Method and device for online prediction of frequency bias extrema based on wide-area measurement information

Abstract

The application discloses a kind of frequency deviation extreme value online prediction method and device based on wide-area measurement information, belong to power system frequency stability control technical field, the application is based on the traditional pure physical analysis model, using wide-area measurement information to the transient change of electromagnetic power on each regional tie line is approximately fitted, the simplified prediction model of physical-data fusion that can be calculated quickly is established, while the influence of wind power and other new energy on frequency response process and the inertia space-time distribution characteristics are considered in frequency analysis model by wide-area measurement information, so the prediction model accuracy is improved.Meanwhile, the index of "prediction error index" is proposed to indirectly quantify the error of each frequency deviation extreme value prediction value, to guide the online prediction model to quickly and intelligently output the effective prediction value that meets the requirements of accuracy.Therefore, the application not only has certain prediction accuracy, and prediction speed is also faster.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of power system frequency stability control, and more particularly relates to a frequency deviation extreme value online prediction method and device based on wide-area measurement information. BACKGROUND

[0002] In recent years, the scale of grid-connected new energy such as wind power has gradually increased, the system inertia level has significantly decreased, and obvious temporal and spatial distribution characteristics have been shown. At the same time, the large-scale commissioning of DC transmission projects further increases the risk of a large power shortage caused by DC blocking. Because new energy units have no primary frequency modulation capability, the transient frequency deviation extreme value of the power grid will significantly increase after a sudden change in active power, and the system frequency security is seriously threatened. Therefore, it is urgent to establish an accurate and fast online frequency stability evaluation model to predict the frequency deviation extreme value of the system in real time after disturbance, and to predict the frequency instability risk of the power grid in advance to ensure the safe and stable operation of the system.

[0003] The current commonly used frequency online prediction methods for new energy systems mainly include equivalent model analysis method, data-driven method based on artificial intelligence, and physical model and data-driven fusion method. The traditional equivalent model analysis method is mostly based on the assumption of "one inertia center", and cannot analyze the temporal and spatial distribution characteristics of frequency. For power grids with uneven spatial distribution of inertia caused by a large number of grid-connected new energy, the prediction accuracy of the "single machine equivalent method" is not enough. The existing pure data-driven method still has high dependence on input data, and the number of samples required for the corresponding high-dimensional training model when analyzing large power grids will increase exponentially. However, the actual system can only collect a small amount of real-time data, and the time-varying nature is strong. Therefore, the pure data-driven method may not achieve the ideal prediction accuracy in engineering applications. Moreover, the operation process of artificial intelligence has a "black box form", and the explainability and traceability still need to be greatly improved.

[0004] And the existing data-physical fusion driven method mostly does not truly delve into the active power-frequency response mechanism of the system, or the fusion method is too simple, and still cannot fully meet the requirements of prediction accuracy and speed of the actual system. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides a frequency deviation extreme value online prediction method and device based on wide-area measurement information, which aims to obtain the transient operating data of the power grid before and after disturbance by using wide-area measurement technology, improve the accuracy of the prediction method, and utilize the advantage of faster calculation speed of the physical-data fusion driven method compared to the pure model analysis method to realize online fast prediction output of the frequency deviation extreme value, and provide a reference basis for subsequent frequency stability quantitative evaluation, thereby solving the technical problems of low prediction accuracy and slow speed of the existing frequency deviation extreme value.

[0006] To achieve the above object, according to one aspect of the present application, a frequency deviation extreme value online prediction method based on wide-area measurement information is provided, comprising:

[0007] S1: an approximate uniform structure transfer function model of a speed governor of each synchronous generator in a power grid is established through offline testing;

[0008] S2: a first electromagnetic power change expression and a first mechanical power change expression before and after active disturbance are obtained by fitting measured data of each synchronous generator PMU with a linear function;

[0009] S3: the first electromagnetic power change expression and the first mechanical power change expression are input into a rotor motion equation, and a frequency deviation transient expression is derived;

[0010] S4: the frequency deviation transient expression is input into the approximate uniform structure transfer function model, and a second mechanical power expression is derived;

[0011] S5: when the frequency deviation reaches an extreme value, the value of the second mechanical power expression is equal to the value of the first electromagnetic power change expression, an equation about the arrival time of the frequency deviation extreme value is obtained, and an iterative solution is used to obtain a predicted value of the arrival time of the frequency deviation extreme value;

[0012] S6: a third electromagnetic power change expression and a third mechanical power change expression of each generator before and after active disturbance are obtained by fitting the measured data of the PMU with a high-order linear function;

[0013] S7: the third electromagnetic power change expression, the third mechanical power change expression and the predicted value of the arrival time are input into the rotor motion equation, and a frequency deviation extreme value prediction value is solved;

[0014] S8: a prediction error index corresponding to the frequency deviation extreme value prediction value at multiple time points is calculated, and a frequency deviation extreme value prediction value corresponding to a frequency error index satisfying accuracy is taken as an effective output.

[0015] In one embodiment, the S1 comprises:

[0016] S11: a step frequency deviation is input into the speed governor of each synchronous generator cluster respectively, step response data of mechanical power is collected, and a ramp response is obtained by discrete integration of the step response data;

[0017] S12: a linear polynomial is used to fit the ramp response of each speed governor, and the following is obtained:

[0018]

[0019] C ramp_i(t) is the ramp response of the generator i speed governor, is the polynomial linear fitting parameter of the ramp response of the generator i speed governor; t fit is the fitting time; the fitting time should be greater than the frequency deviation extreme value reaching time t nadir ;

[0020] S12: the approximate uniform structure transfer function model is derived by using Laplace transform:

[0021]

[0022] In the formula, G′ i (s) is the approximate uniform structure transfer function of the generator i speed governor.

[0023] In one embodiment, the PMU measured data includes electromagnetic power data and mechanical power data of each generator speed governor from each terminal of each synchronous generator from the moment of active disturbance to the frequency deviation extreme value in the transient process; the S2 includes:

[0024] S21: the first electromagnetic power change expression ΔP ei (t) is obtained by using least square method to fit the electromagnetic power data: ei (t0)+l i (t)t,t∈(t0,t nadir ); t0 and t nadir are the moment of disturbance and the frequency deviation extreme value respectively; ΔP ei (t0) is the initial electromagnetic power shortage of the generator i at the moment of disturbance; l i (t) is the least square method adaptive linear fitting parameter;

[0025] S22: the first mechanical power change expression of the generator i is determined by using a linear function with constant slope to model and analyze the mechanical power data:

[0026]

[0027] ΔP mi (t nadir ) is the mechanical power change amount of the generator i at the moment t nadir of the frequency deviation extreme value.

[0028] In one embodiment, the S3 includes: the first electromagnetic power change expression and the first mechanical power change expression are input into the rotor motion equation to obtain the frequency deviation transient expression: wherein, t nadir is the equation variable, Hi is the real-time inertia time constant of the power generation cluster i at time t.

[0029] In one embodiment, the S4 comprises:

[0030] The frequency deviation transient expression is input into the approximate uniform structure transfer function model, and a first mechanical power change expression of each synchronous generator in the frequency domain is derived: wherein C step_i (t) and C ramp_i (t) are the step response and ramp response of the governor transfer function of the generator i, respectively, G i (s) is the transfer function of the equivalent governor of the generator i; through analysis of the active frequency response mechanism, a second mechanical power change expression is derived according to the open-loop transfer function

[0031] In one embodiment, the S5 comprises:

[0032] S51: when the frequency deviation reaches the extreme value, the value of the second mechanical power expression of each synchronous generator is equal to the value of the first electromagnetic power change expression, that is, there is:

[0033]

[0034] wherein t nadir is the equation variable; ΔP ei (t0), H i , l i (t) are calculated based on PMU measurement data and are dynamically updated in real time at the prediction time t; [k i_0 ,k i_1 ,…k i_n ] are obtained through offline data analysis;

[0035] S52: starting from t nadir =0, gradually increasing until the difference between the two sides of the equation in S51 meets the error requirement to obtain t nadir , which is the prediction value of the arrival time of the frequency deviation extreme value.

[0036] In one embodiment, the S7 comprises: inputting the third electromagnetic power change expression ΔP″ ei (t), the third mechanical power change expression ΔP″ mi (t) and the arrival time prediction value t nadir into the rotor motion equation to obtain:

[0037] integrating the same to obtain t nadir_pre_iThe frequency deviation extreme value arrival time prediction value of the power generation cluster i at time t is obtained.

[0038] In one embodiment, the S8 comprises:

[0039] A prediction error index corresponding to the frequency deviation extreme value prediction value at the plurality of time points is calculated.

[0040] When the prediction error index meets the accuracy, the corresponding frequency deviation extreme value prediction value is outputted.

[0041] When the prediction error index does not meet the accuracy, the PMU measured data is updated, and the S2-S7 is repeatedly executed until the prediction error index meets the accuracy, so that the corresponding frequency deviation extreme value prediction value is obtained.

[0042] In one embodiment, the S8 comprises:

[0043] S81: The prediction error index PEI is initially set to 1, and the frequency deviation extreme value prediction value corresponding to the current and the previous n PMU sampling points is taken each time the prediction is performed, and the average value f ave_i (t) is calculated.

[0044] S82: The adjacent n+1 prediction values are normalized:

[0045] S83: The slope of the normalized prediction value is calculated:

[0046] S84: The average value index A1 of the normalized slope is calculated:

[0047] S85: The variance index A2 of the normalized slope is calculated:

[0048]

[0049] S86: The upper and lower limit values of A1 and A2 are determined by discrete simulation, and the real-time calculated A1(t k ) and A2(t k ) are compared with the limit values respectively; when both are less than the upper limit value, the PEI becomes 0; otherwise, the PEI remains 1.

[0050] S87: When the prediction error index PEI becomes 0, the dynamic prediction result is outputted; when the prediction error index PEI remains 1, the PMU measured data is updated, and the S2-S7 is repeatedly executed until the prediction error index PEI becomes 0, so that the corresponding frequency deviation extreme value prediction value is obtained.

[0051] According to another aspect of the present application, a frequency deviation extreme value online prediction device based on wide-area measurement information is provided, which is used to perform the frequency deviation extreme value online prediction method.

[0052] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0053] This invention, based on traditional pure physical analysis models, utilizes wide-area measurement information to approximate the transient changes in electromagnetic power on interconnecting lines in various regions, establishing a simplified prediction model that integrates physical and data fusion for rapid computation. Simultaneously, the influence of new energy sources such as wind power on the frequency response process and the spatiotemporal distribution characteristics of inertia are considered in the frequency analysis model through wide-area measurement information, thus improving the accuracy of the prediction model. Furthermore, a "prediction error index" is proposed to indirectly quantify the error of the predicted extreme values ​​of each frequency deviation, guiding the online prediction model to quickly and intelligently output effective prediction values ​​that meet the required accuracy. Therefore, this invention not only possesses a certain level of prediction accuracy but also offers relatively fast prediction speed. Attached Figure Description

[0054] Figure 1 This is a flowchart of an online prediction method for frequency deviation extreme values ​​based on wide-area measurement information provided in one embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of a method for fitting a linear function of the terminal electromagnetic power in one embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram of the dynamic prediction process of frequency deviation extreme values ​​in one embodiment of the present invention;

[0057] Figure 4 This is a flowchart of online prediction of extreme values ​​of frequency deviation at a single prediction time point in one embodiment of the present invention;

[0058] Figure 5 This is a graph showing the change of the predicted extreme value of frequency deviation and the slope quantization index A1 with the prediction time in one embodiment of the present invention.

[0059] Figure 6 This is a graph showing the changes in the predicted extreme value of frequency deviation and the variance quantification index A2 with the prediction duration in one embodiment of the present invention.

[0060] Figure 7 This is a simulation diagram of the predicted speed of the extreme values ​​of frequency deviation of four synchronous generators in a four-machine two-area system under different wind power penetration rates in one embodiment of the present invention.

[0061] Figure 8 This is a simulation diagram showing the prediction accuracy of the extreme values ​​of frequency deviation for four synchronous generators in a four-machine, two-area system under different wind power penetration rates, according to one embodiment of the present invention. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0063] To achieve the above objectives, the technical solution of the present invention is as follows:

[0064] S1: Offline testing to establish an approximate unified transfer function for the governors of each synchronous generator in the system.

[0065] S2: Based on PMU measured data, the electromagnetic power and mechanical power changes of each synchronous generator in the system are approximately described by using a linear function from the moment the active power disturbance occurs to the point where the frequency deviation reaches its extreme value during the transient process.

[0066] S3: Using the linear function expressions of electromagnetic power and mechanical power calculated in step S2 as input, derive the frequency deviation expression based on the rotor motion equation.

[0067] S4: Based on the approximate unified transfer function of each synchronous generator speed governor in step S1, the mechanical power change expression of each synchronous generator is further derived.

[0068] S5: Establish the arrival time t of the extreme value of frequency deviation nadir The linear equation is solved iteratively.

[0069] S6: Based on PMU measured data, high-order linear functions are used to approximate the changes in electromagnetic power and mechanical power of each synchronous generator in the system during the transient process from the moment it is subjected to active power disturbance to the point where the frequency deviation reaches its extreme value.

[0070] S7: Based on the rotor motion equation and combined with the predicted arrival time of the extreme frequency deviation, the predicted value of the extreme frequency deviation is solved by integration.

[0071] S8: Calculate the "prediction error index" of the current frequency deviation extreme value prediction and analyze the current prediction accuracy. If the current prediction accuracy meets the requirements, output the current frequency deviation extreme value prediction to indicate the subsequent frequency stability analysis process.

[0072] Furthermore, the steps in step S1 for offline testing and establishing an approximate simplified structure for the speed governors of each synchronous generator in the system are as follows:

[0073] S11: Input the step-shaped frequency deviation to the speed governor of each synchronous generator cluster in the multi-machine system, collect the output data of the corresponding mechanical power change, and obtain the ramp response by discrete integration of the measured step response data.

[0074] S12: Fitting the ramp response of various types of speed controllers using linear polynomials:

[0075] C ramp_i (t)=k i_0 +k i_1 t+…k i_n t n ,t∈(0,t fit )

[0076] In the formula, C ramp_i (t) represents the ramp response of the generator i governor transfer function. Here are the polynomial linear fitting parameters for the ramp response of generator i; (0,t) fit This means selecting ramp response data within the corresponding time interval for polynomial fitting. The fitting duration should be greater than the actual time t required to reach the extreme value of the system's frequency deviation. nadir The recommended range is 5–20 seconds. A linear fitting order of 2 to 6 is generally reasonable.

[0077] S13: Using the Laplace transform, derive the unified form of the transfer function for various types of governors, namely:

[0078]

[0079] In the formula, G′ i (s) is the approximate unified structure transfer function of the generator i governor.

[0080] Furthermore, in step S2, based on PMU measured data, the steps of approximating the changes in electromagnetic power and mechanical power of each synchronous generator in the system during the transient process from the moment of active power disturbance to the point where the frequency deviation reaches its extreme value using linear functions are as follows:

[0081] S21: From the moment of disturbance to the current predicted time, the PMU collects multiple terminal electromagnetic power data for each synchronous generator in the system at a fixed sampling frequency. Based on these measured data, the electromagnetic power change expression of each synchronous generator in the form of a linear function is obtained by fitting the least squares method:

[0082] ΔP ei (t)=ΔP ei (t0)+l i (t)t,t∈(t0,t nadir )

[0083] Where t0 and t nadir These are the instant of disturbance and the moment when the frequency deviation reaches its extreme value, respectively; ΔP ei (t0) represents the initial electromagnetic power deficit of generator i at the instant of disturbance; i (t) represents the least squares adaptive linear fitting parameters.

[0084] S22: Using a linear function with a constant slope, a simplified modeling analysis of the change in the mechanical power of generator i is performed to determine the transient change expression of the mechanical power of generator i:

[0085]

[0086] Furthermore, in step S3, the linear function expressions of the electromagnetic power and mechanical power calculated in step S2 are used as inputs, and the frequency deviation expression is derived based on the rotor motion equation.

[0087] S31: According to the rotor motion equation The transient expression for the frequency deviation can be obtained:

[0088]

[0089] Among them, t nadir These are unknown parameters and require further calculations to solve.

[0090] Furthermore, in step S4, based on the approximate unified transfer function of each synchronous generator speed governor obtained in step S1, the step of deriving the expression for the mechanical power change of each synchronous generator is as follows:

[0091] S41: By feeding the parabolic frequency deviation variation formula derived in S31 into the transfer function of the equivalent speed governor of the synchronous generator i, the mechanical power output in the frequency domain can be obtained:

[0092]

[0093] C step_i (t) and C ramp_i (t) represent the step response and ramp response of the transfer function of generator i, respectively. i (s) is the transfer function of the generator i equivalent speed governor.

[0094] S42: Applying the inverse Laplace transform, we can obtain:

[0095]

[0096] In the formula, ΔP′ mi(t) is the change in mechanical power derived from the open-loop transfer function by analyzing the active-frequency response mechanism, and ΔP obtained by fitting the aforementioned PMU measured data. mi (t) are different.

[0097] Furthermore, in step S5, the arrival time t of the extreme value of the frequency deviation is established. nadir The steps for solving the linear equation iteratively are as follows:

[0098] S51: Substituting the approximate unified structure of the generator i equivalent speed governor into the physical-data fusion model, when the frequency deviation reaches its extreme value, the change in mechanical power and the change in electromagnetic power of each synchronous generator are equal. Therefore, we have:

[0099]

[0100] In the formula t nadir It is an unknown parameter; ΔP ei (t0), H i l i (t) is calculated based on PMU measurement data and is dynamically updated in real time following the prediction time t; [k i_0 ,k i_1 ,…k i_n The results are calculated from offline data analysis and then stored in the online prediction model.

[0101] S51: From t nadir The unknown parameter t is gradually increased starting from 0. nadir The value of is taken until the difference between the two sides of the equation in S51 meets the error requirement. At this point, the solution t is obtained. nadir This is the predicted arrival time of the extreme value of frequency deviation.

[0102] Furthermore, in step S6, the PMU collects the electromagnetic power and frequency deviation changes at the terminals of each synchronous generator from the moment of disturbance to the current prediction time, and indirectly calculates the mechanical power changes of each synchronous generator based on the rotor motion equation. Based on the numerous sampling data from the PMU at equal time intervals, the change curves of electromagnetic power and mechanical power are fitted using high-order polynomial functions, with fitting at order 3 to 5 being appropriate.

[0103] Furthermore, in step S7, based on the rotor motion equation and combined with the previously calculated predicted arrival time of the extreme frequency deviation, the predicted value of the extreme frequency deviation is integrally solved:

[0104]

[0105] H i (t) and t nadir_pre_iThese are the real-time inertial time constant and the predicted arrival time of the extreme frequency deviation of power generation cluster i at time t, respectively.

[0106] Furthermore, in step S8, the "prediction error index" of the current frequency deviation extreme value prediction is calculated to analyze the current prediction accuracy. If the current prediction accuracy meets the requirements, the current frequency deviation extreme value prediction is output, indicating the steps of the subsequent frequency stability analysis process:

[0107] S81: Initially set the "Prediction Error Index" (PEI) to 1. With a PMU sampling interval of 0.01s, starting from 0.01*n seconds after the disturbance, for each prediction, take the extreme predicted value of the frequency deviation corresponding to the current and the previous n sampling points, and calculate their average value:

[0108]

[0109] In the formula, [Δf max_i (t k-n ),Δf max_i (t k-n+1 ),…Δf max_i (t k )],(t k <t) represents the most recent n+1 predicted extreme values ​​of frequency deviation; f ave_i (t) is the average of the n+1 predicted values.

[0110] S82: Standardize the next n+1 predicted values:

[0111]

[0112] In the formula, Δf pu_i (t k-i ), i∈[0,1,…n] are the n+1 frequency deviation extreme value predictions after standardization.

[0113] S83: Calculate the slope df of the predicted value after "standardization". pu_i (t k ):

[0114]

[0115] S84: Calculate the per-unit slope average index A1:

[0116]

[0117] S85: Calculate the per-unit slope variance index A2:

[0118]

[0119] S86: Discrete simulation determines reasonable limits for A1 and A2, and the real-time calculated A1(t) is used to... k ) and A2(t k Each value is compared with the limit value. When each value is less than the upper limit value, PEI changes from 1 to 0; otherwise, PEI remains at 1.

[0120] S87: When the "Prediction Error Index" PEI becomes 0, the prediction system outputs the dynamic prediction result; when the "Prediction Error Index" PEI is still 1, return to step S2, wait for the next sampling point data of PMU to be uploaded, execute S2-S7, and calculate the frequency deviation extreme value prediction value again.

[0121] This invention is applied to a four-unit, two-area wind power system. Five wind turbines are added to node 7 of the original system. Each turbine is equivalent to 50 doubly-fed wind turbines with a rated capacity of 2MW. The doubly-fed wind turbines employ a third-order model that ignores stator transients. To fully analyze the model's prediction accuracy under different renewable energy penetration rates, simulations are conducted at wind power penetration rates of 12.98%, 19.47%, 25.96%, and 38.94%. A sudden active power reduction fault of 273.4MW is simulated at node 7, and online prediction of frequency deviation extremes is performed sequentially. The flowchart of the online prediction method for frequency deviation extremes is shown below. Figure 1 As shown, it includes the following steps:

[0122] S1 offline testing establishes an approximate unified structure transfer function for the governors of each synchronous generator in the system.

[0123] Based on PMU measured data, S2 uses linear functions to approximate the changes in electromagnetic power and mechanical power of each synchronous generator in the system during the transient process from the moment it is subjected to an active power disturbance to the point where the frequency deviation reaches its extreme value.

[0124] S3 takes the linear function expressions of electromagnetic power and mechanical power calculated in step S2 as input, and derives the expression of frequency deviation based on the rotor motion equation.

[0125] Based on the approximate unified transfer function of each synchronous generator speed governor in step S1, S4 further derives the expression for the mechanical power change of each synchronous generator.

[0126] S5 establishes information about the arrival time t of the extreme value of frequency deviation. nadir The linear equation is solved iteratively.

[0127] Based on PMU measured data, S6 uses high-order linear functions to approximately describe the changes in electromagnetic power and mechanical power of each synchronous generator in the system during the transient process from the moment it is subjected to an active disturbance to the point where the frequency deviation reaches its extreme value.

[0128] S7 is based on the rotor motion equation, combined with the predicted arrival time of the extreme frequency deviation, and integrally solves for the predicted extreme frequency deviation value.

[0129] S8 calculates the "prediction error index" of the current frequency deviation extreme value prediction and analyzes the current prediction accuracy. If the current prediction accuracy meets the requirements, it outputs the current frequency deviation extreme value prediction, indicating the subsequent frequency stability analysis process.

[0130] like Figure 2 As shown, with the advancement of the prediction time and the increase of PMU sampling data, the linear function fitting parameters of the electromagnetic power at the generator terminals of each synchronous generator in the system are continuously updated.

[0131] like Figure 3 As shown, based on the measured data of the PMU, a higher-order and more accurate high-order function is fitted to the electromagnetic power and mechanical power of each synchronous generator. Combined with the predicted arrival time of the extreme frequency deviation calculated in step S5, the predicted extreme frequency deviation value is solved by integrating the rotor motion equation. As the prediction time progresses, the amount of PMU sampling data increases, and the predicted arrival time of the extreme frequency deviation value is continuously updated, thus continuously updating the predicted extreme frequency deviation value as well.

[0132] like Figure 4 As shown, the prediction process for the extreme value of frequency deviation at a single prediction time mainly includes three stages: data input, data processing, and fusion model analysis to solve for the predicted value. In the data input stage, offline testing is used to determine the unified approximate simplified structural parameters of the governors of each synchronous generator in the system. In the data processing stage, the least squares function is used to fit the transient quantities of the system before and after the disturbance measured by the PMU, including the change in electromagnetic power at the generator terminal and the change in mechanical power of each synchronous generator obtained indirectly. In the fusion model analysis to solve for the predicted value stage, the approximate expressions of electromagnetic power and mechanical power fitted by the data are input into the active power-frequency open-loop decoupling model to establish an equation regarding the arrival time of the extreme value of frequency deviation. After iterative solution, the predicted value of the extreme value of frequency deviation is further solved by integration.

[0133] like Figure 5 As shown, a doubly-fed induction generator (DFIG) wind turbine model is incorporated into node 7 of a classic four-unit, two-region system. Under the condition of a wind power penetration rate of 19.47%, a sudden active power reduction fault of 273.4 MW is simulated at node 7. Simultaneously, the PMU sampling frequency is set to 100 Hz, and the "prediction error index" analysis object is the predicted extreme values ​​of all frequency deviations within a 0.3-second window, i.e., n = 29. Correspondingly, one component of the "prediction error index," the slope quantification index A1, decreases as the prediction duration increases and the amount of sampled data increases, consistent with the changing trend of the prediction error.

[0134] like Figure 6As shown, the slope quantification index A2, one of the components of the "prediction error index," also decreases with increasing prediction duration and more sampled data, consistent with the trend of prediction error. (In summary...) Figure 5 Together, they reflect the effectiveness of the "prediction error index" in indirectly describing prediction accuracy.

[0135] like Figure 7 As shown, the limits for A1 and A2 are set to 4 and 0.05 respectively. The frequency deviation extreme values ​​of each generator are predicted under different new energy penetration rates, and the effectiveness of the online prediction model is analyzed.

[0136] It can be seen that the online prediction models under the four wind power penetration rates can output the predicted values ​​of the extreme frequency deviation at the terminals of the four synchronous generators before the extreme value of frequency deviation is reached, with a prediction lead time of 3 to 6 seconds, indicating that the model prediction speed is relatively fast. Figure 8 The error of the predicted extreme values ​​of frequency deviation was analyzed. The online prediction model proposed in this paper, because it considers the transient changes in electromagnetic power at the turbine terminals after disturbance, reduces the prediction error by more than half compared to the SFR model. The predictions of the extreme values ​​of frequency deviation at the turbine terminals for four different wind power penetration rates and four synchronous turbines are all within the 20% error range. In summary, the online prediction model proposed in this paper can balance prediction speed and accuracy to a certain extent, meeting the requirements of practical systems.

[0137] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 prediction of frequency deviation extreme values ​​based on wide-area measurement information, characterized in that, include: S1: Establish an approximate unified structural transfer function model for the governors of various synchronous generators in the power grid through offline testing; S2: Fit the measured data of the wide-area measurement PMU of each synchronous generator using a linear function to obtain the first electromagnetic power change expression and the first mechanical power change expression before and after the active power disturbance; S3: Input the first electromagnetic power change expression and the first mechanical power change expression into the rotor motion equation to derive the transient expression of frequency deviation; S4: Input the frequency deviation transient expression into the approximate unified structural transfer function model to derive the second mechanical power expression; S5: When the frequency deviation reaches its extreme value, the value of the second mechanical power expression is equal to the value of the first electromagnetic power change expression, thus obtaining an equation about the arrival time of the extreme value of the frequency deviation. The predicted value of the arrival time of the extreme value of the frequency deviation is obtained by iterative solution. S6: Fit the measured data of the PMU using a high-order linear function to obtain the third electromagnetic power change expression and the third mechanical power change expression of each generator before and after the active power disturbance; S7: Input the third electromagnetic power change expression, the third mechanical power change expression, and the arrival time prediction value into the rotor motion equation to solve for the frequency deviation extreme value prediction value; S8: Calculate the prediction error index corresponding to the predicted extreme values ​​of frequency deviation at multiple time points; take the predicted extreme values ​​of frequency deviation that meet the accuracy of the frequency error index as the effective output.

2. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in claim 1, characterized in that, S1 includes: S11: Input the step frequency deviation to the speed governor of each synchronous generator cluster, collect the step response data of mechanical power, and perform discrete integration on the step response data to obtain the ramp response. S12: By fitting the ramp response of each speed controller using a linear polynomial, we obtain: C ramp_i (t)=k i_0 +k i_1 t+…k i_n t n ,t∈(0,t fit ) C ramp_i (t) represents the ramp response of the generator i governor. The parameters for the polynomial linear fit of the ramp response of the generator i governor are: t fit The fitting time should be greater than the time t required to reach the extreme value of the frequency deviation. nadir ; S12: The approximate unified structure transfer function model is derived using the Laplace transform as follows: In the formula, G i '(s) is the approximate unified structure transfer function of the generator i governor.

3. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in claim 1, characterized in that, The PMU measured data includes: electromagnetic power data and mechanical power data of each generator speed governor during the transient process from the moment the active power disturbance occurs to the point where the frequency deviation reaches its extreme value at each generator terminal; S2 includes: S21: Use the least squares method to fit the electromagnetic power data to obtain the expression for the first electromagnetic power change: ΔP ei (t)=ΔP ei (t0)+l i (t)t,t∈(t0,t nadir ); t0 and t nadir These are the instant of disturbance and the moment when the frequency deviation reaches its extreme value, respectively; ΔP ei (t0) represents the initial electromagnetic power deficit of generator i at the instant of disturbance; i (t) represents the least squares adaptive linear fitting parameters; S22: Using a linear function with a constant slope, model and analyze the mechanical power data to determine the first mechanical power change expression for generator i: ΔP mi (t nadir ) represents the time t when the frequency deviation reaches its extreme value. nadir The change in mechanical power of generator i.

4. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in claim 3, characterized in that, S3 includes: inputting the first electromagnetic power change expression and the first mechanical power change expression into the rotor motion equation. The transient expression for the frequency deviation is obtained as follows: Among them, t nadir H is the variable in the equation. i Let be the real-time inertial time constant of power generation cluster i at time t.

5. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in claim 4, characterized in that, S4 includes: By inputting the transient expression of frequency deviation into the approximate unified structural transfer function model, the expression for the first mechanical power change in the frequency domain of each synchronous generator is derived: Among them, C step_i (t) and C ramp_i (t) represent the step response and ramp response of the transfer function of generator i, respectively. i (s) is the transfer function of the equivalent speed governor of generator i; by analyzing the active power frequency response mechanism, the expression for the second mechanical power change is derived based on the open-loop transfer function.

6. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in claim 1, characterized in that, S5 includes: S51: When the frequency deviation reaches its extreme value, the value of the second mechanical power expression of each synchronous generator is equal to the value of the first electromagnetic power change expression, then: In the formula t nadir It is the variable in the equation; ΔP ei (t0), H i l i (t) is calculated based on PMU measurement data and is dynamically updated in real time following the prediction time t; [k i_0 ,k i_1 ,…k i_n This was derived from offline data analysis. S52: From t nadir =Starting from 0, gradually increase until the difference between the two sides of the equation in S51 meets the error requirement, and then solve for t. nadir This is the predicted arrival time of the extreme value of the frequency deviation.

7. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in claim 1, characterized in that, S7 includes: converting the third electromagnetic power change expression ΔP e " i (t), the expression for the change in the third mechanical power ΔP m " i (t) and the predicted arrival time t nadir Inputting the rotor motion equation, we obtain: Integrating it yields t nadir_pre_i Let t be the predicted arrival time of the extreme value of the frequency deviation of power generation cluster i at time t.

8. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in any one of claims 1-7, characterized in that, S8 includes: Calculate the prediction error index corresponding to the extreme predicted values ​​of the frequency deviation at multiple time points; When the prediction error index meets the accuracy requirement, the corresponding frequency deviation extreme value prediction value is output. When the prediction error index does not meet the required accuracy, update the PMU measured data and repeat steps S2-S7 until the corresponding prediction error index meets the required accuracy, thereby obtaining the corresponding frequency deviation extreme value prediction.

9. The online prediction method for frequency deviation extreme values ​​based on wide-area measurement information as described in claim 8, characterized in that, S8 includes: S81: Initially set the prediction error index PEI to 1. For each prediction, take the extreme predicted value of the frequency deviation corresponding to the current and the previous n PMU sampling points, and calculate their average value f. ave_i (t); S82: Standardize the next n+1 predicted values: S83: Calculate the slope of the predicted value after normalization: S84: Calculate the per-unit slope average index A1: S85: Calculate the per-unit slope variance index A2: S86: Discrete simulation determines the upper and lower limits of A1 and A2, and the real-time calculated A1(t) is used to determine the upper and lower limits of A1 and A2. k ) and A2(t k Each value is compared with the limit; when both are less than the upper limit, PEI becomes 0; otherwise, PEI remains 1. S87: Output dynamic prediction results when the prediction error index PEI becomes 0; if the prediction error index PEI is still 1, update the PMU measured data and repeat S2-S7 until the prediction error index PEI becomes 0, thereby obtaining the corresponding frequency deviation extreme value prediction.

10. A frequency deviation extreme value online prediction device based on wide-area measurement information, characterized in that, Used to perform the online prediction method for frequency deviation extremes based on wide-area measurement information as described in any one of claims 1-9.

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