A parameter setting method and system of a PSS based on complex field vector synthesis

Abstract

The application discloses a parameter setting method and system of PSS based on complex domain vector synthesis, and belongs to the technical field of power system automation and control. The method comprises the following steps: obtaining an open-loop frequency response, and extracting a phase lag characteristic curve of a channel; based on a complex domain vector synthesis model and the phase lag characteristic curve, a complex response calculation formula is constructed, a total open-loop phase is defined, a parameter vector is set and a parameter feasible region is determined, a target compensation phase is set, a weighted comprehensive phase error target function is defined, and a boundary value is set; the weighted comprehensive phase error target function is taken as a fitness function, parameter space searching is performed, and a parameter vector that minimizes the fitness function is solved; the parameter searching process of the global optimization algorithm is optimized; the optimal parameter set is verified in multiple dimensions and vector synthesis visual analysis is performed, and parameter setting of a power system stabilizer is completed. The application has correct principles, relatively high efficiency and accuracy in processing, and high engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of power system automation and control technology, specifically relating to a parameter tuning method and system for PSS based on complex field vector synthesis. Background Technology

[0002] Power system stabilizers (PSS) are key devices for ensuring the stability of large-scale interconnected power grids during minor disturbances. They generate positive damping electrical torque to suppress low-frequency power oscillations by injecting a phase-compensated additional signal into the generator excitation system. To effectively cover different oscillation frequency bands from local to inter-regional modes, multi-band PSSs have emerged, with PSS2B and PSS4B models being the most widely used. Although both aim to provide wideband damping, their internal structural designs and phase compensation principles differ fundamentally. This difference has long been overlooked and not properly addressed by existing tuning methods, leading to the common application of empirical methods from PSS2B to PSS4B parameter tuning, resulting in technical misunderstandings and performance defects.

[0003] The PSS2B model is essentially a single-channel structure that utilizes the principle of acceleration synthesis to sum the outputs of the two channels. At any given frequency, its total output phase is the algebraic sum of the phase lags of all series-connected elements within that channel. Therefore, the phase compensation characteristic of PSS2B can be considered as an independent, piecewise effective series phase corrector. Its tuning can follow the classic frequency response method, shaping the phase curve by configuring the zeros and poles of the lead-lag network.

[0004] In stark contrast, the PSS4B model employs a parallel vector synthesis structure. It comprises three completely independent and continuously operating signal processing channels: low-frequency (LB), mid-frequency (IB), and high-frequency (HB). Each channel is itself a bandpass filter formed by subtracting two parallel transfer functions. The outputs of the three channels undergo continuous vector addition in the complex frequency domain, and the resulting vector sum is then processed through a common stage to form the final output. This structure fundamentally alters its core compensation mechanism: the total output phase of PSS4B at frequency ω is not a simple arithmetic average or weighted sum of the phases of the three channels themselves, but rather the argument of the synthesized vector obtained by geometrically adding the three corresponding complex response vectors (each with its own amplitude and phase). That is: ,in , , The vector composition relationship introduces strong nonlinear coupling: adjusting the parameters of any channel not only changes the amplitude and phase of that channel's vector, but also nonlinearly affects the contribution of other channels to the total output and even the total phase by changing the vector composition result. This completely breaks the assumptions of "phase additivity" and "channel independence" upon which PSS2B relies.

[0005] Due to a failure to recognize and properly address this fundamental difference, existing tuning methods for PSS4B have certain limitations: Many engineering practices and some academic research still follow the phase compensation approach of PSS2B, ignoring the vector synthesis effect. This results in a significant deviation between the calculated expected phase and the actual system phase, leading to tuning failure and even negative damping. The PSS4B model contains over 40 adjustable parameters (gains in various frequency bands, multiple time constants). These parameters are highly coupled through vector synthesis, forming an extremely complex nonlinear response surface. Traditional trial-and-error methods, robust tuning methods based on linear matrix inequalities, or local optimization algorithms relying on gradient information are inefficient and prone to getting trapped in local optima in this high-dimensional, non-convex, multi-peak parameter space. Existing commercial or open-source power system analysis software typically provides PSS model libraries, but most of their built-in tuning assistance functions or frequency domain analysis modules do not specifically address the vector synthesis characteristics of PSS4B. While simulation results can verify the performance of specific parameter sets, they cannot provide reverse guidance for efficient and accurate parameter optimization. In summary, current tuning methods for PSS4B may overlook the fundamental nature of vector composition, leading to fundamental errors. High-dimensional, strongly coupled parameters result in relatively low algorithm efficiency and a tendency to get trapped in local optima. Furthermore, the lack of dedicated tools makes it difficult to reverse-engineer precise parameter optimization. Summary of the Invention

[0006] This invention provides a parameter tuning method and system for PSS based on complex field vector synthesis. The purpose is to solve the problems of current tuning methods for PSS4B, which may ignore the essence of vector synthesis and lead to fundamental errors; high-dimensional and strongly coupled parameters make the algorithm relatively inefficient and prone to getting trapped in local optima; and the lack of dedicated tools makes it difficult to reverse guide the precise parameter optimization.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a parameter tuning method for a PSS based on complex field vector synthesis, comprising the following steps: S1. Obtain the open-loop frequency response of the excitation generator controlled object from the PSS output point to the generator electrical torque point forward channel, and extract the phase lag characteristic curve of the channel. S2. Based on the complex domain vector synthesis model and phase lag characteristic curve, construct a complex response calculation formula that includes the series open-loop transfer function of the PSS and the controlled object, define the total open-loop phase, set the parameter vector containing all adjustable parameters of the PSS and determine the parameter feasible region, set the target compensation phase, define the weighted comprehensive phase error objective function at the discrete frequency points of the target oscillation frequency band, and divide the frequency bands of the PSS and set the boundary values ​​of the time constant of each channel. Among them, the complex domain vector synthesis model of PSS is constructed, and the output of the complex domain vector synthesis model is the sum of complex response vectors of multi-band channels; S3. Using the weighted integrated phase error objective function as the fitness function, a global optimization algorithm is used to search the parameter space within the parameter feasible region to find the parameter vector that minimizes the fitness function. S4. The parameter search process of the global optimization algorithm is optimized by adopting a chain-based collaborative optimization mechanism of multi-chain parallelism and intra-chain iteration to obtain the optimal parameters; S5. Perform multi-dimensional verification and vector synthesis visualization analysis on the optimal parameter set to complete the parameter tuning of the power system stabilizer.

[0008] In some implementations, in S1, the open-loop frequency response is obtained by using a frequency domain scanning test method, and the extracted phase hysteresis characteristic curve covers the target oscillation frequency band of the preset frequency.

[0009] In some implementations, in S2, the power system stabilizer is a PSS4B type power system stabilizer. For a given angular frequency, the complex frequency response calculation formula of the PSS4B type power system stabilizer is as follows: ; in, For the gain of each frequency band, , , , , The complex response is the product of the transfer functions of each branch. The imaginary unit, ω is the angular frequency.

[0010] In some implementations, in S2, the complex response of the series open-loop transfer function of PSS4B and the controlled object at the frequency is calculated as follows: ; The total open-loop phase is: ; in, For PSS4B in Complex response at the point, This is a parameter vector containing all adjustable parameters of PSS4B. This is the complex factor corresponding to the phase lag of the controlled object. To calculate the argument of a complex number, This is the phase lag characteristic curve of the controlled object of the excitation generator.

[0011] Furthermore, in S2, the objective function for the weighted synthesis phase error is defined as follows: ; in, The objective function for weighted synthesis phase error is... This is a vector containing all the PSS4B parameters to be optimized. These are the weighting coefficients for each frequency point, used to emphasize the mid-frequency band that is crucial to system stability; The calculation requires a complex field vector composition model and a complex multiplication formula.

[0012] In some implementations, setting the parameter vector containing all adjustable parameters of the power system stabilizer in S2 specifically includes: parameter vector θ Includes all adjustable parameters of PSS4B: ; Each parameter has a physical constraint range, forming the parameter feasible region Ω; θ The first row of the array contains parameters for the low-frequency channel: For low-frequency DC gain, The first row represents the low-frequency time constant; the second row represents the mid-frequency channel parameters; the third row represents the high-frequency channel parameters, defined as for the low-frequency channel; the fourth row represents the filter parameters in the PSS4B model. For the unit's moment of inertia, These are the parameters for the notch filter.

[0013] Furthermore, in S3, the global optimization algorithm employs an improved particle swarm optimization algorithm, and the optimization problem solved within the parameter feasible region is: ; Among them, the improved particle swarm optimization algorithm balances global exploration and local exploitation capabilities by introducing adaptive inertia weights, a perturbation mechanism based on population diversity, and an elite retention strategy.

[0014] In some implementations, the chain-based collaborative optimization mechanism in S4, which involves multi-chain parallelism and intra-chain iteration, includes: Multiple independent optimization chains are initialized, and initial parameter values ​​are randomly generated for each chain. An iterative algorithm is used within each chain to iteratively optimize and retain the optimal solution. Elite migration mechanisms are used between chains to exchange superior individuals to avoid premature convergence. An inheritance strategy is used within chains to use the previous optimization result as the initial value for the next iteration, thereby accelerating convergence.

[0015] In some implementations, S5 includes multi-dimensional verification and vector synthesis visualization analysis, including: Plot the frequency-phase curve of the excitation system after PSS4B correction to verify whether the deviation from the target compensation phase in the target frequency band is within the engineering allowable range. The process of plotting the output vectors of each frequency band on the complex plane at key frequency points and synthesizing the total output vector using vector addition is illustrated. In a nonlinear simulation environment that includes detailed generator, excitation system and load models, typical small disturbances or continuous oscillation disturbances are applied to verify the damping effect and dynamic performance of PSS4B with the optimal parameter set on power oscillations.

[0016] This invention also provides a parameter tuning system for PSS based on complex field vector synthesis, used to implement the above-mentioned parameter tuning method for PSS based on complex field vector synthesis, including an object characteristic interface module, a model configuration and calculation module, a parameter vector calculation module, a parameter optimization module, and a parameter tuning module, wherein: The object characteristic interface module is used to: obtain the open-loop frequency response of the excitation generator controlled object from the PSS output point to the generator electrical torque point forward channel, and extract the phase lag characteristic curve of the channel; The model configuration and calculation module is used to: construct a complex response calculation formula containing the series open-loop transfer function of the PSS and the controlled object based on the complex domain vector synthesis model and the phase lag characteristic curve; define the total open-loop phase; set the parameter vector containing all adjustable parameters of the PSS and determine the parameter feasible region; set the target compensation phase; define the weighted comprehensive phase error objective function at discrete frequency points of the target oscillation frequency band; and divide the frequency bands of the PSS and set the boundary values ​​of the time constant of each channel. Among them, the complex domain vector synthesis model of PSS is constructed, and the output of the complex domain vector synthesis model is the sum of complex response vectors of multi-band channels; The parameter vector calculation module is used to: take the weighted comprehensive phase error objective function as the fitness function, perform a global optimization algorithm to search the parameter space within the parameter feasible region, and solve for the parameter vector that minimizes the fitness function; The parameter optimization module is used to optimize the parameter search process of the global optimization algorithm by using a chain-based collaborative optimization mechanism with multi-chain parallelism and intra-chain iteration to obtain the optimal parameters. The parameter tuning module is used to perform multi-dimensional verification and vector synthesis visualization analysis of the optimal parameter set, and to complete the parameter tuning of the power system stabilizer.

[0017] Compared with the prior art, the parameter tuning method and system of PSS based on complex field vector synthesis of the present invention has the following advantages: This invention presents a parameter tuning method for PSS (Power System Parameters) based on complex field vector synthesis, which improves upon tuning failures caused by conceptual confusion and ensures the mathematical correctness of parameter design. It achieves efficient searching of complex high-dimensional parameter spaces by formalizing the tuning problem into a well-defined optimization problem and employing an improved global optimization algorithm. This automatically and efficiently handles strong nonlinear couplings between PSS4B parameters, overcoming the curse of dimensionality and potentially achieving globally or near-globally optimal parameter configurations. It also provides powerful mechanistic analysis and verification tools. This invention establishes a complete standardized process from data input and automated optimization to comprehensive verification, independent of the personal experience of specific experts. It is easily integrated into existing power system analysis platforms or used as a standalone tool, exhibiting good repeatability and portability, and is applicable to generator sets of different capacities and models. It demonstrates excellent feasibility and applicability. Attached Figure Description

[0018] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0019] Figure 1 This is a flowchart illustrating the parameter tuning method for a PSS based on complex field vector synthesis according to the present invention. Figure 2 This is a schematic diagram of the PSS4B model structure in the PSS parameter tuning method based on complex field vector synthesis of the present invention. Figure 3 This is a detailed flowchart of the parameter search using the particle swarm optimization algorithm in the parameter tuning method of PSS based on complex field vector synthesis of the present invention; Figure 4 This is a schematic diagram showing the comparison of the total open-loop phase of the system before and after tuning, provided as an embodiment of the parameter tuning method for PSS based on complex field vector synthesis of the present invention. Figure 5 This is a visual diagram illustrating the complex domain vector synthesis of PSS4B at a specific frequency point in the PSS parameter tuning method based on complex domain vector synthesis according to the present invention. Figure 6 This is a comparison chart of the simulation dynamic response of a unit with and without PSS4B, provided as an embodiment of the parameter tuning method for PSS based on complex field vector synthesis of the present invention. Figure 7 The output curve of the PSS4B stage of the unit is provided as an embodiment of the parameter tuning method of PSS based on complex field vector synthesis of the present invention. Figure 8This is a diagram showing the hierarchical architecture design of the parameter tuning system in the PSS parameter tuning method based on complex field vector synthesis of the present invention. Figure 9 The optimal parameter set amplitude-frequency curve is provided for an embodiment of the parameter tuning method of PSS based on complex field vector synthesis of the present invention. Figure 10 The optimal parameter set phase-frequency curve is provided for an embodiment of the parameter tuning method of PSS based on complex field vector synthesis of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0021] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0022] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0023] It should be noted that the apparatus and methods disclosed in the embodiments herein can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings show the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments herein. In this regard, each block in a flowchart or block diagram may represent a module, program, or part of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system to perform the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions.

[0024] In addition, the functional modules in the various embodiments of this article can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0025] Developing a dedicated tuning method that is strictly based on the PSS4B vector synthesis mechanism and can automatically handle the strong coupling of high-dimensional parameters has become a key technical requirement for solving its engineering application bottlenecks and fully releasing its broadband damping potential.

[0026] Based on this, the present invention provides a parameter tuning method for a PSS based on complex field vector synthesis, comprising the following steps: S1. Obtain the open-loop frequency response of the excitation generator controlled object from the PSS output point to the generator electrical torque point forward channel, and extract the phase lag characteristic curve of the channel. S2. Based on the complex domain vector synthesis model and phase lag characteristic curve, construct a complex response calculation formula that includes the series open-loop transfer function of the PSS and the controlled object, define the total open-loop phase, set the parameter vector containing all adjustable parameters of the PSS and determine the parameter feasible region, set the target compensation phase, define the weighted comprehensive phase error objective function at the discrete frequency points of the target oscillation frequency band, and divide the frequency bands of the PSS and set the boundary values ​​of the time constant of each channel. Among them, the complex domain vector synthesis model of PSS is constructed, and the output of the complex domain vector synthesis model is the sum of complex response vectors of multi-band channels; S3. Using the weighted integrated phase error objective function as the fitness function, a global optimization algorithm is used to search the parameter space within the parameter feasible region to find the parameter vector that minimizes the fitness function. S4. The parameter search process of the global optimization algorithm is optimized by adopting a chain-based collaborative optimization mechanism of multi-chain parallelism and intra-chain iteration to obtain the optimal parameters; S5. Perform multi-dimensional verification and vector synthesis visualization analysis on the optimal parameter set to complete the parameter tuning of the power system stabilizer.

[0027] This invention presents a parameter tuning method for a Power System (PSS) based on complex-domain vector synthesis. By establishing an accurate complex-domain vector synthesis model of PSS4B, whose multi-band output is essentially a complex vector sum, this method combines the model with the phase lag characteristics of the controlled exciter (GRE) using complex multiplication to construct a total open-loop phase calculation path. This invention defines an optimization function aimed at minimizing the weighted phase error across the entire frequency band and employs an improved global optimization algorithm to achieve automatic searching of the high-dimensional parameter space. It enables comprehensive frequency-domain, complex-plane vector synthesis, and time-domain verification of the tuning results, resolving the failure of traditional tuning methods caused by confusion between the structural differences between PSS4B and PSS2B. This achieves automated and precise parameter tuning, significantly improving the damping stability level of the power system.

[0028] In some embodiments, the present invention provides a parameter tuning method for a PSS based on complex field vector synthesis, which is carried out according to the following steps: S1. Establish an accurate PSS4B complex domain vector synthesis model: Based on the IEEE standard definition, construct the PSS4B model in the complex frequency domain. s The transfer function model is given below. The model must explicitly express that its output is the sum of the three-channel complex responses. For a given angular frequency... Its complex frequency response is calculated as follows: ; in, For the gain of each frequency band, , , , , This represents the complex response corresponding to the product of the transfer functions of each branch. The operations within square brackets [ ] are complex additions, which is a key modeling difference from the PSS2B model; The imaginary unit, It is the angular frequency; and, , .

[0029] S2. Obtain the phase lag characteristics of the controlled excitation generator: Using a frequency domain scanning test method, obtain the open-loop frequency response of the forward path from the PSS output point to the generator's electrical torque point, and accurately extract its phase lag characteristic curve. The frequency range covers the target oscillation band; for example, 0.01Hz to 2Hz. This step is consistent with the method for obtaining the uncompensated characteristics of the excitation system in the power standard guideline DL / T1231, and the obtained... The main input data of the method of this invention; S3. Construct a total open-loop phase and error measurement function based on complex multiplication: Define a series open-loop transfer function containing the PSS4B and the controlled object at frequency... The complex response at point is calculated as follows: ; in, The phase lag of the object is introduced in the form of complex multiplication. Then the total open-loop phase is: ; in, For PSS4B in Complex response at the point, This is a parameter vector containing all adjustable parameters of PSS4B. This is the complex factor corresponding to the phase lag of the controlled object. To calculate the argument of a complex number, The phase lag characteristic curve of the controlled object of the excitation generator; PSS4B in The complex response at point is calculated as follows: ; Let the parameter vector Includes all adjustable parameters of PSS4B; The symbols “+” and “-” represent addition and subtraction operations for vectors in the complex domain. In some embodiments, due to the special nature of complex domain computation, the minimum model structure considered for a single tuning is shown in equation (2), and it is not possible to independently tune a certain frequency band and then splice the parameter set. 。

[0030] ; Each parameter has a physical constraint range, forming the feasible region Ω. In the formula, θ The first row of the array contains parameters for the low-frequency channel: Low-frequency DC gain (unit: pu). The first line represents the low-frequency time constant (in seconds); the second line represents the mid-frequency channel parameters; the third line represents the high-frequency channel parameters, defined as for the low-frequency channel; the fourth line represents the filter parameters in the PSS4B model, where H is the unit's moment of inertia (in seconds). These are the parameters for the notch filter (unit: pu).

[0031] Set the target compensation phase as (e.g., target compensation phase) φ target Set to -90° to provide pure damping torque; the acceptable tolerance for weighted phase error is within the critical frequency band. φ total ( ω , θ *)and φ target The deviation is no greater than ±12°. The transfer function of the PSS4B model has a series-parallel hybrid structure. In the selected... N Discrete frequency points { ω i}( i =1,..., N On the above, define the weighted synthesis phase error objective function. J for: ; in, θ This is a vector containing all the PSS4B parameters to be optimized; m i These are the weighting coefficients for each frequency point, used to emphasize the mid-frequency band that is crucial to system stability; The calculation must strictly follow the vector composition model of S1 and the complex multiplication formula of this step.

[0032] Specifically, S3 needs to practically divide the high, medium, and low frequency bands according to the PSS4B mechanism, and set the time constant boundary values ​​for different channels based on these frequency band partitions. This is the key to the design optimization objective, and specifically includes: The low-frequency and medium-frequency signal inputs originate from the generator speed measurement channel. Following the design of IEEE Std421.5, the effective cutoff frequency of the low-pass digital filter in the speed channel is 0.65Hz, while the cutoff frequency of the high-pass digital filter in the active power measurement channel is above 1.8Hz. Therefore, this invention defines the operating ranges of low frequency (LB), medium frequency (IB), and high frequency (HB) as [0.01Hz, 0.2Hz], [0.2Hz, 1.8Hz], and [1.8Hz, 2.0Hz], respectively. The time constants TL1, TL3, and TL5 in the low-frequency band have boundaries of [1s, 6s], and TL2, TL4, and TL5 have boundaries of [1s, 20s], which are used to suppress oscillations in the range of 0.01~0.2Hz. The time constants TI1, TI3, and TI5 in the mid-frequency band have boundaries of [0.2s, 1s], and the time constants TI2, TI4, and TI6 have boundaries of [0.01s, 1s], which are used to suppress local oscillations in the range of 0.2 to 1.8 Hz. The time constants TH1, TH3, and TH5 in the high-frequency band have boundaries of [0.1s, 1s], and the time constants TH2, TH4, and TH6 have boundaries of [0.01s, 0.5s], which are used to suppress high-frequency oscillations above 1.8Hz. The DC gain coefficient boundaries for high frequency, low frequency, and medium frequency are all [0.1 pu, 200 p.u.]; S4. Perform parameter space search using a global optimization algorithm: The objective function defined in S3... As a fitness function, in the parametric physical feasible region Internally, the following problem is solved using a global optimization algorithm: ; The optimization algorithm needs to be able to handle high-dimensional, nonlinear, and nonconvex problems. Preferably, an improved particle swarm optimization algorithm is adopted, which balances global exploration and local exploitation capabilities and avoids premature convergence by introducing adaptive inertia weights, a perturbation mechanism based on population diversity, and an elite preservation strategy.

[0033] S5. Chain-based collaborative optimization mechanism: Employs a collaborative optimization strategy of multi-chain parallelism and intra-chain iteration. Initialize multiple independent optimization chains, with each chain generating random initial parameter values; Each chain employs an iterative algorithm, such as an improved particle swarm optimization (PSO) or a genetic algorithm (GA), to iteratively optimize and retain the optimal solution; Chains exchange superior individuals through an elite migration mechanism to avoid premature convergence. An inheritance strategy is used within the chain, using the result of the previous optimization as the initial value for the next optimization, which accelerates convergence.

[0034] S6. Verification and Visual Analysis of Tuning Results and Vector Synthesis: This involves analyzing the optimal parameter set obtained through optimization. θ * Conduct multi-dimensional verification; specifically including: Frequency domain performance verification: Plot the frequency and phase curves of the excitation system after PSS4B correction to verify whether it closely follows the target value in the target frequency band and whether the deviation is within the engineering allowable range.

[0035] Visualization of vector synthesis mechanism: At key frequency points (e.g., 0.2Hz, 1.0Hz, 2.0Hz), plot the output vectors for each frequency band on the complex plane. , , The synthesis is illustrated using vector addition. The process is illustrated in the diagram. This diagram visually reveals the formation mechanism of the total phase and contrasts it with the single-vector phase diagram of PSS2B, making it useful for teaching the principles and diagnosing problems.

[0036] Nonlinear time-domain simulation verification: In a nonlinear simulation environment containing detailed generator, excitation system, and load models, typical small disturbances or continuous oscillation disturbances are applied to verify the configuration. θ * The damping effect and dynamic performance of PSS4B on power oscillations.

[0037] This invention also provides a parameter tuning system for PSS based on complex field vector synthesis, including an object characteristic interface module, a model configuration and calculation module, a parameter vector calculation module, a parameter optimization module, and a parameter tuning module, wherein: The object characteristic interface module is used to: obtain the open-loop frequency response of the excitation generator controlled object from the PSS output point to the generator electrical torque point forward channel, and extract the phase lag characteristic curve of the channel; The model configuration and calculation module is used to: construct a complex response calculation formula containing the series open-loop transfer function of the PSS and the controlled object based on the complex domain vector synthesis model and the phase lag characteristic curve; define the total open-loop phase; set the parameter vector containing all adjustable parameters of the PSS and determine the parameter feasible region; set the target compensation phase; define the weighted comprehensive phase error objective function at discrete frequency points of the target oscillation frequency band; and divide the frequency bands of the PSS and set the boundary values ​​of the time constant of each channel. Among them, the complex domain vector synthesis model of PSS is constructed, and the output of the complex domain vector synthesis model is the sum of complex response vectors of multi-band channels; The parameter vector calculation module is used to: take the weighted comprehensive phase error objective function as the fitness function, perform a global optimization algorithm to search the parameter space within the parameter feasible region, and solve for the parameter vector that minimizes the fitness function; The parameter optimization module is used to optimize the parameter search process of the global optimization algorithm by using a chain-based collaborative optimization mechanism with multi-chain parallelism and intra-chain iteration to obtain the optimal parameters. The parameter tuning module is used to perform multi-dimensional verification and vector synthesis visualization analysis of the optimal parameter set, and to complete the parameter tuning of the power system stabilizer.

[0038] In some practical working conditions, the parameter tuning system of PSS based on complex field vector synthesis of the present invention includes the following: The model configuration and management module is used to load the PSS4B standard mathematical model and configure the parameter set to be optimized and its physical constraints. The object characteristic interface module is used to acquire and process the open-loop phase lag frequency characteristic data of the controlled object combining the excitation system and the generator. The core of the complex domain vector synthesis calculation is used to calculate the complex frequency response of PSS4B at a given frequency based on the input PSS4B parameters and strictly according to the principle that its multi-band output is a complex vector sum. It also performs complex multiplication with the phase characteristics of the controlled object to obtain the total open-loop phase of the system. An optimization algorithm engine is used to drive the parameter optimization iteration process and search for the optimal parameter set by using the weighted error between the total open-loop phase output by the vector synthesis calculation core and the target phase as the fitness function. The visualization and analysis platform is used to plot frequency domain response curves, display the complex plane vector synthesis process, and compare time-domain dynamic response simulations of the system performance before and after optimization.

[0039] The core computational process for complex field vector composition is as follows: for parameter vectors... θ and angular frequency ω , Calculate the complex transfer function values ​​for each frequency band (low frequency L, mid frequency I, high frequency H) of PSS4B, and record them separately. , , It is a complex vector; Perform complex field vector addition: ; Introducing phase lag of the controlled object Constructing complex factors ; Performing complex multiplication yields the overall open-loop transfer function: ; Extracting the total open-loop phase: .

[0040] The optimization algorithm engine employs an improved particle swarm optimization algorithm, which introduces a linearly decreasing inertia weight into the standard particle swarm update formula and includes a premature convergence judgment and particle reset mechanism based on population diversity monitoring.

[0041] The visualization and analysis platform includes a vector synthesis graph generation unit. This unit can draw complex vectors representing the output of each frequency band on the complex plane for one or more specified frequency points, and dynamically display the entire process of these vectors being synthesized into a total output vector by connecting them end to end using a geometric graphical method. At the same time, it labels the amplitude and phase information of each vector and the synthesized vector.

[0042] In the method of this invention, the initial parameters and optimization boundaries of PSS4B are set through the model configuration and management module; the open-loop uncompensated phase frequency data phasors of the excitation-generator system are imported through the object characteristic interface module. ; Define a set of discrete frequency points covering the target oscillation frequency band (0.01Hz~2Hz) { ω i}( i =1,..., N ), and assign weight coefficients to each frequency point. m i Among them, the frequency points corresponding to the low-frequency oscillation band (0.4Hz~1Hz) are given higher weights as the most typical oscillation mode. The optimization algorithm engine is launched, and it repeatedly calls the vector synthesis computation core to evaluate the performance of different candidate parameter sets. The performance metric is the weighted phase error objective function. J for: ; The computation process of the PSS4B model requires a collaborative optimization strategy of multi-chain parallelism and intra-chain iteration to avoid the high-dimensional parameter set getting trapped in local optima and thus misjudging. The number of chains should not be less than 2, and the number of intra-chain initiation iterations should not be less than 2.

[0043] The present invention will be further described in detail below through specific embodiments.

[0044] like Figures 1-8 As shown, Figure 1 This demonstrates a simplified signal flow graph and phase calculation path for PSS4B: ​​the low-frequency (LB), intermediate-frequency (IB), and high-frequency (HB) signals are processed independently and then directly summed to obtain the total phase. Three complex numbers , , Argument of vector sum .

[0045] like Figure 2 The overall flowchart shown illustrates that the implementation of this invention mainly includes the following steps: Step 1: Start the tuning system. The user sets the project identifier (e.g., power plant, unit number) through the graphical interface and loads the initial parameter set from PSS4B. These parameters can be derived from manufacturer defaults, parameters from similar units, or the last tuning values. Subsequently, the feasible domain Ω for all parameters to be optimized is defined. For example: The time constants TL1, TL3, and TL5 in the low-frequency band have boundaries of [1s, 6s], and TL2, TL4, and TL5 have boundaries of [1s, 20s], which are used to suppress oscillations in the range of 0.01~0.2Hz. The time constants TI1, TI3, and TI5 in the frequency band are defined as [0.2s, 1s], and the time constants TI2, TI4, and TI6 are defined as [0.01s, 1s], which are used to suppress local oscillations in the range of 0.2 to 1.8 Hz. The time constants TH1, TH3, and TH5 in the high-frequency band have boundaries of [0.1s, 1s], and the time constants TH2, TH4, and TH6 have boundaries of [0.01s, 0.5s], which are used to suppress high-frequency oscillations above 1.8Hz. The DC gain coefficient boundaries for high frequency, low frequency, and medium frequency are all [0.1 pu, 200 p.u.]; Then set the target compensation phase, here we take φ. target =-90°.

[0046] Step 2: Import the open-loop phase lag data of the excitation-generator system, obtained beforehand through frequency domain testing or high-precision simulation, via the system interface. The data format is a frequency-phase pair sequence {( f k , φ obj ( f k The frequency range should cover at least 0.01Hz to 2Hz. The system performs necessary smoothing and interpolation on the data to generate a queryable function within a continuous frequency range. φ obj ( ω ),in ω =2π f .

[0047] Step 3: Configure the optimization target. On a logarithmic coordinate system, within the target frequency band (e.g., 0.01Hz-3Hz), select non-uniformly on the logarithmic coordinate system. N one frequency point { ω 1, ω 2, ..., ω N} is used as the optimization evaluation point. A weight is assigned to each frequency point. m i This emphasizes the frequency bands most critical to system stability.

[0048] For example: for frequencies ≤ 0.4Hz f i Points within the ≤1.0Hz range (common frequency bands for oscillation) are weighted. m i =3.0; for f i <0.1Hz or f i For points >1.8Hz, set weights. mi =0.5; the weights of the remaining points are 1.0.

[0049] Step 4: Refer to Figure 3 The algorithm flowchart shown executes an improved particle swarm optimization algorithm to optimize parameters. The specific process is as follows: 4.1 Algorithm Parameter Settings and Population Initialization: Setting the Particle Swarm Size N =50, maximum number of iterations T max =150. Inertia weight ω Using a linear decreasing strategy, starting from ω start =0.9 decreased to ω end =0.4. Cognitive factor c1 and social factor c2 are both set to 2.0. Within the feasible region Ω, the position of each particle is randomly initialized. Xi (Represents a set of PSS4B parameters) and speed Vi .

[0050] 4.2 Particle Fitness Assessment: For each particle in the population, the vector synthesis computation core is invoked, and the particle fitness is assessed based on its position. Xi The parameters represented are used to calculate the objective function value. J ( Xi This calculation process is the core of this invention; the system calls the complex domain vector synthesis calculation core. First, the three-channel complex responses are calculated and then the vectors are added together to obtain... Multiply by get Finally, take the phase φ total It is absolutely forbidden to directly add the phase of each channel to the phase of the object using algebra.

[0051] 4.3 Update Individual and Population Optimum: Compare and update the historical best position pbest for each particle. i And the global optimal position of the entire group, gbest.

[0052] 4.4 Update Particle State: Update the individual historical best position (pbest) and the group global best position (gbest) for each particle. Update the particle velocity and position according to the standard PSO formula, and reflect out-of-bounds positions.

[0053] 4.5 Application of Adaptive Strategy: Every 10 iterations, update the inertia weights according to the following formula.

[0054] ; Meanwhile, the diversity of the population (such as the average distance between particles) is monitored. If premature convergence is detected (diversity is below the threshold and gbest has not improved for a long time), some particles with poor fitness are randomly reset in order to escape the local optimum.

[0055] 4.6 Iterative Loop: Repeat steps 4.2 to 4.5 until the maximum number of iterations is reached. T max or global optimal fitness J (gbest) has decreased by less than the threshold for 20 consecutive generations. ε =1×10 -5 .

[0056] Step 5, Chain-based Collaborative Optimization Mechanism: Employing a collaborative optimization strategy of multi-chain parallelism and intra-chain iteration. 5.1 Initialize multiple independent optimization chains, with each chain generating random initial parameter values. In this embodiment, three independent chains are generated, and each chain is set to three optimization iterations. The initial value is set randomly within the boundary conditions during the first iteration. 5.2 Each chain employs an iterative algorithm, such as an improved particle swarm optimization (PSO) or a genetic algorithm (GA), to iteratively optimize and retain the optimal solution; 5.3 A merit-based migration mechanism is used between chains to exchange superior individuals, preventing premature convergence. In this example, the best individual in each chain's population is marked and replaced with the individual with the largest residual in the adjacent chain.

[0057] 5.4 An inheritance strategy is adopted within the chain, using the previous optimization result as the initial value for the next iteration to accelerate convergence.

[0058] Step 6: After optimization, output the globally optimal parameters. θ *

[0059] 6.1 Plotting the overall open-loop phase curve: using θ *Calculate the bandwidth φ total ( ω ), generating as Figure 4 The comparison chart shown illustrates the application... θ Afterwards (solid line), the total open-loop phase of the system closely surrounds the -90° target line (dashed line) within the core frequency band of 0.1-2.5Hz, and the vast majority of it falls within the ±12° engineering tolerance band (shaded area), which is significantly better than the chaotic phase characteristics before tuning (dotted line).

[0060] 6.2 Generating a vector composite graph: at a specific frequency point f At frequencies of 0.02, 0.2, 0.5, 1.0, and 2.2 Hz, the following are generated: Figure 5 The diagram shows a complex plane vector image. The blue arrows in the diagram originate from point O. V L Red arrow V I Purple arrow V HThese represent the complex outputs of the low-frequency, mid-frequency, and high-frequency channels, respectively. This is achieved through vector addition (by...). V I The starting point is placed V L The end point V H The starting point is placed V I (The endpoint), resulting in a thick black arrow pointing from the origin O to the endpoint C. V s, i.e. This diagram visually illustrates that... V The phase of s ( The phase values ​​of each phasor are determined entirely by vector geometry and are independent of the arithmetic sum of the phases of each arrow (the text in the diagram marks the phase values ​​of each phasor), which further clarifies the working principle of PSS4B.

[0061] Step 6: Establish a test system in the power system dynamic simulation software PSCAD, including a detailed model of the hydro-generator, excitation system, and the application of... θ *The PSS4B model with specific parameters. First, the PSS is disconnected, and a small step disturbance of ±5% of the terminal voltage is applied between 66s and 75s. Then, the PSS 4B circuit is re-engaged, and the small step disturbance of ±5% of the terminal voltage is repeated once. The active power simulation results of the unit are as follows: Figure 6 As shown, the curves without PSS (before 75 seconds) and with optimized parameters were compared. θ The dynamic response of generator active power under the condition of PSS4B (curve after 75s). Figure 7 The output value monitoring of the PSS4B stage during this process is demonstrated. It is evident that the damping effect of the tuning parameters is significant, proving the effectiveness of the tuning parameters.

[0062] Reference Figure 8 The system of the present invention adopts a layered architecture design, including: Presentation layer: Provides a graphical user interface, including interactive panels for project configuration, data import, parameter settings, optimization control, and result visualization.

[0063] Application service layer: Includes vector composition computation service unit (721), which is specifically responsible for execution Figure 3 The correct calculation path on the right; the optimization engine service unit (722), which is responsible for scheduling the optimization algorithm; and the simulation interface service unit (723), which is responsible for calling external simulation tools or internal simplified models for time-domain verification.

[0064] Data Access Layer: Responsible for managing the case database, model parameter library, object property database, and report template library.

[0065] Output layer: The final output includes an optimized parameter set file and a formatted tuning report. Important process outputs include... Figure 9 and Figure 10 The amplitude-frequency response and phase-frequency response diagrams of the PSS4B after parameter optimization are shown, which can be used to determine whether the tuning effect meets the requirements of the procedure.

[0066] In this embodiment, the final preferred parameter set θ *for:

[0067] In summary, this invention provides a parameter tuning method and system for PSS based on complex domain vector synthesis. By establishing a rigorous mathematical model for PSS4B vector synthesis, a correct phase error evaluation system is constructed. Furthermore, intelligent algorithms are used to achieve adaptive parameter tuning. With comprehensive verification and visualization analysis, a complete, reliable, and efficient PSS4B-specific parameter tuning solution is formed, which has significant engineering practical value.

[0068] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Anyone skilled in the art can readily implement the present invention according to the description and above. Any modifications, alterations, or equivalent variations made using the technical content disclosed above are equivalent embodiments of the present invention. Furthermore, any modifications, alterations, or variations made to the above embodiments based on the essential technology of the present invention are still within the protection scope of the present invention.

Claims

1. A parameter tuning method for a PSS based on complex field vector synthesis, characterized in that, Includes the following steps: S1. Obtain the open-loop frequency response of the excitation generator controlled object from the PSS output point to the generator electrical torque point forward channel, and extract the phase lag characteristic curve of the channel. S2. Based on the complex domain vector synthesis model and phase lag characteristic curve, construct a complex response calculation formula that includes the series open-loop transfer function of the PSS and the controlled object, define the total open-loop phase, set the parameter vector containing all adjustable parameters of the PSS and determine the parameter feasible region, set the target compensation phase, define the weighted comprehensive phase error objective function at the discrete frequency points of the target oscillation frequency band, and divide the frequency bands of the PSS and set the boundary values ​​of the time constant of each channel. Among them, the complex domain vector synthesis model of PSS is constructed, and the output of the complex domain vector synthesis model is the sum of complex response vectors of multi-band channels; S3. Using the weighted integrated phase error objective function as the fitness function, a global optimization algorithm is used to search the parameter space within the parameter feasible region to find the parameter vector that minimizes the fitness function. S4. The parameter search process of the global optimization algorithm is optimized by adopting a chain-based collaborative optimization mechanism of multi-chain parallelism and intra-chain iteration to obtain the optimal parameters; S5. Perform multi-dimensional verification and vector synthesis visualization analysis on the optimal parameter set to complete the parameter tuning of the power system stabilizer.

2. The parameter tuning method for PSS based on complex field vector synthesis according to claim 1, characterized in that, In S1, the open-loop frequency response is obtained by frequency domain scanning test, and the extracted phase hysteresis characteristic curve covers the target oscillation frequency band of the preset frequency.

3. The parameter tuning method for PSS based on complex field vector synthesis according to claim 1, characterized in that, In S2, the power system stabilizer is a PSS4B type power system stabilizer. For a given angular frequency, the complex frequency response calculation formula of the PSS4B type power system stabilizer is as follows: ； in, For the gain of each frequency band, , , , , The complex response is the product of the transfer functions of each branch. The imaginary unit, ω is the angular frequency.

4. The parameter tuning method for PSS based on complex field vector synthesis according to claim 1, characterized in that, In S2, the complex response of the series open-loop transfer function of PSS4B and the controlled object at the specified frequency is calculated as follows: ； The total open-loop phase is: ； in, For PSS4B in Complex response at the point, This is a parameter vector containing all adjustable parameters of PSS4B. This is the complex factor corresponding to the phase lag of the controlled object. To calculate the argument of a complex number, This is the phase lag characteristic curve of the controlled object of the excitation generator.

5. The parameter tuning method for PSS based on complex field vector synthesis according to claim 4, characterized in that, In S2, the objective function for the weighted synthesis phase error is defined as follows: ； in, The objective function for weighted synthesis phase error is... This is a vector containing all the PSS4B parameters to be optimized. These are the weighting coefficients for each frequency point, used to emphasize the mid-frequency band that is crucial to system stability; The calculation requires a complex field vector composition model and a complex multiplication formula.

6. The parameter tuning method for PSS based on complex field vector synthesis according to claim 1, characterized in that, In S2, setting the parameter vector containing all adjustable parameters of the power system stabilizer specifically includes: Parameter vector θ Includes all adjustable parameters of PSS4B: ； Each parameter has a physical constraint range, forming the parameter feasible region Ω; θ The first row of the array contains parameters for the low-frequency channel: For low-frequency DC gain, The first row represents the low-frequency time constant; the second row represents the mid-frequency channel parameters; the third row represents the high-frequency channel parameters, defined as for the low-frequency channel; the fourth row represents the filter parameters in the PSS4B model. For the unit's moment of inertia, These are the parameters for the notch filter.

7. The parameter tuning method for PSS based on complex field vector synthesis according to claim 6, characterized in that, In S3, the global optimization algorithm employs an improved particle swarm optimization algorithm, and the optimization problem solved within the parameter feasible region is: ； Among them, the improved particle swarm optimization algorithm balances global exploration and local exploitation capabilities by introducing adaptive inertia weights, a perturbation mechanism based on population diversity, and an elite retention strategy.

8. The parameter tuning method for PSS based on complex field vector synthesis according to claim 1, characterized in that, In S4, the chain-based collaborative optimization mechanism with multi-chain parallelism and intra-chain iteration includes: Multiple independent optimization chains are initialized, and initial parameter values ​​are randomly generated for each chain. An iterative algorithm is used within each chain to iteratively optimize and retain the optimal solution. Elite migration mechanisms are used between chains to exchange superior individuals to avoid premature convergence. An inheritance strategy is used within chains to use the previous optimization result as the initial value for the next iteration, thereby accelerating convergence.

9. The parameter tuning method for PSS based on complex field vector synthesis according to claim 1, characterized in that, In S5, the multi-dimensional verification and vector synthesis visualization analysis includes: Plot the frequency-phase curve of the excitation system after PSS4B correction to verify whether the deviation from the target compensation phase in the target frequency band is within the engineering allowable range. The process of plotting the output vectors of each frequency band on the complex plane at key frequency points and synthesizing the total output vector using vector addition is illustrated. In a nonlinear simulation environment that includes detailed generator, excitation system and load models, typical small disturbances or continuous oscillation disturbances are applied to verify the damping effect and dynamic performance of PSS4B with the optimal parameter set on power oscillations.

10. A parameter tuning system for a PSS based on complex field vector synthesis, used to implement the parameter tuning method for a PSS based on complex field vector synthesis as described in any one of claims 1-9, characterized in that, It includes an object characteristic interface module, a model configuration and calculation module, a parameter vector calculation module, a parameter optimization module, and a parameter tuning module, among which: The object characteristic interface module is used to: obtain the open-loop frequency response of the excitation generator controlled object from the PSS output point to the generator electrical torque point forward channel, and extract the phase lag characteristic curve of the channel; The model configuration and calculation module is used to: construct a complex response calculation formula containing the series open-loop transfer function of the PSS and the controlled object based on the complex domain vector synthesis model and the phase lag characteristic curve; define the total open-loop phase; set the parameter vector containing all adjustable parameters of the PSS and determine the parameter feasible region; set the target compensation phase; define the weighted comprehensive phase error objective function at discrete frequency points of the target oscillation frequency band; and divide the frequency bands of the PSS and set the boundary values ​​of the time constant of each channel. Among them, the complex domain vector synthesis model of PSS is constructed, and the output of the complex domain vector synthesis model is the sum of complex response vectors of multi-band channels; The parameter vector calculation module is used to: take the weighted comprehensive phase error objective function as the fitness function, perform a global optimization algorithm to search the parameter space within the parameter feasible region, and solve for the parameter vector that minimizes the fitness function; The parameter optimization module is used to optimize the parameter search process of the global optimization algorithm by using a chain-based collaborative optimization mechanism with multi-chain parallelism and intra-chain iteration to obtain the optimal parameters. The parameter tuning module is used to perform multi-dimensional verification and vector synthesis visualization analysis of the optimal parameter set, and to complete the parameter tuning of the power system stabilizer.

Images