A transient synchronization dynamic characteristics modeling method for doubly-fed wind turbines
By modeling doubly-fed wind turbines as grid-following converters, the method simplifies the analysis of transient synchronous stability, addressing the challenge of complex nonlinear characteristics and improving stability during grid faults.
Patent Information
- Application Number
- CN202310694715.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-12
- Publication Date
- 2024-12-27
- Estimated Expiration
- 2043-06-12
AI Technical Summary
Existing technologies fail to adequately model the transient synchronous stability of doubly-fed wind turbines, which exhibit complex nonlinear characteristics during faults, making it difficult to analyze their stability during grid disturbances.
A method is developed to model doubly-fed wind turbines as grid-following converters under the transient synchronization time scale, simplifying the analysis by equating the rotor-side converter to a grid-following converter, filter inductor, and current controller to a unit gain, using phase angle dynamic expressions and transient differential equations to characterize the system's dynamic response.
This approach simplifies the analysis of instability boundaries and improves transient synchronization stability of doubly-fed wind turbines, providing a reference for enhancing their stability under large disturbances.
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Figure CN116738914B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of wind power generation control, and in particular relates to a transient synchronous dynamic characteristic modeling method of a doubly-fed wind turbine generator set. Background Art
[0002] With the increase in the number and power level of wind power and photovoltaic power, in order to prevent large-scale grid disconnection accidents of new energy and ensure the safety and reliability of the power grid, relevant national standards require that wind power and photovoltaic converters have a longer grid fault tolerance time to maintain the continuity of output power, and the converter cannot be locked at will during the fault ride-through period. However, the overload capacity of the new energy grid-connected system that relies on power electronic devices is much smaller than that of the traditional synchronous machine, and compared with the rotor motion equation of the synchronous machine, the transient characteristics of the new energy equipment will be affected by the grid synchronization control parameters and the switching protection strategy; therefore, whether the new energy device can maintain transient stability after a grid fault has become the focus of domestic and foreign scholars.
[0003] In recent years, there have been some transient faults caused by the loss of synchronization between new energy equipment and the power grid after being affected by large disturbances such as voltage drops. For example, in 2016 and 2017, a 900MW photovoltaic power station in Southern California, the United States, lost power. In a 2018 report, the North American Electric Reliability Council (NERC) pointed out that the accident was related to the failure of the phase-locked loop to maintain synchronization during the fault. In 2021, the European power grid experienced a "1.8" disconnection accident. Relevant reports pointed out that the accident was caused by power angle instability. The continued increase in the penetration rate of new energy will reduce the stability of the power system under large disturbances, resulting in cascading failures and unplanned disconnections.
[0004] In actual projects, the problem of transient out-of-step in doubly-fed wind power grid-connected systems has not been fully reported. There are two main reasons for this: ① In the past, doubly-fed wind turbines had weak fault ride-through capabilities. When the grid voltage dropped deeply, the crowbar circuit and the locking converter would be triggered to limit the rotor overcurrent. At this time, the grid phase and frequency information obtained by the grid-connected synchronization link would not directly affect the control system of the doubly-fed wind turbine. ② The control time scale of power electronic devices is fast. Even if a transient out-of-step fault occurs, it will dissipate in a very short time, and then trigger nonlinear controls such as overvoltage or overcurrent protection, which is difficult to identify and judge.
[0005] Through searching and research, it is found that the Chinese patent application with publication number CN116070403A in the related prior art proposes an equivalent modeling method for a multi-converter system suitable for transient synchronous stability analysis, by equivalentizing the multi-converter system to a star structure, extracting the key characteristic quantity of the transient response curve of the q-axis component of the voltage at each converter terminal, determining the synchronization criterion of the multi-converter system, and finally simplifying each synchronous converter group into a single-machine equivalent aggregation model. The Chinese patent application with publication number CN115954927A proposes a method for determining the transient synchronous stability coefficient of a phase-locked synchronous grid-connected converter, by obtaining the corresponding equivalent circuit when the grid-connected converter fails, determining the voltage drop amplitude generated by the output current of the grid-connected converter through the line impedance and the voltage amplitude generated by the grid voltage through the equivalent circuit when the fault occurs according to the equivalent circuit, and finally determining the transient synchronous stability coefficient of the phase-locked synchronous grid-connected converter corresponding to the grid-connected converter failure.
[0006] In summary, the existing technologies mainly focus on the transient synchronous stability of traditional inverters, but rarely focus on the transient synchronous stability analysis and modeling of doubly-fed wind turbines. Doubly-fed wind turbines exhibit more complex nonlinear characteristics during transient faults. Due to the multi-time scale coupling and control mode switching of the converter, it is difficult to establish a complete model to analyze the transient characteristics of doubly-fed wind turbines during faults. A complete system has not yet been formed at home and abroad. Summary of the invention
[0007] In view of the above, the present invention provides a method for modeling the transient synchronization dynamic characteristics of a doubly-fed wind turbine set, which equates the doubly-fed wind power to a grid-following converter at the transient synchronization time scale to simplify the analysis, improves the analysis method of the instability boundary of the doubly-fed wind power at the transient synchronization time scale, and provides a reference for improving the transient synchronization stability of the doubly-fed wind power under large disturbances.
[0008] A transient synchronous dynamic characteristic modeling method for a doubly-fed wind turbine generator system comprises the following steps:
[0009] (1) Under the transient synchronization time scale, the doubly-fed wind turbine generator system is equivalent to a simplified model based on a grid-following converter;
[0010] (2) Based on the simplified model, the phase angle dynamic expression is used to qualitatively describe the transient synchronization characteristics of the doubly fed wind turbine generator system;
[0011] (3) Based on the transient synchronization characteristics, the transient differential equation is used to accurately characterize the dynamic response waveform of the grid-following converter phase angle and the phase-locked loop output frequency.
[0012] Furthermore, the simplified model in step (1) is to make the rotor-side converter in the doubly-fed wind turbine generator set equivalent to a grid-following converter, the doubly-fed asynchronous wind turbine generator equivalent to a filter inductor, and the current controller equivalent to a unit gain.
[0013] Furthermore, the grid-following converter ignores the internal structure of the current controller, that is, it is assumed that the input current I dq In the transient synchronization time scale, it can always follow the upper reference value, I dq is the current vector at the common coupling point in the dq coordinate system.
[0014] Furthermore, the model parameters of the simplified model include two parts: grid parameters and converter parameters. The grid parameters include the three-phase voltage U at the common coupling point. PCC and three-phase current I PCC , the three-phase voltage U of the remote AC power grid GCP And the grid impedance Z g , the converter parameters include the DC bus voltage V dc 、Filter inductor L f , the proportional gain K of the phase-locked loop pp And the integral gain K ip And the output angle θ of the phase-locked loop PLL and the output angular frequency ω PLL .
[0015] Furthermore, the dynamic expression of the phase angle in step (2) is as follows:
[0016] δ=∫[K pp (-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)+K ip ∫(-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)] where: U GCP is the voltage amplitude of the remote AC grid, K pp and K ip are the proportional coefficient and integral coefficient of the PI link in the phase-locked loop, δ is the output angle θ of the phase-locked loop PLL Phase angle θ with the remote AC grid voltage GCP The phase angle difference is δ = θ PLL -θ GCP , R g is the grid resistance, L g is the grid inductance, I d and Iq are the d-axis current component and q-axis current component at the common coupling point, I q ' is the q-axis current component I q The differential result of PLL is the output angular frequency of the phase-locked loop.
[0017] Furthermore, the transient synchronization characteristic of the doubly-fed wind turbine in step (2) is the phase-locked loop output angle θ PLL Phase angle θ with the remote AC grid voltage GCP The phase angle difference δ, the phase-locked loop output angle θ in steady state PLL The phase angle θ with the voltage at the common coupling point PCC However, when a grid voltage drop occurs, the voltage of the remote AC grid drops instantly, and the voltage drop on the grid impedance will cause θ PLL ≠θ PCC , when the phase difference between these two angles exceeds 180°, out-of-step phenomenon will occur; therefore, according to the dynamic expression of the phase angle, it is iteratively solved. If the phase angle difference δ converges to a constant, it means that the doubly fed wind turbine has achieved transient synchronous stability at this time; if the phase angle difference δ cannot converge, it means that the doubly fed wind turbine has a out-of-step fault.
[0018] Furthermore, the transient differential equation in step (3) is as follows:
[0019]
[0020] Where: x1 and x2 are two state variables of the transient differential equation, corresponding to the phase angle of the grid-following converter and the phase-locked loop output angular frequency, respectively. The superscript ' represents the differential operator. δ is the phase angle difference between the phase-locked loop output angle and the phase angle of the remote AC grid voltage. U fault is the voltage amplitude of the remote AC power grid under fault, K pp and K ip are the proportional coefficient and integral coefficient of the PI link in the phase-locked loop, L g is the grid inductance, ω g is the grid angular frequency, is the d-axis current reference value at the common coupling point.
[0021] Furthermore, the initial value expressions of the phase angle difference δ and its differential result δ' are as follows:
[0022]
[0023] Among them: δ0 and δ0' correspond to the initial values of δ and δ' respectively, I max is the maximum current amplitude output by the rotor-side converter before the fault, U nom is the voltage amplitude of the remote AC power grid before the fault.
[0024] The present invention equates the doubly-fed wind turbine unit to a grid-following converter under the transient synchronization time scale to simplify the analysis, verifies the influence of transient flux linkage based on the models before and after simplification, and thus verifies the rationality of the simplified model. It further qualitatively describes the transient synchronization characteristics based on the phase angle dynamic expression, and accurately characterizes the dynamic response waveform based on the transient differential equation, improves the analysis method of the doubly-fed wind power instability boundary under the transient synchronization time scale, and provides a reference for improving the transient synchronization stability of doubly-fed wind power under large disturbances. BRIEF DESCRIPTION OF THE DRAWINGS
[0025] Figure 1 Schematic diagram of a doubly-fed wind turbine connected to a weak power grid.
[0026] Figure 2 Schematic diagram of the simplified model of the doubly-fed wind turbine generator system under the transient synchronization time scale.
[0027] Figure 3 (a) is a schematic diagram of the dynamic waveforms of the phase angle and frequency of the doubly fed wind power system under a low impedance ratio grid voltage drop fault.
[0028] Figure 3 (b) is a schematic diagram of the dynamic waveforms of the phase angle and frequency of the grid-following converter under a low impedance ratio grid voltage drop fault.
[0029] Figure 4 (a) is a schematic diagram of the dynamic waveforms of the phase angle and frequency of the doubly fed wind power system under a high impedance ratio grid voltage drop fault.
[0030] Figure 4 (b) is a schematic diagram of the dynamic waveforms of the phase angle and frequency of the grid-following converter under a high impedance ratio grid voltage drop fault.
[0031] Figure 5 It is a schematic diagram of the dynamic waveform of the phase angle and frequency of the grid-type converter when the voltage drops to 414V.
[0032] Figure 6 It is a schematic diagram of the dynamic waveform of the phase angle and frequency of the grid-type converter when the voltage drops to 345V. DETAILED DESCRIPTION
[0033] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.
[0034] The method for modeling transient synchronous dynamic characteristics of doubly-fed wind power of the present invention comprises the following steps:
[0035] (1) Under the transient synchronization time scale, the doubly-fed wind power plant is equivalent to a simplified grid-following converter model.
[0036] In order to establish a complete mathematical model to describe the transient characteristics of the doubly fed wind turbine, it is first assumed that the unloading circuit of the doubly fed wind power can maintain the DC bus voltage of the doubly fed wind turbine constant during the fault period. Therefore, the influence of the grid-side converter is ignored in the transient synchronization time scale. The doubly fed wind turbine connected to the grid after the grid-side converter is ignored. Figure 1 shown.
[0037] When a doubly-fed wind turbine is affected by a large disturbance such as a voltage drop, a transient magnetic flux will be generated on the stator side, as shown in the following equation:
[0038]
[0039] Among them: U s and I s represents the stator voltage and stator current, R s is the stator resistance, ψ s is the stator flux, ω g =100πrad / s is the fundamental angular frequency of the power grid, the subscripts d and q represent the components of the two-phase rotating coordinate system, and the superscript ' represents the derivative with respect to time t.
[0040] Q-axis stator transient flux ψ' during transient process sq It will affect the input voltage of the phase-locked loop, thereby affecting the output angle of the phase-locked loop, and affecting the phase angle and the output frequency waveform of the phase-locked loop during the transient process. However, the response speed of the transient magnetic flux is relatively fast, and the doubly fed wind turbine can be simplified into a grid-following converter on the transient synchronization time scale, retaining only the conversion relationship between the stator and rotor currents.
[0041] Figure 2 A simplified model and control block diagram of a grid-following converter connected to a weak grid are given, where U PCC and I PCC It represents the three-phase voltage and current at the common coupling point, U GCP Indicates the three-phase voltage of the remote AC power grid. DC bus voltage V dc Assuming a constant value, Z g =R g +jω g L g Represents the grid impedance, where R g is the grid resistance, L g is the grid inductance. f Represents the filter inductance, K pp and K ip is the phase-locked loop proportional and integral gain, θ PLL and ω PLL is the phase-locked loop output angle and output angular frequency. In steady state, θ PLL The phase angle θ with the voltage at the common coupling point PCC Equal, but in the event of a grid voltage drop or other faults, such as UGCP The voltage drop on the grid impedance will cause θ PLL ≠θ PCC When the phase difference between the two angles exceeds 180°, a step-out phenomenon will occur. The phase angle δ=θ between the phase-locked loop output and the remote AC grid voltage can be used. PLL -θ GCP to measure this transient synchronization process; since the dynamic characteristics of the out-of-step fault are in the low-frequency range and the bandwidth of the current controller is usually very high, the out-of-step fault is mainly related to the dynamics of the phase-locked loop. Figure 2 The internal structure of the current controller is omitted, and it is assumed that the controller current I dq Always able to follow the upper reference value in the transient synchronization time scale
[0042] (2) Verify the impact of transient magnetic flux based on the model before and after simplification.
[0043] In order to analyze the impact of transient flux on synchronous stability, we established a double-fed wind power and a simplified grid-following converter EMT simulation model in Matlab / Simulink to compare the voltage amplitude U GCP The transient synchronous waveform drops from 690V to 345V. Both use a 45Hz phase-locked loop bandwidth and operate at full rated active power.
[0044] Depend on Figure 3 (a) It can be found that in the low impedance ratio grid (R g >L g ) when a voltage drop fault occurs, the transient waveform of the synchronous link of the doubly fed wind power system has a transient flux disturbance of 50Hz, but compared with Figure 3 (b) The transient waveform of the grid-type converter, the change trends of the phase angle and frequency of the two are similar. For example, the phase angle δ of the double-fed wind turbine is 0.48rad at 0.023s, and the output frequency f PLL At the moment of fault, it is 54.4Hz; the phase angle δ of the grid-type converter is 0.47rad at 0.023s, and the output frequency f PLL At the moment of fault, it is 54.1Hz. Figure 4 (a) and Figure 4 (b) It can be found that the high impedance ratio grid (L g >R g ) the transient waveforms of the two are also similar, and both have out-of-step faults. For example, the output frequency f PLL At the moment of fault, they are 63.1Hz and 63.4Hz respectively, and then f PLL First decrease, then increase, and finally diverge.
[0045] In summary, it is indeed possible to simplify the doubly-fed wind power system into a grid-following converter within the time scale of transient synchronous stability analysis.
[0046] (3) Qualitatively describe the transient synchronization characteristics based on the phase angle dynamic expression.
[0047] Remote AC grid voltage U in two-phase rotating coordinate system GCP As shown below:
[0048]
[0049]
[0050] The grid impedance voltage drop in the two-phase rotating coordinate system is shown as follows:
[0051]
[0052] Combining the above formula, the grid connection point voltage in the two-phase rotating coordinate system can be obtained as follows:
[0053]
[0054] The output angle of the phase-locked loop is shown as follows:
[0055] θ PLL =∫[(K pp +K ip ∫)U PCCq +ω g ]
[0056] When the double-fed wind power is subject to a large disturbance, θ PLL With θ PCC are not equal; if θ PLL I can't keep up with θ PCC , then the doubly-fed wind power cannot complete synchronization with the grid and causes a step-out fault. The phase angle δ=θ PLL -θ GCP To measure this transient synchronization process, where θ GCP =∫ω g dt, we can get the following formula:
[0057] δ=∫[(K pp +K ip ∫)(-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)]
[0058] If δ can eventually converge to a constant, it means that transient synchronous stability has been achieved; if δ cannot converge, it means that the system has a loss of synchronization failure.
[0059] (4) Accurately characterize the dynamic response waveform based on transient differential equations.
[0060] When the grid short-circuit ratio is relatively high, the grid inductance L g The current transient time is short and it will reach steady state soon. At this time, L can be ignored in the time scale of transient synchronous stability analysis. g I q ', so we can get the following formula:
[0061] δ′=(K pp +K ip ∫)[-U GCP sinδ+(ω g +δ′)L g I d ]
[0062] Where: PLL In transient processes, ω g +δ', and then differentiate once more to obtain:
[0063] δ″=K pp (-U GCP cosδδ′+δ″L g I d )+K ip [-U GCP sinδ+(ω g +δ′)L g I d ]
[0064] Therefore, the voltage drop fault U GCP From U nom =1p.u. drops to U fault The second-order differential equation is as follows:
[0065]
[0066] The initial value calculation of the differential equation is shown as follows:
[0067]
[0068] We established the grid inductance L in Matlab / Simulink g =0.51mH (0.5pu) grid-following converter EMT simulation model, the phase angle dynamics and phase-locked loop output frequency dynamics under different voltage drop depths are shown in Figure 5 and Figure 6As shown; Figure 5 and Figure 6 The second-order transient synchronization model analytical waveform is also given, where the phase-locked loop output frequency f PLL =(δ' / 2π+50)Hz, it can be found that the second-order transient synchronization model matches the EMT simulation model, and accurately predicts that the system will eventually stabilize after the voltage drops from 690V to 414V, and predicts that there will be a loss of step when the voltage drops from 690V to 345V.
[0069] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.
Claims
1. A transient synchronous dynamic characteristic modeling method for a doubly-fed wind turbine generator system, comprising the following steps: (1) Under the transient synchronization time scale, the doubly-fed wind turbine generator system is equivalent to a simplified model based on a grid-following converter; (2) Based on the simplified model, the following phase angle dynamic expression is used to qualitatively describe the transient synchronization characteristics of the doubly fed wind turbine generator system; δ=∫[K pp (-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)+K ip ∫(-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)] in: U GCP is the voltage amplitude of the remote AC grid, K pp and K ip are the proportional coefficient and integral coefficient of the PI link in the phase-locked loop, δ is the output angle θ of the phase-locked loop PLL Phase angle θ with the remote AC grid voltage GCP The phase angle difference is δ = θ PLL -θ GCP , R g is the grid resistance, L g is the grid inductance, I d and I q are the d-axis current component and q-axis current component at the common coupling point, I q ' is the q-axis current component I q The differential result of PLL is the output angular frequency of the phase-locked loop; (3) Based on the transient synchronization characteristics, the following transient differential equation is used to accurately characterize the dynamic response waveform of the grid-following converter phase angle and phase-locked loop output frequency; Where: x1 and x2 are two state variables of the transient differential equation, corresponding to the phase angle of the grid-following converter and the phase-locked loop output angular frequency, respectively. The superscript ' represents the differential operator. δ is the phase angle difference between the phase-locked loop output angle and the phase angle of the remote AC grid voltage. U fault is the voltage amplitude of the remote AC power grid under fault, K pp and K ip are the proportional coefficient and integral coefficient of the PI link in the phase-locked loop, L g is the grid inductance, ω g is the grid angular frequency, I d ref is the d-axis current reference value at the common coupling point.
2. The transient synchronous dynamic characteristic modeling method according to claim 1 is characterized in that: The simplified model in step (1) is to make the rotor-side converter in the doubly-fed wind turbine generator set equivalent to a grid-following converter, the doubly-fed asynchronous wind turbine generator equivalent to a filter inductor, and the current controller equivalent to a unit gain.
3. The transient synchronous dynamic characteristic modeling method according to claim 2 is characterized in that: The grid-following converter ignores the internal structure of the current controller, that is, it is assumed that the input current I dq In the transient synchronization time scale, it can always follow the upper reference value, I dq is the current vector at the common coupling point in the dq coordinate system.
4. The transient synchronous dynamic characteristic modeling method according to claim 1 is characterized in that: The model parameters of the simplified model include two parts: grid parameters and converter parameters. The grid parameters include the three-phase voltage U at the common coupling point. PCC and three-phase current I PCC , the three-phase voltage U of the remote AC power grid GCP And the grid impedance Z g , the converter parameters include the DC bus voltage V dc 、Filter inductor L f , the proportional gain K of the phase-locked loop pp And the integral gain K ip And the output angle θ of the phase-locked loop PLL and the output angular frequency ω PLL .
5. The transient synchronous dynamic characteristic modeling method according to claim 1, characterized in that: The transient synchronization characteristic of the doubly-fed wind turbine in step (2) is the phase-locked loop output angle θ PLL Phase angle θ with the remote AC grid voltage GCP The phase angle difference δ, the phase-locked loop output angle θ in steady state PLL The phase angle θ with the voltage at the common coupling point PCC However, when a grid voltage drop occurs, the voltage of the remote AC grid drops instantly, and the voltage drop on the grid impedance will cause θ PLL ≠θ PCC , when the phase difference between these two angles exceeds 180°, out-of-step phenomenon will occur; therefore, according to the dynamic expression of the phase angle, it is iteratively solved. If the phase angle difference δ converges to a constant, it means that the doubly fed wind turbine has achieved transient synchronous stability at this time; if the phase angle difference δ cannot converge, it means that the doubly fed wind turbine has a out-of-step fault.
6. The transient synchronous dynamic characteristic modeling method according to claim 1, characterized in that: The initial value expressions of the phase angle difference δ and its differential result δ' are as follows: Among them: δ0 and δ0' correspond to the initial values of δ and δ' respectively, I max is the maximum current amplitude output by the rotor-side converter before the fault, U nom is the voltage amplitude of the remote AC power grid before the fault.