A parameter setting method for a speed regulating system controller balancing damping characteristics and frequency modulation performance

Abstract

The present application relates to the technical field of power system stability control, and proposes a speed regulating system controller parameter setting method balancing damping characteristics and frequency modulation performance. The method establishes a frequency oscillation model of a hydroelectric generator system containing a proportional integral (PI) controller, calculates the damping torque contribution of an automatic generation control (AGC) link and a primary frequency regulation (PFR) link to the generator for the system dominant oscillation mode, and extracts the corresponding damping performance index. Based on the relationship between the damping performance index and a preset damping safety threshold, an adaptive weight mechanism is constructed to impose a higher penalty weight on the frequency regulation link with weaker damping performance. On this basis, a comprehensive objective function containing a frequency modulation performance index and a damping characteristic penalty term is constructed, and is optimized to obtain the PI controller parameters of the speed regulating system. The present application realizes closed-loop optimization of damping characteristic analysis and parameter setting, can effectively suppress ultra-low frequency oscillation while ensuring frequency modulation performance, and improves system operation stability.

Description

Technical Field

[0001] This invention relates to the field of power system automatic control and optimization technology, and in particular to a method for tuning controller parameters for a hydropower unit speed regulation system, specifically a method for tuning controller parameters of a speed regulation system that balances damping characteristics and frequency regulation performance. Background Technology

[0002] During the construction of a new power system primarily based on new energy sources, the large-scale integration of intermittent power sources such as wind and solar power has significantly reduced the equivalent rotational inertia of the power system, decreased the system damping level, and made frequency stability issues increasingly prominent. In actual power grid operation, ultra-low frequency oscillations with frequencies between 0.01Hz and 0.10Hz have gradually emerged. These oscillations typically manifest as continuous alternating fluctuations in system active power and frequency, which not only degrade power quality but may also induce generator shaft fatigue or even trigger protection devices, seriously threatening the safe and stable operation of the power system.

[0003] Against this backdrop, hydropower units, due to their rapid adjustment speed and strong response capabilities, are widely used in primary frequency regulation (PFR) and automatic generation control (AGC) of power grids. However, due to the non-minimum phase characteristics of the turbine system, such as the "water hammer effect," short-term power reversal can easily occur during rapid adjustment, potentially causing the speed control system to exhibit negative damping characteristics in the ultra-low frequency range. Under specific operating conditions, if the control parameters of the speed control system are not set appropriately, the dynamic coupling effect between different frequency control links will further amplify system oscillations, increasing the risk of ultra-low frequency oscillations.

[0004] To address the above problems, existing technologies mainly focus on the following two aspects: Firstly, there are methods for identifying frequency oscillation modes in power systems. These methods are typically based on Damping Torque Analysis (DTA) theory. By constructing a dynamic model of the power system, they analyze the contribution of different frequency regulation components to system damping, thereby identifying whether the current system oscillation is dominated by the AGC (Automatic Generation Control) component or the PFR (Power Frequency Regulating) component. While this technique can provide a basis for oscillation mechanism analysis, it primarily remains at the level of oscillation mode identification and does not further utilize the identification results for optimizing speed regulation system control parameters, making it difficult to form a closed-loop control mechanism.

[0005] Secondly, there are optimization methods for the control parameters of speed regulation systems. These methods typically construct a comprehensive objective function that includes primary frequency regulation response performance indicators and damping performance indicators, and then employ intelligent optimization algorithms to optimize the governor parameters to improve the system's frequency regulation performance and damping level. However, these methods are usually based on simplified or open-loop models, failing to fully consider the dynamic coupling relationship between AGC and PFR control loops. Furthermore, they often use fixed weighting coefficients in the objective function construction process, making it impossible to adaptively adjust different frequency regulation loops according to the actual operating state and oscillation mode of the system.

[0006] Therefore, the aforementioned prior art has at least the following shortcomings: On the one hand, the oscillation mode identification method and the parameter optimization method are independent of each other and lack effective integration, which makes it impossible for the damping characteristic analysis results to directly guide the tuning of the speed regulation system control parameters, and makes it difficult to form a closed-loop technical system from oscillation mechanism analysis to control parameter optimization. On the other hand, existing parameter optimization methods do not fully incorporate key control links (such as PI regulation links) in the speed regulation system into the system modeling process. The established models are difficult to truly reflect the coupling characteristics between AGC and PFR in actual operation, which in turn affects the accuracy and engineering applicability of the optimization results. Furthermore, the objective function with fixed weights is difficult to dynamically adjust according to the changes in the dominant oscillation mode and damping characteristics of the system. Under complex operating conditions, it is easy for the optimization direction to deviate, making it difficult to simultaneously achieve both frequency modulation performance and ultra-low frequency oscillation suppression effect.

[0007] Therefore, there is an urgent need for a speed control system controller parameter tuning method that can combine damping characteristic analysis with speed control system parameter tuning and can adaptively adjust the optimization strategy according to the system oscillation characteristics, so as to improve the frequency regulation performance and system stability of hydropower units under complex operating conditions. Summary of the Invention

[0008] In view of this, the purpose of the present invention is to provide a method for tuning the controller parameters of a speed control system that balances damping characteristics and frequency modulation performance, so as to solve the problem that the tuning of speed control system parameters in the prior art fails to fully consider the coupling relationship between damping characteristics and frequency modulation performance, and it is difficult to take into account both the suppression effect of ultra-low frequency oscillation and the dynamic performance of frequency modulation.

[0009] To achieve the above objectives, the present invention provides the following technical solution: In one possible implementation, a method for tuning the controller parameters of a speed control system that balances damping characteristics and frequency modulation performance includes the following steps: S1. Establish a frequency oscillation model of the hydropower unit system. The model includes an automatic generation control (AGC) link, a primary frequency regulation (PFR) link, a speed regulation system, a prime mover and a generator. The integral link of the proportional-integral (PI) controller in the speed regulation system is introduced as a state variable into the system state-space equation. S2, Based on the system frequency oscillation model, calculate the characteristics of each oscillation mode of the system, and for the dominant oscillation mode, determine the damping torque contribution of the AGC link and PFR link to the generator, so as to obtain the corresponding AGC damping performance index and PFR damping performance index. S3. Based on the AGC damping performance index and the PFR damping performance index, construct a penalty term related to the damping characteristics, and based on the relationship between the damping performance index and the preset damping safety threshold, determine the adaptive weight corresponding to the penalty term, so that the penalty weight corresponding to the frequency modulation link with weaker damping performance is increased. S4. Construct a comprehensive objective function that includes the primary frequency regulation performance evaluation index and the penalty term, and solve the comprehensive objective function based on the adaptive weights to obtain the PI controller parameters of the speed regulation system.

[0010] In one possible implementation, in step S1, the state variables include at least the system frequency deviation, the prime mover mechanical power deviation, the prime mover opening deviation, and the PI controller integral state variable.

[0011] In one possible implementation, step S1 further includes approximate modeling of the AGC instruction execution delay to incorporate the delay element into the system state-space equations to construct an extended-order model.

[0012] In one possible implementation, the delay modeling is achieved using the Padé approximation method.

[0013] In one possible implementation, in step S2, the dominant oscillation mode is determined by solving the eigenvalues ​​through the system state-space equations.

[0014] In one possible implementation, in step S2, the damping torque contribution is calculated based on the damping torque analysis method through the transmission relationship from the control loop to the generator.

[0015] In one possible implementation, in step S3, the adaptive weight is dynamically adjusted according to the changes in the AGC damping performance index and the PFR damping performance index, so as to increase the weight ratio of the dominant negative damping frequency modulation link in the comprehensive objective function.

[0016] In one possible implementation, the process of determining the adaptive weights includes introducing basic weight parameters, mode-dominant penalty amplification parameters, and adjustment parameters to ensure computational stability.

[0017] In one possible implementation, in step S4, the comprehensive objective function simultaneously considers the primary frequency modulation dynamic performance index and the damping characteristic constraint.

[0018] In one possible implementation, a speed control system controller parameter tuning device includes: a modeling module for establishing a frequency oscillation model of a hydropower unit system including a PI controller; a damping analysis module for calculating the damping performance indicators of the AGC and PFR links for the dominant oscillation modes; a weight determination module for determining adaptive weights based on the damping performance indicators and a preset damping safety threshold; and a parameter solving module for constructing a comprehensive objective function and solving it to obtain the PI controller parameters of the speed control system.

[0019] Based on the above technical solution, the present invention provides a method for tuning controller parameters of a speed regulation system that balances damping characteristics and frequency regulation performance. This method establishes a frequency oscillation model of a hydropower unit system including a PI controller, incorporating the speed regulation system control components into a unified modeling framework. Based on this, for the dominant oscillation mode of the system, the damping torque contribution of the Automatic Generation Control (AGC) component and the Primary Frequency Regulation (PFR) component to the generator are extracted, obtaining damping performance indicators that characterize the damping characteristics of each frequency regulation component. Furthermore, based on the relationship between the damping performance indicators and a preset damping safety threshold, an adaptive weighting mechanism is constructed, allowing frequency regulation components with weaker damping performance or exhibiting a negative damping trend to receive higher weights in the comprehensive objective function, thereby achieving dynamic penalty and targeted adjustment of the speed regulation system control parameters. Finally, by solving the comprehensive objective function that includes the primary frequency regulation performance evaluation index and the damping characteristic penalty term, the optimal PI controller parameters that balance frequency regulation dynamic performance and damping suppression effect are obtained.

[0020] Compared to existing technologies that only identify oscillation modes or optimize parameters based on fixed weights, this invention directly incorporates the damping characteristic analysis results into the parameter tuning process, constructing a closed-loop optimization mechanism consisting of "oscillation characteristic analysis - damping performance evaluation - adaptive weight adjustment - parameter optimization solution". This effectively overcomes the technical defects of existing technologies, such as incomplete speed control system modeling, insufficient consideration of coupling relationships between frequency regulation links, and lack of adaptability in the optimization process.

[0021] Furthermore, since the present invention introduces the dynamic characteristics of the PI controller integral link and the frequency modulation control link in the system modeling process, and reflects the coupling relationship between AGC and PFR through the extended state space model, the obtained damping performance index can more accurately characterize the influence of each control link on the system oscillation characteristics under actual operating conditions, thereby improving the engineering applicability and accuracy of the parameter tuning results.

[0022] Furthermore, by introducing an adaptive weighting mechanism based on a damping safety threshold, this invention can differentiate the frequency modulation links according to the current oscillation state of the system. Even when the dominant oscillation mode changes or the operating conditions fluctuate, it can still maintain the effective suppression capability of key control links, thereby significantly improving the robustness and stability of the system under complex operating conditions.

[0023] In summary, this invention not only effectively improves the damping level of the system in the ultra-low frequency band and suppresses frequency oscillation while ensuring the primary frequency regulation response speed and regulation accuracy, but also enables adaptive optimization and global coordination of the speed regulation system control parameters, thereby improving the safety, stability and reliability of hydropower units and power system operation, and has good engineering application value. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the damping torque transmission used in the automatic generation control (AGC) stage of this invention. Figure 2 This is a schematic diagram of the speed control system controller parameter optimization process in an embodiment of the present invention; Figure 3 This is a schematic diagram of the convergence curve of the speed regulation system control parameter optimization process in an embodiment of the present invention; Figure 4 This is a schematic diagram comparing the simulation curves of the system response before and after optimization in an embodiment of the present invention. Detailed Implementation

[0025] To enable those skilled in the art to more clearly understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the technical concept, technical means, and beneficial effects of the present invention, and are not intended to limit the scope of protection of the present invention. Without departing from the spirit and essence of the present invention, those skilled in the art can make various modifications, substitutions, and improvements based on the content disclosed in the present invention.

[0026] This embodiment describes a method for tuning the controller parameters of a speed control system that balances damping characteristics and frequency modulation performance.

[0027] To clearly illustrate the implementation process of this method, the following will be presented in the logical order of "establishing the system frequency oscillation model—calculating the system oscillation mode and damping torque contribution—constructing the penalty term and adaptive weights—constructing the comprehensive objective function and solving the parameter optimization problem," and will be combined with... Figures 1 to 4 The document also includes relevant formulas and tables to explain the implementation process, key parameters, and simulation verification results for each step.

[0028] I. General Description This embodiment provides a method for tuning the controller parameters of a speed control system that balances damping characteristics and frequency regulation performance. Based on the damping torque analysis theory, this method models and analyzes the dynamic characteristics of the hydropower unit speed control system under the action of Automatic Generation Control (AGC) and Primary Frequency Regulation (PFR) links, thereby achieving optimized tuning of the speed control system control parameters.

[0029] In power systems, with the increasing proportion of new energy sources and the decrease in system inertia, the problem of ultra-low frequency oscillations is becoming increasingly prominent. Traditional speed control system parameter tuning methods struggle to simultaneously consider frequency regulation performance and damping characteristics, easily triggering or amplifying low-frequency oscillations during rapid adjustments. This embodiment introduces a damping torque analysis method to quantify the damping contribution of different frequency control components under the dominant oscillation mode. The analysis results are directly used in the controller parameter optimization process, achieving coordinated adjustment of system damping characteristics and frequency regulation performance, thereby effectively suppressing ultra-low frequency oscillations and improving system operational stability.

[0030] The overall flow of the method described in this embodiment is as follows: Figure 2 As shown, the main components include: establishing a frequency oscillation model of a hydropower unit system containing a proportional-integral (PI) controller, extracting the damping performance indicators of the AGC and PFR links, constructing an adaptive weighting mechanism based on damping characteristics, and on this basis, constructing a comprehensive objective function for optimization and solution to obtain the optimal parameters of the PI controller of the speed regulation system.

[0031] II. Step S1: Establish a system frequency oscillation model containing a PI controller This embodiment first establishes a frequency oscillation model of a hydropower unit system containing a proportional-integral (PI) controller. The system frequency oscillation model includes a frequency regulation component, a speed regulation system, a prime mover, and a generator. Figure 1 This diagram illustrates the damping torque transmission, primarily focusing on the analysis of the AGC control loop. By introducing an integral element of the PI controller into the speed regulation system and considering the AGC execution delay, a system state-space model reflecting the dynamic coupling relationship between AGC and PFR can be constructed. This provides a foundation for subsequent feedback signal derivation, damping performance index extraction, and parameter optimization.

[0032] (a) Determine the input and output of the PI controller In this embodiment, the combined error signal (e(t)) at the confluence point is as shown in formula (1).

[0033] (1); To construct the state equation, the state variable of the integral element of the PI controller is introduced, and its definition is shown in formula (2).

[0034] (2); The control signal output by the PI controller is shown in formula (3).

[0035] (3); Based on the above definition, the proportional and integral control effects of the PI controller can be incorporated into the system dynamic model to more accurately characterize the influence of the speed regulation system control element on the system frequency oscillation characteristics.

[0036] (ii) Define the system state vector After introducing the integral state variable of the PI controller, the system state vector of the PI controller of the speed regulation system is extended to four dimensions, and its expression is shown in formula (4).

[0037] (4); In this state vector, each state variable represents the system frequency deviation, the prime mover mechanical power deviation, the prime mover opening deviation, and the PI controller integral state variable, respectively. By uniformly defining these state variables, a foundation can be provided for establishing the system state-space equations.

[0038] (III) Generator Component Equations According to the rotor motion equation, the dynamic relationship of the generator components is shown in formula (5).

[0039] (5); By rearranging formula (5), we can obtain the first state equation, as shown in formula (6).

[0040] (6); The first state equation is used to describe the dynamic relationship between the system frequency deviation and the mechanical power deviation.

[0041] (iv) Equations of the governor actuator after introducing PI According to the equation of the speed governor's execution link, its expression is shown in formula (7).

[0042] (7); Substituting the PI controller output signal into formula (7) and rearranging it, we can obtain the second state equation, as shown in formula (8).

[0043] (8); The second state equation describes the adjustment process of the governor actuator to the change in the prime mover opening and reflects the influence of the PI controller parameters on the dynamic response of the speed control system.

[0044] (V) Equations of the turbine components Based on the non-minimum phase transfer function of the water turbine, it is transformed into a differential equation, the expression of which is shown in formula (9).

[0045] (9); Substituting the aforementioned derivation results into formula (9) and expanding and merging them, we can obtain the third state equation, as shown in formula (10).

[0046] (10); The third state equation is used to describe the dynamic characteristics of the turbine under the influence of factors such as the "water hammer effect", thereby improving the model's accuracy in representing the actual operation of the hydropower unit.

[0047] (vi) Equation of the integral element of the PI controller According to the definition of the integral state variable, the fourth state equation can be obtained by taking its derivative, as shown in formula (11).

[0048] (11); Thus far, four state equations have been obtained, including system frequency deviation, prime mover mechanical power deviation, prime mover opening deviation, and PI controller integral state variables.

[0049] (vii) Complete matrix form The above derivation results are then presented in a standard state-space expression. The corrected matrix form is shown in formula (12).

[0050] (12); The state-space expression shown in formula (12) can be used to integrate the frequency regulation link, speed regulation system, prime mover and generator into the same analysis framework so that subsequent system oscillation mode analysis can be performed.

[0051] (viii) Modeling of AGC execution delay In actual grid operation, the unit execution delay of AGC commands significantly affects the dominant oscillation mode of the power system. The expression describing this delay in the Laplace domain is shown in equation (13).

[0052] (13); Since this form is not conducive to the analysis of system damping characteristics, the Padé approximation method is used to make it equivalent to a finite-order rational polynomial model, and its third-order expansion is shown in formula (14).

[0053] (14); By approximating the delay term, the delay term can be incorporated into the state-space model for unified analysis while preserving the main dynamic characteristics of the system.

[0054] (ix) Constructing a complete 8th-order state matrix Substituting the third-order Padé approximation equation shown in formula (14) into the original state equation, we can obtain the complete 8th-order state matrix, as shown in formula (15).

[0055] (15); Thus, a frequency oscillation model of a hydropower unit system, including the integral element of the PI controller and the execution delay characteristics of AGC, has been established. This model can relatively completely reflect the dynamic coupling relationship between the AGC, PFR, speed control system, prime mover, and generator, providing a modeling foundation for subsequent steps such as feedback signal derivation, damping torque calculation, damping performance index extraction, and comprehensive objective function construction.

[0056] III. Step S2: Calculate the characteristics of each oscillation mode of the system, and determine the damping torque contribution of the AGC and PFR components to the generator. In this embodiment, after completing the system frequency oscillation model construction, the system oscillation mode characteristics are first solved based on the system state-space model established in step S1, and the oscillation mode with the largest real part or the weakest damping is selected as the dominant oscillation mode of the system. Furthermore, in order to analyze the influence of the automatic generation control (AGC) link and the primary frequency regulation (PFR) link on the system damping characteristics, the AGC control signal and its feedback path are derived and reconstructed, and the damping torque contribution of the AGC link and the PFR link to the generator is calculated based on the damping torque analysis method to obtain the corresponding AGC damping performance index and PFR damping performance index.

[0057] (a) Feedback signal expression The feedback signal can be expressed as shown in formula (16).

[0058] (16); The feedback signal is used to characterize the output response characteristics of the AGC control action in the system and is an important basis for subsequent damping torque analysis. These are the AGC signal reconstruction coefficients.

[0059] (II) Expression of AGC control signals The AGC control signal can be expressed as shown in formula (17).

[0060] (17); Furthermore, the transmission relationship of AGC control signals can be expressed as shown in formula (18).

[0061] (18); Formula (18) is the transfer function expression of the AGC controller, which describes the dynamic relationship between the AGC control signal and the system error signal.

[0062] (III) State variable expansion expression Based on the state-space model established in step S1, the AGC control signal can be further represented as a function of the system state variables.

[0063] The expression for the PI integral state variable is shown in formula (19); (19); The expression for the state variable of the prime mover opening deviation is shown in formula (20); (20); The expression for the state variable of the mechanical power deviation of the prime mover is shown in formula (21).

[0064] (twenty one); The above state variable expressions can be used to uniformly transform AGC control signals into a form directly related to system state variables, thus facilitating subsequent unified analysis.

[0065] (iv) Construction of output equations To represent the AGC feedback signal as a function of the system state variables, its output equation is constructed. The output equation is of fourth order, and its expression is shown in formula (22).

[0066] (twenty two); In formula (22), the feedback signal is composed of a linear combination of the system's state variables, where C1, C2, C3, C4, and d are the coefficients of the AGC output variables after reconstruction.

[0067] The above output equations can realize the mapping relationship between AGC feedback signals and system state variables.

[0068] (v) Derivation of the feedback signal reconstruction function Substituting equations (22) to (16) into the feedback signal expression, and combining them with the transfer function of the AGC controller for simplification and reorganization, we can obtain the reconstruction function of the feedback signal, the expression of which is shown in equation (23).

[0069] (twenty three); The reconstruction function is used to characterize the dynamic mapping relationship of the AGC control signal in the system state space and is an important input for subsequent damping torque calculation.

[0070] (vi) Explanation of Function Through the above-mentioned feedback signal derivation and reconstruction process, the AGC control link was transformed from the original control signal form into an expression form directly related to the system state variables, so that the AGC control action can be embedded into the system dynamic model for unified analysis.

[0071] Meanwhile, the constructed feedback signal reconstruction function provides the necessary mathematical basis for subsequent calculation of the damping contribution of the AGC and PFR links to the system oscillation modes based on the damping torque analysis method.

[0072] In this embodiment, after completing the derivation and reconstruction of the feedback signal, the damping contribution of the automatic generation control (AGC) link and the primary frequency regulation (PFR) link in the system oscillation process is quantitatively calculated based on the damping torque analysis method, thereby extracting damping performance indicators that can characterize the damping characteristics of each frequency regulation link.

[0073] (I) Calculation of damping torque in AGC process Substituting the feedback signal reconstruction function obtained in step S2 into the damping torque calculation model, the damping torque provided by the AGC control loop to the (j)th generator under the (i)th oscillation mode of the system can be calculated, and its expression is shown in formula (24).

[0074] (twenty four); The damping torque is characterized by the transmission relationship between the AGC control signal and the generator, and is used to describe the ability of the AGC control action to suppress system oscillations.

[0075] The corresponding transfer function expression of the AGC control signal to the generator is shown in formula (25).

[0076] (25); (II) Calculation of damping torque of PFR link Using the same method as the AGC link, the primary frequency regulation PFR control link is analyzed, and the damping torque provided by the PFR link to the (j)th generator under the (i)th oscillation mode can be obtained. Its expression is shown in formula (26).

[0077] (26); The PFR damping torque is used to characterize the damping contribution of the primary frequency modulation control element during system oscillation.

[0078] (III) Definition of Damping Performance Indicators In order to uniformly evaluate the impact of different frequency modulation links on the system oscillation characteristics, in this embodiment, damping performance indicators are defined for the AGC link and the PFR link respectively, and their expressions are shown in formula (27).

[0079] (27); in, , respectively representing the automatic generation control link and the primary frequency regulation link.

[0080] (iv) Selection of dominant oscillation mode In the actual calculation process, by solving the eigenvalues ​​of the system state-space model established in step S1, the oscillation modes of the system are obtained, and the oscillation mode with the largest real part or the weakest damping is selected as the dominant oscillation mode of the system.

[0081] Under the dominant oscillation mode, the damping torque of the AGC link and the PFR link are calculated based on formula (24) and formula (26) respectively, and the corresponding damping performance index is obtained by combining formula (27).

[0082] (V) Explanation of Functions Through the above process of calculating damping torque and extracting damping performance indicators, a quantitative analysis of the damping effect of different frequency modulation control links in system oscillation is realized, so that the influence of AGC and PFR links on system stability can be compared and evaluated in a unified index form.

[0083] The damping performance index not only reflects the ability of each frequency regulation element to suppress oscillations, but also serves as an important basis for the subsequent construction of an adaptive weighting mechanism and a comprehensive objective function, thus providing key support for the optimization and tuning of the speed regulation system controller parameters.

[0084] IV. Step S3: Construct a penalty term based on the AGC damping performance index and the PFR damping performance index, and determine the adaptive weights. In this embodiment, after obtaining the damping performance indices of the AGC and PFR stages, in order to reflect the degree of deviation of the damping performance of different frequency modulation stages from the preset damping safety threshold, penalty terms related to the damping characteristics are constructed respectively; and based on the relationship between the AGC damping performance indices, the PFR damping performance indices and the preset damping safety threshold, the adaptive weight of the corresponding penalty terms is determined, so that the frequency modulation stage with weaker damping performance can obtain higher weight in subsequent optimization.

[0085] (a) Definition of Damping Safety Threshold To measure whether the system damping level meets the requirements for stable operation, a target damping safety threshold is preset. Under the current PI controller parameter X, the damping characteristics of the AGC link are defined as shown in formula (28).

[0086] (28); Wherein, the ΔD AGC This represents the amount by which the damping performance index of the corresponding frequency modulation stage is insufficient relative to the damping safety threshold, and is used as the basis for constructing the damping penalty term in the future.

[0087] (II) Construction of Adaptive Weight Mechanism Based on the AGC damping performance index and PFR damping performance index obtained in step S3, an adaptive weighting mechanism is constructed to dynamically adjust the influence of different frequency modulation links in the comprehensive objective function.

[0088] The calculation expression for the adaptive weight is shown in formula (29).

[0089] (29); Among them, W 30 W 40 The fundamental weight constants for PFR and AGC damping penalties; The penalty amplification factor is determined by the pattern. It should be a very small positive number to prevent the denominator from being zero.

[0090] The adaptive weights are related to the damping performance indicators of each frequency modulation stage, and the weights are dynamically adjusted by introducing basic weight parameters, mode-dominant penalty amplification parameters, and adjustment parameters to avoid the denominator being zero.

[0091] w2(X) and w3(X) represent the adaptive weights for the PFR and AGC stages, respectively, and their values ​​are based on the degree of damping insufficiency ΔD. AGC Dynamic adjustment.

[0092] Specifically: When the damping performance index of a certain frequency modulation link is lower than the damping safety threshold, the weight of the corresponding frequency modulation link is increased. When a certain frequency modulation element exhibits a weakly damped or negatively damped trend under the dominant oscillation mode, its weight is further increased; Based on the relative relationship between AGC and PFR damping performance indicators, the weights of the two are adaptively allocated.

[0093] (III) Construction of the comprehensive objective function Based on the adaptive weighting mechanism, a comprehensive objective function is constructed to uniformly describe the frequency regulation performance and damping characteristic constraints of the speed regulation system. Its expression is shown in formula (30).

[0094] (30); The integrated objective function includes: A comprehensive index for evaluating primary frequency regulation performance is used to characterize the dynamic response performance of the system. The damping characteristic penalty term of the AGC stage is used to constrain the impact of the AGC control stage on system oscillation. The damping characteristic penalty term of the PFR stage is used to constrain the influence of the primary frequency control stage on system oscillation.

[0095] The damping penalty terms of the AGC and PFR links are multiplied by their corresponding adaptive weights, which are used to adjust the influence of each frequency modulation link on the comprehensive objective function according to the degree of insufficient damping performance.

[0096] Where w1 is a pre-set fixed weight coefficient, used to characterize the basic weight of the primary frequency regulation performance evaluation index in the comprehensive objective function; w2(X) and w3(X) are adaptive weights that change with the current controller parameter X, and their values ​​are dynamically determined according to the damping performance state of the AGC and PFR links in formula (29). In addition, D AGC (X) and D PFR (X) represents the damping performance index of the corresponding frequency modulation stage. To explicitly incorporate the impact of insufficient damping performance on the optimization objective into the comprehensive objective function, a damping penalty can be further constructed based on the deviation between the damping performance index and the preset damping safety threshold. In other words, the damping-related terms in the comprehensive objective function are used to reflect the constraint strength corresponding to insufficient damping in the AGC and PFR stages, rather than simply repeating the damping performance index itself.

[0097] (iv) Optimization Objectives By constructing the above-mentioned comprehensive objective function, the system frequency regulation performance index and damping characteristic index are incorporated into the same optimization framework, thereby achieving multi-objective coordinated optimization.

[0098] In the subsequent parameter solution process, by minimizing the comprehensive objective function shown in formula (30), the PI controller parameters of the speed regulation system can meet the frequency regulation performance requirements while improving the system damping level, thereby effectively suppressing ultra-low frequency oscillations.

[0099] (V) Explanation of Functions By introducing an adaptive weighting mechanism based on damping characteristics, this embodiment can dynamically adjust the weight allocation of each part in the optimization objective according to the current oscillation state of the system and the damping contribution of different frequency modulation links, thus avoiding the problem of inconsistent optimization effects of the traditional fixed weight method under different operating conditions.

[0100] Meanwhile, this method realizes a closed-loop optimization process of "damping characteristic analysis - adaptive weight adjustment - parameter optimization solution", which enables the speed control system control parameters to be dynamically adjusted according to the actual operating state, thereby significantly improving the stability and robustness of the system under complex operating conditions.

[0101] V. Step S4: Construct a comprehensive objective function that includes primary frequency regulation performance evaluation indicators and penalty terms, and solve for the parameters. In this embodiment, after determining the penalty term and its adaptive weight related to the damping characteristics, a comprehensive objective function containing the primary frequency regulation performance evaluation index and the penalty term is constructed, and the comprehensive objective function is solved based on the adaptive weight to obtain the PI controller parameters of the speed regulation system.

[0102] (a) Optimizing variable definitions The proportional coefficient and integral coefficient of the PI controller of the speed regulation system are taken as variables to be optimized, and their expression is shown in formula (31).

[0103] (31); The optimization variables are used to describe the parameter space of the speed control system controller and serve as the search objects for subsequent optimization processes.

[0104] (II) Optimization Objectives Using the comprehensive objective function constructed in step S4 as the optimization objective, the controller parameters shown in formula (31) are adjusted to make the comprehensive objective function reach the optimal value, thereby achieving coordinated optimization of frequency modulation performance and damping characteristics.

[0105] (III) Selection of Optimization Algorithm In this embodiment, an optimization algorithm is used to solve the comprehensive objective function. The optimization algorithm iteratively updates the controller parameters, causing the objective function to gradually converge to the optimal solution.

[0106] In the specific implementation process, the following optimization parameters are set: The optimization variable dimension is set to 2; The population size is 20; The maximum number of iterations is 100.

[0107] By setting the parameters as described above, the stability and convergence speed of the optimization process can be improved while ensuring computational efficiency.

[0108] (iv) Parameter optimization process Combination Figure 2 The speed control system controller parameter optimization process shown includes the following steps: 1. Initialize the PI controller parameters; 2. Based on the current parameters, execute steps S1 to S4 sequentially to calculate the system state-space model, damping performance index, adaptive weights, and comprehensive objective function value; 3. Update the PI controller parameters according to the optimization algorithm; 4. Determine whether the convergence condition is met. If it is, output the optimal parameters; otherwise, return to step 2 to continue iterative calculation.

[0109] The above process enables the step-by-step optimization of the speed control system controller parameters.

[0110] (v) Explanation of convergence characteristics During the optimization process, the convergence process of the comprehensive objective function value as the number of iterations changes is as follows: Figure 3 As shown, with the increase of the number of iterations, the objective function value gradually decreases and tends to stabilize, indicating that the optimization method can effectively converge to the optimal solution.

[0111] (vi) Explanation of optimization results Through the above optimization process, the optimal parameter combination of the PI controller of the speed regulation system is obtained, so that the system can effectively improve the damping level and suppress ultra-low frequency oscillations while meeting the dynamic performance requirements of primary frequency regulation.

[0112] The optimization results can be directly applied to the tuning of control parameters of the hydropower unit speed regulation system, thereby improving the stability and reliability of the system under complex operating conditions.

[0113] VI. Simulation Verification To verify the effectiveness of the speed control system controller parameter tuning method described in this embodiment, a frequency oscillation analysis model of a hydropower unit was constructed in the MATLAB-R2024b / Simulink environment, and the method was verified by simulation.

[0114] (a) Setting simulation model parameters During the simulation, the main system parameters were set as shown in Table 1: Table 1. Main parameter values ​​of the frequency oscillation analysis model System parameters D <![CDATA[T J ]]> <![CDATA[T w ]]> R <![CDATA[T y ]]> τ β numerical values 1 8 0.2 0.15 0.1 6.5 2.5 The above parameters are used to construct the system state-space model in step S1 to reflect the dynamic characteristics of the hydropower unit under actual operating conditions.

[0115] (II) Oscillation Mode Analysis Based on the system state-space model established in step S1, its eigenvalues ​​are solved to obtain the system's oscillation modes, as shown in Table 2: Table 2 Oscillation Modes of Frequency Oscillation Analysis Model Oscillation mode numerical values <![CDATA[λ1]]> -13.4476 <![CDATA[λ2]]> -6.4231 <![CDATA[λ3]]> -0.5918+1.1486i <![CDATA[λ4]]> -0.5918-1.1486i <![CDATA[λ5]]> -1.1457 <![CDATA[λ6]]> 0.0407+0.7476i <![CDATA[λ7]]> 0.0407-0.7476i <![CDATA[λ8]]> -1.1474 As shown in Table 2, λ6 and λ7 are a pair of conjugate complex eigenvalues ​​with positive real parts, indicating that this mode exhibits an oscillatory amplification trend. Therefore, the oscillation mode corresponding to λ6 is selected as the dominant oscillation mode of the system for subsequent damping performance analysis.

[0116] (III) Calculation of Damping Performance Indicators After determining the dominant oscillation mode, based on steps S2 and S3, the damping torques of the AGC and PFR components are calculated, and the corresponding damping performance indices are extracted. The results are shown in Table 3. Table 3 Calculation results of damping performance indices under the dominant oscillation mode Control Link Dominant Oscillation Pattern Damping performance indicators AGC 0.0407+0.7476i 4.361 PFR 0.0407+0.7476i 3.422 As shown in Table 3, under the dominant oscillation mode, the contributions of the AGC and PFR components to the system damping differ, providing a basis for subsequent adaptive weight allocation.

[0117] (iv) Optimization results and convergence characteristics In step S4, the Newton-Raphson optimization algorithm is used to solve the comprehensive objective function. The convergence curve of the objective function during the optimization process is shown in the figure. Figure 3 As shown. By Figure 3 As can be seen, the objective function value gradually converges with the increase of the number of iterations, indicating that the optimization method has good convergence performance.

[0118] (V) Comparative Analysis of Optimization Effects To further verify the effectiveness of the method in this embodiment, a comparative analysis of the system response before and after optimization was performed, and the results are as follows: Figure 4 As shown.

[0119] Depend on Figure 4 As can be seen, compared to before optimization: The amplitude of system frequency oscillations has decreased significantly; The oscillation decay rate is significantly increased; The system stabilization time has been significantly shortened; This embodiment demonstrates that by introducing an adaptive weighting mechanism based on damping characteristics, the control parameters of the speed regulation system are optimized and tuned, which can effectively improve the system damping level, suppress ultra-low frequency oscillations, and maintain good frequency regulation dynamic performance.

[0120] (vi) Conclusion The simulation results show that the speed control system controller parameter tuning method proposed in this embodiment can achieve synergistic optimization of frequency regulation performance and damping characteristics under complex operating conditions, and has good engineering application value.

[0121] The above description is merely a preferred embodiment of the present invention, used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Those skilled in the art can make various modifications, equivalent substitutions, or improvements to the above embodiments without departing from the spirit and substance of the present invention, and all such modifications, substitutions, or improvements should fall within the scope of protection of the present invention.

[0122] It should be noted that the various technical features involved in this invention can be combined arbitrarily, provided they do not contradict each other. This invention does not exhaustively list the combinations of the various technical features; therefore, any equivalent combination based on the technical solution of this invention should be considered to fall within the protection scope of this invention.

[0123] Furthermore, the references to the accompanying drawings in the specification are only for assisting in understanding the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention; the structures, processes or parameter relationships shown in the drawings can be appropriately adjusted without affecting the technical effects of the present invention.

[0124] Without departing from the inventive concept, those skilled in the art can make various equivalent substitutions or modifications to the above embodiments, and all such substitutions or modifications should fall within the protection scope of this invention. For example: (1) In terms of system delay modeling, in addition to using the third-order Padé approximation to model the AGC instruction execution delay, the first-order, second-order or higher-order Padé approximation model can also be used, or other equivalent modeling methods that can characterize the dynamic characteristics of the delay can be used, as long as the delay element can be incorporated into the system state space model and used for subsequent oscillation mode analysis, damping performance evaluation and parameter optimization.

[0125] (2) Regarding the form of the speed control system controller, in addition to using a PI controller, a PID controller or other controller structures with integral regulation characteristics can also be used; accordingly, it is only necessary to introduce the key dynamic links in the controller as state variables into the system model, and carry out damping characteristic analysis and parameter tuning accordingly.

[0126] (3) In terms of constructing damping performance indicators, in addition to using the damping performance indicators of the AGC and PFR links obtained based on damping torque analysis, other evaluation quantities that can characterize the contribution of the frequency modulation control link to the damping of the dominant oscillation mode can also be used, as long as the influence of different frequency modulation links on the system damping characteristics can be distinguished and used as the basis for subsequent adaptive weight allocation and objective function construction.

[0127] (4) In terms of adaptive weight construction, in addition to using the weight allocation method based on the damping safety threshold, piecewise functions, proportional functions or exponential functions can also be used to construct weights so that the weights can be dynamically adjusted as the damping performance changes.

[0128] (5) In terms of constructing the comprehensive objective function, in addition to combining the primary frequency modulation performance evaluation index with the damping penalty term, dynamic performance indicators such as overshoot, settling time, and steady-state error can also be introduced as needed for multi-objective optimization.

[0129] (6) In terms of parameter solving, in addition to the Newton-Raphson optimization algorithm, particle swarm optimization, genetic algorithm, differential evolution algorithm or other optimization algorithms can also be used to solve the problem.

Claims

1. A method for tuning controller parameters of a speed control system that balances damping characteristics and frequency modulation performance, characterized in that, Includes the following steps: S1. Establish a frequency oscillation model of the hydropower unit system. The model includes an automatic generation control (AGC) link, a primary frequency regulation (PFR) link, a speed regulation system, a prime mover and a generator. The integral link of the proportional-integral (PI) controller in the speed regulation system is introduced as a state variable into the system state-space equation. S2, Based on the system frequency oscillation model, calculate the characteristics of each oscillation mode of the system, and for the dominant oscillation mode, determine the damping torque contribution of the AGC link and PFR link to the generator, so as to obtain the corresponding AGC damping performance index and PFR damping performance index. S3. Based on the AGC damping performance index and the PFR damping performance index, construct a penalty term related to the damping characteristics, and based on the relationship between the damping performance index and the preset damping safety threshold, determine the adaptive weight corresponding to the penalty term, so that the penalty weight corresponding to the frequency modulation link with weaker damping performance is increased. S4. Construct a comprehensive objective function that includes the primary frequency regulation performance evaluation index and the penalty term, and solve the comprehensive objective function based on the adaptive weights to obtain the PI controller parameters of the speed regulation system.

2. The method according to claim 1, characterized in that: In step S1, the state variables include at least the system frequency deviation, the prime mover mechanical power deviation, the prime mover opening deviation, and the PI controller integral state variables.

3. The method according to claim 1, characterized in that: Step S1 also includes approximate modeling of the AGC instruction execution delay, so as to introduce the delay element into the system state space equation to construct an extended-order model.

4. The method according to claim 3, characterized in that: The delay modeling is implemented using the Padé approximation method.

5. The method according to claim 1, characterized in that: In step S2, the dominant oscillation mode is determined by solving the eigenvalues ​​through the system state-space equations.

6. The method according to claim 1, characterized in that: In step S2, the damping torque contribution is calculated based on the damping torque analysis method through the transmission relationship from the control loop to the generator.

7. The method according to claim 1, characterized in that: In step S3, the adaptive weights are dynamically adjusted according to the changes in the AGC damping performance index and the PFR damping performance index, so as to increase the weight ratio of the dominant negative damping frequency modulation link in the comprehensive objective function.

8. The method according to claim 7, characterized in that: The process of determining the adaptive weights includes introducing basic weight parameters, mode-dominant penalty amplification parameters, and adjustment parameters to ensure computational stability.

9. The method according to claim 1, characterized in that: In step S4, the comprehensive objective function simultaneously considers the primary frequency modulation dynamic performance index and damping characteristic constraints.

10. A speed control system controller parameter tuning device, characterized in that, include: The modeling module is used to build a frequency oscillation model of a hydropower unit system that includes a PI controller. The damping analysis module is used to calculate the damping performance indices of the AGC and PFR components for the dominant oscillation modes. The weight determination module is used to determine adaptive weights based on damping performance indicators and preset damping safety thresholds. The parameter solving module is used to construct the comprehensive objective function and solve it to obtain the parameters of the PI controller of the speed control system.

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