A small signal modeling and analysis method for grid-connected wind power system considering control time delay

Abstract

The application provides a kind of wind power grid-connected system small disturbance modeling and stability analysis method considering control delay, the method introduces sampling delay, zero-order hold and switch delay link in small disturbance linearization modeling process, linearization is handled using first-order inertia link, and a unified state space model is established;Direct drive wind turbine and double-fed wind turbine control delay mathematical model is constructed respectively, the influence of control delay on system oscillation mode and stability is identified through eigenvalue and impedance analysis;Finally, time domain simulation is carried out in simulation platform, and the accuracy of the model is verified by comparing the calculation results and simulation results. The method can accurately reflect the small disturbance characteristics of wind power grid-connected system in sub-synchronous and super-synchronous frequency band, provide a theoretical basis for wind turbine control parameter optimization and grid-connected stability evaluation, and solve the technical problem that the influence of control delay is generally ignored in existing wind power grid-connected system modeling.

Description

Technical Field

[0001] This invention belongs to the field of new energy power system modeling and stability analysis, and more specifically, relates to a method for small disturbance modeling and stability analysis of wind power grid-connected systems considering control delay. Background Technology

[0002] With the continuous growth of new energy installed capacity, wind farms are increasingly accounting for a larger share of the power system, making the dynamic characteristics of wind power grid-connected systems increasingly prominent. Wind turbine control systems generally adopt digital control structures based on digital signal processors and drive power converters through pulse width modulation. In this process, unavoidable control delays are introduced in signal sampling, data calculation, zero-order hold, and switching actions, causing shifts in the system's phase and amplitude response, thus altering the dynamic characteristics and stability boundaries of the wind power system. Failure to accurately consider these delay effects during modeling often leads to discrepancies between the system's small-disturbance model and actual operating characteristics.

[0003] When wind power systems operate in weak grid environments or transmit power over long distances via series capacitor compensation lines, the additional phase lag caused by control delays can affect the system's phase margin and damping ratio, making the grid-connected system more prone to dynamic instability problems such as subsynchronous / supersynchronous oscillations. Typical engineering cases include: in 2009, a large doubly-fed wind farm in Texas, USA, experienced a subsynchronous oscillation accident in its transmission system via a series compensation line, causing hundreds of wind turbines to disconnect from the grid due to control instability; since 2012, wind farms in Zhangbei and Hami regions of my country have also experienced similar oscillation phenomena multiple times, sometimes even triggering unit protection actions and regional voltage fluctuations.

[0004] In traditional dynamic modeling and small-disturbance analysis, researchers often simplify the impact of control delay or ignore its effect on system phase characteristics in time-domain simulations. This results in models that fail to accurately reflect the dynamic response characteristics of wind power systems under different operating conditions. Especially in multi-site, large-scale wind power grid-connected systems, the coupling of delay effects with factors such as network impedance, control parameters, and short-circuit ratio becomes more complex, making it difficult for traditional modeling to accurately identify the dominant oscillation modes and stability boundaries. Therefore, there is an urgent need to establish a dynamic modeling and analysis method for wind power grid-connected systems that can consider the control delay effect in small-disturbance analysis. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method for small-disturbance modeling and stability analysis of wind power grid-connected systems that considers control delay. This solves the technical problem of generally neglecting the influence of control delay in existing wind power grid-connected system modeling. This method introduces sampling delay, zero-order hold, and switching delay elements into the small-disturbance linearization model, establishing a unified dynamic model that accurately reflects the interaction and coupling relationship between control characteristics and the power grid, providing a basis for wind power system oscillation mode identification and stability analysis.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay is provided, comprising the following steps:

[0007] (1) The converter control delay element in the wind turbine is mathematically modeled using the first-order Taylor expansion to obtain the mathematical model of converter control delay.

[0008] (2) Construct an equivalent linear model of wind turbine control delay by using the mathematical model of converter control delay established in the linearization process (1);

[0009] (3) Perform eigenvalue calculation on the equivalent linear model of wind turbine control delay to identify the dominant oscillation mode frequency and key state variables of the dominant oscillation mode of the equivalent linear model of wind turbine control delay;

[0010] (4) Using impedance analysis, construct the equivalent impedance model of the wind turbine control delay equivalent linear model; perform linearization modeling of the power grid subsystem of the wind power grid connection system, and use impedance analysis to obtain the power grid equivalent impedance model of the power grid subsystem;

[0011] Plot the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine, and the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid. The phase difference between the equivalent impedance model of the wind turbine and the equivalent impedance model of the power grid is obtained based on the intersection frequency value of the intersection point of the amplitude-frequency curves.

[0012] (5) Build a unified simulation model of the wind power grid-connected system in the simulation software, and obtain the actual oscillation frequency of the wind power grid-connected system through time-domain simulation; compare the dominant oscillation mode frequency and the intersection frequency value with the actual oscillation frequency respectively. When the difference between the dominant oscillation mode frequency and the actual oscillation frequency, and the difference between the intersection frequency value and the actual oscillation frequency are both within 1Hz, it indicates that the converter control delay mathematical model can accurately characterize the influence of the wind power grid-connected system under small disturbances.

[0013] Preferably, step (1) specifically includes:

[0014] (1-1) The sampling and modulation delays of the converter in the frequency domain can be established based on the physical delays in the time domain using the transfer function. and the zero-order hold transfer function ;

[0015] ;

[0016]

[0017] in, The sampling period is s, where s represents the complex variable introduced in the Laplace transform;

[0018] (1-2) Based on the available transfer function and the zero-order hold transfer function Obtain the total delay transfer function ;

[0019] ;

[0020] (1-3) By transferring the zero-order hold function The approximated zero-order hold transfer function is obtained by performing an approximation. By considering the complete sampling control delay, the transfer function of the sampling control loop is obtained. ; , They are represented as follows:

[0021] ;

[0022] ;

[0023] (1-4) Transfer function of the sampling control loop After performing equivalent and linearization on a first-order inertial element, the specific mathematical model of the converter control delay is obtained as follows:

[0024] ;

[0025] in, T d The set equivalent delay time constant.

[0026] Preferably, in step (2), the equivalent linear model of the wind turbine control delay is:

[0027] ;

[0028] in, , These represent the voltage of the wind turbine. d, q Quantity, , These represent the voltage of the wind turbine. d, q Component reference values.

[0029] Preferably, step (3) specifically includes:

[0030] (3-1) The state-space model for the equivalent linear model of the wind turbine control delay is as follows: ,

[0031] Where A is the system matrix, B is the input matrix, and x is the state variable vector. Let be the first derivative of the state variable vector, and u be the input vector;

[0032] (3-2) By performing eigenvalue decomposition on the system matrix A, the eigenvalues ​​of the wind power grid-connected system are obtained. It can be represented as:

[0033] ;

[0034] in, Ω represents damping. i The modal oscillation frequency; It represents the imaginary unit.

[0035] Preferably, in step (4):

[0036] The equivalent impedance model of the wind turbine is as follows:

[0037] ;

[0038] in, This is the equivalent small-signal voltage at the grid connection point of the wind turbine. Inject current into the corresponding small signal;

[0039] The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine are as follows:

[0040] ;

[0041] ;

[0042] in, , Im Equivalent impedance models of wind turbines The real and imaginary parts, Represents the imaginary unit; It represents angular frequency.

[0043] Preferably, in step (4):

[0044] The equivalent impedance model of the power grid is as follows:

[0045] ;

[0046] in, , These represent the equivalent resistance and inductance of the grid-connected power grid at the grid connection point, respectively.

[0047] The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid are as follows:

[0048] ;

[0049] ;

[0050] Preferably, the wind turbine is a direct-drive wind turbine or a doubly-fed wind turbine.

[0051] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0052] (1) This invention proposes a method for small disturbance modeling and stability analysis of wind power grid-connected systems that considers control delay. By performing equivalent linearization modeling of sampling delay, zero-order hold, and switching delay in the digital control system of wind turbine generators, and uniformly introducing the delay model into the small disturbance state-space equation of the wind power grid-connected system, an explicit description and unified modeling of the control delay is achieved. Since the above modeling process retains the influence of control delay on the phase and damping characteristics of the system within the small disturbance linearization framework, the established model can accurately reflect the dynamic characteristics of the wind power grid-connected system in the subsynchronous and supersynchronous frequency bands, thereby avoiding the distortion of small disturbance characteristics caused by ignoring control delay in existing models.

[0053] (2) Based on the linearized modeling described above, this invention further combines eigenvalue analysis, impedance analysis, and time-domain simulation to conduct system stability assessment. Eigenvalue analysis quantitatively identifies the dominant oscillation modes and their damping characteristics, impedance analysis determines the coupling relationship between the wind turbine subsystem and the power grid subsystem from a frequency domain perspective, and time-domain simulation verifies the analysis results. Since these multiple analysis methods corroborate each other within the same modeling framework, not only is the reliability and accuracy of small-disturbance stability analysis results improved, but the analysis efficiency is also effectively enhanced, providing reliable technical support for wind farm control parameter tuning and grid-connected stability assessment. Attached Figure Description

[0054] Figure 1 A schematic diagram illustrating the modeling principle of a wind power grid-connected system that takes into account control delay.

[0055] Figure 2To linearize the Bode plot of the transfer function of a wind power grid-connected system that takes control delay into account.

[0056] Figure 3 This is a schematic diagram of a direct-drive wind power grid-connected system.

[0057] Figure 4 The impedance amplitude-frequency curves and phase-frequency curves of the direct drive system and the power grid are shown.

[0058] Figure 5 The output power waveform for the time-domain simulation of a direct-drive wind turbine grid-connected system.

[0059] Figure 6 This is a schematic diagram of a doubly fed wind power system connected to the grid via series compensation.

[0060] Figure 7 The diagram shows the impedance amplitude-frequency curves and phase-frequency curves of the doubly fed system and the power grid.

[0061] Figure 8 The output power waveform for the time-domain simulation of a doubly fed wind turbine grid-connected system. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0063] This invention first establishes a mathematical model of digital control delay based on the timing characteristics of the digital control system of wind turbine generators, and uses a first-order inertial element to linearize and equivalently process the delay characteristics, introducing it into the control system of direct-drive wind turbines and doubly-fed wind turbines; then, in a synchronous rotating coordinate system, the electrical equations and control elements of the system are linearized to form a state-space model, and the damping and frequency characteristics of the main oscillation modes of the system are obtained by eigenvalue decomposition of the system matrix, combined with participation factor analysis to determine the key state variables and control elements most significantly affected by the control delay.

[0064] Building upon this foundation, the present invention further employs the impedance method for frequency domain verification. The system is divided into a wind turbine subsystem and a power grid subsystem. Equivalent impedance models are established for each subsystem, and amplitude-frequency and phase-frequency characteristic curves are plotted. When the phase difference at the intersection of the amplitude-frequency curves is greater than 180°, the system is deemed to have an oscillation risk. This result is consistent with the oscillation frequency variation law observed in eigenvalue analysis, demonstrating the rationality of linearized modeling.

[0065] Finally, a unified simulation model of the direct-drive wind turbine and the doubly-fed induction generator (DFIG) was built in the PSCAD / EMTDC electromagnetic transient simulation software. The system output power waveform was obtained through time-domain simulation, and the simulation results were compared with the calculation results of the linearized model. If the oscillation frequency error is within 1Hz, the linearized model considering control delay is considered to accurately reflect the dynamic characteristics of the system. The method of this invention can effectively reveal the impact of control delay on the stability of wind power grid-connected systems and has high theoretical research and engineering application value.

[0066] Example 1

[0067] A method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay includes the following steps:

[0068] (1) The converter control delay element in the direct-drive wind turbine is mathematically modeled using the first-order Taylor expansion to obtain the mathematical model of converter control delay.

[0069] (2) Construct an equivalent linear model of wind turbine control delay by using the mathematical model of converter control delay established in the linearization process (1);

[0070] (3) Perform eigenvalue calculation on the equivalent linear model of wind turbine control delay to identify the dominant oscillation mode frequency and key state variables of the dominant oscillation mode of the equivalent linear model of wind turbine control delay;

[0071] (4) Using impedance analysis, construct the equivalent impedance model of the wind turbine control delay equivalent linear model; perform linearization modeling of the power grid subsystem of the wind power grid connection system, and use impedance analysis to obtain the power grid equivalent impedance model of the power grid subsystem;

[0072] Plot the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine, and the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid. The phase difference between the equivalent impedance model of the wind turbine and the equivalent impedance model of the power grid is obtained based on the intersection frequency value of the intersection point of the amplitude-frequency curves.

[0073] (5) Build a unified simulation model of the wind power grid-connected system in the simulation software, and obtain the actual oscillation frequency of the wind power grid-connected system through time-domain simulation; compare the dominant oscillation mode frequency and the intersection frequency value with the actual oscillation frequency respectively. When the difference between the dominant oscillation mode frequency and the actual oscillation frequency, and the difference between the intersection frequency value and the actual oscillation frequency are both within 1Hz, it indicates that the converter control delay mathematical model can accurately characterize the influence of the wind power grid-connected system under small disturbances.

[0074] Step (1) specifically includes:

[0075] This embodiment takes a grid-side converter as an example. In digital control, to avoid the influence of switching transistor noise, the output current of the grid-side converter is adjusted at the peaks and troughs of the triangular carrier wave. i g Sampling was carried out at the sampling point. k General i g The sampled signal is sent to a digital signal processor, where it is processed by a control algorithm to obtain the modulated signal. v m The modulated signal at the next sampling point ( k+1 The actual output occurs only at point ( ), causing the actual output modulated signal to be delayed by one sampling period compared to the calculated modulated signal. Therefore, the sampling and modulation delay of the grid-side converter can be represented by the transfer function G. h (s) is represented as:

[0076] (1)

[0077] In the formula, T s The sampling period is s, where s represents the complex variable introduced in the Laplace transform;

[0078] During the modulation process, the modulating signal v m This modulation phenomenon remains unchanged within one sampling period and is compared with a triangular carrier until the next sampling period arrives. A zero-order hold is introduced to describe this modulation phenomenon, and its zero-order hold transfer function is expressed as:

[0079] (2)

[0080] The total delay transfer function generated in the sampling control stage is:

[0081] (3)

[0082] A zero-order hold is introduced into the system model, which enables the control signal to remain constant during the sampling period, thus contributing to stable system control. Approximating equation (2), the approximate transfer function is:

[0083] (4)

[0084] As shown in equation (4), the entire delay process can be simplified to a fixed delay of 0.5 sampling periods using the zero-order hold model. Therefore, the transfer function of the sampling control loop can be expressed as:

[0085] (5)

[0086] Furthermore, a first-order inertial element is introduced for equivalent linearization, resulting in the following mathematical model for the converter control delay:

[0087] (6)

[0088] In the formula, T d The set equivalent delay time constant.

[0089] Step (2) includes the following steps:

[0090] Based on the linearized mathematical model of control delay established in step (1), the equivalent linear model of control delay for direct-drive wind turbines is established as follows:

[0091] (7)

[0092] in, u gcd and u gcq For direct-drive wind turbine grid-side voltage d, q Quantity; u gcdref and u gcqref These represent the grid-side voltage of the direct-drive wind turbine. d, q Component reference values.

[0093] Step (3) specifically includes:

[0094] Taking into account the delay in digital control, a grid-connected power transmission system for a direct-drive wind turbine is constructed, operating synchronously. dq A state-space model is established by linearizing the steady-state operating point with small perturbations in the coordinate system. ,in A For the system matrix, B For the input matrix, x For the state variable vector, u The input vector; through the matrix A Perform eigenvalue decomposition to obtain the full-dimensional eigenvalues ​​of the system. The oscillation frequency, damping characteristics, and dominant oscillation mode of the system are determined. The eigenvalue calculation results considering the digital control delay element are obtained.

[0095] Step (4) specifically includes:

[0096] Considering the delay in digital control, the wind power grid-connected system is divided into a wind turbine subsystem and a grid subsystem at the grid connection point, and their equivalent impedance models are established separately; wherein, the equivalent impedance of the wind turbine subsystem is expressed as... Z s (j )The dynamic characteristics of the fan and its control system at different frequencies are calculated from the relationship between the voltage and current at the fan output port. ,in, This is the equivalent small-signal voltage at the grid connection point of the wind turbine. Inject current into the corresponding small signal;

[0097] The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine are as follows:

[0098] (8)

[0099] (9)

[0100] in, , Im Equivalent impedance models of wind turbines The real and imaginary parts, Represents the imaginary unit; It represents angular frequency.

[0101] The equivalent impedance of the power grid subsystem is expressed as: Z g (j ) Determined by the equivalent voltage source of the power grid and the network impedance parameters, it reflects the frequency response characteristics of the power grid side, and its expression is: .

[0102] The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid are as follows:

[0103] (10)

[0104] (11)

[0105] By drawing Z s (j ) The amplitude-frequency curve and phase-frequency curve, and Z g (j ) The amplitude-frequency curves and phase-frequency curves are compared. When the phase difference at the intersection of the amplitude-frequency curves is greater than 180°, it indicates that the wind turbine subsystem and the power grid subsystem generate negative damping at that frequency point, and the system is at risk of oscillation. If the phase difference is less than 180°, the system is in a stable operating state. The impedance analysis results considering the digital control delay are obtained.

[0106] Step (5) specifically includes:

[0107] Perform time-domain simulation in PSCAD / EMTDC, keeping the operating conditions consistent with the linearized model, record the system output power waveform, and compare the oscillation frequency and amplitude of the eigenvalue analysis, impedance characteristic analysis and simulation results. If the frequency difference between the linear model considering the control loop and the time-domain simulation system is within 1Hz, it indicates that the linearized model considering the control delay can accurately reflect the dynamic characteristics of the system.

[0108] like Figure 1 The figure shows the digital control timing diagram of the grid-side converter. In the digital control system, the current signal is usually sampled at the peak and trough of the carrier wave. The sampled data is calculated by the controller and output in the next cycle, thus introducing a delay of one sampling cycle. In order to describe the holding effect of sampling control, this invention introduces a zero-order hold model; at the same time, the switching delay caused by the triggering time of the switching device is considered. The total delay is approximately 1.5 sampling cycles. In order to simplify the calculation and maintain the consistency of the amplitude and phase characteristics in the low frequency band, a first-order inertial element is used to perform equivalent linearization of the delay process. The equivalent transfer function is shown in Equation (12).

[0109] (12)

[0110] Figure 2 The Bode plots of the transfer function of the delay element and the first-order inertial approximation model are compared. The amplitude and phase frequency characteristics show that they almost overlap in the 0–100Hz frequency band, verifying the feasibility and rationality of using the first-order inertial element in the linearization modeling of control delay.

[0111] Direct-drive fan control delay modeling and dynamic characteristic analysis:

[0112] like Figure 3 The diagram shown is a grid-connected structure diagram of a direct-drive wind farm. To study the impact of control delay on the dynamic characteristics of the system, an equivalent direct-drive wind turbine is used to represent the wind farm for analysis. The main system parameters are shown in Table 1.

[0113] Table 1 Typical parameters of direct-drive fans

[0114]

[0115] This invention introduces the linearized control delay element into the converter voltage control equation, forming a complete state-space equation, and calculates the eigenvalues ​​of the system matrix. Table 2 shows the comparison results of the eigenvalues ​​considering and ignoring the control delay. The calculation results show that the system exhibits unstable modes after considering the control delay. λ 9,10 =0.73±j2 ×36.91 corresponds to an oscillation frequency of approximately 36.9Hz, indicating that the unstable oscillation mode was obtained by calculating the eigenvalues ​​after considering the control delay model.

[0116] Table 2 Calculation results of characteristic values ​​of direct-drive wind turbine grid-connected system

[0117]

[0118] Based on the same parameter conditions, plot the impedance amplitude-frequency curves and phase-frequency curves of the wind turbine and power grid subsystems, considering and ignoring control delay, as follows: Figure 4 As shown in the figure. The results show that, considering the delay, the phase difference at the intersection of the amplitude-frequency curves at a frequency of 36.6 Hz exceeds 180°, indicating a risk of system oscillation; ignoring the delay, the phase difference at the intersection is less than 180°, indicating that the system is operating stably.

[0119] Subsequently, a system was created in PSCAD / EMTDC as follows: Figure 3 The simulation model is shown, and the short-circuit ratio is changed from 4 to 2 after 3 seconds. Figure 5 The simulated waveform of the system output power is presented. Waveform analysis shows that the power oscillation frequency is approximately 36.87 Hz, which is consistent with the eigenvalue and impedance analysis results. The oscillation frequency error is within 1 Hz, verifying the accuracy of the linearized delay model.

[0120] Example 2

[0121] A method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay, characterized by the following steps:

[0122] (1) The converter control delay element in the doubly fed wind turbine is mathematically modeled using the first-order Taylor expansion to obtain the mathematical model of converter control delay.

[0123] (2) Construct an equivalent linear model of wind turbine control delay by using the mathematical model of converter control delay established in the linearization process (1);

[0124] (3) Perform eigenvalue calculation on the equivalent linear model of wind turbine control delay to identify the dominant oscillation mode frequency and key state variables of the dominant oscillation mode of the equivalent linear model of wind turbine control delay;

[0125] (4) Using impedance analysis, construct the equivalent impedance model of the wind turbine control delay equivalent linear model; perform linearization modeling of the power grid subsystem of the wind power grid connection system, and use impedance analysis to obtain the power grid equivalent impedance model of the power grid subsystem;

[0126] Plot the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine, and the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid. The phase difference between the equivalent impedance model of the wind turbine and the equivalent impedance model of the power grid is obtained based on the intersection frequency value of the intersection point of the amplitude-frequency curves.

[0127] (5) Build a unified simulation model of the wind power grid-connected system in the simulation software, and obtain the actual oscillation frequency of the wind power grid-connected system through time-domain simulation; compare the dominant oscillation mode frequency and the intersection frequency value with the actual oscillation frequency respectively. When the difference between the dominant oscillation mode frequency and the actual oscillation frequency, and the difference between the intersection frequency value and the actual oscillation frequency are both within 1Hz, it indicates that the converter control delay mathematical model can accurately characterize the influence of the wind power grid-connected system under small disturbances.

[0128] In step (1), the specific mathematical model for the converter control delay is as follows:

[0129] (13)

[0130] Step (2) includes the following steps:

[0131] Based on the converter control delay mathematical model established in step (1), the equivalent linear model of the doubly fed wind turbine control delay is established as follows:

[0132] (14)

[0133] (15)

[0134] in, u rd and u rq The rotor-side voltage of the doubly fed wind turbine d, q Quantity, u gd and u gq Output voltage of the grid-side converter for doubly fed wind turbines d, q Quantity; u gdref and u gqref Indicates the output voltage of the grid-side converter of the doubly fed wind turbine. d, q Component reference value; u rdref and u rqref Indicates the rotor-side voltage of the doubly fed wind turbine. d, q Component reference values.

[0135] Step (3) specifically includes:

[0136] Considering the delay in digital control, a grid-connected power transmission system for the doubly-fed wind turbine is constructed, operating synchronously. dq A state-space model is established by linearizing the steady-state operating point with small perturbations in the coordinate system. ,in A For the system matrix, B For the input matrix, x For the state variable vector, u The input vector; through the matrix A Perform eigenvalue decomposition to obtain the full-dimensional eigenvalues ​​of the system. The oscillation frequency, damping characteristics, and dominant oscillation mode of the system are determined. The eigenvalue calculation results considering the digital control delay element are obtained.

[0137] Step (4) specifically includes:

[0138] Considering the delay in digital control, the wind power grid-connected system is divided into a wind turbine subsystem and a grid subsystem at the grid connection point, and their equivalent impedance models are established separately; wherein, the equivalent impedance of the wind turbine subsystem is expressed as... Z s (j ) The dynamic characteristics of the fan and its control system at different frequencies are calculated from the relationship between the voltage and current at the fan's output port. ;in, This is the equivalent small-signal voltage at the grid connection point of the wind turbine. Inject current into the corresponding small signal;

[0139] The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine are as follows:

[0140] (16)

[0141] (17)

[0142] in, , Im Equivalent impedance models of wind turbines The real and imaginary parts, Represents the imaginary unit; It represents angular frequency.

[0143] The equivalent impedance of the power grid subsystem is expressed as: Z g (j ) Determined by the equivalent voltage source of the power grid and the network impedance parameters, it reflects the frequency response characteristics of the power grid side, and its expression is: .

[0144] The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid are as follows:

[0145] (18)

[0146] (19)

[0147] By drawing Z s (j ) The amplitude-frequency curve and phase-frequency curve, and Z g (j ) The amplitude-frequency curves and phase-frequency curves are compared. When the phase difference at the intersection of the amplitude-frequency curves is greater than 180°, it indicates that the wind turbine subsystem and the power grid subsystem generate negative damping at that frequency point, and the system is at risk of oscillation. If the phase difference is less than 180°, the system is in a stable operating state. The impedance analysis results considering the control delay are obtained.

[0148] Step (5) specifically includes:

[0149] Perform time-domain simulation in PSCAD / EMTDC, keeping the operating conditions consistent with the linearized model, record the system output power waveform, and compare the oscillation frequency and amplitude of the eigenvalue analysis, impedance characteristic analysis and simulation results. If the frequency difference between the linear model considering the control loop and the time-domain simulation system is within 1Hz, it indicates that the linearized model considering the control delay can accurately reflect the dynamic characteristics of the system.

[0150] like Figure 6 The diagram shows the grid-connected system structure of a doubly-fed induction generator (DFIG) with series capacitor compensation. Line and control parameters are shown in Table 3. Eigenvalues ​​of the system state matrix are calculated for both cases considering and ignoring control delay, and the results are listed in Table 4. It can be seen that control delay leads to a decrease in damping for multiple modes, including the subsynchronous oscillation mode modeled with control delay consideration. λ 23,24 =6.07±j2 ×41.66 corresponds to an oscillation frequency of approximately 41.6 Hz, which is the main unstable mode.

[0151] Table 3 Typical parameters of doubly-fed wind turbines

[0152]

[0153] Table 4. Calculation results of characteristic values ​​of doubly fed wind turbines connected to the grid via series compensation.

[0154]

[0155] Figure 7 Based on the impedance analysis results, the frequency of the intersection of the amplitude-frequency curves is consistent with that of the eigenvalue analysis, verifying the consistency of the linearization modeling of the digital control delay. Considering that the phase difference between the intersection of the impedance curve of the new energy side and the impedance curve of the AC line in the digital control delay stage is greater than 180°, it is determined that the system has the risk of subsynchronous oscillation.

[0156] PSCAD / EMTDC time-domain simulation was performed under the same operating parameters, with a 35% series compensation capacitor added at 4s. The simulation results are as follows. Figure 8 As shown, the power waveform oscillation frequency is approximately 41.6 Hz, which is consistent with the eigenvalue calculation and impedance analysis results considering the modeling of digital control components. The oscillation frequency error is within 1 Hz, verifying the correctness of the linearized delay model.

[0157] This invention should be able to mathematically describe the impact of time delay on the system state equation, and combine eigenvalue analysis, impedance analysis and time-domain simulation to accurately identify the system oscillation mode, thereby providing reliable theoretical support for the optimization of wind turbine control parameters and the stable operation of the power grid.

[0158] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay, characterized in that, Includes the following steps: (1) The converter control delay element in the wind turbine is mathematically modeled using the first-order Taylor expansion to obtain the mathematical model of converter control delay. (2) Construct an equivalent linear model of wind turbine control delay by using the mathematical model of converter control delay established in the linearization process (1); (3) Perform eigenvalue calculation on the equivalent linear model of wind turbine control delay to identify the dominant oscillation mode frequency and key state variables of the dominant oscillation mode of the equivalent linear model of wind turbine control delay; (4) Using impedance analysis, construct the equivalent impedance model of the wind turbine control delay equivalent linear model; perform linearization modeling of the power grid subsystem of the wind power grid connection system, and use impedance analysis to obtain the power grid equivalent impedance model of the power grid subsystem; Plot the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine, and the amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid. The phase difference between the equivalent impedance model of the wind turbine and the equivalent impedance model of the power grid is obtained based on the intersection frequency value of the intersection point of the amplitude-frequency curves. (5) Build a unified simulation model of the wind power grid-connected system in the simulation software, and obtain the actual oscillation frequency of the wind power grid-connected system through time-domain simulation; compare the dominant oscillation mode frequency and the intersection frequency value with the actual oscillation frequency respectively. When the difference between the dominant oscillation mode frequency and the actual oscillation frequency, and the difference between the intersection frequency value and the actual oscillation frequency are both within 1Hz, it indicates that the converter control delay mathematical model can accurately characterize the influence of the wind power grid-connected system under small disturbances.

2. The method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay as described in claim 1, characterized in that, Step (1) is as follows: (1-1) The sampling and modulation delays of the converter in the frequency domain can be established based on the physical delays in the time domain using the transfer function. and zero-order hold transfer function ; ; in, The sampling period is s, where s represents the complex variable introduced in the Laplace transform; (1-2) Based on the available transfer functions and zero-order hold transfer function Obtain the total delay transfer function ; ； (1-3) By transferring the zeroth-order hold function The approximated zero-order hold transfer function is obtained by performing an approximation. By considering the complete sampling control delay, the transfer function of the sampling control loop is obtained. ; , They are represented as follows: ； ； (1-4) Transfer function of the sampling control loop After performing equivalent and linearization on a first-order inertial element, the specific mathematical model of the converter control delay is obtained as follows: ； in, T d The set equivalent delay time constant.

3. The method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay as described in claim 2, characterized in that, In step (2), the equivalent linear model of the wind turbine control delay is: ； in, , These represent the voltage of the wind turbine. d, q Quantity, , These represent the voltage of the wind turbine. d, q Component reference values.

4. The method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay as described in claim 3, characterized in that, Step (3) specifically includes: (3-1) The state-space model for the equivalent linear model of the wind turbine control delay is as follows: , Where A is the system matrix, B is the input matrix, and x is the state variable vector. Let be the first derivative of the state variable vector, and u be the input vector; (3-2) By performing eigenvalue decomposition on the system matrix A, the eigenvalues ​​of the wind power grid-connected system are obtained. It can be represented as: ； in, Ω represents damping. i The modal oscillation frequency; It represents the imaginary unit.

5. The method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay as described in claim 4, characterized in that, In step (4): The equivalent impedance model of the wind turbine for: ; in, This is the equivalent small-signal voltage at the grid connection point of the wind turbine. Inject current into the corresponding small signal; The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the wind turbine are as follows: ; ; in, , Im Equivalent impedance models of wind turbines The real part and the imaginary part, Represents the imaginary unit; It represents angular frequency.

6. The method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay as described in claim 5, characterized in that, In step (4): The power grid equivalent impedance model for: ; in, , These represent the equivalent resistance and inductance of the grid-connected power grid at the grid connection point, respectively. The amplitude-frequency curve and phase-frequency curve of the equivalent impedance model of the power grid are as follows: ; 。 7. The method for small disturbance modeling and stability analysis of a wind power grid-connected system considering control delay as described in claim 1, characterized in that, The wind turbine is either a direct-drive wind turbine or a doubly-fed wind turbine.

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