CN115764928A - Wide-area measurement information-based frequency deviation extreme value online prediction method and device - Google Patents

Wide-area measurement information-based frequency deviation extreme value online prediction method and device Download PDF

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CN115764928A
CN115764928A CN202211484684.8A CN202211484684A CN115764928A CN 115764928 A CN115764928 A CN 115764928A CN 202211484684 A CN202211484684 A CN 202211484684A CN 115764928 A CN115764928 A CN 115764928A
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frequency deviation
value
prediction
extreme value
expression
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柯贤波
姚伟
张钢
邓贤哲
王吉利
马晓伟
程林
文劲宇
黄远超
任冲
施秀萍
卫琳
刘诗雨
陈翔宇
谢醉冰
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Northwest Branch Of State Grid Corp Of China
Huazhong University of Science and Technology
China EPRI Electric Power Engineering Co Ltd
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Northwest Branch Of State Grid Corp Of China
Huazhong University of Science and Technology
China EPRI Electric Power Engineering Co Ltd
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Abstract

The invention discloses a frequency deviation extreme value online prediction method and device based on wide area measurement information, and belongs to the technical field of power system frequency stability control. Meanwhile, an index of 'prediction error index' is provided to indirectly quantify the error of the predicted value of each frequency deviation extreme value and guide the on-line prediction model to rapidly and intelligently output an effective predicted value with the accuracy meeting the requirement. Therefore, the method has certain prediction accuracy and high prediction speed.

Description

Wide-area measurement information-based frequency deviation extreme value online prediction method and device
Technical Field
The invention belongs to the technical field of power system frequency stability control, and particularly relates to a frequency deviation extreme value online prediction method and device based on wide area measurement information.
Background
In recent years, the grid-connected scale of new energy such as wind power generation and the like is gradually increased, the system inertia level is obviously reduced, and the characteristic of obvious space-time distribution is presented. Meanwhile, the large-scale production of the direct-current transmission project further increases the risk of occurrence of large-scale power shortage faults caused by direct-current blocking, and because the new energy unit has no primary frequency modulation capability, the transient frequency deviation extreme value of the power grid is remarkably increased after active mutation, and the system frequency safety is seriously threatened. Therefore, an accurate and rapid frequency stability online evaluation model is urgently needed to be established, the frequency instability risk of the power grid is predicted in advance by carrying out real-time dynamic prediction on the frequency deviation extreme value of the disturbed system, and the safe and stable operation of the system is ensured.
At present, a commonly used frequency online prediction method for a new energy system mainly comprises an equivalent model analysis method, a data driving method based on artificial intelligence and a physical model and data driving fusion method. Most of the traditional equivalent model analysis methods are based on the assumption of one inertia center, and cannot analyze the space-time distribution characteristics of the frequency. For a power grid with uneven inertia space distribution caused by a large amount of new energy grid connection, the prediction precision of a single-machine equivalence method is insufficient. The existing pure data driving method is still high in dependency on input data, the number of samples required by a corresponding high-dimensional training model is exponentially increased when a large power grid is analyzed, real-time collected data of an actual system are few, and time-varying property is strong, so that the pure data driving method cannot achieve the prediction accuracy of an ideal model in engineering application. Moreover, the operation process of artificial intelligence has a black box form, so that interpretability and traceability still need to be greatly improved.
Most of the existing data-physical fusion driving methods are not really deep into an active-frequency response mechanism of a system, or the fusion method is too simple, so that the requirements of an actual system on prediction precision and speed cannot be completely met.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a frequency deviation extreme value online prediction method and a frequency deviation extreme value online prediction device based on wide area measurement information, and aims to obtain transient operation data before and after a power grid is disturbed by using the wide area measurement technology, improve the accuracy of the prediction method, realize online rapid prediction output of the frequency deviation extreme value by using the advantage that a physical-data fusion driving method has higher calculation speed compared with a pure model analysis method, provide a reference basis for subsequent frequency stabilization quantitative evaluation, and solve the technical problems of low precision and low speed of the conventional frequency deviation extreme value prediction.
In order to achieve the above object, according to an aspect of the present invention, there is provided an online prediction method for an extreme value of frequency deviation based on wide-area measurement information, comprising:
s1: establishing an approximate uniform structure transfer function model of each synchronous generator speed regulator of the power grid through an offline test;
s2: fitting actual measurement data of PMUs of the synchronous generators by using a linear function to obtain a first electromagnetic power change expression and a first mechanical power change expression before and after active disturbance;
s3: inputting the first electromagnetic power change expression and the first mechanical power change expression into a rotor motion equation, and deducing to obtain a frequency deviation transient expression;
s4: inputting the frequency deviation transient expression into the approximate uniform structure transfer function model, and deducing a second mechanical power expression;
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 to obtain an equation about the arrival time of the frequency deviation extreme value, and iterative solution is carried out to obtain a predicted arrival time value of the frequency deviation extreme value;
s6: fitting the PMU measured data by using a high-order linear function to obtain a third electromagnetic power change expression and a third mechanical power change expression of each generator before and after active disturbance;
s7: inputting the third electromagnetic power change expression, the third mechanical power change expression and the predicted value of the arrival time into the rotor motion equation, and solving a predicted value of a frequency deviation extreme value;
s8: calculating a prediction error index corresponding to the predicted value of the frequency deviation extreme value at a plurality of time points; and taking the frequency deviation extreme value predicted value corresponding to the frequency error index meeting the precision as effective output.
In one embodiment, the S1 includes:
s11: step frequency deviation is respectively input to speed controllers of all synchronous generator clusters, step response data of mechanical power is collected, and discrete integration is carried out on the step response data to obtain slope response;
s12: the slope response of each speed regulator is fitted by using a linear polynomial to obtain:
Figure BDA0003961571750000031
C ramp_i (t) is the ramp response of the generator i governor,
Figure BDA0003961571750000032
a polynomial linear fit parameter for generator i-governor ramp response; t is t fit Is the fitting duration; the fitting time length should be greater than the arrival time length t of the frequency deviation extreme value nadir ；
S12: and utilizing Laplace transform to derive the approximate uniform structure transfer function model as follows:
Figure BDA0003961571750000033
in formula (II), G' i (s) is an approximately uniform structural transfer function of the generator i speed governor.
In one embodiment, the PMU measurement data includes: electromagnetic power data and mechanical power data of each generator speed regulator in the transient process from the moment when each generator end of each synchronous generator is subjected to active disturbance to the moment when the frequency deviation reaches an extreme value; the S2 comprises the following steps:
s21: fitting the electromagnetic power data by using a least square method to obtain the first electromagnetic power change expression: delta P ei (t)＝ΔP ei (t 0 )+l i (t)t,t∈(t 0 ,t nadir )；t 0 And t nadir Respectively, the disturbed instant and when the frequency deviation reaches the extreme valueEngraving; delta P ei (t 0 ) Is the initial electromagnetic power shortage of the disturbed transient generator i; l i (t) is a least square method adaptive linear fitting parameter;
s22: performing modeling analysis on the mechanical power data by using a linear function with a constant slope, and determining a first mechanical power change expression of the generator i:
Figure BDA0003961571750000034
ΔP mi (t nadir ) For the moment t at which the frequency deviation reaches the extreme value nadir The amount of change in the mechanical power of the generator i.
In one embodiment, the S3 includes: inputting the first electromagnetic power variation expression and the first mechanical power variation expression into a rotor motion equation
Figure BDA0003961571750000041
Obtaining the frequency deviation transient expression:
Figure BDA0003961571750000042
Figure BDA0003961571750000043
wherein, t nadir Is a variable of an equation, H i And the real-time inertia time constant of the power generation cluster i at the moment t.
In one embodiment, the S4 includes:
inputting the frequency deviation transient expression into the approximate uniform structure transfer function model, and deducing a first mechanical power change expression on the frequency domain of each synchronous generator:
Figure BDA0003961571750000044
wherein, C step_i (t) and C ramp_i (t) step response and ramp response of generator i speed regulator transfer function, G i (s) is the transfer function of the equivalent speed governor of the generator i; by analysing active frequenciesRate response mechanism, and a second mechanical power change expression obtained by derivation according to open-loop transfer function
Figure BDA0003961571750000045
In one embodiment, the S5 includes:
s51: when the frequency deviation reaches an 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, and then:
Figure BDA0003961571750000046
in the formula t nadir Is an equation variable; delta P ei (t 0 )、H i 、l i (t) calculating based on PMU measurement data, and dynamically updating in real time along with the predicted time t; [ k ] A i_0 ,k i_1 ,…k i_n ]Is obtained by off-line data analysis;
s52: from t nadir =0 starts to increase gradually until the difference between both sides of the equation in S51 satisfies t obtained by solving the error requirement nadir Namely, the predicted value is the arrival time of the frequency deviation extremum.
In one embodiment, the S7 includes: changing the third electromagnetic power into an expression delta P ″ ei (t) the third mechanical power variation expression Δ P ″ mi (t) and the arrival time prediction value t nadir Inputting the rotor motion equation to obtain:
Figure BDA0003961571750000051
integral solution is carried out on the obtained product to obtain t nadir_pre_i And (4) obtaining a predicted value of the arrival time of the frequency deviation extreme value of the power generation cluster i at the time t.
In one embodiment, the S8 includes:
calculating a prediction error index corresponding to the predicted value of the frequency deviation extreme value at a plurality of time points;
when the prediction error index meets the precision, outputting a corresponding frequency deviation extreme value prediction value;
and when the prediction error index does not meet the precision, updating the actual measurement data of the PMU to repeatedly execute S2-S7 until the corresponding prediction error index meets the precision, thereby obtaining the predicted value of the corresponding frequency deviation extreme value.
In one embodiment, the S8 includes:
s81: initially setting the prediction error index PEI to be 1, taking the frequency deviation extreme value prediction values corresponding to the current and the previous n PMU sampling points in each prediction, and calculating the average value f of the frequency deviation extreme value prediction values ave_i (t)；
S82: performing per unit on the adjacent n +1 predicted values:
Figure BDA0003961571750000052
s83: calculate predicted value slope after per-unit:
Figure BDA0003961571750000053
s84: calculating a per-unit slope average index A1:
Figure BDA0003961571750000054
s85: calculating a per-unit slope variance index A2:
Figure BDA0003961571750000055
s86: discrete simulation determines the upper and lower limit values of A1 and A2, and A is calculated in real time 1 (t k ) And A 2 (t k ) Respectively comparing with a limit value; PEI becomes 0 when both are less than the upper limit value; whereas PEI still maintained 1;
s87: outputting a dynamic prediction result when the prediction error index PEI becomes 0; and when the prediction error index PEI is still 1, updating the actual measurement data of the PMU and repeatedly executing S2-S7 until the prediction error index PEI becomes 0, thereby obtaining the corresponding frequency deviation extreme value prediction value.
According to another aspect of the present invention, an apparatus for on-line prediction of frequency deviation extremum based on wide-area measurement information is provided, which is used for executing the method for on-line prediction of frequency deviation extremum.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
on the basis of a traditional pure physical analysis model, the transient state change of the electromagnetic power on each regional interconnection line is approximately fitted by utilizing wide-area measurement information, a physical-data fusion simplified prediction model capable of being rapidly calculated is established, and meanwhile, the influence of new energy such as wind power on a frequency response process and the characteristics of inertia space-time distribution are considered into the frequency analysis model through the wide-area measurement information, so that the accuracy of the prediction model is improved. Meanwhile, an index of 'prediction error index' is provided to indirectly quantify the error of the predicted value of each frequency deviation extreme value and guide the on-line prediction model to rapidly and intelligently output an effective predicted value with the accuracy meeting the requirement. Therefore, the method has certain prediction accuracy and high prediction speed.
Drawings
FIG. 1 is a flowchart of an exemplary method for on-line prediction of frequency deviation extremum based on wide-area measurement information;
FIG. 2 is a schematic diagram of a fitting method of a linear function of electromagnetic power at the generator end according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a dynamic prediction process of extreme frequency deviation according to an embodiment of the present invention;
FIG. 4 is a flow chart of the online prediction of the extreme frequency deviation value at a single predicted time point according to an embodiment of the present invention;
FIG. 5 is a graph showing the predicted value of the frequency deviation extremum and the slope quantization index A1 varying with the predicted duration according to an embodiment of the present invention;
FIG. 6 is a graph of the predicted extreme value of frequency deviation and the variance quantization index A2 varying with the predicted duration according to an embodiment of the present invention;
FIG. 7 is a simulation diagram of the predicted speed of the extreme frequency deviation value of 4 synchronous generators of the four-generator two-region system under different wind permeability according to an embodiment of the present invention;
fig. 8 is a simulation diagram of the prediction accuracy of the frequency deviation extremum of 4 synchronous generators in the four-generator two-region system under different wind permeability in one embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
s1: and (5) performing off-line test, and establishing an approximate uniform structure transfer function of each synchronous generator speed regulator of the system.
S2: based on PMU measured data, a linear function is respectively utilized to approximately describe the electromagnetic power and mechanical power change of each synchronous generator in the system in the transient process from the moment of receiving active disturbance to the moment of reaching an extreme value of frequency deviation.
S3: and (3) taking the linear function expression of the electromagnetic power and the mechanical power obtained by calculation in the step (S2) as input, and deducing a frequency deviation expression based on a rotor motion equation.
S4: and further deducing and obtaining a mechanical power change expression of each synchronous generator based on the approximate uniform transfer function of each synchronous generator speed regulator in the step S1.
S5: establishing an arrival time t for an extreme value of a frequency deviation nadir And iteratively solving.
S6: based on actual measurement data of PMUs, high-order linear functions are respectively utilized to approximately describe the electromagnetic power and mechanical power changes of each synchronous generator in the system in the transient process from the moment of receiving active disturbance to the moment of reaching an extreme value of frequency deviation.
S7: and on the basis of a rotor motion equation, integrating and solving the predicted value of the frequency deviation extreme value by combining the predicted value of the arrival time of the frequency deviation extreme value.
S8: and calculating the 'prediction error index' index of the predicted value of the current frequency deviation extreme value, and analyzing the current prediction precision. And if the current prediction precision meets the requirement, outputting a current frequency deviation extreme value prediction value and indicating the subsequent frequency stability analysis process.
Further, the step S1 of off-line testing and establishing an approximate simplified structure of each synchronous generator speed regulator of the system comprises the following steps:
s11: and respectively inputting the frequency deviation in a step form to the speed regulators of all the synchronous generator clusters of the multi-machine system, collecting output data corresponding to the mechanical power variation, and performing discrete integration on actually measured step response data to obtain slope response.
S12: and (3) fitting the slope response of each structure speed regulator by using a linear polynomial:
C ramp_i (t)＝k i_0 +k i_1 t+…k i_n t n ,t∈(0,t fit )
in the formula, C ramp_i (t) is the ramp response of the generator i governor transfer function,
Figure BDA0003961571750000081
polynomial linear fit parameters for generator i governor ramp response; (0,t) fit ) Meaning that the ramp response data in the corresponding time interval is selected for polynomial fitting. The fitting time duration is longer than the actual frequency deviation extreme value arrival time duration t of the system nadir A range of 5 to 20s is recommended. It is reasonable to choose 2 to 6 linear fitting orders.
S13: by utilizing Laplace transform, a unified form of each type of speed regulator transfer function is deduced, namely:
Figure BDA0003961571750000082
in the formula (II), G' i (s) is a near uniform structural transfer of generator i speed governorA function.
Further, the step S2 of approximately describing the electromagnetic power and mechanical power changes of each synchronous generator in the system in a transient process from the instant of receiving the active disturbance to the time when the frequency deviation reaches the extreme value by using the linear function of the first order based on the actual measurement data of the PMU is as follows:
s21: in the system, a PMU (power management unit) acquires electromagnetic power data of a plurality of machine ends at a fixed sampling frequency from the disturbed moment to the current prediction moment of each synchronous generator. Based on the measured data, obtaining an electromagnetic power change expression in a linear function form of each synchronous generator by using least square fitting:
ΔP ei (t)＝ΔP ei (t 0 )+l i (t)t,t∈(t 0 ,t nadir )
wherein, t 0 And t nadir Respectively the disturbed moment and the moment when the frequency deviation reaches the extreme value; delta P ei (t 0 ) Is the initial electromagnetic power shortage of the disturbed transient generator i; l i And (t) is a least square method adaptive linear fitting parameter.
S22: the method comprises the following steps of carrying out simplified modeling analysis on the change of the mechanical power of the generator i speed regulator by utilizing a linear function with a constant slope, and determining a transient change expression of the mechanical power of the generator i:
Figure BDA0003961571750000091
further, in step S3, the step of taking the linear function expression of the electromagnetic power and the mechanical power calculated in step S2 as input, and deriving a frequency deviation expression based on the rotor motion equation includes:
s31: according to the equation of motion of the rotor
Figure BDA0003961571750000092
A transient expression for the frequency deviation can be found:
Figure BDA0003961571750000093
wherein, t nadir Is an unknown parameter and needs to be solved by subsequent calculation.
Further, in step S4, based on the approximately uniform transfer function of the speed regulators of the synchronous generators in step S1, the step of further deriving and obtaining the mechanical power variation expression of each synchronous generator is as follows:
s41: and (3) sending the parabolic frequency deviation variation formula deduced in the step (S31) to an equivalent speed regulator transfer function of the synchronous generator i to obtain mechanical power output on a frequency domain:
Figure BDA0003961571750000094
C step_i (t) and C ramp_i (t) step response and ramp response, G, of the generator i governor transfer function, respectively i (s) is the transfer function of the equivalent governor for the generator i.
S42: applying an inverse laplace variation can result in:
Figure BDA0003961571750000101
in the formula,. DELTA.P' mi (t) is the delta P obtained by analyzing the active-frequency response mechanism, deducing the mechanical power variable quantity according to the open-loop transfer function and fitting the variable quantity with the actual measurement data based on the PMU mi (t) is different.
Further, the arrival time t of the extreme value of the frequency deviation is established in step S5 nadir The steps of linear equation and iterative solution of (a) are:
s51: substituting an approximate uniform structure of the generator i equivalent speed regulator into a physical-data fusion model, wherein when the frequency deviation reaches an extreme value, the mechanical power variable quantity and the electromagnetic power variable quantity of each synchronous generator are equal, so that the method comprises the following steps:
Figure BDA0003961571750000102
in the formula t nadir Is an unknown parameter; delta P ei (t 0 )、H i 、l i (t) calculating based on PMU measurement data, and dynamically updating in real time along with the predicted time t; [ k ] A i_0 ,k i_1 ,…k i_n ]The data is obtained by analyzing and calculating the off-line data and then stored in the on-line prediction model.
S51: from t nadir =0 starting to gradually increase the unknown parameter t nadir Until the difference between the two sides of the equation in S51 meets the error requirement, at this time, the solved t is obtained nadir Namely the predicted value of the arrival time of the frequency deviation extreme value.
Further, the PMU in step S6 collects the electromagnetic power and frequency deviation change at the end of each synchronous generator from the disturbed moment to the current prediction moment, and the mechanical power change of each synchronous generator is indirectly calculated based on the rotor motion equation. Based on a plurality of sampling data of PMU at equal time intervals, the variation curves given by the electromagnetic power and the mechanical power are respectively fitted by using a high-order polynomial function, and the fitting is more suitable when the fitting is finished for 3-5 times.
Further, in step S7, based on the rotor motion equation, and in combination with the predicted value of the arrival time of the frequency deviation extremum obtained by the calculation, the predicted value of the frequency deviation extremum is solved through integration:
Figure BDA0003961571750000111
H i (t) and t nadir_pre_i And respectively obtaining a real-time inertia time constant and a predicted value of the arrival time of the frequency deviation extreme value of the power generation cluster i at the time t.
Further, in step S8, a "prediction error index" index of the predicted value of the current frequency deviation extremum is calculated, and the current prediction accuracy is analyzed. If the current prediction precision meets the requirement, outputting a current frequency deviation extreme value prediction value, and indicating the subsequent frequency stability analysis process as follows:
s81: the method comprises the following steps of initially setting a 'prediction error index' PEI to be 1, starting from 0.01 x n seconds after disturbance on the premise that PMU sampling interval is 0.01s, taking frequency deviation extreme value prediction values corresponding to the current and the previous n sampling points during each prediction, and calculating the average value of the frequency deviation extreme value prediction values:
Figure BDA0003961571750000112
wherein, [ Delta f [ ] max_i (t k-n ),Δf max_i (t k-n+1 ),…Δf max_i (t k )],(t k < t) is the nearest n +1 frequency deviation extreme value predicted values; f. of ave_i (t) is the average of n +1 predicted values.
S82: performing per unit on the adjacent n +1 predicted values:
Figure BDA0003961571750000113
in the formula,. DELTA.f pu_i (t k-i ),i∈[0,1,…n]Respectively, the predicted values of the n +1 frequency deviation extreme values after the per-unit operation.
S83: predicted value slope df after calculation of per unit pu_i (t k )：
Figure BDA0003961571750000114
S84: calculating a per-unit slope average index A1:
Figure BDA0003961571750000121
s85: calculating a per-unit slope variance index A2:
Figure BDA0003961571750000122
s86: discrete simulations determine reasonable limits for A1 and A2,a to be calculated in real time 1 (t k ) And A 2 (t k ) Respectively comparing with the limit value, and when the values are all smaller than the upper limit value, changing the PEI from 1 to 0; otherwise, the PEI remains 1.
S87: when the 'prediction error index' PEI is changed into 0, the prediction system outputs a dynamic prediction result; and when the 'prediction error index' PEI is still 1, continuing to return to the step S2, waiting for uploading of data of the next sampling point of the PMU, executing S2-S7, and calculating the predicted value of the frequency deviation extreme value again.
The method is applied to a four-machine two-region system containing wind power, 5 fans are merged into a No. 7 node of an original system, each fan is equivalent to 50 doubly-fed wind generators with rated capacity of 2MW, and the doubly-fed wind generators adopt a three-order model ignoring stator transient state. In order to fully analyze model prediction accuracy under different new energy permeabilities, simulation verification is respectively carried out on four working conditions of 12.98%, 19.47%, 25.96% and 38.94% of wind power permeability, 273.4MW active sudden-reduction fault of the No. 7 node is set, and online prediction of a frequency deviation extreme value is sequentially carried out. The flow chart of the frequency deviation extreme value online prediction method is shown in fig. 1, and comprises the following steps:
s1, performing offline test, and establishing an approximate uniform structure transfer function of each synchronous generator speed regulator of the system.
And S2, based on PMU measured data, respectively utilizing a linear function to approximately describe the electromagnetic power and mechanical power changes of each synchronous generator in the system in a transient process from the moment of receiving active disturbance to the moment of reaching an extreme value of frequency deviation.
And S3, taking the linear function expression of the electromagnetic power and the mechanical power obtained by calculation in the step S2 as input, and deducing a frequency deviation expression based on a rotor motion equation.
And S4, further deducing and obtaining a mechanical power change expression of each synchronous generator based on the approximate uniform transfer function of each synchronous generator speed regulator in the step S1.
S5 establishing the arrival time t of the extreme value related to the frequency deviation nadir And iteratively solving.
And S6, based on actual measurement data of the PMU, respectively utilizing high-order linear functions to approximately describe the electromagnetic power and mechanical power changes of each synchronous generator in the system in a transient process from the moment when the synchronous generator is subjected to active disturbance to the moment when the frequency deviation reaches an extreme value.
And S7, based on the rotor motion equation, integrating and solving the predicted value of the frequency deviation extreme value by combining the predicted value of the arrival time of the frequency deviation extreme value.
And S8, calculating a prediction error index of the predicted value of the current frequency deviation extreme value, and analyzing the current prediction precision. And if the current prediction precision meets the requirement, outputting a current frequency deviation extreme value prediction value and indicating a subsequent frequency stability analysis process.
As shown in fig. 2, as the prediction time goes by, the PMU sampling data increases, and the fitting parameters of the linear function of the electromagnetic power at the synchronous generator end in the system are updated continuously.
As shown in fig. 3, based on the actual measurement data of PMU, higher-order and more accurate high-order function fitting is performed on the electromagnetic power and the mechanical power of each synchronous generator, and the predicted value of the frequency deviation extremum is solved based on the integration of the rotor motion equation in combination with the predicted value of the arrival time of the frequency deviation extremum calculated in step S5. Along with the lapse of the prediction time, PMU sampling data is increased, the predicted value of the arrival time of the frequency deviation extremum is continuously updated, and the predicted value of the frequency deviation extremum is also continuously updated.
As shown in fig. 4, the process of predicting the extreme value of the frequency deviation at a single predicted time mainly includes three stages: and analyzing and solving a predicted value by data input, data processing and a fusion model. In the data input stage, uniform approximate simplified structure parameters of the speed regulators of the synchronous generators in the system are determined through off-line testing; in the data processing stage, performing function fitting of a least square method on transient state quantity before and after system disturbance actually measured by a PMU, wherein the function fitting comprises machine end electromagnetic power variation and variation of mechanical power of each synchronous generator obtained by indirect calculation; and a stage of analyzing and solving the predicted value by the fusion model, inputting an approximate expression of electromagnetic power and mechanical power based on data fitting into an active-frequency open-loop decoupling model, establishing an equation about the arrival time of the frequency deviation extreme value, and further integrating and solving the predicted value of the frequency deviation extreme value after iterative solution.
As shown in FIG. 5, a node 7 of a classic four-machine two-region system is merged into a doubly-fed wind turbine model, and under the working condition that the wind power permeability is 19.47%, a 273.4MW active sudden-reduction fault is set to occur on the node 7. Meanwhile, the PMU sampling frequency is set to be 100Hz, the 'prediction error index' analysis object is a predicted value of all frequency deviation extreme values within 0.3s, namely n =29, and a slope quantization index A1 corresponding to one of the components of the 'prediction error index' index is increased along with the increase of the prediction duration, the sampling data is reduced along with the increase of the prediction data, and the change trend of the prediction error is consistent with the change trend of the prediction error.
As shown in fig. 6, a slope quantization index A2, which is one of the components of the "prediction error index" index, also decreases as the prediction duration increases and the number of sampled data increases, and coincides with the variation trend of the prediction error. And by combining the figure 5, the effectiveness of the prediction precision indirectly described by the index of the prediction error index is reflected.
As shown in fig. 7, the limit values of A1 and A2 are set to be 4 and 0.05, respectively, the extreme value of the frequency deviation of each generator is predicted under different new energy permeabilities, and the effectiveness of the online prediction model is analyzed.
It can be seen that the on-line prediction models under the 4 kinds of wind power permeability can output predicted values of the frequency deviation extreme value at the ends of the 4 synchronous generators before the frequency deviation extreme value reaches, the prediction advance time is 3-6 s, and the model prediction speed is high. The error of the predicted value of the output frequency deviation extreme value is analyzed in fig. 8, the online prediction model provided by the invention takes the transient change of the electromagnetic power at the machine end after disturbance into consideration, so that the prediction error is reduced by more than half compared with that of an SFR model, and the predictions of the frequency deviation extreme value at the machine end of 4 synchronous machines under 4 wind power permeabilities are within the error range of 20%. In conclusion, the online prediction model provided by the invention can give consideration to both the prediction speed and the prediction precision to a certain extent, and meets the requirements of an actual system.
It will be understood by those skilled in the art that the foregoing is only an exemplary embodiment of the present invention, and is not intended to limit the invention to the particular forms disclosed, since various modifications, substitutions and improvements within the spirit and scope of the invention are possible and within the scope of the appended claims.

Claims (10)

1. An online prediction method for frequency deviation extremum based on wide area measurement information is characterized by comprising the following steps:
s1: establishing an approximate uniform structure transfer function model of each synchronous generator speed regulator of the power grid through an offline test;
s2: fitting measured data of the wide-area measurement PMU of each synchronous generator by using a linear function to obtain a first electromagnetic power change expression and a first mechanical power change expression before and after active disturbance;
s3: inputting the first electromagnetic power change expression and the first mechanical power change expression into a rotor motion equation, and deducing to obtain a frequency deviation transient expression;
s4: inputting the frequency deviation transient expression into the approximate uniform structure transfer function model, and deducing a second mechanical power expression;
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 to obtain an equation about the arrival time of the frequency deviation extreme value, and iterative solution is carried out to obtain a predicted arrival time value of the frequency deviation extreme value;
s6: fitting the PMU measured data by using a high-order linear function to obtain a third electromagnetic power change expression and a third mechanical power change expression of each generator before and after active disturbance;
s7: inputting the third electromagnetic power change expression, the third mechanical power change expression and the predicted value of the arrival time into the rotor motion equation, and solving a predicted value of a frequency deviation extreme value;
s8: calculating a prediction error index corresponding to the predicted value of the frequency deviation extreme value at a plurality of time points; and taking the predicted value of the frequency deviation extreme value corresponding to the frequency error index meeting the precision as effective output.
2. The wide-area measurement information-based online prediction method of frequency deviation extremum as claimed in claim 1, wherein the S1 comprises:
s11: step frequency deviation is respectively input to speed controllers of all synchronous generator clusters, step response data of mechanical power is collected, and discrete integration is carried out on the step response data to obtain slope response;
s12: the slope response of each speed regulator is fitted by using a linear polynomial to 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) is the ramp response of the generator i governor,
Figure FDA0003961571740000021
a polynomial linear fit parameter for generator i-governor ramp response; t is t fit Is the fitting duration; the fitting time length should be greater than the arrival time length t of the frequency deviation extreme value nadir ；
S12: and utilizing Laplace transform to derive the approximate uniform structure transfer function model as follows:
Figure FDA0003961571740000022
in the formula, G i '(s) is an approximately uniform structural transfer function of the generator i speed governor.
3. The method of claim 1, wherein the PMU measured data includes: electromagnetic power data and mechanical power data of speed regulators of the generators in the transient process from the moment when the generator ends of the synchronous generators are subjected to active disturbance to the moment when the frequency deviation reaches an extreme value; the S2 comprises the following steps:
s21: fitting the electromagnetic power data by using a least square method to obtain the first electromagnetic power change expression: delta P ei (t)＝ΔP ei (t 0 )+l i (t)t,t∈(t 0 ,t nadir )；t 0 And t nadir Respectively the disturbed moment and the moment when the frequency deviation reaches the extreme value; delta P ei (t 0 ) The initial electromagnetic power shortage of the disturbed instantaneous generator i; l i (t) is a least square method adaptive linear fitting parameter;
s22: modeling and analyzing the mechanical power data by using a linear function with a constant slope, and determining a first mechanical power change expression of a generator i:
Figure FDA0003961571740000023
ΔP mi (t nadir ) For the moment t at which the frequency deviation reaches the extreme value nadir The amount of change in the mechanical power of the generator i.
4. The wide-area measurement information-based online prediction method of frequency deviation extremum as claimed in claim 3, wherein the step S3 comprises: inputting the first electromagnetic power variation expression and the first mechanical power variation expression into a rotor motion equation
Figure FDA0003961571740000024
Obtaining the frequency deviation transient expression:
Figure FDA0003961571740000031
wherein, t nadir Is an equation variable, H i Is the real-time inertia time constant of the power generation cluster i at the moment t.
5. The wide-area measurement information-based online prediction method of frequency deviation extremum as claimed in claim 4, wherein the step S4 comprises:
inputting the frequency deviation transient expression into the approximate uniform structure transfer function model, and deducing a first mechanical power change expression on the frequency domain of each synchronous generator:
Figure FDA0003961571740000032
wherein, C step_i (t) and C ramp_i (t) step response and ramp response, G, of the generator i governor transfer function, respectively i (s) is the transfer function of the equivalent speed governor of generator i; a second mechanical power change expression obtained by analyzing the active frequency response mechanism and deducing according to the open-loop transfer function
Figure FDA0003961571740000033
6. The method according to claim 1, wherein the S5 comprises:
s51: when the frequency deviation reaches an 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, and then:
Figure FDA0003961571740000034
in the formula t nadir Is an equation variable; delta P ei (t 0 )、H i 、l i (t) calculating based on PMU measurement data, and dynamically updating in real time along with the predicted time t; [ k ] A i_0 ,k i_1 ,…k i_n ]Is obtained by off-line data analysis;
s52: from t nadir =0 starts to increase gradually until the difference between both sides of the equation in S51 satisfies t obtained by solving the error requirement nadir Namely, the predicted value of the arrival time of the frequency deviation extreme value is obtained.
7. The method according to claim 1, wherein the S7 comprises: varying the third electromagnetic power by an expression Δ P e ” i (t) the third mechanical power variation expression Δ P m ” i (t) and the arrival time predicted value t nadir Inputting the equation of motion of the rotor,obtaining:
Figure FDA0003961571740000041
integral solution is carried out on the obtained product to obtain t nadir_pre_i And (4) obtaining a predicted value of the arrival time of the frequency deviation extreme value of the power generation cluster i at the time t.
8. The method for on-line prediction of frequency deviation extremum based on wide-area measurement information of any one of claims 1-7, wherein the S8 comprises:
calculating a prediction error index corresponding to the predicted value of the frequency deviation extreme value at a plurality of time points;
when the prediction error index meets the precision, outputting a corresponding frequency deviation extreme value prediction value;
and when the prediction error index does not meet the precision, updating the actual measurement data of the PMU to repeatedly execute S2-S7 until the corresponding prediction error index meets the precision, thereby obtaining the predicted value of the corresponding frequency deviation extreme value.
9. The method of claim 8, wherein the step S8 comprises:
s81: initially setting the prediction error index PEI to be 1, taking frequency deviation extreme value prediction values corresponding to the current and the previous n PMU sampling points during each prediction, and calculating the average value f of the frequency deviation extreme value prediction values ave_i (t)；
S82: performing per unit on the adjacent n +1 predicted values:
Figure FDA0003961571740000042
s83: calculating the predicted value slope after per unit:
Figure FDA0003961571740000043
s84: calculating a per-unit slope average index A1:
Figure FDA0003961571740000044
s85: calculating a per-unit slope variance index A2:
Figure FDA0003961571740000045
s86: discrete simulation determines the upper and lower limit values of A1 and A2, and A to be calculated in real time 1 (t k ) And A 2 (t k ) Respectively comparing with a limit value; PEI becomes 0 when both are smaller than the upper limit value; whereas PEI still maintained 1;
s87: outputting a dynamic prediction result when the prediction error index PEI becomes 0; and when the prediction error index PEI is still 1, updating the actual measurement data of the PMU and repeatedly executing S2-S7 until the prediction error index PEI becomes 0, thereby obtaining the corresponding frequency deviation extreme value prediction value.
10. An on-line prediction apparatus for frequency deviation extremum based on wide-area measurement information, which is used to perform the on-line prediction method for frequency deviation extremum based on wide-area measurement information as claimed in any one of claims 1 to 9.
CN202211484684.8A 2022-11-24 2022-11-24 Wide-area measurement information-based frequency deviation extreme value online prediction method and device Pending CN115764928A (en)

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