A method for optimizing multi-channel additional damping control parameters of a DFIG considering time delay
By refining time delay calculations and optimizing control parameters, the problems of time delay inconsistency and interactive coupling in multi-channel additional damping control were solved, improving the stability of the wind power grid-connected system and enabling safe and stable operation in complex scenarios.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI UNIV OF TECH
- Filing Date
- 2026-03-13
- Publication Date
- 2026-06-12
AI Technical Summary
Existing multi-channel additional damping control technology fails to effectively consider time delay inconsistency and interactive coupling in wind power grid-connected systems, leading to conflicting control parameter adjustments and making it difficult to ensure system stability in complex scenarios.
By establishing a linear model, calculating the modal selectivity index to select the optimal observation station, refining the time delay calculation, constructing a time delay sensitivity analytical model, optimizing control parameters to offset the eigenvalue drift caused by time delay fluctuations, and using the interior point method to solve for the optimal parameters.
It enables coordinated adjustment of multiple control parameters in complex time-delay scenarios, improves the safety and stability of wind power grid-connected systems, and ensures that the system can remain stable even under extreme time-delay fluctuations.
Smart Images
Figure CN122203249A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system stability control technology, specifically to a method for optimizing DFIG multi-channel additional damping control parameters by calculating time delay. Background Technology
[0002] With the high proportion of wind turbines connected to the grid, power system stability issues are becoming increasingly prominent, exhibiting complex characteristics of low-frequency oscillations and multiple dangerous modes coexisting near the virtual axis. While existing multi-channel additional damping control technology achieves coverage of different critical oscillation modes by configuring multiple independent channels, its parameter design is often based on ideal communication assumptions, neglecting the unavoidable time delay problem in the wide-area feedback loop. In actual operation, due to differences in physical paths, the time delays of different control channels are significantly inconsistent. If traditional multi-channel parameter tuning methods that ignore time delays or only consider fixed time delays are directly used, it is very easy for the regulating actions of each channel to conflict during time delay fluctuations, even leading to instability of the wind power grid-connected system.
[0003] Furthermore, existing multi-channel parameter optimization methods still have significant shortcomings at the level of refined design. On the one hand, the selection strategy for observation stations is relatively coarse, often focusing only on the observability of the target mode while ignoring the mutual interference between multi-mode signals, making it difficult to select high-purity feedback signals. On the other hand, existing studies have not considered the interactive coupling between time-delay fluctuations and control parameters. This leads to the current controller parameter optimization design mostly adopting a passive margin preservation strategy, lacking a compensation mechanism based on an accurate analytical model. It is impossible to use the adjustment of control parameters to offset the eigenvalue drift caused by the worst-case time-delay fluctuations, making it difficult to ensure the stable operation of wind power grid-connected systems in complex scenarios. Summary of the Invention
[0004] This invention addresses the shortcomings in the tuning process of DFIG multi-channel additional damping control parameters considering wide-area time delay. It proposes an optimization method for DFIG multi-channel additional damping control parameters that takes time delay into account. The aim is to achieve coordinated adjustment of multiple control parameters in complex time delay scenarios, thereby effectively improving the safety and stability of wind power grid-connected systems under time delay fluctuation conditions.
[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: The present invention provides a method for optimizing DFIG multi-channel additional damping control parameters by calculating time delay, characterized by the following steps: Step 1: Establish a linearized model of the wind power grid-connected system containing a synchronous generator (SG) and a doubly fed induction generator (DFIG), and perform eigenvalue analysis on the linearized model to obtain the dangerous modes where the damping ratio is lower than the preset safety threshold or the real part of the eigenvalue is greater than the preset safety threshold. Step 2: Construct the observation matrix of the wind power grid-connected system, and use the observation matrix to calculate the target observability of each algebraic variable for each hazardous mode and the interference observability for other non-target hazardous modes; thereby calculate the ratio between the target observability and the interference observability, and use it as the mode selectivity index; select the algebraic variable with the largest mode selectivity index as the optimal observation signal, and take the observation station corresponding to the optimal observation signal as the optimal observation station. Step 3: Determine the signal transmission path from the optimal observation station to the additional damping controller of the multi-control channel. Calculate the measurement processing time delay, network transmission time delay, and control execution time delay on each signal transmission path, and then superimpose them to obtain the time delay of each control channel on the additional damping controller. Step 4, using second-order The time delay elements of each control channel are approximately expanded into differential algebraic equations; Step 5: Combine the differential-algebraic equations of the time-delay elements of each control channel, the differential-algebraic equations of the multi-control channel additional damping controller, and the differential-algebraic equations of the wind power grid-connected system, and then linearize them to obtain the closed-loop linearized model of the entire system and the closed-loop state matrix of the entire system. ; Step 6, based on The first-order sensitivity of the eigenvalues of each hazardous mode to time delay and the first-order sensitivity to the control parameters of the additional damping controller are calculated. Then, using the first-order sensitivity as the initial value, the second-order sensitivity and the mixed second-order sensitivity are calculated and linearly approximated to obtain the sensitivity analytical expression. Then, using the sensitivity analytical expression, the eigenvalue offset analytical function of each hazardous mode is constructed to obtain the offset of the eigenvalues. Step 7: Construct the worst-case time-delay fluctuation vector using the real part sign of the first-order time-delay sensitivity; substitute the worst-case time-delay fluctuation vector into the eigenvalue offset analytical function to obtain the eigenvalue offset function only with respect to the control parameter increment; superimpose the eigenvalue offset function with the initial eigenvalue to obtain the actual real part of the eigenvalue affected by the worst-case time-delay fluctuation and the actual damping ratio; thereby establishing a parameter optimization model with the goal of minimizing the control parameter increment and the constraint that the actual real part of the eigenvalue and the actual damping ratio satisfy a preset critical value; and solve the parameter optimization model using the interior point method to obtain the optimal control parameters.
[0006] The characteristic of the DFIG multi-channel additional damping control parameter optimization method with time delay described in this invention is that the selection of the optimal observation station in the dangerous mode in step 2 is determined according to the following steps: Step 2.1: Select the bus voltage and line power under the dangerous mode as algebraic variables to construct the observation matrix. Thus, the first equation is obtained using equation (1). y The algebraic variable for the th iObservability of each hazard pattern : (1) In equation (1), This represents the total number of state variables in the wind power grid-connected system. k The index of the state variable; for The Middle y Line number k Column elements; For the first i Characteristic values of each hazard mode The corresponding right eigenvector The k One element; For the first i Characteristic values of each hazard mode The corresponding left eigenvector The k One element; Step 2.2, calculate the first step using equation (2). y The algebraic variable for the th i Modal selectivity index of each hazard mode : (2) In equation (2), The total number of hazardous modes; j This is the sequence number of the non-target hazard mode; For the first y The algebraic variable for the th j The observability of individual non-target hazard patterns; A tiny positive number is set to prevent the denominator from being zero; Step 2.3: Select the algebraic variable with the largest modal selectivity index value as the optimal observation signal, and designate the observation station that collected the optimal observation signal as the first... i The optimal observation station for each dangerous mode.
[0007] Furthermore, the calculation of the time delay of each control channel in step 3 is determined according to the following steps: Step 3.1, calculate the first step using equation (3). i The first danger mode corresponds to the first i Processing time delay of phasor measurement unit (PMU) in the optimal observation station of each control channel : (3) In equation (3), The sampling frequency of the PMU; These are the digital filter characteristic coefficients; This is a constant related to the measurement window in the PMU device; For the first i Maximum data load under each dangerous mode; This refers to the amount of data in the communication protocol packet header; The transmission rate of the PMU communication interface; For the transmission interface delay; Step 3.2: Determine the signal transmission path along the wide area communication network. Calculate the first using equation (4) i Wide-network transmission delay under dangerous modes : (4) In equation (4), E A set of links in a wide area communication network; This is a routing indicator function, representing a node. and nodes Links between Is it in the signal transmission path? Above, if in Above, then Take 1, otherwise Set to 0; For link Length; The speed of light in the medium; For the signal at the node To the node Processing time delay; For worst-case queuing delays; Step 3.3, combining the synchronization waiting time delay of the wide area communication network. Processing time delay of control stations at each node in a wide area communication network Calculate the first using equation (5) i The first danger mode corresponds to the first i Time delay of each control channel : (5).
[0008] Furthermore, step 4 includes: Step 4.1, use equation (6) to... i Time delay element of each control channel Convert to frequency domain transfer function : (6) In equation (6), s For the Laplace operator; Step 4.2, use equation (7) to transform equation (6) into a differential algebraic equation: (7) In equation (7), For the first i The output signal of the optimal observation station corresponding to each control channel; The observed signal after the time delay; , For the first i Two time-delayed state variables for each control channel.
[0009] Furthermore, step 6 includes: Step 6.1, calculate the first step using equation (8). i Characteristic values of each hazard mode For the first j Each control channel time delay First-order time delay sensitivity : (8) In equation (8), The state matrix of the entire system; This is the input matrix for the entire system; This is the output matrix of the entire system; This is the direct transmission matrix for the entire system; , They are respectively For the first i The left and right eigenvectors of each dangerous pattern; the superscript T denotes transpose, and the superscript -1 denotes the inverse of the matrix; Step 6.2 introduces the second-order sensitivity of the eigenvalues to the control parameters, the second-order sensitivity to the time delay, and the mixed second-order sensitivity to the time delay-parameter. Using equation (9), a linear approximation of the sensitivity is obtained, yielding an analytical expression for the sensitivity that includes the effects of interactive coupling: (9) In equation (9), For the first to the second N The time delay of each control channel; For the first to the second M One control parameter; For the first q One control parameter; For the first r One control parameter; For the first c The time delay of each control channel; For the first h The time delay of each control channel; N The number of control channels for the additional damping controller; M The number of control parameters for the additional damping controller; Let be the initial control parameter vector, and ,in, Indicates the first One initial control parameter; Let be the initial time delay vector of the control channel, and ,in, Indicates the first Initial time delay of each control channel; For the first h The time delay fluctuation of each control channel; For the first r The increment of each control parameter; for right and Second-order sensitivity; for right and Second-order sensitivity; for right and The mixed second-order sensitivity, for right and The mixed second-order sensitivity; Step 6.3, construct the first using equation (10). i Eigenvalues under each dangerous mode offset : (10) In equation (10), for The first-order sensitivity vector is formed by the first-order sensitivity of each control parameter under the initial control parameters and the initial time delay of the control channel. for The first-order sensitivity vector is composed of the first-order sensitivity of each control channel delay under the initial control parameters and the initial time delay of the control channel. This is the increment vector of the control parameters; This represents the time-delay fluctuation vector for each control channel; for The second-order sensitivity matrix is composed of the second-order sensitivities to each control parameter; for The second-order sensitivity matrix is composed of the second-order sensitivities to the time delay of each control channel; for The mixed second-order sensitivity matrix is composed of the mixed second-order sensitivities of each control parameter and the control channel time delay, and we have: (11).
[0010] Furthermore, the construction of the parameter optimization model and the solution process in step 7 are determined as follows: Step 7.1, construct the worst-case time-delay fluctuation vector that causes the real part of the eigenvalue to increase using equation (12): : (12) In equation (12), is the maximum allowable time-delay fluctuation amplitude for the N th control channel; is the sign function; is the operation of taking the real part; is the N th eigenvalue of the th dangerous mode N with respect to the first-order time-delay sensitivity of the time-delay of the th control channel; Step 7.2, substitute i into equation (10), and then use equation (13) to establish the eigenvalue offset of the th dangerous mode that only depends on the increment of the control parameter, so as to obtain the eigenvalue offset vector (13) Step 7.3, construct the objective function of the parameter optimization model using equation (14): : (14) In equation (14), is the increment vector of the control parameter to be optimized; is the weight diagonal matrix of the control parameter; is the weight coefficient of the th control parameter; ]>[[]]END]]Step 7.4, establish the inequality constraint conditions of the parameter optimization model using equation (15): (15) In equation (15), is the critical damping ratio vector; is the initial eigenvalue vector of the entire system under [[ID=7(]](11).
[0010] Furthermore, the construction of the parameter optimization model and the solution process in step 7 are determined as follows: Step 7.1, construct the worst-case time-delay fluctuation vector that causes the real part of the eigenvalue to increase using equation (12): : (12) In equation (12), is the maximum allowable time-delay fluctuation amplitude for the N th control channel; is the sign function; is the operation of taking the real part; is the N th eigenvalue of the th dangerous mode N with respect to the first-order time-delay sensitivity of the time-delay of the th control channel; Step 7.2, substitute i into equation (10), and then use equation (13) to establish the eigenvalue offset of the th dangerous mode that only depends on the increment of the control parameter, so as to obtain the eigenvalue offset vector (13) Step 7.3, construct the objective function of the parameter optimization model using equation (14): : (14) In equation (14), is the increment vector of the control parameter to be optimized; is the weight diagonal matrix of the control parameter; is the weight coefficient of the th control parameter; Step 7.4, establish the inequality constraint conditions of the parameter optimization model using equation (15): (15) In equation (15), is the critical damping ratio vector; is the initial eigenvalue vector of the entire system under and conditions, and ; is the real part critical value vector; , are the upper and lower limit vectors of the parameters to be tuned respectively; , These are operations that extract the real part and the imaginary part, respectively. Step 7.5: Solve the parameter optimization model composed of equations (14) and (15) using the interior point method, and output the optimal control parameter increment vector. ,Will and The control parameters of the multi-channel additional damping controller are superimposed to update the control parameters, thereby achieving effective suppression of multiple dangerous modes.
[0011] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in performing the method described therein, and the processor is configured to execute the program stored in the memory.
[0012] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program is executed by a processor to perform the steps of the method described thereon.
[0013] Compared with the prior art, the beneficial effects of the present invention are reflected in: 1. This invention proposes a modal selectivity index, which quantifies the ability of observation stations to extract target modes and accurately determines the optimal observation station for each dangerous mode, providing a clear spatial topology basis for subsequent calculation of the time delay of each independent control channel based on the physical architecture.
[0014] 2. This invention innovatively proposes a time-delay sensitivity method. Compared with the traditional first-order linearization method that ignores parameter-time-delay coupling, it constructs an eigenvalue offset analytical model containing interaction terms, providing a high-precision mathematical model for the optimization and tuning of multi-channel parameters under complex time-delay fluctuation environments, and solving the problem of poor adjustment effect of additional damping controller due to time-delay fluctuations.
[0015] 3. This invention defines the worst-case time delay fluctuation vector based on time delay sensitivity, and offsets the characteristic value shift caused by the worst-case time delay fluctuation by adjusting parameters. This active offsetting idea ensures that the wind power grid-connected system can still maintain safety and stability when the time delay fluctuates extremely. Attached Figure Description
[0016] Figure 1 This is a schematic diagram of the control structure of the DFIG multi-channel SDC system that measures time delay in this invention; Figure 2 This is a schematic diagram illustrating the eigenvalue offset cancellation principle and optimization effect in this invention; Figure 3 Flowchart for refined modeling and analytical calculation of time delay; Figure 4 This is a flowchart of the DFIG multi-channel SDC control parameter optimization algorithm for time delay in this invention. Detailed Implementation
[0017] In this embodiment, a method for optimizing the additional damping control parameters of a DFIG multi-channel system that considers time delay is described, such as... Figure 4 As shown, in this embodiment, a modal selectivity index is proposed to select the optimal observation station for each hazardous mode, and combined with... Figure 3 The time-delay refined modeling process shown involves independently calculating the time delay of each control channel. For each channel's time delay element, a second-order Padé approximation is used to establish the closed-loop augmented state matrix of the entire system. By calculating the time delay sensitivity and considering the parameter-time delay interaction, an eigenvalue offset analytical function containing coupling characteristics is constructed. Based on the idea of compensating for and offsetting time delay disturbances using control parameters, an optimization model is established. The interior-point method is used to solve for the optimal parameters of each channel, thereby achieving the suppression of multiple dangerous modes under the worst time delay fluctuation conditions. The comparison of the offsetting idea and the effect before and after optimization is shown in the figure below. Figure 2 As shown. Specifically, as... Figure 4 As shown, the method includes the following steps: Step 1: Establish a linearized model of the wind power grid-connected system containing a synchronous generator (SG) and a doubly fed induction generator (DFIG), and perform eigenvalue analysis on the linearized model to obtain the dangerous modes where the damping ratio is lower than the preset safety threshold or the real part of the eigenvalue is greater than the preset safety threshold. Step 1.1, the mathematical model of the power system after the wind turbine is connected to the grid is expressed by state equations and algebraic equations as equation (1): (1) In equation (1), p Represents the differential operator; x , y These represent the vector forms of state variables and algebraic variables, respectively. f , g These represent the functional forms of the state equation and the algebraic equation, respectively; the subscripts SG, DFIG, and sys represent the synchronous generator, the doubly fed induction generator, and the wind power grid-connected system network, respectively.
[0018] Step 1.2: Linearize equation (1) at the steady-state operating point, and obtain the linearized model of the wind power grid-connected system using equation (2): (2) In equation (2), , , , is the coefficient matrix; Δ represents the increment.
[0019] Eliminate the algebraic vectors and use equation (3) to calculate the closed-loop system coefficient matrix. : (3) Step 1.3, the closed-loop system coefficient matrix obtained according to equation (3) The characteristic values, damping ratio, and oscillation frequency of the wind power grid-connected system are obtained using equation (4): (4) In equation (4), For eigenvalues; , These are the real and imaginary parts of the eigenvalues, respectively. The damping ratio; The oscillation frequency of the oscillation mode; , They are respectively The corresponding left and right feature vectors.
[0020] Step 1.4: Based on the distribution of system eigenvalues, a basic judgment of dangerous modes is made. Dangerous modes are selected according to the obtained eigenvalues, damping ratio, and upper and lower limits of oscillation frequency. Eigenvalues near the imaginary axis mean that any small parameter change may cause the eigenvalue to cross the imaginary axis instantaneously and be located on the right side of the imaginary axis, causing system instability. Oscillation modes with small damping ratios have slow decay rates and are prone to causing system oscillations. Low-frequency oscillation modes with damping ratios less than the critical value or near-imaginary axis modes with real parts of eigenvalues greater than the critical value are considered dangerous modes. In order to determine dangerous modes, a danger judgment function is defined using equation (5). : (5) In equation (5), Let be the danger determination function, when When this occurs, the oscillation mode is determined to be a dangerous mode; For the first i The real part of each oscillation mode; The critical value for the real part of the set eigenvalue; This represents the upper limit of the oscillation frequency in the oscillation mode. For the first i Damping ratio of each oscillation mode; This is the critical value for the set damping ratio.
[0021] Step 2: Construct the observation matrix of the wind power grid-connected system, and use the observation matrix to calculate the target observability of each algebraic variable for each hazardous mode and the interference observability for other non-target hazardous modes; thereby calculate the ratio between the target observability and the interference observability, and use it as the mode selectivity index; select the algebraic variable with the largest mode selectivity index as the optimal observation signal, and take the observation station corresponding to the optimal observation signal as the optimal observation station.
[0022] Step 2.1: Since state variables such as generator speed and power angle are difficult to measure in actual power systems, bus voltage and line power under dangerous modes are selected as algebraic variables to construct the observation matrix. Thus, by using equation (6), the first... y The algebraic variable for the th i Observability of each hazard mode : (6) In equation (6), This represents the total number of state variables in the wind power grid-connected system. k The index of the state variable; for The Middle y Line number k Column elements; For the first i Characteristic values of each hazard mode The corresponding right eigenvector The k One element; For the first i Characteristic values of each hazard mode The corresponding left feature vector The k Each element.
[0023] Step 2.2, calculate the first step using equation (7). y The algebraic variable for the th i Modal selectivity index of each hazard mode : (7) In equation (7), The total number of hazardous modes; j This is the sequence number of the non-target hazard mode; For the first y The algebraic variable for the th j The observability of individual non-target hazard patterns; A tiny positive number is set to prevent the denominator from being zero.
[0024] Step 2.3: Select the algebraic variable with the largest modal selectivity index value as the optimal observation signal, and designate the observation station that collected the optimal observation signal as the first... i The optimal observation station for each dangerous mode.
[0025] Step 3: Determine the signal transmission path from the optimal observation station to the additional damping controller of the multi-control channel. Calculate the measurement processing time delay, network transmission time delay, and control execution time delay on each signal transmission path, and then superimpose them to obtain the time delay of each control channel on the additional damping controller. Step 3.1, calculate the first step using equation (8). i The first danger mode corresponds to the first i Processing time delay of phasor measurement unit (PMU) in the optimal observation station of each control channel : (8) In equation (8), The sampling frequency of the PMU; These are the digital filter characteristic coefficients; This is a constant related to the measurement window in the PMU device; For the first i Maximum data load under each dangerous mode; This refers to the amount of data in the communication protocol packet header; The transmission rate of the PMU communication interface; This refers to the latency of the sending interface.
[0026] Step 3.2: Determine the signal transmission path along the wide area communication network. Calculate the first using equation (9) i Wide-network transmission delay under dangerous modes : (9) In equation (9), E A set of links in a wide area communication network; This is a routing indicator function, representing a node. and nodes Links between Is it in the signal transmission path? Above, if in Above, then Take 1, otherwise, Set to 0; For link Length; The speed of light in the medium; For the signal at the node To the node Time delay in processing; This is for the worst-case queuing delay.
[0027] Step 3.3, combining the synchronization waiting time delay of the wide area communication network. Processing time delay of control stations at each node in a wide area communication network Calculate the first using equation (10) i The first danger mode corresponds to the first i Time delay of each control channel : (10) Step 4: Use the second-order Padé approximation to expand the time delay elements of each control channel into differential algebraic equations; Step 4.1, use equation (11) to... i Time delay element of each control channel Convert to frequency domain transfer function : (11) In equation (11), s For the Laplace operator.
[0028] Step 4.2, use equation (12) to transform equation (11) into a differential algebraic equation: (12) In equation (12), For the first i The output signal of the optimal observation station corresponding to each control channel; The observed signal after the time delay; , For the first i Two time-delayed state variables for each control channel.
[0029] Step 5: Combine the differential-algebraic equations of the time-delay elements of each control channel, the differential-algebraic equations of the multi-control channel additional damping controller, and the differential-algebraic equations of the wind power grid-connected system, and then linearize them to obtain the closed-loop linearized model of the entire system and the closed-loop state matrix of the entire system. .
[0030] Step 5.1: To suppress multiple dangerous modes, a multi-channel additional damping controller is constructed. i The damping control circuit of each channel refers to the typical SDC structure, including a gain circuit, a DC blocking circuit, and a lead-lag circuit, and its transfer function is shown in equation (13): (13) In equation (13), For controller gain; The time constant of the DC blocking element; , , , This is the time constant for the lead-lag compensation process.
[0031] Step 5.2: Combine the differential-algebraic equations of the wind turbine grid-connected system obtained in Step 1.1, the differential-algebraic equations of the time delay elements of each channel obtained in Step 4.2, and the SDC controller equations of each channel obtained in Step 5.1, and perform unified linearization on the combined equations at the steady-state operating point to obtain the following result: Figure 1 The structure shows the whole system closed-loop linearized model and the whole system closed-loop augmented state matrix. .
[0032] Step 6, based on The first-order sensitivity of the eigenvalues of each hazardous mode to time delay and the first-order sensitivity to the control parameters of the additional damping controller are calculated. Using the first-order sensitivity as the initial value, the second-order sensitivity and the mixed second-order sensitivity are calculated and then linearly approximated to obtain the sensitivity analytical expression. Then, using the sensitivity analytical expression, the eigenvalue offset analytical function of each hazardous mode is constructed to obtain the offset of the eigenvalues.
[0033] Step 6.1, calculate the first step using equation (14). i Characteristic values of each hazard mode For the j Each control channel time delay First-order time delay sensitivity : (14) In equation (14), The state matrix of the entire system; This is the input matrix for the entire system; This is the output matrix of the entire system; This is the direct transmission matrix for the entire system; , They are respectively For the i The left and right eigenvectors of each dangerous pattern; the superscript T denotes transpose, and the superscript -1 denotes the inverse of the matrix.
[0034] Step 6.2, use equation (15) to calculate the first... i Characteristic values of each hazard mode For the w Control parameters of an additional damping controller First-order control parameter sensitivity : (15) Step 6.3 introduces the second-order sensitivity of the eigenvalues to the control parameters, the second-order sensitivity to the time delay, and the mixed second-order sensitivity to the time delay-parameter. Using equation (16), the sensitivity is linearly approximated to obtain the analytical expression of the sensitivity including the effects of interactive coupling: (16) In equation (16), For the first to the second N The time delay of each control channel; For the first to the second M One control parameter; For the first q One control parameter; For the first r One control parameter; For the first c The time delay of each control channel; For the first h The time delay of each control channel; N The number of control channels for the additional damping controller; M The number of control parameters for the additional damping controller; Let be the initial control parameter vector, and ,in, Indicates the first One initial control parameter; Let be the initial time delay vector of the control channel, and ,in, Indicates the first Initial time delay of each control channel; For the first h The time delay fluctuation of each control channel; For the first r The increment of each control parameter; for right and Second-order sensitivity; for right and Second-order sensitivity; for right and The mixed second-order sensitivity, for right and The mixed second-order sensitivity; To obtain the second-order sensitivity required in equation (16), combining equations (14) and (15), the first-order sensitivity formula is derived by second-order differentiation using equation (17): (17) In equation (17), It is the identity matrix; , , , The eigenvectors are respectively about , , , The sensitivity is obtained by solving equation (18): (18) Step 6.4: To describe the comprehensive impact of small fluctuations in control parameters and time delay parameters on the oscillation mode eigenvalues of the wind power grid-connected system, an approximate expansion of the relationship between the eigenvalues and the control parameters and time delay parameters is performed. Based on the idea of multivariable Taylor expansion, the first equation (19) is used to construct the... i Eigenvalues under each dangerous mode offset : (19) In equation (19), for The first-order sensitivity vector is formed by the first-order sensitivity of each control parameter under the initial control parameters and the initial time delay of the control channel. for The first-order sensitivity vector is composed of the first-order sensitivity of each control channel delay under the initial control parameters and the initial time delay of the control channel. This is the increment vector of the control parameters; This represents the time-delay fluctuation vector for each control channel; for The second-order sensitivity matrix is composed of the second-order sensitivities to each control parameter; for The second-order sensitivity matrix is composed of the second-order sensitivities to the time delay of each control channel; for The mixed second-order sensitivity matrix is composed of the mixed second-order sensitivities of each control parameter and the control channel time delay, and we have: (20) Step 7: Construct the worst-case time-delay fluctuation vector using the real part sign of the first-order time-delay sensitivity; substitute the worst-case time-delay fluctuation vector into the eigenvalue offset analytical function to obtain the eigenvalue offset function only with respect to the control parameter increment; superimpose the eigenvalue offset function with the initial eigenvalue to obtain the actual real part of the eigenvalue affected by the worst-case time-delay fluctuation and the actual damping ratio; thereby establishing a parameter optimization model with the goal of minimizing the control parameter increment and the constraint that the actual real part of the eigenvalue and the actual damping ratio satisfy a preset critical value; and solve the parameter optimization model using the interior point method to obtain the optimal control parameters.
[0035] Step 7.1: Construct the worst-case time-delay fluctuation vector that causes the real part of the eigenvalue to increase using equation (12). : (twenty one) In equation (21), For the first N The maximum allowable time delay fluctuation range for each control channel; It is a symbolic function; To perform the operation of taking the real part; For the first N Characteristic values of each hazard mode For the N Each control channel time delay The first-order time delay sensitivity.
[0036] Step 7.2, will Substituting into equation (19), we can then use equation (22) to establish the first... i The eigenvalue offset of each hazardous mode with respect to the increment of control parameters only. This yields the eigenvalue offset vector composed of the eigenvalue offsets of each hazardous mode under the worst operating condition. : (twenty two) Step 7.3: Construct the objective function of the parameter optimization model using equation (23). : (twenty three) In equation (23), This is the increment vector of the control parameters to be optimized; The weights are a diagonal matrix for the control parameters; For the first The weighting coefficients of each control parameter; For the first One initial control parameter; Step 7.4, use equation (24) to establish the inequality constraints for the parameter optimization model: (twenty four) In equation (24), The damping ratio critical value vector; For the whole system and The initial eigenvalue vector, and ; The vector of critical values of the real part; , These are the upper and lower limit vectors of the parameter to be tuned, respectively; , These are operations that extract the real part and the imaginary part, respectively.
[0037] Step 7.5: Solve the parameter optimization model composed of equations (23) and (24) using the interior point method, including: Step 7.5.1, Define the optimization variable vector By introducing slack variables, the inequality constraints are transformed into equality constraints, specifically addressing the damping ratio constraint in equation (24). Real part constraint In addition to upper and lower bound constraints on parameters, a nonnegative slack variable vector is introduced. , , , The following equation constraints are constructed using equation (25): (25) In equation (25), This is the increment vector of the control parameters to be optimized.
[0038] Step 7.5.2, introduce the corresponding Lagrange multiplier vectors. , , , ,make , Construct the Lagrangian function using equation (26): (26) In equation (26), For disturbance factor; , They are respectively N peacekeeping M A column vector of all 1s.
[0039] To solve the optimization model containing the logarithmic obstacle term, according to Kuhn-Tucker theory, the optimal solution is obtained by taking the partial derivatives of the Lagrangian function with respect to the control parameter increment, slack variable, and Lagrangian multiplier and setting them to zero, as shown in equation (27): (27) In equation (27), , , , , , , , , These are the residual vector functions after differentiating the Lagrange function with respect to each variable; , , , These are diagonal matrices formed by the corresponding slack variable vectors; , , , These are diagonal matrices formed by the corresponding Lagrange multiplier vectors; For gradient.
[0040] Step 7.5.3: The above nonlinear equations are solved using the Newton-Raphson method. After linearization, equation (28) can be obtained: (28) In equation (28), The Hessian matrix is calculated using the formula (29): (29) In equation (29), It is a second-order gradient; , The first a The, the b Lagrange multiplier components of each dangerous mode constraint; , The first a The damping ratio constraint function of the first dangerous mode and the first b Real part constraint functions for each dangerous mode.
[0041] Step 7.5.4: The search direction of the current iteration is obtained by solving the system of linear equations. In order to ensure that the iteration point is always within the feasible region, that is, to satisfy the hard constraint that the slack variables and Lagrange multipliers are always positive, the step size is controlled by equation (30): (30) In equation (30), , These are the iteration step sizes for the primal problem and the dual problem, respectively; and They are the first o Each slack variable component and a Lagrange multiplier.
[0042] Step 7.5.5: Update the value of the current iteration point using equation (31) and proceed to the next iteration cycle: (31) In equation (31), and These are all the slack variables and Lagrange multipliers, respectively.
[0043] Step 7.5.6: Determine whether the convergence condition is met. If the condition is not met, return to step 7.5.3 to continue the iteration; Step 7.6: Output the optimal control parameter vector. ,Will and The control parameters of the multi-channel additional damping controller are superimposed to update the control parameters, thereby effectively suppressing multiple dangerous modes.
[0044] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.
[0045] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.
Claims
1. A method for optimizing DFIG multi-channel additional damping control parameters based on time delay, characterized in that, Includes the following steps: Step 1: Establish a linearized model of the wind power grid-connected system containing a synchronous generator (SG) and a doubly fed induction generator (DFIG), and perform eigenvalue analysis on the linearized model to obtain the dangerous modes where the damping ratio is lower than the preset safety threshold or the real part of the eigenvalue is greater than the preset safety threshold. Step 2: Construct the observation matrix of the wind power grid-connected system, and use the observation matrix to calculate the target observability of each algebraic variable for each hazardous mode and the interference observability for other non-target hazardous modes; thereby calculate the ratio between the target observability and the interference observability, and use it as the mode selectivity index; select the algebraic variable with the largest mode selectivity index as the optimal observation signal, and take the observation station corresponding to the optimal observation signal as the optimal observation station. Step 3: Determine the signal transmission path from the optimal observation station to the additional damping controller of the multi-control channel. Calculate the measurement processing time delay, network transmission time delay, and control execution time delay on each signal transmission path, and then superimpose them to obtain the time delay of each control channel on the additional damping controller. Step 4: Use the second-order Padé approximation to expand the time delay elements of each control channel into differential algebraic equations; Step 5: Combine the differential-algebraic equations of the time-delay elements of each control channel, the differential-algebraic equations of the multi-control channel additional damping controller, and the differential-algebraic equations of the wind power grid-connected system, and then linearize them to obtain the closed-loop linearized model of the entire system and the closed-loop state matrix of the entire system. ; Step 6, based on The first-order sensitivity of the eigenvalues of each hazardous mode to time delay and the first-order sensitivity to the control parameters of the additional damping controller are calculated. Then, using the first-order sensitivity as the initial value, the second-order sensitivity and the mixed second-order sensitivity are calculated and linearly approximated to obtain the sensitivity analytical expression. Then, using the sensitivity analytical expression, the eigenvalue offset analytical function of each hazardous mode is constructed to obtain the offset of the eigenvalues. Step 7: Construct the worst-case time-delay fluctuation vector using the real part sign of the first-order time-delay sensitivity; substitute the worst-case time-delay fluctuation vector into the eigenvalue offset analytical function to obtain the eigenvalue offset function only with respect to the control parameter increment; superimpose the eigenvalue offset function with the initial eigenvalue to obtain the actual real part of the eigenvalue affected by the worst-case time-delay fluctuation and the actual damping ratio; thereby establishing a parameter optimization model with the goal of minimizing the control parameter increment and the constraint that the actual real part of the eigenvalue and the actual damping ratio satisfy the preset critical value. The interior point method is then used to solve the parameter optimization model to obtain the optimal control parameters.
2. The method for optimizing DFIG multi-channel additional damping control parameters based on time delay as described in claim 1, characterized in that, The selection of the optimal observation station under the dangerous mode in step 2 is determined according to the following steps: Step 2.1: Select the bus voltage and line power under the dangerous mode as algebraic variables to construct the observation matrix. Thus, the first equation is obtained using equation (1). y The algebraic variable for the th i Observability of each hazard pattern : (1) In equation (1), This represents the total number of state variables in the wind power grid-connected system. k The index of the state variable; for The Middle y Line 1 k Column elements; For the first i Characteristic values of each hazard mode The corresponding right eigenvector The k One element; For the first i Characteristic values of each hazard mode The corresponding left eigenvector The k One element; Step 2.2, calculate the first step using equation (2). y The algebraic variable for the th i Modal selectivity index of each hazard mode : (2) In equation (2), The total number of hazardous modes; j This is the sequence number of the non-target hazard mode; For the first y The algebraic variable for the th j The observability of individual non-target hazard patterns; A tiny positive number is set to prevent the denominator from being zero; Step 2.3: Select the algebraic variable with the largest modal selectivity index value as the optimal observation signal, and designate the observation station that collected the optimal observation signal as the first... i The optimal observation station for each dangerous mode.
3. The method for optimizing DFIG multi-channel additional damping control parameters based on time delay as described in claim 1, characterized in that, The calculation of the time delay of each control channel in step 3 is determined according to the following steps: Step 3.1, calculate the first step using equation (3). i The first danger mode corresponds to the first i Processing time delay of phasor measurement unit (PMU) in the optimal observation station of each control channel : (3) In equation (3), The sampling frequency of the PMU; These are the digital filter characteristic coefficients; This is a constant related to the measurement window in the PMU device; For the first i Maximum data load under each dangerous mode; This refers to the amount of data in the communication protocol packet header; The transmission rate of the PMU communication interface; For the transmission interface delay; Step 3.2: Determine the signal transmission path along the wide area communication network. Calculate the first using equation (4) i Wide-network transmission delay under dangerous modes : (4) In equation (4), E A set of links in a wide area communication network; This is a routing indicator function, representing a node. and nodes Links between Is it in the signal transmission path? Above, if in Above, then Take 1, otherwise Set to 0; For link Length; The speed of light in the medium; For the signal at the node To the node Processing time delay; For worst-case queuing delays; Step 3.3, combining the synchronization waiting time delay of the wide area communication network. Processing time delay of control stations at each node in a wide area communication network Calculate the first using equation (5) i The first danger mode corresponds to the first i Time delay of each control channel : (5)。 4. The method for optimizing DFIG multi-channel additional damping control parameters based on time delay as described in claim 3, characterized in that, Step 4 includes: Step 4.1, use equation (6) to... i Time delay element of each control channel Convert to frequency domain transfer function : (6) In equation (6), s For the Laplace operator; Step 4.2, use equation (7) to transform equation (6) into a differential algebraic equation: (7) In equation (7), For the first i The output signal of the optimal observation station corresponding to each control channel; The observed signal after the time delay; , For the first i Two time-delayed state variables for each control channel.
5. The method for optimizing DFIG multi-channel additional damping control parameters based on time delay as described in claim 1, characterized in that, Step 6 includes: Step 6.1, calculate the first step using equation (8). i Characteristic values of each hazard mode For the j Each control channel time delay First-order time delay sensitivity : (8) In equation (8), The state matrix of the entire system; This is the input matrix for the entire system; This is the output matrix of the entire system; This is the direct transmission matrix for the entire system; , They are respectively For the i The left and right eigenvectors of each dangerous pattern; the superscript T denotes transpose, and the superscript -1 denotes the inverse of the matrix; Step 6.2 introduces the second-order sensitivity of the eigenvalues to the control parameters, the second-order sensitivity to the time delay, and the mixed second-order sensitivity to the time delay-parameter. Using equation (9), a linear approximation of the sensitivity is obtained, yielding the analytical expression of the sensitivity including the effects of interactive coupling: (9) In equation (9), For the first to the second N The time delay of each control channel; For the first to the second M One control parameter; For the first q One control parameter; For the first r One control parameter; For the first c The time delay of each control channel; For the first h The time delay of each control channel; N The number of control channels for the additional damping controller; M The number of control parameters for the additional damping controller; Let be the initial control parameter vector, and ,in, Indicates the first One initial control parameter; Let be the initial time delay vector of the control channel, and ,in, Indicates the first Initial time delay of each control channel; For the first h The time delay fluctuation of each control channel; For the first r The increment of each control parameter; for right and Second-order sensitivity; for right and Second-order sensitivity; for right and The mixed second-order sensitivity, for right and The mixed second-order sensitivity; Step 6.3, construct the first using equation (10). i Eigenvalues under each dangerous mode offset : (10) In equation (10), for The first-order sensitivity vector is formed by the first-order sensitivity of each control parameter under the initial control parameters and the initial time delay of the control channel. for The first-order sensitivity vector is composed of the first-order sensitivity of each control channel delay under the initial control parameters and the initial time delay of the control channel. This is the increment vector of the control parameters; This represents the time-delay fluctuation vector for each control channel; for The second-order sensitivity matrix is composed of the second-order sensitivities to each control parameter; for The second-order sensitivity matrix is composed of the second-order sensitivities to the time delay of each control channel; for The mixed second-order sensitivity matrix is composed of the mixed second-order sensitivities of each control parameter and the control channel time delay, and we have: (11)。 6. The method for optimizing DFIG multi-channel additional damping control parameters based on time delay as described in claim 1, characterized in that, The construction and solution process of the parameter optimization model in step 7 is determined as follows: Step 7.1: Construct the worst-case time-delay fluctuation vector that causes the real part of the eigenvalue to increase using equation (12). : (12) In equation (12), For the first N The maximum allowable time delay fluctuation range for each control channel; It is a symbolic function; This is for the operation of taking the real part; For the first N Characteristic values of each hazard mode For the N Each control channel time delay First-order time-delay sensitivity; Step 7.2, will Substituting into equation (10), we can then use equation (13) to establish the first... i The eigenvalue offset of each hazardous mode with respect to the increment of control parameters only. This yields the eigenvalue offset vector composed of the eigenvalue offsets of each hazardous mode under the worst operating condition. : (13) Step 7.3: Construct the objective function of the parameter optimization model using equation (14). : (14) In equation (14), This is the increment vector of the control parameters to be optimized; The weights are a diagonal matrix for the control parameters; For the first The weighting coefficients of each control parameter; Step 7.4, use equation (15) to establish the inequality constraints for the parameter optimization model: (15) In equation (15), The damping ratio critical value vector; For the whole system and The initial eigenvalue vector, and ; The vector of critical values of the real part; , These are the upper and lower limit vectors of the parameter to be tuned, respectively; , These are operations that extract the real part and the imaginary part, respectively. Step 7.5: Solve the parameter optimization model composed of equations (14) and (15) using the interior point method, and output the optimal control parameter increment vector. ,Will and The control parameters of the multi-channel additional damping controller are superimposed to update the control parameters, thereby achieving effective suppression of multiple dangerous modes.
7. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports a processor in executing the method of any one of claims 1-6, the processor being configured to execute the program stored in the memory.
8. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by a processor to perform the steps of the method according to any one of claims 1-6.