Y-axis square; L s , L r and L mare stator inductance, rotor inductance and mutual inductance respectively; the superscript “·” indicates the parameter; the superscript “··” indicates the second-order derivative of the parameter; Im indicates the imaginary part; k p_PLL 、k i_PLL is the proportional and integral coefficient of the PI controller in the phase-locked loop; L g is the line inductance; ω s is the synchronous angular frequency; ω sl is the slip angular frequency.
[0037] In one embodiment, the second-order slow subsystem model is
[0038]
[0039] Among them, k PLL =k i_PLL / k p_PLL ; Indicates the reference value of the d-axis current control quantity of the doubly fed wind turbine rotor; u gq represents the q-axis component of the grid voltage; u gd represents the d-axis component of the grid voltage.
[0040] According to a second aspect of the present application, an electronic device is provided, including:
[0041] at least one processor; and
[0042] a memory communicatively connected to the at least one processor; wherein,
[0043] The memory stores instructions that can be executed by the at least one processor. The instructions are executed by the at least one processor to enable the at least one processor to perform the method described in this application.
[0044] According to a third aspect of the present application, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to enable the computer to execute the method described in the present application.
[0045] According to a fourth aspect of the present application, a computer program product is provided, comprising a computer program or instructions, which implement the method described in the present application when executed by a processor.
[0046] Utilizing the technical solution of this application helps to enhance the transient stability of the doubly-fed wind turbine system.
[0047] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present application, nor is it intended to limit the scope of the present application. Other features of the present application will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS
[0048] The above and other objects, features and advantages of the exemplary embodiments of the present application will become readily understood by reading the detailed description below with reference to the accompanying drawings. In the accompanying drawings, several embodiments of the present application are shown in an illustrative and non-limiting manner, in which:
[0049] In the drawings, the same or corresponding reference numerals denote the same or corresponding parts.
[0050] Figure 1 A schematic diagram of the topological structure of a doubly-fed wind turbine in an embodiment of the present application is shown;
[0051] Figure 2 A schematic diagram of the implementation process of the transient stability analysis method based on a doubly fed wind turbine in an embodiment of the present application is shown;
[0052] Figure 3 shows a coordinate transformation vector diagram in an embodiment of the present application;
[0053] Figure 4 A three-dimensional stability boundary diagram of a doubly-fed wind turbine considering different parameters according to an embodiment of the present application is shown;
[0054] Figure 5 A phase-locked loop output frequency diagram is shown in accordance with an embodiment of the present application, taking into account changes in phase-locked loop control parameters;
[0055] Figure 6 A schematic diagram of active power output under varying line inductance according to an embodiment of the present application is shown;
[0056] Figure 7 A schematic diagram of active power output under grid voltage changes according to an embodiment of the present application is shown;
[0057] Figure 8 A schematic diagram of the structure of an electronic device in an embodiment of the present application is shown. DETAILED DESCRIPTION
[0058] In order to make the purpose, features, and advantages of this application more obvious and easy to understand, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making creative efforts shall fall within the scope of protection of this application.
[0059] In order to make the purpose, technical solutions and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. The described embodiments should not be regarded as limiting this application. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.
[0060] In the following description, reference is made to “some embodiments”, which describes a subset of all possible embodiments, but it will be understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.
[0061] In the following description, the terms "first\second" involved are merely used to distinguish similar objects and do not represent a specific ordering of the objects. It is understandable that "first\second" can be interchanged with a specific order or sequence where permitted, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein.
[0062] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application pertains. The terms used herein are for the purpose of describing the embodiments of this application only and are not intended to limit this application.
[0063] It should be understood that in the various embodiments of the present application, the size of the serial number of each implementation process does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.
[0064] In related technologies, transient stability research on doubly fed wind turbines is mostly based on full-order mathematical models. Full-order mathematical models can generally be high-order state equation models of electromagnetic transients, mechanical torsional vibrations, and dual converter control loops. Although full-order models can accurately characterize the dynamic behavior of doubly fed wind turbine systems, due to their high order and complex variable coupling, they are difficult to be directly used for stability analysis and calculations. Therefore, it is necessary to reduce the order of the full-order mathematical model, such as the singular perturbation method, modal analysis method, and Routh approximation method. Among them, the singular perturbation method can effectively extract the dominant dynamic characteristics by separating the fast and slow subsystems. However, this method often ignores the model reduction of the phase-locked loop dynamics or simplifies the control link, and pays insufficient attention to the interaction between the phase-locked loop and the current controller in the actual power system. As a result, the transient stability characteristics of the doubly fed wind turbine in the face of disturbances are not accurate enough.
[0065] The following describes the transient stability analysis method and electronic equipment based on a doubly-fed wind turbine provided by the present application in conjunction with the accompanying drawings.
[0066] like Figure 1As shown, the present application provides a transient stability analysis method based on a doubly fed wind turbine, wherein the doubly fed wind turbine includes a doubly fed induction generator, a back-to-back converter, and a control circuit, wherein the doubly fed induction generator and the back-to-back converter are respectively connected to the control circuit; the back-to-back converter includes a rotor-side converter and a grid-side converter, and the stator side of the doubly fed induction generator is coupled with an inverter and then connected in parallel to the grid;
[0067] like Figure 2 As shown, the method includes:
[0068] S201, constructing a full-order model of the doubly-fed wind turbine based on a control circuit, a rotor-side converter, and a target phase-locked loop state equation of the doubly-fed wind turbine;
[0069] Specifically, the topology of the doubly fed wind turbine is as follows: Figure 1 As shown in Figure 2, a doubly-fed wind turbine includes a doubly-fed induction generator (DFIG), a back-to-back converter (BBC), and control circuitry. The BBC consists of a rotor-side converter (RSC) and a grid-side converter (GSC). The stator side of the DFIG and the inverter are connected in parallel to the grid via the point of common coupling (PCC). Figure 1 In, θ r is the rotor speed of the doubly fed induction generator, I s is the stator side current phasor of the doubly fed induction generator, I r is the rotor side current phasor of the doubly fed induction generator, I g is the output current phasor of the back-to-back converter; U g is the grid voltage phasor, U s is the voltage phasor of the PCC grid connection point; L g is the line inductance, L f The three slashes to the left of the PCC point indicate that all control circuits in the topology diagram are three-phase circuits, abc. The parameters with the superscript "c" represent the control circuit, rotor-side converter, and target phase-locked loop state equations, which are used to construct the full-order model of the doubly fed wind turbine. This parameter is a control parameter and has a certain phase angle difference with the control circuit.
[0070] This application constructs a full-order model of a doubly-fed wind turbine using its control circuit, rotor-side converter, and target phase-locked loop (PLL) state equations. The full-order model constructed in this application is based on the rotor-side converter and target PLL state equations, taking into account the PLL state, making the stability parameters calculated subsequently more accurate.
[0071] S202, performing order reduction processing on the full-order model of the doubly fed wind turbine to obtain a second-order slow subsystem model;
[0072] In this application, the full-order model of the doubly fed wind turbine is reduced to obtain a second-order slow subsystem model, wherein the full-order model is a sixth-order model of the doubly fed wind turbine.
[0073] S203: Analyze the second-order slow subsystem model to determine the stability boundary of the doubly fed wind turbine under different stability parameters.
[0074] Finally, by analyzing the second-order slow subsystem model, the stability parameters that affect the stability of the second-order slow subsystem can be determined. Furthermore, the stability boundary of the doubly fed wind turbine under different stability parameters is determined.
[0075] This application provides a transient stability analysis method for a doubly-fed wind turbine. Taking into account the dynamics of the phase-locked loop (PLL) and current loop control, a sixth-order model of the doubly-fed wind turbine is established and then reduced to a second-order slow subsystem. The transient stability of the second-order slow subsystem is analyzed, and the impact of stability parameters on transient stability is determined. Further determination of the impact of different stability parameters on the stability of the doubly-fed wind turbine helps enhance the transient stability of the doubly-fed wind turbine system.
[0076] In some embodiments, the state equations based on the control circuit, rotor-side converter, and phase-locked loop of the doubly-fed wind turbine are used to construct a full-order model of the doubly-fed wind turbine, including:
[0077] Based on the control circuit and rotor-side converter of the doubly-fed wind turbine, the state equation of the rotor current loop is determined;
[0078] Determining a first voltage and a first magnetic flux phasor of the doubly-fed wind turbine on the dq axis based on a control circuit of the doubly-fed wind turbine;
[0079] determining a target stator voltage based on the first voltage, the magnetic flux phasor, and the grid voltage;
[0080] Transform the state equation of the phase-locked loop to the dq axis of the control circuit to obtain the target phase-locked loop state equation;
[0081] Based on the state equation of the rotor current loop, the target stator voltage equation and the target phase-locked loop state equation, the full-order model of the doubly fed wind turbine is obtained.
[0082] In the present application, the state equation of the rotor current loop can be determined based on the control circuit and rotor-side converter of the doubly fed wind turbine. Then, based on the control circuit of the doubly fed wind turbine, the first voltage and magnetic flux phasor of the doubly fed wind turbine on the dq axis are determined, thereby determining the target stator voltage. The state equation of the phase-locked loop is transformed to the dq axis of the control circuit to obtain the target phase-locked loop state equation. Based on the state equation of the rotor current loop, the target stator voltage equation, and the target phase-locked loop state equation, a full-order model of the doubly fed wind turbine is obtained. The first voltage includes the first stator voltage and the first rotor voltage, and the magnetic flux phasor includes the stator flux phasor and the rotor flux phasor.
[0083] Specifically, the first voltage equation of the doubly fed wind turbine under the dq axis is:
[0084]
[0085] The flux equation of the doubly fed wind turbine under the dq axis is:
[0086]
[0087] Among them, U s 、U r are the stator voltage and rotor voltage phasors of the doubly fed wind turbine, I s , I r are the stator current and rotor current phasors, ψ s , ψ r are the stator flux and rotor flux phasors respectively. s 、R r are the stator resistance and rotor resistance respectively, L s , L r and L m They are stator inductance, rotor inductance and mutual inductance respectively. s is the synchronous angular frequency, ω sl is the slip angular frequency, j represents the unit vector of the Y-axis square, and is represented in the phasor diagram as leading the reference phasor by 90°.
[0088] In some embodiments, the determining of the state equation of the rotor current loop based on the control circuit and the rotor-side converter of the doubly-fed wind turbine includes:
[0089] Ignoring rotor resistance transformation of the first voltage, a second voltage is obtained; the second voltage includes a second stator voltage and a second rotor voltage;
[0090] Determine the feedback electromotive force in the control circuit based on the three-phase balanced fault on the grid side;
[0091] Based on the control circuit of the doubly-fed wind turbine, determine the rotor voltage control quantity;
[0092] Considering the dynamic response of the phase-locked loop, determining the conversion relationship between the control circuit dq rotating coordinate system of the doubly fed wind turbine and the phase-locked loop dq rotating coordinate system;
[0093] The state equation of the rotor current loop is obtained based on the first voltage, magnetic flux phasor, second voltage, feedback electromotive force, rotor voltage control variable and the conversion relationship between the control circuit dq rotating coordinate system and the phase-locked loop dq rotating coordinate system.
[0094] In this application, if the rotor resistance R in formula (1) is ignored, r , combined with formula (2), the rotor voltage can be expressed as
[0095]
[0096] If the rotor resistance R in formula (1) is ignored s , combined with formula (2), the stator voltage can be expressed as
[0097]
[0098] This application also introduces feedback electromotive force E in the rotor side control r In the case of a three-phase balanced fault on the grid side, E r It can be expressed as
[0099]
[0100] in, is the stator voltage control quantity, which is based on the control coordinate system d c q c In the rotating coordinate, the stator voltage U in the grid side dq rotating coordinate in equation (4) is s A certain angle difference. The rotor voltage control quantity in the following formula (6) is This is also the case.
[0101] Based on the control circuit of the doubly fed wind turbine, determine the rotor voltage control quantity U r c ,
[0102]
[0103] in, is the magnetic flux leakage coefficient, k p 、k i are the proportional and integral coefficients of the PI controller in vector control, is the control quantity of the rotor current reference value.
[0104] Furthermore, in the weak network,
[0105] like Figure 3As shown in the figure, considering the dynamic response of the phase-locked loop, two dq rotating coordinate systems are introduced in this doubly fed induction wind turbine system: one is the main circuit dq rotating coordinate system, and the other is the PLL control dq rotating coordinate system. c q c Rotating coordinate system. PLL output frequency angle θ PLL The actual rotor angle θ in the main circuit dq axis s There is an angle deviation δ, that is, δ = θ PLL -θ s For the variable X, the transformation relationship between the two dq coordinate systems can be expressed as:
[0106] X c =Xe -jδ (7)
[0107] According to formulas (1)-(7), the rotor voltage on the dq axis of the main circuit is eliminated, and the state space equation of the rotor current loop can be obtained:
[0108]
[0109] The superscript “·” on a parameter indicates the first-order derivative of the parameter, which can also be expressed as “d / dt”; the superscript “··” on a parameter indicates the second-order derivative of the parameter, which can also be expressed as “d 2 / dt 2 ”.
[0110] Considering the line resistance R g <<ω s L g , so only the line inductance L is considered g , that is, the line impedance Z g =jω s L g , the grid voltage can be expressed as:
[0111]
[0112] Substituting formula (1) and (2) into formula (9), the target stator voltage equation is obtained as follows:
[0113]
[0114] Then, the differential equation of formula (10) is obtained as
[0115]
[0116] Among them, the state equation of the phase-locked loop can be expressed as:
[0117]
[0118] Among them, Im represents the imaginary part, kp_PLL 、k i_PLL are the proportional and integral coefficients of the PI controller in the phase-locked loop.
[0119] According to the transformation relationship between the two dq coordinate systems in formula (7), the state equation of the phase-locked loop can be transformed to the dq axis of the main circuit, which is expressed as
[0120]
[0121] In summary, formulas (8), (10), and (13) constitute the full-order model of the doubly fed wind turbine.
[0122] In some embodiments, the full-order model of the doubly-fed wind turbine is reduced to obtain a second-order slow subsystem model, including:
[0123] Based on the preset condition of rotor transient inductance, the state equation of the rotor current loop is transformed by using the singular perturbation method to obtain the transformation equation;
[0124] Solving the transformation equation to obtain a first rotor current;
[0125] The first rotor current is transformed based on a constant reference current and a linearly varying angle difference to obtain a second rotor current; the angle difference is the angle difference between the phase-locked loop output frequency angle and the actual rotor angle in the dq axis of the control circuit;
[0126] performing integration processing on the second rotor current to obtain an integrated rotor current;
[0127] Based on the preset conditions of rotor transient inductance, target stator voltage, differential equation of target stator voltage, integrated rotor current and target phase-locked loop state equation, a second-order slow subsystem model is obtained.
[0128] In this application, in the full-order model, the rotor current I r It can be regarded as a fast state, and the angle difference δ between the phase-locked loop output frequency angle and the actual rotor angle in the dq axis of the control circuit can be regarded as a slow state. r It can be regarded as a time scale parameter ε, satisfying 0<σL r <<1. Therefore, the entire model can be simplified and reduced using the singular perturbation method. The reduction method is as follows:
[0129] Let σLr=0, then formula (8) is transformed into:
[0130]
[0131] If the solution of equation (14) is required, the integral factor μ(t) is constructed and the speed is set to δ, that is:
[0132] μ(t)=e-kt+jδ (15)
[0133] where k = k i / k p The general solution of the equation can be obtained as:
[0134]
[0135] where the constant C is determined by the initial condition. When t tends to infinity and is constant, the transient term decays. For constant reference current and linearly varying δ, the solution is obtained as:
[0136]
[0137] From the above, it can be seen that I r Steady-state tracking of reference signal From equation (17), it can be seen that dI r / dt is:
[0138]
[0139] Substituting equation (10), equation (11), equation (20) and σL r = 0 into equation (13), ignoring the decay term of the rotor current, and using the Taylor formula approximation, the state space equation of the phase-locked loop output angle can be re-expressed as:
[0140]
[0141] where k PLL = k i_PLL / k p_PLL .
[0142] Since the second-order slow subsystem model has lower computational complexity compared to the complete model, a typical nonlinear analysis method, such as the Lyapunov direct method, can be used to analyze the stability of the slow subsystem.
[0143] In some embodiments, analyzing the second-order slow subsystem model to determine the stability boundary of the doubly-fed wind turbine under different stability parameters comprises:
[0144] Transforming the second-order slow subsystem model using the Lyapunov second method to obtain a standard model;
[0145] Constructing an energy function based on the angle difference;
[0146] Determining the stability parameters of the second-order slow subsystem model based on the positive definiteness of the energy function;
[0147] Determining the stability boundary of the doubly-fed wind turbine under different stability parameters.
[0148] The stability parameters include current reference, phase-locked loop controller, grid voltage, line inductance and phase-locked loop control parameters; the phase-locked loop control parameters include the proportional and integral coefficients of the PI controller in the phase-locked loop.
[0149] In this application, the Lyapunov energy function is constructed based on the idea of a positive quadratic function V(x1,x2), that is, the stability of the system is identified by judging the sign of the derivative of V(x1,x2). The details are as follows:
[0150]
[0151] From a dynamics perspective, M is the inertia term, C is the damping term, K is the stiffness term, and the nonhomogeneous term is the external force term.
[0152] Considering dδ / dt and δ as x1 and x2 respectively, the energy function of the slow subsystem can be constructed as:
[0153]
[0154] in:
[0155]
[0156] According to formula (21) and formula (22), we can calculate The derivative of is:
[0157]
[0158] According to the Lyapunov direct method, for the second-order slow subsystem model, x = f(x) has an equilibrium point at x = 0, that is, the function V(x) satisfies:
[0159] (1) V(x) = 0, if and only if x = 0;
[0160] (2) V(x)>0, if and only if x≠0;
[0161] (3) For all values of x≠0, V(x) / dt≤.
[0162] The second-order slow subsystem model satisfies the first condition, so when the energy function (21) is positive definite and its derivative (23) is negative definite, the slow subsystem is stable. Therefore, the stability parameter of the slow subsystem can be derived as:
[0163]
[0164] In summary, stability is mainly affected by the current reference The proportional parameter k of the phase-locked loop control p_PLL and the integration parameter ki_PLL , grid voltage U g and line inductance L g Furthermore, the stiffness function K always satisfies , since all elements in K are positive. Thus, a three-dimensional stability boundary considering different stability parameters can be drawn.
[0165] like Figure 4 (a) Figure 4 (b) Figure 4 (c) Figure 4 (d) shows the effect of different stability parameters on the stability of the second-order slow subsystem model. The red and blue planes represent the M function and C function in Equation (24), respectively. The stable region S is above the blue plane and below the red plane.
[0166] In summary, this application considers the dynamics of the phase-locked loop and the current loop control, establishes a sixth-order model of the doubly fed wind turbine, and reduces the sixth-order model to a second-order slow subsystem based on the singular perturbation method. The Lyapunov direct method is used to analyze the transient stability of the slow subsystem and the line inductance L is analyzed. g , grid voltage UU g , d-axis rotor current reference value Proportional and integral parameters k of phase-locked loop control p_PLL 、k i_PLL Impact on transient stability. Grid voltage U g The larger the grid inductance L g The smaller it is, the stronger the transient stability of the doubly fed wind turbine is. p_PLL and the integration parameter k i_PLL , which helps to enhance the transient stability of the doubly fed wind turbine system.
[0167] As a specific embodiment, this application conducts a simulation experiment on the transient stability analysis method based on the doubly fed wind turbine. Figure 1 The specific parameters of the medium-sized double-fed wind turbine are shown in Table 1.
[0168] Table 1 2MW doubly-fed wind turbine simulation parameters
[0169]
[0170]
[0171] Figure 5 (a) Figure 5 (b) Consider the phase-locked loop ratio parameter k p_PLL Variation and integration parameter k i_PLLThe time domain simulation curve of the changing phase-locked loop output frequency. When the frequency disturbance is added at 0.5 seconds, the phase-locked loop output frequency decreases with the grid frequency and decreases with the proportional parameter k. p_PLL Increase or integrate parameter k i_PLL The proportional parameter k p_PLL Too large or the integral parameter k i_PLL If the value is too small, the system stability will be reduced.
[0172] like Figure 6 As shown, the present application also makes a line inductor L g The time domain simulation curve of active output under the change of frequency disturbance is shown in Figure 2. When the frequency disturbance is added at 0.5 seconds, it can be clearly seen that as the line inductance L g With the increase of , the oscillation of active power is obviously strengthened, and the stability of the doubly fed wind turbine system is obviously deteriorated.
[0173] like Figure 7 As shown, the grid voltage U g Time-domain simulation curve of active power output under varying voltage conditions. A voltage disturbance is added at 0.5 seconds. As the grid voltage drops further, the active power overshoot increases, and system stability deteriorates.
[0174] According to an embodiment of the present application, the present application also provides an electronic device and a readable storage medium.
[0175] The electronic device includes at least one processor and a memory in communication with the at least one processor. The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the transient stability analysis method based on a doubly fed wind turbine described in this application. The computer instructions are used to cause the computer to perform the transient stability analysis method based on a doubly fed wind turbine described in this application.
[0176] The present application also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the transient stability analysis method based on a doubly-fed wind turbine of the present application.
[0177] Figure 8A schematic block diagram of an example electronic device 800 that can be used to implement embodiments of the present application is shown. The electronic device is intended to represent various forms of digital computers, such as laptops, desktops, tablets, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device can also represent various forms of mobile electronic devices, such as personal digital processors, cellular telephones, smartphones, wearable devices, and other similar computing electronic devices. The components shown here, their connections and relationships, and their functions, are meant to be examples only, and are not intended to limit the implementations of the present application described and / or claimed in this document.
[0178] As shown in Figure 8 The device 800 includes a computing unit 801 that can perform various appropriate actions and processes in accordance with a computer program stored in a read-only memory (ROM) 802 or a computer program loaded into a random access memory (RAM) 803 from a storage unit 808. Various programs and data required for the operation of the device 800 can also be stored in the RAM 803. The computing unit 801, the ROM 802, and the RAM 803 are connected to each other through a bus 804. An input / output (I / O) interface 805 is also connected to the bus 804.
[0179] Various components in the device 800 are connected to the I / O interface 805, including an input unit 806, such as a keyboard, a mouse, etc.; an output unit 807, such as various types of displays, speakers, etc.; the storage unit 808, such as a magnetic disk, an optical disk, etc.; and a communication unit 809, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 809 allows the device 800 to exchange information / data with other devices through a computer network, such as the Internet, and / or various telecommunication networks.
[0180] The computing unit 801 can be various general and / or special purpose processing components with processing and computing capabilities. Some examples of the computing unit 801 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various specialized artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 801 performs various methods and processes described above, such as the transient stability analysis method based on a doubly-fed wind turbine. For example, in some embodiments, the transient stability analysis method based on a doubly-fed wind turbine can be implemented as a computer software program tangibly embodied in a machine-readable medium, such as the storage unit 808. In some embodiments, part or all of the computer program can be loaded and / or installed onto the device 800 via the ROM 802 and / or the communication unit 809. When the computer program is loaded onto the RAM 803 and executed by the computing unit 801, one or more steps of the transient stability analysis method based on a doubly-fed wind turbine described above can be performed. Alternatively, in other embodiments, the computing unit 801 can be configured to perform the transient stability analysis method based on a doubly-fed wind turbine by any other suitable means, such as by means of firmware.
[0181] Various implementations of the systems and techniques described above can be realized in digital electronic circuitry, integrated circuitry, a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a system on a chip (SOC), a programmable logic device (CPLD), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and / or interpretable on a programmable system including at least one programmable processor, which can be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.
[0182] Program code for carrying out methods of the present application can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing electronic device to produce a machine, such that the program code, when executed by the processor or controller, produces a means for implementing the functions / acts specified in the flowcharts and / or block diagrams. The program code can be executed entirely on a machine, partially on a machine, partially on a machine and partially on a remote machine or entirely on a remote machine or server.
[0183] In the context of the present application, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in combination with an instruction execution system, an electronic device or an apparatus. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium can include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
[0184] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display electronic device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of electronic devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).
[0185] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (LAN), a wide area network (WAN), and the Internet.
[0186] A computer system may include a client and a server. The client and server are generally remote from each other and typically interact through a communication network. The client-server relationship arises through computer programs running on the respective computers and having a client-server relationship with each other. The server may be a cloud server, a server in a distributed system, or a server integrated with a blockchain.
[0187] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.
Claims
1. A transient stability analysis method based on a doubly fed wind turbine, characterized in that: The doubly-fed wind turbine includes a doubly-fed induction generator, a back-to-back converter, and a control circuit. The doubly-fed induction generator and the back-to-back converter are respectively connected to the control circuit. The back-to-back converter includes a rotor-side converter and a grid-side converter. The stator side of the doubly-fed induction generator is coupled with an inverter and then connected in parallel to the grid. The method includes: Based on the control circuit, rotor-side converter and target phase-locked loop state equation of the doubly-fed wind turbine, a full-order model of the doubly-fed wind turbine is constructed; Performing order reduction processing on the full-order model of the doubly fed wind turbine to obtain a second-order slow subsystem model; The second-order slow subsystem model is analyzed to determine the stability boundary of the doubly fed wind turbine under different stability parameters.
2. The method according to claim 1, characterized in that The state equations of the control circuit, rotor-side converter and phase-locked loop of the doubly-fed wind turbine are used to construct a full-order model of the doubly-fed wind turbine, including: Based on the control circuit and rotor-side converter of the doubly-fed wind turbine, the state equation of the rotor current loop is determined; Determining a first voltage and a first magnetic flux phasor of the doubly-fed wind turbine on the dq axis based on a control circuit of the doubly-fed wind turbine; determining a target stator voltage based on the first voltage, the magnetic flux phasor, and the grid voltage; Transform the state equation of the phase-locked loop to the dq axis of the control circuit to obtain the target phase-locked loop state equation; Based on the state equation of the rotor current loop, the target stator voltage equation and the target phase-locked loop state equation, the full-order model of the doubly fed wind turbine is obtained.
3. The method according to claim 2, characterized in that The first voltage includes a first stator voltage and a first rotor voltage, and the magnetic flux phasor includes a stator flux phasor and a rotor flux phasor. The state equation of the rotor current loop is determined based on the control circuit and the rotor-side converter of the doubly fed wind turbine, including: Ignoring rotor resistance transformation of the first voltage, a second voltage is obtained; the second voltage includes a second stator voltage and a second rotor voltage; Determine the feedback electromotive force in the control circuit based on the three-phase balanced fault on the grid side; Based on the control circuit of the doubly-fed wind turbine, determine the rotor voltage control quantity; Considering the dynamic response of the phase-locked loop, determining the conversion relationship between the control circuit dq rotating coordinate system of the doubly fed wind turbine and the phase-locked loop dq rotating coordinate system; The state equation of the rotor current loop is obtained based on the first voltage, magnetic flux phasor, second voltage, feedback electromotive force, rotor voltage control variable and the conversion relationship between the control circuit dq rotating coordinate system and the phase-locked loop dq rotating coordinate system.
4. The method according to claim 2, characterized in that The full-order model of the doubly-fed wind turbine is subjected to order reduction processing to obtain a second-order slow subsystem model, including: Based on the preset condition of rotor transient inductance, the state equation of the rotor current loop is transformed by using the singular perturbation method to obtain the transformation equation; Solving the transformation equation to obtain a first rotor current; The first rotor current is transformed based on a constant reference current and a linearly varying angle difference to obtain a second rotor current; the angle difference is the angle difference between the phase-locked loop output frequency angle and the actual rotor angle in the dq axis of the control circuit; performing integration processing on the second rotor current to obtain an integrated rotor current; Based on the preset conditions of rotor transient inductance, target stator voltage, differential equation of target stator voltage, integrated rotor current and target phase-locked loop state equation, a second-order slow subsystem model is obtained.
5. The method according to claim 4, characterized in that The second-order slow subsystem model is analyzed to determine the stability boundary of the doubly fed wind turbine under different stability parameters, including: Lyapunov's second method is used to transform the second-order slow subsystem model to obtain a standard model; Construct an energy function based on the angle difference; Determining stability parameters of the second-order slow subsystem model based on the positive definiteness of the energy function; Determine the stability boundary of the doubly fed wind turbine under different stability parameters.
6. The method according to claim 5, characterized in that The stability parameters include current reference, phase-locked loop controller, grid voltage, line inductance and phase-locked loop control parameters; the phase-locked loop control parameters include the proportional and integral coefficients of the PI controller in the phase-locked loop.
7. The method according to claim 5, characterized in that The energy function is in, is the energy function, M is the inertia term, K is the stiffness term, δ is the angle difference, is the first derivative of the angle difference δ.
8. The method according to claim 2, characterized in that The full-order model is Where σ is the magnetic flux leakage coefficient, k p 、k i are the proportional and integral coefficients of the PI controller in vector control respectively; is the control quantity of the rotor current reference value; U s 、U r are the stator voltage and rotor voltage of the doubly fed wind turbine respectively; I s , I r are the stator current and rotor current phasors respectively; j represents the unit vector of the Y-axis square; L s 、L r and L m are stator inductance, rotor inductance and mutual inductance respectively; the superscript "·" indicates the parameter; the superscript "··" indicates the second-order derivative of the parameter; Im indicates the imaginary part; k p_PLL 、k i_PLL is the proportional and integral coefficient of the PI controller in the phase-locked loop; L g is the line inductance; ω s is the synchronous angular frequency; ω sl is the slip angular frequency.
9. The method according to claim 1, characterized in that The second-order slow subsystem model is Among them, k PLL =k i_PLL / k p_PLL ; Indicates the reference value of the d-axis current control quantity of the doubly fed wind turbine rotor; u gq represents the q-axis component of the grid voltage; u gd Represents the d-axis component of the grid voltage.
10. An electronic device, characterized in that: at least one processor; as well as a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 9.