An online identification method for equivalent rotational inertia of pumped storage unit based on active micro-perturbation and water-mechanical coupling model

Abstract

The application discloses an online identification method and system for equivalent rotational inertia of a pumped storage unit based on active micro-perturbation and a water-mechanical-electric coupling model and a storage medium. The method comprises the following steps: in a stable operation state of the unit, a micro-perturbation test signal is injected into an active power regulation control loop to stimulate a local transient response of the unit, and operation data in a disturbance period is synchronously collected; a water-mechanical-electric coupling dynamic model considering hydraulic transient characteristics is constructed; based on measured rotational speed data and model simulation rotational speed data, a double-target identification function group considering global response error and local transient extreme error is constructed; a multi-target optimization algorithm is used for iterative solution to obtain a Pareto optimal solution set, and a compromise equilibrium solution is selected through fuzzy membership evaluation, and equivalent rotational inertia under a current working condition is output. The application can reduce the influence of background disturbance on the identification result, and improve the accuracy and working condition adaptability of the online identification of the equivalent rotational inertia.

Description

Technical Field

[0001] This invention relates to the field of online identification of power system parameters and operation control technology of pumped storage, and particularly to an online identification method for the equivalent rotational inertia of pumped storage units based on an active micro-perturbation and hydro-mechanical coupling model. Background Technology

[0002] With the accelerated construction of a new power system dominated by new energy sources, large-scale grid connection of intermittent power sources such as wind power and photovoltaics, and the widespread replacement of traditional synchronous generator sets by power electronic equipment, the power grid exhibits the "dual high" characteristics of high proportion of new energy and high proportion of power electronic equipment. Traditional synchronous generator sets with high physical rotational inertia are gradually being phased out, and new energy units such as wind power and photovoltaics have almost no mechanical rotational inertia support, resulting in a continuous decrease in the overall equivalent rotational inertia of the power grid, a significant decline in the system's frequency support capability, and severe challenges to frequency regulation and stability control. Pumped storage units, as large-capacity, fast-response, and high-performance rotating reserve and energy storage power sources in the power grid, have rotor physical rotational inertia as an inherent structural parameter; while equivalent rotational inertia can comprehensively reflect the superimposed effects of hydraulic transients, electromechanical coupling, speed control, and multiple operating conditions, and is a core parameter for conducting power grid inertia assessment, frequency stability analysis, and operation control strategy formulation. Therefore, real-time and accurate acquisition of the equivalent rotational inertia of pumped storage units under different operating conditions such as power generation and pumping has become an urgent engineering requirement for the safe and stable operation of the power grid.

[0003] Currently, the methods for obtaining the physical moment of inertia of generating units (including synchronous generator units and pumped storage units) are mainly divided into three categories: offline physical measurement, grid-level macroscopic estimation, and passive small disturbance identification. All of these methods have significant limitations in the application of pumped storage units. 1. Offline physical measurements rely on shutdown and disconnection, and cannot be obtained online in real time. Traditional rotational inertia testing requires the unit to enter power generation or pumping phase-shifting operation, performing a shutdown and disconnection operation. It then utilizes the transient process of electromagnetic power returning to zero after the circuit breaker is opened to infer the inertia parameters from the rate of change of rotational speed. This method necessitates interrupting normal grid-connected operation and cannot be implemented under continuous operation conditions such as power generation or pumping. Furthermore, the calculation typically simplifies the resistance torque to a constant value, neglecting the dynamic coupling characteristics of the turbine, water circuit, and governor, making it difficult to reflect the unit's true equivalent inertia.

[0004] II. Grid-level macroscopic estimation focuses on the total system inertia and cannot be accurate down to the individual pumped-storage unit. Methods based on large disturbances, such as the generator tripping method, power loss method, or unit parameter accumulation method, are mostly used for assessing the overall inertia level of regional power grids. These methods rely on grid faults or large-power disturbances, and the models are highly simplified. They do not consider the unique characteristics of pumped storage units, such as the four-quadrant operation of pump-turbines, hydraulic transients in the water intake pipeline, and strong coupling between water and electricity. They cannot separate the inertia parameters of individual units, nor can they reflect the differences in inertia under different operating conditions and loads.

[0005] Third, passive small disturbance identification is easily submerged by background noise from the power grid, resulting in low identification accuracy. In a multi-machine strongly coupled power grid environment, relying solely on passive small disturbances such as daily load fluctuations for single-machine inertia identification results in weak unit response signals that are easily "overwhelmed" by the total system inertia and massive disturbances. At the same time, the closed-loop regulation of the speed governor and excitation system will generate strong interference, leading to an extremely low measurement signal-to-noise ratio. Parameter identification exhibits serious ill-conditioned inverse problems, with large errors and poor robustness, making it difficult to meet the requirements of engineering applications.

[0006] Furthermore, existing research on pumped storage unit modeling and parameter identification largely focuses on governor parameters, hydraulic parameters, or unit control strategy optimization, lacking an online identification scheme for equivalent rotational inertia that considers active excitation, high-precision hydro-turbine coupling models, and global optimization. Some methods fail to consider the multi-valued nature of the pump-turbine anti-S characteristic region, and do not incorporate elastic water hammer and full characteristic curves, resulting in significant dynamic deviations between the model and the actual unit. Some identification methods employ single-objective optimization, making it difficult to simultaneously consider the fitting accuracy of the global steady-state response and local transient extrema, thus affecting the accuracy of inertia identification.

[0007] In summary, existing technologies cannot achieve high-precision online identification of the equivalent rotational inertia of pumped storage units that consider the complex hydroelectric coupling characteristics without shutdown, disconnection, or grid impact. This makes it difficult to meet the needs of new power systems for real-time perception and precise control of unit parameters. Summary of the Invention

[0008] The purpose of this invention is to address the aforementioned problems in the existing technology by providing an online identification method for the equivalent rotational inertia of pumped storage units based on an active micro-perturbation and hydro-mechanical coupling model. This method involves actively injecting micro-perturbation signals to excite the transient response of the unit, constructing a hydro-mechanical coupling dynamic model, and building a dual-objective function set based on measured and simulated rotational speed data for multi-objective optimization. This achieves uninterrupted and high-precision online identification of the equivalent rotational inertia of the pumped storage unit, while also considering both steady-state operating conditions and transient dynamic characteristics, thus improving the adaptability and engineering practicality of the identification results.

[0009] The above-mentioned technical objectives of this invention are mainly achieved through the following technical solutions: A method for online identification of the equivalent rotational inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model, comprising the following steps: Under the stable grid-connected operation of the pumped storage unit, a micro-perturbation test signal is injected into the active power control loop of the unit to induce the unit to generate a local transient response, and the unit's operating data during the disturbance period is collected simultaneously. Based on the local transient operating characteristics formed by the excitation and the operating data, a hydraulic-mechanical coupling dynamic model considering the transient characteristics of hydraulics is constructed. Based on the measured rotational speed data and the simulated rotational speed data calculated by the hydro-mechanical coupling dynamic model, a dual-objective identification function set that takes into account both global steady-state response error and local transient extreme value error is constructed. The dual-objective identification function set is iteratively optimized to construct a Pareto optimal front solution set; The compromise equilibrium solution is selected from the Pareto optimal front solution set and output as the equivalent moment of inertia under the current operating condition, thereby realizing the online identification of the equivalent moment of inertia of the pumped storage unit.

[0010] This technical solution utilizes actively injected micro-perturbation test signals (with extremely small amplitudes, such as 1%~2%, and a mean of zero) to avoid substantial impact on the overall frequency security of the power grid and the mechanical lifespan of the generating unit. It also successfully induces a high signal-to-noise ratio transient response locally at the generator terminal, reducing the influence of background noise on the identification results. Furthermore, a hydro-electromechanical coupling dynamic model incorporating the elastic water hammer effect is established, ensuring that the identified equivalent inertia accurately reflects the actual support capacity of complex hydraulic dynamics for the power grid, thus improving the model's ability to characterize the dynamic processes of the generating unit. Moreover, by combining measured and simulated rotational speeds to construct a dual-objective function optimization model, the accuracy of equivalent rotational inertia identification can be improved, balancing steady-state and transient operating condition adaptability, and ensuring that the identification results closely match the actual operating state of the generating unit.

[0011] As a further improvement and supplement to the above technical solution, the present invention adopts the following technical measures: The micro-perturbation test signal is a pseudo-random binary sequence signal. The amplitude of the micro-perturbation test signal is 1% to 2% of the rated active power of the pumped storage unit, and the signal mean is zero. The operating data is collected synchronously using a phasor measurement device with a sampling frequency greater than or equal to 100Hz.

[0012] This technical solution, by limiting the type and amplitude range of the micro-perturbation signal and using a high-frequency phasor measurement device to collect data, helps to ensure the effectiveness of the excitation signal and the accuracy of the operational data acquisition, providing reliable raw data support for subsequent modeling and calculation.

[0013] As a preferred embodiment, the hydro-mechanical coupling dynamic model includes a governor sub-model, a pressurized water system sub-model, a hydraulic power sub-model, and a synchronous generator sub-model. The speed governor sub-model receives micro-perturbation test signals and unit speed feedback signals, and outputs control command signals; The control command signal is processed sequentially by the pressurized water system sub-model and the hydraulic power sub-model to obtain the mechanical power or mechanical torque input to the synchronous generator sub-model. The synchronous generator sub-model calculates the simulated rotational speed data based on the mechanical power or mechanical torque. Based on the deviation between the simulated rotational speed data and the measured rotational speed data, the equivalent moment of inertia to be identified is iteratively optimized.

[0014] This technical solution constructs a multi-sub-model collaborative hydro-mechanical coupling dynamic model to form a closed loop of signal transmission and computational feedback. Based on the deviation correction mechanism, it reduces the gap between simulation and actual working conditions, thereby improving the overall model's dynamic simulation fit.

[0015] Preferably, the pressurized water system sub-model adopts an approximate elastic water hammer model to characterize the dynamic coupling relationship between the head deviation and flow deviation in the pressure pipeline, thereby depicting the transient hydraulic characteristics of the pipeline. Using an approximate elastic water hammer model to characterize the dynamic hydraulic correlation of the pipeline accurately reproduces the transient changes in head and flow in the water transmission pipeline, which helps ensure the realism of the hydraulic modeling.

[0016] As a preferred embodiment, the hydraulic dynamic sub-model adopts a full characteristic curve model equipped with an improved Suter transform; Based on the improved Suter transform, the original full characteristic curve of the unit is normalized and corrected to obtain a uniformly distributed dimensionless single-value characteristic curve. The hydraulic dynamic sub-model calculates the nonlinear dynamic parameters of the unit based on the single-value characteristic curve, and obtains the single-value characteristics of the unit under all operating conditions.

[0017] This technical solution eliminates the multi-valued defect of characteristic curves by improving the Suter transformation, and transforms them into dimensionless single-valued characteristic curves. This results in regular single-valued curves, which can stably complete the calculation of nonlinear parameters of the unit and meet the hydraulic characteristic calculation requirements under all operating conditions.

[0018] As a preferred embodiment, the synchronous generator sub-model adopts a third-order transient model; The dynamic relationship between the unit speed and the power angle is calculated and obtained based on the rotor motion equation in the third-order transient model. Based on the transient electropotential equation of the excitation system in the third-order transient model, the dynamic change relationship of the unit's electromagnetic power is calculated and obtained. Based on the dynamic relationship between the unit's rotational speed and power angle and the dynamic relationship between the unit's electromagnetic power, the dynamic coupling transient relationship of the unit's electromechanical energy is obtained.

[0019] This technical solution is based on the calculation rules of the rotor motion equation and excitation system transient electromotive force equation built into the third-order transient model. It extracts the transient relationship of electromechanical energy coupling, fully restores the dynamic process of electromechanical conversion of the unit, and consolidates the electromechanical theoretical foundation for the identification of rotational inertia.

[0020] Preferably, the dual-objective identification function set includes a first objective function and a second objective function; The first objective function is the root mean square error function of rotational speed, which is used to characterize the global steady-state fitting accuracy; The second objective function is the maximum absolute deviation function of rotational speed, which is used to characterize the ability to capture local transient extrema.

[0021] By using two differentiated objective functions, we can simultaneously consider both the global fitting effect and the ability to capture local extrema, which is conducive to a comprehensive evaluation of the identification ability and avoids the one-sidedness of identification caused by a single evaluation standard.

[0022] As a preferred option, the iterative optimization solution for the dual-target identification function set is as follows: A multi-objective particle swarm optimization algorithm is used to initialize the position and velocity of particles within the physical constraint interval of equivalent rotational inertia. The particles are sorted non-dominated based on the Pareto dominance relation. The diversity of the front solution set is maintained by combining the crowding distance. The algorithm is iterated and updated multiple times until convergence, and the Pareto optimal front solution set is obtained. The Pareto optimal frontier solution set is normalized and its satisfaction is evaluated using a fuzzy membership function to select the compromise equilibrium solution.

[0023] This technical solution relies on the multi-objective particle swarm optimization algorithm to constrain the optimization range, uses sorting and crowding to ensure the richness of the solution set, and combines fuzzy evaluation to screen the optimal solution, which helps to improve the comprehensive rationality and optimality of the identification results.

[0024] The technical solution of the second technical subject matter involved in this invention: An online identification system for the equivalent rotational inertia of a pumped-storage unit is provided for executing the aforementioned online identification method for the equivalent rotational inertia of a pumped-storage unit based on an active micro-perturbation and hydro-mechanical coupling model. The system includes: The signal injection and data acquisition module is used to inject micro-perturbation test signals into the active power control loop of the pumped storage unit under the stable grid-connected operation state, to excite the local transient response of the unit, and simultaneously acquire the active power and speed data of the unit during the disturbance period. The coupling model construction module is used to build a dynamic model of hydraulic-turbine coupling considering hydraulic transient characteristics based on the collected operational data, and to simulate the dynamic response characteristics of the unit in all dimensions. The objective function construction module is used to calculate the speed deviation information based on the collected measured speed data and the simulated speed data obtained from the model simulation, and to construct a dual-objective identification function set including global root mean square error and maximum absolute deviation. The multi-objective optimization solution module is used to iteratively optimize the dual-objective identification function set using a multi-objective optimization algorithm to obtain a converged Pareto optimal frontier solution set; The result filtering and output module is used to evaluate the satisfaction of the Pareto optimal front solution set through fuzzy membership functions, determine the compromise equilibrium solution, and output the equivalent moment of inertia under the current working condition.

[0025] The technical solution of the third technical subject matter involved in this invention: A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the aforementioned method for online identification of the equivalent moment of inertia of a pumped storage unit are implemented.

[0026] The beneficial effects of this invention are as follows: by injecting micro-perturbation signals to excite the transient response of the unit, a multi-sub-model coupled system is constructed to accurately restore the hydraulic and electromechanical dynamic characteristics; by adopting a dual objective function to take into account both steady-state and transient identification accuracy, and by combining a multi-objective optimization algorithm to select the optimal solution, the accuracy of equivalent moment of inertia identification and the adaptability to operating conditions are effectively improved, and online efficient identification can be achieved, which has good engineering applicability. Attached Figure Description

[0027] Figure 1 This invention relates to a logic flowchart of an online identification method for the equivalent inertia of pumped-storage units based on an active micro-perturbation and hydro-mechanical coupling model.

[0028] Figure 2 The equivalent moment of inertia optimization trajectory obtained through simulation software, as well as the time-series verification diagram of rotational speed ω and guide vane opening y, are shown. Detailed Implementation

[0029] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0030] Example 1: An online identification method for the equivalent rotational inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model, comprising the following steps: When the pumped-storage unit is in stable grid-connected operation, a micro-perturbation test signal is injected into the unit's active power control circuit. The active power control circuit includes a power setpoint circuit of the speed governor, a regulator circuit, or an active power control circuit of the speed governor. The micro-perturbation test signal is preferably a pseudo-random binary sequence signal with an amplitude of 1% to 2% of the unit's rated active power and a signal mean of zero. Simultaneously with the injection of the micro-perturbation test signal, a phasor measurement device installed at the unit terminal is used to synchronously collect the unit's active power and unit speed data during the disturbance period at a sampling frequency of not less than 100Hz. Based on the local transient operating characteristics formed by the excitation and the operating data, a hydraulic-mechanical coupling dynamic model considering the transient characteristics of hydraulics is constructed. Based on the measured rotational speed data and the simulated rotational speed data calculated by the hydro-mechanical coupling dynamic model, a dual-objective identification function set that takes into account both global steady-state response error and local transient extreme value error is constructed. The dual-objective identification function set is iteratively optimized to construct a Pareto optimal front solution set; The compromise equilibrium solution is selected from the Pareto optimal front solution set and output as the equivalent moment of inertia under the current operating condition, thereby realizing the online identification of the equivalent moment of inertia of the pumped storage unit.

[0031] Furthermore, the hydro-mechanical coupling dynamic model includes: a governor sub-model, a pressurized water system sub-model, a hydraulic power sub-model, and a synchronous generator sub-model; The speed governor sub-model receives micro-perturbation test signals and outputs control command signals; the control command signals are sequentially processed by the pressurized water system sub-model and the hydraulic power sub-model before being input into the synchronous generator sub-model; the synchronous generator sub-model processes the signals and outputs simulated speed data. The governor sub-model receives micro-perturbation test signals and unit speed feedback signals, and outputs control command signals. The control command signals are processed sequentially by the pressurized water system sub-model and the hydraulic power sub-model to obtain the mechanical power or mechanical torque input to the synchronous generator sub-model. The synchronous generator model calculates the simulated speed data based on the mechanical power or mechanical torque. An objective function is constructed based on the deviation between the simulated speed data and the measured speed data, and the parameters to be identified are updated through iterative optimization.

[0032] Furthermore, the pressurized water system sub-model adopts an approximate elastic water hammer model to characterize the dynamic coupling relationship between the head deviation and flow deviation in the pressure pipeline, thereby describing the hydraulic transient characteristics of the pipeline.

[0033] Furthermore, the hydraulic sub-model adopts a full characteristic curve model equipped with an improved Suter transform; Based on the improved Suter transform, the original full characteristic curve of the unit is normalized and corrected, and transformed into a dimensionless single-valued characteristic curve with uniform distribution and no multivalues. The hydraulic dynamic sub-model calculates the nonlinear dynamic parameters of the unit based on the single-value characteristic curve, and obtains the single-value characteristics of the unit under all operating conditions.

[0034] As a preferred embodiment, the synchronous generator sub-model adopts a third-order transient model; The dynamic relationship between the unit speed and the power angle is calculated and obtained based on the rotor motion equation in the third-order transient model. Based on the transient electropotential equation of the excitation system in the third-order transient model, the dynamic change relationship of the unit's electromagnetic power is calculated and obtained. Based on the dynamic relationship between the unit's rotational speed and power angle and the dynamic relationship between the unit's electromagnetic power, the dynamic coupling transient relationship of the unit's electromechanical energy is obtained.

[0035] Preferably, the dual-objective identification function set includes a first objective function and a second objective function; The first objective function is the root mean square error function of rotational speed, which is used to characterize the global steady-state fitting accuracy; The second objective function is the maximum absolute deviation function of rotational speed, which is used to characterize the ability to capture local transient extrema.

[0036] By using two differentiated objective functions, we can simultaneously consider both the global fitting effect and the ability to capture local extrema, which is conducive to a comprehensive evaluation of the identification ability and avoids the one-sidedness of identification caused by a single evaluation standard.

[0037] As a preferred option, the iterative optimization solution for the dual-target identification function set is as follows: A multi-objective particle swarm optimization algorithm is used to initialize the position and velocity of particles within the physical constraint interval of equivalent rotational inertia. The particles are sorted non-dominated based on the Pareto dominance relation. The diversity of the front solution set is maintained by combining the crowding distance. The algorithm is iterated and updated multiple times until convergence, and the Pareto optimal front solution set is obtained. The Pareto optimal frontier solution set is normalized and its satisfaction is evaluated using a fuzzy membership function to select the compromise equilibrium solution.

[0038] Next, each of the above steps will be explained in detail: Step 1, Active micro-perturbation signal injection and data acquisition: When the pumped storage unit is in a stable grid-connected operation state (including but not limited to power generation and pumping conditions), a micro-perturbation test signal is injected into the active power control circuit of the unit's speed governor through a micro-perturbation signal generator; the active power control circuit includes a power setpoint circuit, a regulator circuit, or an active power control circuit (hereinafter referred to as: test signal). This is done to ensure that a transient response with a sufficient signal-to-noise ratio is generated without affecting grid security or causing mechanical wear on the guide vanes of hydraulic power components (such as water turbines).

[0039] In practical applications, the preferred test signal is a pseudo-random binary sequence (PRBS) with a very small amplitude, set to 1% to 2% of the unit's rated active power, and with a signal mean of zero. Simultaneously with the injection of the test signal, a phasor measurement unit (PMU) installed at the generator terminal is used to synchronously acquire the generator terminal active power P during the disturbance period at a high sampling rate of no less than 100Hz. e and the actual speed of the unit oh means .

[0040] Step 2: Construct a dynamic model of hydraulic-mechanical coupling that takes into account the transient characteristics of hydraulics.

[0041] For the local transient process excited by the micro-perturbation test signal, the mechanical power of the unit is no longer a constant, but undergoes a complex evolution with the dynamics of the water flow and the action of the governor.

[0042] The measured active power P collected e Using the initial state variables of the system as input, a complete hydraulic-electrical coupling model is established, comprising four main components: speed governor, water circuit, hydraulic turbine, and electrical system. First, in the governor (such as a microcomputer regulator) and actuator (such as an electro-hydraulic follow-up system) stages: a micro-perturbation test signal u is injected, and the microcomputer regulator and electro-hydraulic follow-up system will respond, outputting the unit's guide vane opening command. The actuator's comprehensive transfer function (which is within the scope of existing technology) takes into account the inertial time constants of the main pressure regulating valve and the main servo valve, outputting the relative value y of the guide vane opening deviation.

[0043] Secondly, regarding the pressurized water system: considering the long water intake pipeline of the pumped storage power station, and the significant impact of the elasticity of the water body and pipe wall on the transient process, this embodiment uses an approximate elastic water hammer model to characterize the dynamic transmission relationship between pipeline water pressure and flow rate: (1) In the formula, G h ( s () is the head-flow transfer function. h This represents the relative value of the head deviation. q This is the relative value of the flow deviation; Tw The inertial time constant of the water flow; T r Water and water interact and grow together; s For the Laplace operator.

[0044] Secondly, the pump-turbine stage: As the key hub for energy conversion in pumped-storage units, the pump-turbine exhibits complex four-quadrant operating characteristics and highly nonlinear inverse "S" characteristics. If a traditional Taylor series linear expansion model is used, a non-negligible truncation error will occur when operating conditions fluctuate significantly. Therefore, this embodiment employs a high-precision full-characteristic curve model equipped with an improved Suter transform.

[0045] Because traditional full characteristic curves (or existing full characteristic curves) are composed of multiple lines of equal opening for flow and torque characteristics, there is a multi-valued problem in the inverse "S" region where a given unit rotational speed corresponds to multiple unit flow rates and unit torques, making conventional interpolation calculations impossible. To solve this mapping singularity problem, this invention employs an improved Suter transform method. By introducing dimensionless parameters, the multi-valued full characteristic curve is transformed into a uniformly distributed, dimensionless, single-valued characteristic curve, including the dimensionless head function WH and the dimensionless torque function WM. The specific mathematical model of the improved Suter transform is as follows: (2) (3) The definition of the abscissa characteristic parameter x (characteristic angle variable) is determined by the direction of the relative value ω of the rotational speed: when oh≥ 0:00 (4) when oh< 0:00 (5) In the formula, oh , q , h , m , y These are the relative values ​​of rotational speed, flow rate, water pressure, dynamic mechanical torque, and guide vane opening; the preferred range for each constant parameter is k1 > |M 11max | / M 11r k2 [0.5, 1.2], C y [0.1, 0.3], C h [0.4, 0.6].

[0046] During dynamic simulation and identification, based on the rotational speed and water pressure status of the model at the previous time step, the current dynamic mechanical torque m and flow rate q are interpolated through the above mapping relationship, thereby providing high-precision driving torque boundary conditions for the downstream generator model.

[0047] In this technical solution, the improved Suter transform (one of the core improvements) solves the multivalued problem of traditional full-characteristic curves in the inverse "S" region through the arctan transform, enabling stable simulation calculations. Combined with the curve fitting model with correction coefficients k1, k2, and C, the correction coefficients k1, k2, and C are given. C h The general form of the formula is given, along with its optimal range. Based on the rotational speed and head state at the previous moment, the current dynamic torque and flow rate are interpolated to provide high-precision driving boundary conditions for the generator model. This constructs a complete nonlinear dynamic model of the pump-turbine, which can flexibly adapt to different types of pump-turbines, improving the model's versatility and accuracy. In other words, these formulas are embedded into the closed-loop simulation of the hydroelectric coupling model through a closed-loop dynamic application method of "excitation-simulation-correction," calculating the dynamic torque and flow rate in real time and providing high-precision driving signals for the identification of equivalent moment of inertia.

[0048] Finally, the synchronous generator stage. Regarding electromagnetic transients, to accurately characterize the dynamic coupling relationship between the decay of the internal magnetic flux and power output under micro-disturbances, this embodiment employs a third-order transient model. The generator model receives the main driving torque transmitted from the pump-turbine and maps it to mechanical power P. m Simultaneously, by combining the voltage regulation dynamics of the excitation system and simultaneously solving the rotor motion equations and the q-axis transient electromotive force equations, the dynamic evolution of rotational speed and electromagnetic power is calculated: (6) (7) (8) (9) In the formula, J The equivalent moment of inertia to be identified; d For the angle of attack; E' q for q Axis transient potential; E fd This is the excitation voltage; T' d0 for d Shaft open-circuit transient time constant; X d , X' d , X qThese are the reactance parameters of each shaft system of the generator; i d , i q This represents the direct and quadrature axis components of the stator current. At this point, the guide vane micro-motion triggered by the governor control signal undergoes elastic water hammer (from the hydraulic system) h , q ), mechanical torque conversion of water turbine ( P m ), ultimately related to the electromagnetic transients of the generator ( E' q , P e This forms a complete closed-loop coupling. By performing time-domain numerical integration on the above nonlinear differential-algebraic equations (e.g., using the Runge-Kutta method), the equations can be solved with the given parameters. J Below, the model accurately outputs the calculated rotational speed, which includes the dynamic characteristics of the entire system. oh model .

[0049] In other words, this technical solution identifies the equivalent moment of inertia to be determined. J Embedded in a complete hydro-mechanical coupling model, the nonlinear differential equations are solved by time-domain numerical integration, and a high-precision model speed curve is output under micro-perturbation conditions, providing reliable dynamic response data for subsequent parameter identification.

[0050] Step 3: Construct a set of multi-objective parameter identification functions.

[0051] Given that the aforementioned hydro-mechanical coupling model contains highly nonlinear characteristics (such as improved Suter transform and elastic water hammer), the conventional single-objective residual sum of squares easily obscures local transient dynamic details. Therefore, this technical solution transforms the identification of rotational inertia into a multi-objective extremum optimization problem, constructing the following two complementary objective functions: First objective function f 1 (J) The aim is to minimize the root mean square error (RMSE) between the measured and calculated rotational speeds over the entire time window, with a focus on evaluating global steady-state tracking accuracy. (10) Second objective function f 2 (J) The aim is to minimize the maximum absolute deviation (MaxError) throughout the process, focusing on evaluating the model's accuracy in capturing transient extreme points such as speed overshoot. (11) In the formula, N is the total number of sampling points; k Time series index (sampling point number); JThe equivalent moment of inertia of the pumped storage unit to be identified; oh meas ( k ) is the first k The measured relative value of rotational speed at each moment. oh model ( k, J ) is the first k At a given moment, with equivalent moment of inertia J The model simulates the relative rotational speed as a parameter.

[0052] During the optimization process, for values ​​exceeding the physically reasonable range of equivalent moment of inertia (e.g., [J]), min J max The variable ]) is directly assigned a very large penalty fitness value, which limits the optimization space.

[0053] Step 4: Solve for the equivalent inertia using the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm.

[0054] Due to the difficulty in differentiating the strongly coupled hydroelectric model, this technical solution preferably employs the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to globally optimize the aforementioned nonlinear multi-objective function set. The specific execution process is as follows: First, parameter initialization. The particle swarm size and maximum number of iterations are set, and the equivalent moment of inertia position J represented by each particle is randomly initialized within the physical boundary of the moment of inertia. i and its search speed V i .

[0055] Secondly, fitness evaluation and non-dominated ranking. In each iteration, the J of each particle is... i Input the hydroelectric coupling dynamic model and perform time-domain simulation calculations to obtain their respective f1(J) values. i ) and f2(J i The Pareto dominance rule is used to compare the fitness of all particles. The optimal solutions that are not mutually dominated are extracted into the external archive. The crowding distance of each solution in the external archive is calculated to maintain the diversity of solutions.

[0056] Then, the particle state is updated. Using either a roulette wheel or a tournament-style approach based on crowding distance, the globally optimal guiding particle (gbest) is selected from the external archive, and its current position is compared to its individual historical best position (pbest). The velocity (V) of the next generation of the particle swarm is then updated using velocity and position update formulas. i and J i .

[0057] Finally, the optimal solution is selected. The above simulation calculations, non-dominated sorting, and state updates are repeated until convergence is achieved after the maximum number of iterations. At this point, the Pareto optimal front solution set consisting of f1 and f2 is stored in the external archive. To obtain a unique identification result, this embodiment uses the fuzzy membership function method to normalize the satisfaction evaluation of all non-dominated solutions on the Pareto front, selecting the optimal compromise solution with the highest satisfaction. The J value corresponding to this solution is the high-precision equivalent moment of inertia identified under the current micro-perturbation condition.

[0058] Example 2: Technical solution of the second technical subject matter involved in this invention: An online identification system for the equivalent rotational inertia of a pumped-storage unit is provided for executing the online identification method for the equivalent rotational inertia of a pumped-storage unit based on an active micro-perturbation and hydro-mechanical coupling model as described in Example 1. The system includes: The signal injection and data acquisition module is used to inject micro-perturbation test signals into the active power control loop of the pumped storage unit under the stable grid-connected operation state, to excite the local transient response of the unit, and simultaneously acquire the active power and speed data of the unit during the disturbance period. The coupling model construction module is used to build a dynamic model of hydraulic-turbine coupling considering hydraulic transient characteristics based on the collected operational data, and to simulate the dynamic response characteristics of the unit in all dimensions. The objective function construction module is used to calculate the speed deviation information based on the collected measured speed data and the simulated speed data obtained from the model simulation, and to construct a dual-objective identification function set including global root mean square error and maximum absolute deviation. The multi-objective optimization solution module is used to iteratively optimize the dual-objective identification function set using a multi-objective optimization algorithm to obtain a converged Pareto optimal frontier solution set; The result filtering and output module is used to evaluate the satisfaction of the Pareto optimal front solution set through fuzzy membership functions, determine the compromise equilibrium solution, and output the equivalent moment of inertia under the current working condition.

[0059] Example 3: The technical solution of the third technical subject matter involved in this invention: A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the online identification method for the equivalent moment of inertia of a pumped storage unit as described in Embodiment 1 are implemented.

[0060] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Various modifications and variations can be made to the above embodiments. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for online identification of the equivalent rotational inertia of a pumped-storage unit based on an active micro-perturbation and hydro-mechanical coupling model, characterized in that, The steps include: Under the stable grid-connected operation of the pumped storage unit, a micro-perturbation test signal is injected into the active power control loop of the unit to induce the unit to generate a local transient response, and the unit's operating data during the disturbance period is collected simultaneously. Based on the local transient operating characteristics formed by the excitation and the operating data, a hydraulic-mechanical coupling dynamic model considering the transient characteristics of hydraulics is constructed. Based on the measured rotational speed data and the simulated rotational speed data calculated by the hydro-mechanical coupling dynamic model, a dual-objective identification function set that takes into account both global steady-state response error and local transient extreme value error is constructed. The dual-objective identification function set is iteratively optimized to construct a Pareto optimal front solution set; The compromise equilibrium solution is selected from the Pareto optimal front solution set and output as the equivalent moment of inertia under the current operating condition, thereby realizing the online identification of the equivalent moment of inertia of the pumped storage unit.

2. The method for online identification of the equivalent rotational inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model according to claim 1, characterized in that, The micro-perturbation test signal is a pseudo-random binary sequence signal. The amplitude of the micro-perturbation test signal is 1% to 2% of the rated active power of the pumped storage unit, and the signal mean is zero. The operating data is collected synchronously using a phasor measurement device, the sampling frequency of which is greater than or equal to 100Hz.

3. A method for online identification of the equivalent rotational inertia of a pumped-storage unit based on an active micro-perturbation and hydro-mechanical coupling model, as described in claim 1 or 2, characterized in that, The hydro-mechanical coupling dynamic model includes a governor sub-model, a pressurized water system sub-model, a hydraulic power sub-model, and a synchronous generator sub-model. The speed governor sub-model receives micro-perturbation test signals and unit speed feedback signals, and outputs control command signals; The control command signal is processed sequentially by the pressurized water system sub-model and the hydraulic power sub-model to obtain the mechanical power or mechanical torque input to the synchronous generator sub-model. The synchronous generator sub-model calculates the simulated rotational speed data based on the mechanical power or mechanical torque. Based on the deviation between the simulated rotational speed data and the measured rotational speed data, the equivalent moment of inertia to be identified is iteratively optimized.

4. The method for online identification of the equivalent rotational inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model according to claim 3, characterized in that, The pressurized water system sub-model adopts an approximate elastic water hammer model to characterize the dynamic coupling relationship between the head deviation and flow deviation in the pressure pipeline, thereby describing the hydraulic transient characteristics of the pipeline.

5. The method for online identification of the equivalent rotational inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model according to claim 1, characterized in that, The hydraulic dynamic sub-model adopts a full characteristic curve model equipped with an improved Suter transform; Based on the improved Suter transform, the original full characteristic curve of the unit is normalized and corrected to obtain a uniformly distributed dimensionless single-value characteristic curve. The hydraulic dynamic sub-model calculates the nonlinear dynamic parameters of the unit based on the single-value characteristic curve, and obtains the single-value characteristics of the unit under all operating conditions.

6. A method for online identification of the equivalent moment of inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model, as described in claim 1 or 2, characterized in that, The synchronous generator sub-model adopts a third-order transient model; The dynamic relationship between the unit speed and the power angle is calculated and obtained based on the rotor motion equation in the third-order transient model. Based on the transient electropotential equation of the excitation system in the third-order transient model, the dynamic change relationship of the unit's electromagnetic power is calculated and obtained. Based on the dynamic relationship between the unit's rotational speed and power angle and the dynamic relationship between the unit's electromagnetic power, the dynamic coupling transient relationship of the unit's electromechanical energy is obtained.

7. The method for online identification of the equivalent moment of inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model according to claim 1, characterized in that, The dual-objective identification function set includes a first objective function and a second objective function; The first objective function is the root mean square error function of rotational speed, which is used to characterize the global steady-state fitting accuracy; The second objective function is the maximum absolute deviation function of rotational speed, which is used to characterize the ability to capture local transient extrema.

8. The method for online identification of the equivalent moment of inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model according to claim 1, characterized in that, The steps for iteratively optimizing the dual-target identification function set are as follows: A multi-objective particle swarm optimization algorithm is used to initialize the position and velocity of particles within the physical constraint interval of equivalent rotational inertia. The particles are sorted non-dominated based on the Pareto dominance relation. The diversity of the front solution set is maintained by combining the crowding distance. The algorithm is iterated and updated multiple times until convergence, and the Pareto optimal front solution set is obtained. The Pareto optimal frontier solution set is normalized and its satisfaction is evaluated using a fuzzy membership function to select the compromise equilibrium solution.

9. An online identification system for the equivalent moment of inertia of a pumped storage unit, characterized in that, The system is used to perform the online identification method for the equivalent rotational inertia of a pumped storage unit based on an active micro-perturbation and hydro-mechanical coupling model as described in any one of claims 1-8, and comprises: The signal injection and data acquisition module is used to inject micro-perturbation test signals into the active power control loop of the pumped storage unit under the stable grid-connected operation state, to excite the local transient response of the unit, and simultaneously acquire the active power and speed data of the unit during the disturbance period. The coupling model construction module is used to build a dynamic model of hydraulic-turbine coupling considering hydraulic transient characteristics based on the collected operational data, and to simulate the dynamic response characteristics of the unit in all dimensions. The objective function construction module is used to calculate the speed deviation information based on the collected measured speed data and the simulated speed data obtained from the model simulation, and to construct a dual-objective identification function set including global root mean square error and maximum absolute deviation. The multi-objective optimization solution module is used to iteratively optimize the dual-objective identification function set using a multi-objective optimization algorithm to obtain a converged Pareto optimal frontier solution set; The result filtering and output module is used to evaluate the satisfaction of the Pareto optimal front solution set through fuzzy membership functions, determine the compromise equilibrium solution, and output the equivalent moment of inertia under the current working condition.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the online identification method for the equivalent moment of inertia of a pumped storage unit as described in any one of claims 1 to 8.

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