A method and system for estimating system frequency response based on fault location

Abstract

The application provides a system frequency response estimation method and system based on fault location, and belongs to the technical field of new energy power grids, and comprises the following steps: constructing a new energy multi-operation state model; solving the node voltage after the fault based on the superposition principle and iterative calculation on the state model, establishing a mapping model of the fault location and the low penetration cluster, obtaining the initial value of the active power shortage, and comprehensively considering the initial value of the active power shortage between stations and the difference in active power recovery rate under different fault locations, and calculating the total active power shortage of the system level considering the difference in the low penetration characteristics of the stations; constructing a system frequency response model based on the difference in the frequency modulation capability caused by the fault location, and estimating the system frequency response by using the response model. The application realizes quantitative description of the active power shortage after disturbance of different fault locations and the loss of equivalent frequency modulation capability of the system, so that the accuracy of frequency response analysis is improved.

Description

Technical Field

[0001] This invention belongs to the field of new energy power grid technology, and in particular relates to a system frequency response estimation method and system based on fault location. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the continuous integration of high-proportion renewable energy sources, traditional power systems dominated by synchronous machines are transforming into new power systems based on power electronics. This leads to a decline in system inertia and frequency regulation capabilities, making frequency security under fault disturbances increasingly prominent. In high-proportion renewable energy grids, renewable energy sources are required to actively participate in frequency regulation. When a large number of renewable energy units capable of actively participating in frequency regulation enter low-voltage ride-through (LVRT) conditions, they no longer possess frequency support capabilities. The resulting large-capacity power deficit may cause the system frequency to drop more deeply and change more rapidly, even triggering low-frequency load shedding, threatening the safe and stable operation of the system.

[0004] In large-scale power grids with increasing penetration rates, the range of generating units entering low-voltage control mode varies depending on the fault location. Besides the active power deficit, the overall frequency regulation capability of renewable energy units in the system also exhibits complex variations depending on the fault location. Therefore, accurately calculating the frequency response of high-proportion renewable energy systems after large disturbances becomes more complex. Existing frequency response methods for systems involving active wind turbine participation in frequency regulation tend to aggregate or simplify the response of distributed wind power, which improves computational efficiency but neglects the spatial dimension of fault disturbance propagation in the grid and fails to comprehensively consider the differentiated active power deficit characteristics caused by varying voltage dips and active power recovery rates at different fault locations. Summary of the Invention

[0005] To overcome the shortcomings of the existing technologies, this invention proposes a system frequency response estimation method and system based on fault location. It constructs an improved system frequency response model that considers the differences in active power deficit and frequency regulation capability loss and recovery caused by fault location, and quantifies the initial active power deficit and frequency regulation capability loss. By introducing the frequency regulation state switching coefficient of new energy power plants, the system's equivalent frequency regulation capability availability rate is formed by weighted aggregation, thereby realizing the fault location-based correction of the traditional frequency response model.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0007] In a first aspect, the present invention discloses a system frequency response estimation method based on fault location, comprising:

[0008] A multi-operational-state model for new energy is constructed, which includes steady-state operation, fault ride-through state, and frequency regulation state.

[0009] Based on the superposition principle and iterative calculation, the node voltage after the fault is solved by the state model, and a mapping model between the fault location and the low-voltage cluster is established. Based on the mapping model, the voltage drop of the unit is determined to obtain the initial value of the active power deficit. Taking into account the differences in the initial value of the active power deficit and the active power recovery rate between the stations under different fault locations, the total active power deficit at the system level considering the differences in the low-voltage characteristics of the stations is calculated.

[0010] The system frequency response model is constructed based on the frequency regulation capability status switching coefficient of the new energy power station, and the equivalent frequency regulation capability availability rate of the system is formed by weighted aggregation. The system frequency response model is then used to estimate the system frequency response.

[0011] Secondly, this invention discloses a system frequency response estimation system based on fault location, comprising:

[0012] The state construction module is configured to: construct a new energy multi-operation state model, wherein the multi-operation states include steady-state operation, fault ride-through state and frequency regulation state;

[0013] The parameter calculation module is configured to: solve the node voltage after the fault based on the superposition principle and iterative calculation of the state model, establish a mapping model between the fault location and the low-voltage trunking cluster, determine the voltage drop degree of the unit based on the mapping model to obtain the initial value of the active power deficit, and comprehensively consider the differences in the initial value of the active power deficit and the active power recovery rate between the stations under different fault locations, and calculate the total active power deficit of the system level considering the differences in the low-voltage characteristics of the stations.

[0014] The frequency response module is configured to: use the frequency regulation capability state switching coefficient of the new energy power station, weighted aggregate to form the system equivalent frequency regulation capability availability rate, construct a system frequency response model based on the frequency regulation capability difference caused by the fault location, and use the response model to estimate the system frequency response.

[0015] Thirdly, the present invention discloses an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, complete the steps of the above-described system frequency response estimation method based on fault location.

[0016] Fourthly, the present invention discloses a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the above-described system frequency response estimation method based on fault location.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] This invention provides a method for accurately solving the node voltage after a fault based on the superposition principle and iterative calculation. The established mapping model between the fault location and the low-voltage cluster can effectively identify the low-voltage range and provide initial conditions, while avoiding the high time consumption problem of traditional time-domain simulation traversing the fault scenario.

[0019] This invention, based on a mapping model between fault location and low-voltage power grid clusters, considers the differences in the initial value of active power deficit and active power recovery rate among power plants under different fault scenarios when calculating the total wind power active power deficit. This allows for a more realistic simulation of the time-varying recovery process of wind power active power deficit after fault clearance. It avoids the errors caused by simplifying all renewable energy power plants into a single aggregated model, thus providing a more accurate description of frequency variation curves.

[0020] The improved system frequency response model proposed in this invention can accurately reflect the differentiated impact of fault location on system frequency dynamics. Compared with traditional models, this model significantly improves the calculation accuracy of key indicators such as the lowest frequency point and voltage drop rate by finely characterizing the range of new energy clusters entering the low-voltage state under different fault points.

[0021] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0023] Figure 1 This is a flowchart of the system frequency response estimation method based on fault location as described in Embodiment 1 of the present invention.

[0024] Figure 2 This is the voltage ride-through curve of the wind turbine generator described in Embodiment 1 of the present invention.

[0025] Figure 3 This is a block diagram of the integrated inertia control described in Embodiment 1 of the present invention.

[0026] Figure 4 This is a logic block diagram of switching between multiple operating states of new energy as described in Embodiment 1 of the present invention.

[0027] Figure 5 This is a flowchart of the fault analysis and low-voltage cluster mapping model with nonlinear output characteristics of new energy sources as described in Embodiment 1 of the present invention.

[0028] Figure 6 This is the characteristic curve showing the difference between the low penetration drop and the active recovery rate as described in Embodiment 1 of the present invention.

[0029] Figure 7 This is a logic block diagram of the average frequency response equivalent model described in Embodiment 1 of the present invention.

[0030] Figure 8 This refers to the ASF model with wind power frequency regulation state switching as described in Embodiment 1 of the present invention.

[0031] Figure 9 This is an equivalent block diagram of the system frequency response described in Embodiment 1 of the present invention.

[0032] Figure 10 This is the IEEE 10 machine 39-node system with new energy source in Embodiment 1 of the present invention.

[0033] Figure 11 This is the active power deficit curve of the low-voltage generator unit under scenario A in Embodiment 1 of the present invention.

[0034] Figure 12 The frequency response curves are shown under different wind power active power deficit calculation methods in Embodiment 1 of the present invention.

[0035] Figure 13 These are the frequency response curves of each model under scenario A in Embodiment 1 of the present invention.

[0036] Figure 14 These are the frequency response curves of each model in scenario B of Embodiment 1 of the present invention. Detailed Implementation

[0037] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0038] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0039] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0040] Existing research on improved frequency response models for systems considering active frequency regulation by wind turbines has the following methods and their limitations:

[0041] Existing research considers the frequency regulation characteristics of wind power and the effect of virtual inertia, proposing improved system frequency response models suitable for high-proportion renewable energy grids. However, none of these studies consider the correction of the system frequency response model by wind turbines entering low-voltage ripple (LVRT). For the system frequency response considering wind power LVRT after system disturbance, existing research focuses on analyzing the impact of active power recovery rate on active power deficit. Existing methods demonstrate the feasibility of reducing the power deficit caused by faults and mitigating the impact of LVRT by adjusting the active power recovery rate. Other methods consider dividing wind turbines into LVRT-affected units and units unaffected by faults, quantifying the lowest point of system frequency. However, these methods only consider the distinction between LVRT-affected units under fixed fault scenarios and do not consider the differentiated characteristics caused by different fault locations. Existing simplified methods that ignore the dynamic characteristics of LVRT (Low Voltage Recovery Time) and assume that all power plants have the same active power recovery rate are no longer applicable as new projects are continuously put into operation and the differences in active power recovery rates among different power plants become increasingly significant. Other methods use the principles of energy conservation and common-mode frequency to aggregate the transient micro-processes of wind power LVRT, which take into account differences in active power recovery, into a macro-equivalent model to concisely describe the magnitude of active power disturbances. However, these methods tend to aggregate or simplify the response of distributed wind power as a whole, which improves computational efficiency but ignores the spatial dimension of fault disturbance propagation in the grid and does not comprehensively consider the differentiated active power deficit characteristics caused by different voltage drops and active power recovery rates at different fault locations. In the future, in scenarios where renewable energy frequency regulation capabilities become dominant, the active power deficit and frequency regulation capability loss and recovery process caused by renewable energy units entering low-voltage control after a fault will exhibit significantly differentiated characteristics depending on the fault location. The existing system frequency response model does not fully consider the differences in frequency regulation capability loss and active power deficit of each unit after a fault at different locations, and the accuracy of the frequency response description after disturbance needs to be improved.

[0042] Example 1

[0043] In one or more embodiments, a system frequency response estimation method based on fault location is disclosed, such as Figure 1 As shown, it includes the following steps:

[0044] Step S1: Construct a new energy multi-operation state model, which includes steady-state operation, fault ride-through state and frequency regulation state. The transition between each state is triggered based on grid voltage and frequency conditions.

[0045] To accurately characterize the frequency response characteristics of new energy sources, this embodiment takes a representative direct-drive permanent magnet synchronous generator (PMSG) as an example and establishes a mathematical model of its multiple operating states. The dynamic behavior of the PMSG during system disturbances can be summarized into three typical operating states: steady-state operation, fault ride-through state, and frequency regulation state.

[0046] First, steady-state operation:

[0047] When a wind turbine is operating in a steady state, its output mechanical power can be described by the following formula:

[0048] (1)

[0049] In the formula, Mechanical power; To output mechanical torque for the wind turbine; The angular velocity of the wind turbine; The average density of air; The radius of the wind turbine's impeller; Indicates wind speed; The wind energy utilization coefficient, For the tip speed ratio, The pitch angle is a coefficient used to characterize the efficiency of a wind turbine in converting wind energy into mechanical energy. Its value depends on the mathematical relationship between the tip speed ratio and the pitch angle, and can be approximated by the following formula:

[0050] (2)

[0051] In the formula, The tip speed ratio is an intermediate variable used to calculate the influence of the blade tip speed ratio and pitch angle on the wind energy utilization coefficient. To describe the operating state of the wind turbine at different wind speeds, the ratio of the wind turbine blade linear velocity to the wind speed is defined as the tip speed ratio. It can be calculated using the following formula:

[0052] (3)

[0053] In the formula, This refers to the mechanical rotational speed of the wind turbine.

[0054] Combining equations (2) and (3), it can be seen that in the variable speed operating range below the rated wind speed, the rotor speed follows the optimal... When the value changes, the wind turbine will operate under maximum power point tracking (MPPT) control, which is the stable operating state for grid-connected wind turbines. At this time, the output power is:

[0055] (4)

[0056] In the formula, Output power for stable operation; The optimal tip speed ratio; This represents the maximum wind energy utilization factor. The maximum power factor under stable operating conditions.

[0057] Second, fault-crossing state:

[0058] When the grid voltage drops or rises above the voltage ride-through threshold, the wind turbine fault ride-through control system is immediately triggered, switching from normal operation mode to fault ride-through mode. The wind turbine voltage ride-through curve is shown below. Figure 2 As shown.

[0059] When the grid connection point voltage drops to When the unit enters a low-voltage ride-through, the dynamic reactive current increment of the wind farm responds to the voltage change at the grid connection point. During a voltage fault, the continuous injection of capacitive reactive current should meet the following requirements:

[0060] (5)

[0061] In the formula, It is capacitive reactive current; This refers to the grid connection voltage of the wind turbine generator. This is the rated current of the wind turbine.

[0062] When the grid connection point voltage drops to When a wind turbine enters a high-voltage ride-through, the wind farm supports voltage recovery by actively absorbing dynamic reactive current from the power system. During a voltage fault, it continuously injects inductive reactive current, which should meet the following requirements:

[0063] (6)

[0064] In the formula, It is the inductive reactive current.

[0065] Due to the equipment's maximum output current limitation, the active current output by the fan during a fault must meet the following requirements:

[0066] (7)

[0067] In the formula, This refers to the active current output by the wind turbine. This represents the maximum output current during the fault ride-through of the wind turbine.

[0068] Wind farms that did not disconnect during the fault will have their active power restored after the fault is cleared, at least [percentage missing]. The power change rate recovers to its pre-fault value. In summary, after the wind turbine enters fault ride-through mode, its active power output can be expressed as:

[0069] (8)

[0070] In the formula, This refers to the active power output of the wind turbine during fault ride-through. The time when the fault occurred; This is the time to clear the fault; This refers to the moment when the active power of the wind turbine unit recovers. This refers to the rated active power of the wind farm. This refers to the steady-state active power during faults. This represents the active power recovery rate.

[0071] Third, frequency adjustment status:

[0072] When the unit is operating under normal conditions or after the fault has been cleared and restored, and the power system frequency deviation is greater than the dead zone range, and the active power of the wind farm is greater than... At that time, the wind farm should provide an inertial response under the condition of satisfying equation (9), and the change in active power of the wind farm should satisfy equation (10):

[0073] (9)

[0074] (10)

[0075] In the formula, This refers to the system frequency deviation. The frequency at the wind farm's grid connection point; This represents the change in active power of the wind farm. The equivalent inertial time constant of the wind farm; The system's rated frequency; The active power of the wind farm; This represents the change in active power of the wind farm.

[0076] At the same time, wind farms should have the capability to participate in the primary frequency regulation of the power system, and the change in active power of wind farms should be considered. The formula should be satisfied:

[0077] (11)

[0078] In the formula, This is the active frequency regulation coefficient.

[0079] Traditional integrated inertia control block diagram as follows Figure 3 As shown, its effective output is:

[0080] (12)

[0081] In the formula, This refers to the change in active power of a wind farm that takes into account the overall inertia control.

[0082] When the wind turbine provides frequency support to the system, the active power reference value of the wind turbine is:

[0083] (13)

[0084] In the formula, This is the active power reference value for the wind turbine; This represents the active power of the wind turbine operating under MPPT conditions.

[0085] Furthermore, the transitions between states are triggered by grid voltage and frequency conditions, directly affecting the system's frequency response characteristics. Its overall logical framework is as follows: Figure 4 As shown, the specific logic for switching between multiple operating states of new energy sources is as follows: When the wind speed is between the rated wind speed and the cut-in wind speed, the unit first enters the maximum power point tracking (MPPT) control state to maximize wind energy capture; when a large disturbance occurs in the power grid and the voltage at the power plant's grid connection point is lower than the undervoltage threshold, the system switches to the fault ride-through control state. The main objective of this stage is to support the recovery of the grid voltage, during which a large amount of active power deficit will occur; at the same time, if the voltage recovers to above the undervoltage threshold and the frequency deviation exceeds the dead zone, the inertial response and primary frequency regulation functions are triggered, utilizing the unit's frequency regulation capability to participate in grid frequency regulation; when the grid frequency recovers to above the minimum allowable frequency and the duration exceeds the minimum required time, the system exits the fault ride-through and frequency regulation states, returns to MPPT control, and resumes normal power generation operation.

[0086] Step S2: Based on the superposition principle and iterative calculation, solve the node voltage after the fault in the state model, establish a mapping model between the fault location and the low-voltage cluster, determine the voltage drop degree of the unit based on the mapping model to obtain the initial value of the active power deficit, and comprehensively consider the differences in the initial value of the active power deficit and the active power recovery rate between the stations under different fault locations, calculate the total active power deficit at the system level considering the differences in the low-voltage characteristics of the stations.

[0087] Step S2-1, as follows Figure 5 As shown, a calculation method based on the superposition principle and iterative calculation is used to solve the node voltage after the fault, and a mapping model between the fault location and the low-voltage cluster containing the nonlinear output characteristics of new energy is established.

[0088] Accurately characterizing the extent of low-voltage ride-through (LVRT) in a power grid after a fault hinges on precisely calculating the post-fault voltage at each renewable energy access node. However, the dynamic response of renewable energy units during LVRT introduces significant nonlinear characteristics: their reactive power control mode switches from the constant power mode under normal operating conditions to a constant current mode that prioritizes the injection of supporting reactive current, causing their equivalent model and output current to dynamically change with the terminal voltage. This nonlinear behavior makes it impossible to directly solve the post-fault network using a fixed-structure admittance matrix.

[0089] This embodiment employs a computational method combining the superposition principle and iterative calculation, ensuring model accuracy while maintaining computational efficiency. The complex post-fault network state is decomposed into two independent, linearly superimposed parts: the pre-fault network influenced by the original power source and the fault-incremental network influenced only by the current injected at the fault point. In each iteration, the nonlinear components in the system are locally linearized at the current operating point, approximating the entire network as a linear system for rapid solution. The linearized operating point is then updated based on the solution results, and this process is iterated until convergence.

[0090] Step S2-1-1: Calculate the steady-state voltage distribution after the fault using an algorithm combining the superposition principle and iterative calculation.

[0091] 1. Initialization: Set the number of iterations ; Flow analysis before the fault As the initial node voltage column vector .based on The equivalent model of each new energy node is initialized according to the control logic of each new energy node.

[0092] 2. Linearized Network Construction and Solution: Forming the Node Admittance Matrix Based on the Running Topology Based on the type and location of the fault, a fault is viewed as adding one or more new branches to the network, thereby changing the network topology and correcting... Forming the nodal admittance matrix under fault conditions Solve the equation Obtain the node voltage correction amount , where the injected current vector Including fault point current and the change in current injected by new energy units The updated voltage yields a new solution for the voltage of all nodes in the network. .

[0093] 3. State determination and model update: based on Reassess whether each new energy node meets the requirements. Dynamically update low-voltage cluster For the dynamic switching of new energy unit modes, the equivalent expression of the injected current at this node is adjusted and iterative calculation is performed.

[0094] 4. Convergence Judgment: Verify whether the node voltage and the low-throughput cluster output current both tend to stabilize. If the convergence tolerance is met... and If the iteration fails, stop and output the iteration result; otherwise, increment the value. Then return to step 2.

[0095] Step S2-1-2: Based on the post-fault steady-state voltage distribution obtained from the above iterative calculations, the identification of low-voltage power consumption clusters and the calculation of the initial value of active power deficit can be systematically completed. This is specifically achieved through the following structured steps:

[0096] 1. Construct the core criteria for low-voltage clustering. Based on the node voltage vector after a fault. As the core input, it is compared with a preset low-voltage ride-through threshold. By comparing the data, the low-speed cluster corresponding to the fault location f can be determined. The composition of this decision. This decision logic can be expressed as:

[0097] (14)

[0098] in, This represents the set of all new energy nodes in the system. This judgment criterion completes the crucial transformation from electrical quantities to equipment operating status.

[0099] 2. Calculate the initial value of the active power deficit. Based on the accurate solution model of node voltage, determine the degree of voltage drop at the new energy node, and calculate the initial value of the active power deficit by combining equations (5) and (7):

[0100] (15)

[0101] In the formula, This is the initial value for the active power deficit; and These are the reactive and active currents injected into the wind turbine during the low-voltage period, respectively. and These are the rated voltage and rated current of the new energy node, respectively. The current limit for wind turbine units; The grid connection voltage for new energy sources; This represents the direct-axis component of the voltage at the grid connection point of new energy sources. This represents the initial value of the active power of new energy sources; This refers to the active power of new energy sources during a fault.

[0102] Step S2-2: Identify low-voltage clusters at different fault locations and aggregate active power deficits based on the mapping model.

[0103] In a real power grid, a low-voltage ride-through cluster is defined by a specific fault location f. A wind farm typically consists of numerous geographically dispersed wind farms with varying turbine configurations and control parameters. To accurately characterize the overall dynamics of this cluster, two levels of equivalent modeling are required: For turbine equivalents within a wind farm, it is assumed that turbines within the same wind farm have similar operating characteristics and experience similar voltage drops under the same fault, thus aggregating turbines within the same wind farm into a single equivalent turbine; for active power deficit aggregation between wind farms, the significant differences in initial active power deficits and operating characteristics among all equivalent wind farms at different fault locations must be considered.

[0104] Therefore, to accurately assess the system frequency response, it is necessary to quantify the active power deficit at different fault locations, considering the differences in the degree of low-voltage drop and active power recovery rate of new energy sources, and to comprehensively characterize its combined output and dynamic behavior, such as... Figure 6 As shown. This embodiment, based on the solution results of low-voltage ride-through clustering, uses a segmented aggregation method to calculate the actual total active power deficit of the system at different fault locations as the input to the system frequency response model.

[0105] Based on the low-penetration cluster discrimination method in step S2-1, the low-penetration wind field range is obtained, and the important parameter set is extracted. Low-passage station number Rated capacity Voltage drop degree Initial value of active power deficit Active recovery rate Time of failure Fault clearance time }

[0106] During the fault persistence phase, the system voltage drop is constant, and the active power deficit is a fixed value. Assuming that substations numbered {1, 2, ..., n} simultaneously enter low voltage ride-through control, the initial active power deficit values ​​extracted for each substation can be directly used as the reference. Summing these values ​​yields the total active power deficit for this stage:

[0107] (16)

[0108] In the formula, This represents the initial value of the total active power deficit of wind power during the fault duration phase.

[0109] During the fault recovery phase, the initial active power and recovery rate vary from station to station, resulting in different active power recovery completion times. They are also different, so the active power recovery completion time for each station is calculated first:

[0110] (17)

[0111] In the formula, For station i Time required for successful recovery; For station i Active power output during low-voltage operation.

[0112] Sort by size from largest to smallest. Based on this time series, the total active power deficit is calculated:

[0113] (18)

[0114] In the formula, This represents the total active power deficit of wind power. for Step function at time unit, .

[0115] Combining the above two equations, the active power deficit of wind farms entering low-lying areas is... It can be expressed as a piecewise continuous function as shown in equation (19):

[0116] (19)

[0117] In the formula, Let be the initial value of the active power of the i-th wind farm station; for Step function per second; m is the number of stations entering the low-voltage tunnel; The active power restoration completion time for the m-th power station.

[0118] In traditional power system stability analysis, the impact of faults on frequency stability is often simplified to a fixed power deficit. However, in systems with a high proportion of renewable energy integration, the impact mechanism of faults is not only reflected in the imbalance of total power, but also in the differentiated suppression of frequency response resources in the system by the fault location. Accurately assessing the degree of suppression requires quickly determining the operating status of each renewable energy node after the fault to precisely delineate the low-voltage crossing cluster, which is a prerequisite for quantifying the system's active power deficit and effective frequency regulation resources. Therefore, this invention utilizes a method for accurately solving the node voltage after a fault based on the superposition principle and iterative calculation to establish a mapping model between the fault location and the low-voltage crossing cluster, avoiding the time-consuming problem of traditional time-domain simulations that traverse fault scenarios. Furthermore, it segments and aggregates the active power deficit of renewable energy, providing key disturbance boundaries and input quantities for subsequent system frequency response analysis.

[0119] Step S3: Using the frequency regulation capability state switching coefficient of the new energy power station, weighted aggregation is used to form the system equivalent frequency regulation capability availability rate. A system frequency response model based on the frequency regulation capability difference caused by the fault location is constructed, and the system frequency response is estimated using the response model.

[0120] Step S3-1: Construct an average system frequency model with active frequency support from new energy sources.

[0121] To construct an accurate dynamic model of the system frequency response that considers wind power frequency regulation, this invention first requires establishing a fundamental model capable of describing the system's frequency dynamics. Therefore, an average system frequency (ASF) model supporting active frequencies from renewable energy sources is first established. Through reasonable model aggregation and generalization, the model significantly reduces its order and computational complexity while accurately characterizing the system's inertial response and the core process of primary frequency regulation, laying the foundation for subsequent analysis of more complex frequency response characteristic differences.

[0122] To balance the dynamic process of the speed governor with calculation accuracy and efficiency, the speed control system of a traditional thermal power unit is equivalent to a first-order inertial element:

[0123] (20)

[0124] In the formula, This refers to the frequency adjustment coefficient of the speed controller; The time constant of the speed controller; This is for frequency deviation; This represents the power variation of each thermal power unit.

[0125] To establish a single-unit equivalent model of a wind farm, the dynamic process of wind turbines with inertial response and sag capability participating in frequency regulation is equivalent to:

[0126] (twenty one)

[0127] In the formula, and These are the equivalent virtual inertial time constant and droop control coefficient for each wind field; This represents the power variation of each wind farm.

[0128] The overall frequency response dynamics of the system are described by the rotor motion equations of the equivalent generator:

[0129] (twenty two)

[0130] In the formula, This represents the change in the active power output of the thermal power unit. This represents the change in the active power output of the wind turbine generator. This represents the change in active power consumed by the load. In summary, the equivalent model of the average frequency response is obtained as follows: Figure 7 As shown.

[0131] Step S3-2: Construct a system frequency response model based on the difference in frequency modulation capability caused by the fault location.

[0132] Traditional frequency response models aggregate the system into an idealized model, failing to characterize the differences in wind power frequency regulation capability caused by fault locations. To represent this characteristic, a state switching coefficient is introduced. A value of 1 indicates that the wind turbine's frequency regulation function is normally engaged; a value of 0 indicates that the frequency regulation capability is temporarily blocked due to low-voltage ride-through, resulting in an ASF model incorporating wind power frequency regulation state switching, such as... Figure 8 As shown.

[0133] However, while the aforementioned multi-machine ASF model can accurately characterize the complex characteristics of frequency, its solution process involves a high-dimensional differential-algebraic equation system, resulting in high computational complexity and long simulation time. This inherent limitation makes it difficult to meet the requirements for rapid prediction of system frequency trajectories in scenarios such as system frequency stability control.

[0134] To resolve the conflict between model accuracy and computational efficiency, and to simultaneously consider the heterogeneity and dynamic evolution of wind turbine frequency regulation capabilities during disturbances, this invention proposes a weighted aggregation-based single-unit equivalent modeling method by introducing state switching coefficients characterizing wind power frequency regulation capabilities. The core idea of ​​this method is to weighted aggregate all wind and thermal power units with frequency regulation capabilities in the system into single-unit equivalent models. The parameters of the wind turbine single-unit model are no longer fixed values, but rather variables that reflect the overall frequency regulation status of the entire network's wind turbines under different fault locations. The specific implementation is as follows:

[0135] Step S3-2-1: Aggregate equivalent parameters. Using unit capacity as the weight, aggregate the wind power and thermal power multi-site models with different system parameters into single-unit models. The aggregation of equivalent parameters of the system's wind power and thermal power frequency regulation capabilities is as follows:

[0136] The virtual inertia time constant and droop control coefficient of the wind turbine are shown in equations (23) and (24), respectively.

[0137] (twenty three)

[0138] (twenty four)

[0139] In the formula, The virtual inertial time constant of the wind turbine; This refers to the sag control coefficient for wind turbine units. Let be the rated capacity of the i-th unit.

[0140] The frequency regulation coefficient and time constant of the governor of the thermal power unit are as follows:

[0141] (25)

[0142] (26)

[0143] In the formula, This is the equivalent frequency regulation coefficient of the thermal power unit speed governor; It is the equivalent inertial time constant of the governor of the thermal power unit.

[0144] The moment of inertia and damping coefficient of the thermal power unit are:

[0145] (27)

[0146] (28)

[0147] In the formula, This represents the equivalent inertia of a thermal power unit. Let be the inertia of the i-th thermal power unit; This is the equivalent damping coefficient of the thermal power unit; Let be the damping coefficient of the i-th thermal power unit.

[0148] Step S3-2-2, Frequency regulation capability mapping. Map the previously defined single-unit state switching coefficients of the wind turbine. Through weighted aggregation, it is mapped to an equivalent frequency regulation coefficient that characterizes the availability of wind power frequency regulation capability of the entire system. :

[0149] (29)

[0150] In the formula, Let be the virtual inertia of the i-th wind farm entering the low-voltage tunnel; , denoted as the rated capacity of the i-th and j-th wind farms; n represents the total number of wind farms in the entire system; m represents the number of wind farms that enter the low-voltage circuit after a fault.

[0151] By concatenating this coefficient with the basic equivalent model, a complete dynamic equivalent wind turbine model is finally constructed, and its output is:

[0152] (30)

[0153] The obtained system frequency response equivalent block diagram is as follows: Figure 9 As shown.

[0154] Each fault location corresponds to a different A constant. Therefore, the system frequency response transfer function under each fault scenario can be written as:

[0155] (31)

[0156] In the formula, This represents the total active power deficit of the system. The transfer function describing the power-frequency dynamic characteristics of a thermal power unit, and ; The transfer function describing the power-frequency dynamic characteristics of the speed governor, and ; The transfer function describes the power-frequency dynamic characteristics of a wind turbine. .

[0157] Simplifying the above expression into a rational fraction, we get:

[0158] (32)

[0159] In the formula, A, B, and C are coefficients, and , , .

[0160] This leads to the construction of the system frequency response model transfer function expression considering the frequency modulation capability switching caused by the fault location. Using the residue theorem, it is partially decomposed into a sum of several simple rational fractions, as follows:

[0161] (33)

[0162] In the formula, k represents the number of terms in a simple rational fraction; Represents the transfer function The j-th residue; Represents the transfer function The j-th pole.

[0163] Adding the power disturbances of each type together, where the active power disturbance from wind power is the multi-stage active power deficit obtained in step S2-2, and substituting equation (19) into the equation, we obtain the time-domain expression for the system's active power deficit:

[0164] (34)

[0165] In the formula, m represents the number of wind farms entering the low-lying area; This refers to the active power deficit of the load during a fault.

[0166] The time-domain expression for the above power perturbation is obtained by performing a Laplace transform:

[0167] (35)

[0168] Substituting into equation (33), we get:

[0169] (36)

[0170] The inverse Laplace transform yields the time-domain expression of the system frequency response for each stage:

[0171] (37)

[0172] In the formula, Represents the transfer function The j-th residue; Represents the transfer function The j-th pole; Let represent the active power recovery rate of the i-th wind turbine entering low-voltage operation. By continuously calculating the final value of each stage as the initial value of the next stage, the complete frequency response trajectory of the system can be fitted.

[0173] The above schemes establish the mapping relationship between the fault location and the low-voltage trunking, as well as the active power deficit and frequency regulation capability loss and recovery considering the differences. They also establish a system frequency response model considering the differences in frequency regulation capability, laying a solid foundation for the system frequency response analysis considering the fault location.

[0174] Step S3-3: Establish the fault location location f as the core input variable of the model. By coupling the mapping relationship between the fault location and the low-voltage range, calculating the active power deficit, and improving the system frequency response model, a complete "fault location-low-voltage range-frequency response" evaluation method that can be used for fine simulation of frequency response is realized, enabling accurate analysis of the system frequency response trajectory considering different fault locations.

[0175] To illustrate the fault location-based system frequency response estimation method proposed in this embodiment, and to verify the applicability and effectiveness of the established "location-low-voltage penetration-frequency" response model for refined frequency response simulation, this invention builds a simulation model of an IEEE 10-machine 39-bus system with renewable energy sources on the Matlab / Simulink simulation platform. Based on the standard system, the rated capacity of the traditional generator sets is reduced to 50% of their original capacity. Near-field nodes 17 and 27-29 of the 38th synchronous machine and near-field nodes 21-24 of the 36th synchronous machine are connected to wind turbines. The wind turbines are direct-drive models equipped with LVRT control and integrated inertia control. The detailed topology of the system is shown below. Figure 10 As shown.

[0176] Under normal operating conditions, the wind turbines at nodes 28 and 29 generate 300MW of power, while the remaining wind turbines at the other nodes generate 200MW each, accounting for 37.2% of the total power generation. Two different fault locations, the midpoint between lines 26-28 and 22-23, are set up as Scenario A and Scenario B, respectively. The disturbances in both scenarios occur... A three-phase short-circuit fault occurs at a certain time (grounding impedance is 0), and the fault is cleared after 100ms.

[0177] To verify the inherent adaptability of the model constructed in this paper to different fault locations, this section analyzes the key state variables of the model under different fault scenarios from two dimensions: dynamic process response and equivalent system parameters.

[0178] Furthermore, simulations verified that the location of the fault caused differences in wind power deficit among the units.

[0179] When scenario A disturbance occurs, the grid connection voltage of each wind turbine is calculated via short circuit, and the range of turbines entering the low-voltage breakdown is obtained as follows: Figure 10 The generator units in area A and the generator units in area B have grid connection point voltages higher than the low-voltage ride-through threshold and have not entered low-voltage ride-through control. In this scenario, the calculated active power deficits for each wind turbine unit and the total active power deficit in area A are as follows: Figure 11 As shown.

[0180] like Figure 11 As shown in the power deficit data of various low-voltage wind turbine units, under grid fault disturbances, the power deficit of each wind turbine unit exhibits significant spatial non-uniformity. This non-uniformity stems from the differences in node voltage drops caused by the fault point. Through comparison... Figure 11 The aggregation curves of the three power deficits show that there is a significant error between the superposition calculation that does not consider the differences in the initial value of the active power deficit and the differences in the active power recovery rate, and the superposition calculation that comprehensively considers the differences in the characteristics of the units. Figure 11 As shown in the shaded area. This phenomenon indicates that the voltage drop depth of each node is determined by the electrical distance of the fault location, and this depth, together with the unit's own capacity, determines the magnitude of its power deficit. The initial magnitude of the power deficit and its subsequent recovery rate together determine the active power recovery dynamics of each unit, which in turn superimpose to form the total wind power active power disturbance of the system, and ultimately affect the transient response characteristics of the frequency.

[0181] like Figure 12 As shown, if the difference in the initial value of the active power deficit is not considered when calculating the total active power deficit, a smaller frequency deviation and a lower frequency minimum point will be obtained after superimposing the active power disturbance of the load in the early stage of the fault; if the difference in the active power recovery rate is not considered when calculating the total active power deficit, a higher frequency minimum point will be obtained in the later stage of the fault.

[0182] In summary, traditional response models that treat wind power as a homogeneous whole or only consider aggregated power fail to accurately characterize frequency response dynamics due to neglecting spatial differences. By coupling fault location information, a more accurate characterization of frequency response dynamics can be achieved. The complete characterization of the difference characteristics, that is: not only accurately obtaining the impact amount at the initial moment of the disturbance. This more accurately describes the dynamic path of the impact decay over time. This provides an accurate power disturbance input for subsequent precise simulation of frequency dynamics.

[0183] Furthermore, another core innovation of the model proposed in this invention lies in the introduction of an equivalent frequency regulation coefficient that characterizes the overall frequency regulation capability availability of the wind turbine cluster. This coefficient is a key dynamic link connecting the "fault location - low-speed cluster - frequency response". To comprehensively evaluate the predictive performance of the constructed model in actual dynamic processes, this section compares it with traditional single-machine equivalent models and detailed time-domain simulation models as benchmarks to verify the accuracy of the proposed model. Figure 13-14 As shown, the frequency response curves of each model are displayed in scenario A and scenario B, respectively.

[0184] contrast Figure 13-14 The frequency response curves show that the lowest frequency point in scenario A is lower than that in scenario B. This indicates that in scenario A, the fault results in a larger affected wind turbine capacity and a more severe active power deficit in low-voltage transmission area A. Meanwhile, area B has weaker frequency regulation capabilities, posing a greater challenge to system frequency stability. Through comparison... Figure 13-14 The frequency response curves of various models under different scenarios show that traditional system frequency response models that do not consider the frequency regulation capability of wind turbines or assume that the frequency regulation capability of wind turbines is fixed have significant deviations.

[0185] In both scenarios, the traditional model, which does not consider the frequency regulation capability of the wind turbine, severely underestimates the system frequency level because it does not take into account the frequency regulation power provided by the wind turbine. The predicted minimum frequency differs from the detailed model by 0.163Hz and 0.06Hz. This deviation may lead to a misjudgment in actual operation that the system has entered the low-frequency danger zone, thereby prematurely triggering the low-frequency load shedding device and cutting off unnecessary loads.

[0186] The model that assumes the wind turbine's frequency regulation capability remains constant fails to reflect the actual loss of this capability and overestimates the system's frequency regulation resources. Its predicted minimum frequency differs from the detailed model by 0.089 Hz and 0.11 Hz. Such errors may mask the true frequency risks of the system, causing low-frequency load shedding devices to fail to operate in a timely manner, further deteriorating the system frequency and increasing the risk of widespread power outages.

[0187] In contrast, the proposed model, by introducing an equivalent frequency regulation coefficient for wind power, accurately characterizes the dynamic changes in the frequency regulation capability of wind turbines. Its predicted minimum frequencies are 49.685Hz and 49.733Hz, respectively, which are highly consistent with the detailed model. This helps to more reliably assess whether the system has truly reached the low-frequency load shedding threshold, thereby improving the accuracy of protection coordination and avoiding false trips or failures to trip.

[0188] Example 2

[0189] In one or more embodiments, a system frequency response estimation system based on fault location is disclosed, specifically including:

[0190] The state construction module is configured to: construct a new energy multi-operation state model, wherein the multi-operation states include steady-state operation, fault ride-through state and frequency regulation state;

[0191] The parameter calculation module is configured to: solve the node voltage after the fault based on the superposition principle and iterative calculation of the state model, establish a mapping model between the fault location and the low-voltage trunking cluster, determine the voltage drop degree of the unit based on the mapping model to obtain the initial value of the active power deficit, and comprehensively consider the differences in the initial value of the active power deficit and the active power recovery rate between the stations under different fault locations, and calculate the total active power deficit of the system level considering the differences in the low-voltage characteristics of the stations.

[0192] The frequency response module is configured to: use the frequency regulation capability state switching coefficient of the new energy power station, weighted aggregate to form the system equivalent frequency regulation capability availability rate, construct a system frequency response model based on the frequency regulation capability difference caused by the fault location, and use the response model to estimate the system frequency response.

[0193] Example 3

[0194] This embodiment provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, they complete the steps of the above-described system frequency response estimation method based on fault location.

[0195] Example 4

[0196] This embodiment provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the above-described system frequency response estimation method based on fault location.

[0197] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0198] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0199] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0200] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0201] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. 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 system frequency response estimation method based on fault location, characterized in that, include: A multi-operational-state model for new energy is constructed, which includes steady-state operation, fault ride-through state, and frequency regulation state. Based on the superposition principle and iterative calculation, the node voltage after the fault is solved by the state model, and a mapping model between the fault location and the low-voltage cluster is established. Based on the mapping model, the voltage drop of the unit is determined to obtain the initial value of the active power deficit. Taking into account the differences in the initial value of the active power deficit and the active power recovery rate between the stations under different fault locations, the total active power deficit at the system level considering the differences in the low-voltage characteristics of the stations is calculated. The system frequency response model is constructed based on the frequency regulation capability state switching coefficient of the new energy power station, and the equivalent frequency regulation capability availability rate of the system is formed by weighted aggregation. The system frequency response model is then used to estimate the system frequency response. The determination of the voltage drop of the unit based on the mapping model to obtain the initial value of the active power deficit is specifically as follows: Using the post-fault node voltage vector as the core input, it is compared with the preset low-voltage ride-through threshold to determine the composition of the low-voltage ride-through cluster corresponding to the fault location. Based on the nodal voltage solution model, the degree of voltage drop at the renewable energy nodes is determined, and the initial value of the active power deficit is calculated: In the formula, This is the initial value for the active power deficit; and These are the reactive and active currents injected into the wind turbine during the low-voltage period, respectively. and These are the rated voltage and rated current of the new energy node, respectively. The current limit for wind turbine units; The grid connection voltage for new energy sources; This represents the direct-axis component of the voltage at the grid connection point of new energy sources. This represents the initial value of the active power of new energy sources; This represents the active power of new energy sources during a fault; n represents the total number of wind farms in the entire system. The expression for the system frequency response model based on the difference in frequency modulation capability caused by the fault location is: In the formula, This is for frequency deviation; Represents the transfer function The j-th residue; Represents the transfer function The j-th pole; This represents the active power recovery rate of the i-th wind turbine unit that enters the low-voltage circuit. Let be the initial value of the active power of the i-th wind farm station; is the active power deficit of the load during the fault; m is the number of wind farms entering the low-voltage tunnel. The time when the fault occurred; This is the time to clear the fault; The active power restoration completion time for the m-th power station.

2. The system frequency response estimation method based on fault location as described in claim 1, characterized in that, The method of solving the post-fault node voltage of the state model based on the superposition principle and iterative calculation includes the following steps: Step 1: Set the number of iterations, use the power flow solution before the fault as the initial node voltage column vector, and initialize the equivalent model of each new energy node according to the control logic of each new energy node based on the initial node voltage column vector. Step 2: Based on the running topology, form a node admittance matrix. According to the fault type and location, the fault is regarded as adding one or more new branches in the network. Correct the node admittance matrix under the fault state. Based on the node admittance matrix under the fault state and the injected current vector, solve for the node voltage correction amount. Based on the node voltage correction amount, update the voltage to obtain a new solution for the node voltage of the entire network. Step 3: Based on the new solution of the network node voltage, re-determine whether each new energy node meets the conditions and dynamically update the low-voltage cluster; for the dynamic switching of new energy unit mode, adjust the equivalent expression of the injected current of the node and perform iterative calculation. Step 4: Check if the node voltage and the low-throughput cluster output current both tend to stabilize. If the convergence tolerance is met, stop the iteration and output the iteration result; otherwise, increment... Then return to step 2.

3. The system frequency response estimation method based on fault location as described in claim 1, characterized in that, The expression for the total active power deficit at the system level is: In the formula, This is due to the active power deficit of wind turbine units; Let be the initial value of the active power of the i-th wind farm station; for Step function per second; m is the number of stations entering the low-voltage tunnel; The time of the failure; This refers to the fault clearance time; Let m be the active power restoration completion time for the m-th power station; This refers to the active power recovery rate; for Step function at time unit.

4. The system frequency response estimation method based on fault location as described in claim 1, characterized in that, The method of using the frequency regulation capability status switching coefficient of new energy power stations to form the system's equivalent frequency regulation capability availability rate through weighted aggregation is as follows: Define the individual wind turbine state switching coefficient, and through weighted aggregation, map it to an equivalent frequency regulation coefficient representing the availability of the wind power frequency regulation capability of the entire system: In the formula, This is the equivalent frequency modulation coefficient; This represents the single-unit state switching coefficient for the wind turbine. Let be the virtual inertia of the i-th wind farm entering the low-voltage tunnel; Let be the virtual inertia of the j-th wind farm entering the low-voltage tunnel; , denoted as the rated capacity of the i-th and j-th wind farms; n represents the total number of wind farms in the entire system; m represents the number of wind farms that enter the low-voltage circuit after a fault.

5. The system frequency response estimation method based on fault location as described in claim 4, characterized in that, Based on the aforementioned equivalent frequency regulation coefficient and the basic equivalent model connected in series, a complete dynamic equivalent wind turbine model is constructed, and its output is: In the formula, For frequency deviation, The virtual inertial time constant of the wind turbine. This is the sag control coefficient for wind turbine units.

6. A system frequency response estimation system based on fault location, characterized in that, include: The state construction module is configured to: construct a new energy multi-operation state model, wherein the multi-operation states include steady-state operation, fault ride-through state and frequency regulation state; The parameter calculation module is configured to: solve the node voltage after the fault based on the superposition principle and iterative calculation of the state model, establish a mapping model between the fault location and the low-voltage trunking cluster, determine the voltage drop degree of the unit based on the mapping model to obtain the initial value of the active power deficit, and comprehensively consider the differences in the initial value of the active power deficit and the active power recovery rate between the stations under different fault locations, and calculate the total active power deficit of the system level considering the differences in the low-voltage characteristics of the stations. The frequency response module is configured to: use the frequency regulation capability state switching coefficient of the new energy power station, weighted aggregate to form the system equivalent frequency regulation capability availability rate, construct a system frequency response model based on the frequency regulation capability difference caused by the fault location, and use the response model to estimate the system frequency response; The determination of the voltage drop of the unit based on the mapping model to obtain the initial value of the active power deficit is specifically as follows: Using the post-fault node voltage vector as the core input, it is compared with the preset low-voltage ride-through threshold to determine the composition of the low-voltage ride-through cluster corresponding to the fault location. Based on the nodal voltage solution model, the degree of voltage drop at the renewable energy nodes is determined, and the initial value of the active power deficit is calculated: In the formula, This is the initial value for the active power deficit; and These are the reactive and active currents injected into the wind turbine during the low-voltage period, respectively. and These are the rated voltage and rated current of the new energy node, respectively. The current limit for wind turbine units; The grid connection voltage for new energy sources; This represents the direct-axis component of the voltage at the grid connection point of new energy sources. This represents the initial value of the active power of new energy sources; This represents the active power of new energy sources during a fault; n represents the total number of wind farms in the entire system. The expression for the system frequency response model based on the difference in frequency modulation capability caused by the fault location is: In the formula, This is for frequency deviation; Represents the transfer function The j-th residue; Represents the transfer function The j-th pole; This represents the active power recovery rate of the i-th wind turbine unit that enters the low-voltage circuit. Let be the initial value of the active power of the i-th wind farm station; is the active power deficit of the load during the fault; m is the number of wind farms entering the low-voltage tunnel. The time when the fault occurred; This is the time to clear the fault; The active power restoration completion time for the m-th power station.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the system frequency response estimation method based on fault location as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the system frequency response estimation method based on fault location as described in any one of claims 1-5.

Images