CN115764928A - Method and device for online prediction of frequency deviation extremum based on wide-area measurement information - Google Patents

Method and device for online prediction of frequency deviation extremum based on wide-area measurement information 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
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extreme value
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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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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

基于广域量测信息的频率偏差极值在线预测方法和装置Method and device for online prediction of frequency deviation extremum based on wide-area measurement information

技术领域technical field

本发明属于电力系统频率稳定控制技术领域,更具体地,涉及一种基于广域量测信息的频率偏差极值在线预测方法和装置。The invention belongs to the technical field of power system frequency stability control, and more specifically relates to a method and device for online prediction of frequency deviation extremum based on wide-area measurement information.

背景技术Background technique

近年来,风力发电等新能源并网规模逐渐增大,系统惯量水平显著下降,且呈现出明显的时空分布特点。同时,直流输电工程的大规模投产进一步增加了直流闭锁导致的大幅功率缺额故障发生的风险,因为新能源机组无一次调频能力,故有功突变后电网暂态频率偏差极值将显著增大,系统频率安全受到严重威胁。故迫切需要建立精确、快速的频率稳定在线评估模型,通过对受扰后系统进行频率偏差极值的实时动态预测,提前预判电网的频率失稳风险,保证系统的安全稳定运行。In recent years, the grid-connected scale of wind power and other new energy sources has gradually increased, and the system inertia level has dropped significantly, showing obvious characteristics of temporal and spatial distribution. At the same time, the large-scale commissioning of DC transmission projects has further increased the risk of large power shortage faults caused by DC blocking. Because new energy units have no primary frequency regulation capability, the extreme value of transient frequency deviation of the power grid will increase significantly after a sudden change in active power. Frequency security is seriously threatened. Therefore, it is urgent to establish an accurate and fast online evaluation model of frequency stability. Through real-time dynamic prediction of the frequency deviation extreme value of the disturbed system, the frequency instability risk of the power grid can be predicted in advance to ensure the safe and stable operation of the system.

目前常用的针对新能源系统的频率在线预测方法主要包括等值模型分析法、基于人工智能的数据驱动法以及物理模型与数据驱动融合法。传统的等值模型分析法大多基于“一个惯量中心”的假设,不能分析频率的时空分布特性。对于新能源的大量并网导致惯量空间分布不均的电网,“单机等值法”的预测精度不够。现有纯数据驱动方法对输入数据的依赖性依旧较高,分析大电网时对应的高维训练模型所需的样本数量更是将呈指数增长,而实际系统可实时采集的数据少且时变性强,故纯数据驱动的方法在工程应用中可能达不到理想模型的预测精度。且人工智能的运算过程具有“黑盒形式”,可解释性和可追溯性仍需大幅提升。Currently commonly used online frequency prediction methods for new energy systems mainly include equivalent model analysis, data-driven methods based on artificial intelligence, and physical model and data-driven fusion methods. Most of the traditional equivalent model analysis methods are based on the assumption of "one center of inertia", which cannot analyze the spatial and temporal distribution characteristics of frequency. For grids with uneven spatial distribution of inertia caused by a large number of grid-connected new energy sources, the prediction accuracy of the "single machine equivalent method" is not enough. The existing pure data-driven methods are still highly dependent on the input data, and the number of samples required for the corresponding high-dimensional training model when analyzing large power grids will increase exponentially, while the real-time data that can be collected by the actual system is small and time-varying Therefore, the purely data-driven method may not achieve the prediction accuracy of the ideal model in engineering applications. Moreover, the calculation process of artificial intelligence has a "black box form", and the interpretability and traceability still need to be greatly improved.

而现有数据-物理融合驱动的方法大多未真正深入系统的有功-频率响应机理,或融合方法过于简单,尚无法完全满足实际系统对预测精度和速度的要求。However, most of the existing data-physics fusion-driven methods have not really penetrated into the active power-frequency response mechanism of the system, or the fusion method is too simple to fully meet the requirements of the actual system for prediction accuracy and speed.

发明内容Contents of the invention

针对现有技术的以上缺陷或改进需求,本发明提供了一种基于广域量测信息的频率偏差极值在线预测方法和装置,其目的在于,利用广域量测技术获取电网受扰前后的暂态运行数据,提高预测方法的准确性,同时利用物理-数据融合驱动方法相较于纯模型分析方法计算速度更快的优势,实现频率偏差极值的在线快速预测输出,为后续频率稳定量化评估提供参考依据,由此解决现有的频率偏差极值预测精度低和速度慢的技术问题。Aiming at the above defects or improvement needs of the prior art, the present invention provides a method and device for online prediction of frequency deviation extremum based on wide-area measurement information, the purpose of which is to use wide-area measurement technology to obtain Transient operation data, improve the accuracy of the prediction method, and at the same time, take advantage of the faster calculation speed of the physics-data fusion drive method compared with the pure model analysis method, to realize the online rapid prediction output of the frequency deviation extreme value, and to stabilize and quantify the subsequent frequency The evaluation provides a reference basis, thereby solving the existing technical problems of low precision and slow speed of frequency deviation extreme value prediction.

为实现上述目的,按照本发明的一个方面,提供了一种基于广域量测信息的频率偏差极值在线预测方法,包括:In order to achieve the above object, according to one aspect of the present invention, an online prediction method of frequency deviation extremum based on wide-area measurement information is provided, including:

S1:通过离线测试建立电网各同步发电机调速器的近似统一结构传递函数模型;S1: Establish an approximate unified structural transfer function model of each synchronous generator governor in the power grid through offline testing;

S2:利用一次线性函数对各同步发电机PMU实测数据进行拟合,获取有功扰动前后的第一电磁功率变化表达式和第一械功率变化表达式;S2: Use a linear function to fit the PMU measured data of each synchronous generator, and obtain the first electromagnetic power change expression and the first mechanical power change expression before and after the active power disturbance;

S3:将所述第一电磁功率变化表达式和所述第一机械功率变化表达式输入转子运动方程,推导得到频率偏差暂态表达式;S3: input the first electromagnetic power change expression and the first mechanical power change expression into the rotor motion equation, and derive a frequency deviation transient expression;

S4:将所述频率偏差暂态表达式输入所述近似统一结构传递函数模型,推导出第二机械功率表达式;S4: Input the frequency deviation transient expression into the approximate unified structure transfer function model, and derive a second mechanical power expression;

S5:当频率偏差达到极值时所述第二机械功率表达式的值与第一电磁功率变化表达式的值相等得到关于频率偏差极值到达时间的方程,迭代求解得到频率偏差极值的到达时间预测值;S5: When the frequency deviation reaches the 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 iteratively solve to obtain the arrival of the frequency deviation extreme value time forecast value;

S6:利用高次线性函数对所述PMU实测数据进行拟合,得到有功扰动前后各发电机的第三电磁功率变化表达式和第三机械功率变化表达式;S6: Using a high-order linear function to fit the measured data of the PMU 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:将所述第三电磁功率变化表达式、所述第三机械功率变化表达式和所述到达时间预测值输入所述转子运动方程,求解频率偏差极值预测值;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, and solve the frequency deviation extreme value prediction value;

S8:计算多个时刻点所述频率偏差极值预测值对应的预测误差指标;将频率误差指标满足精度对应的频率偏差极值预测值作为有效输出。S8: Calculate the prediction error index corresponding to the frequency deviation extreme value prediction value at multiple time points; use the frequency deviation extreme value prediction value corresponding to the frequency error index to meet the accuracy as an effective output.

在其中一个实施例中,所述S1包括:In one of the embodiments, the S1 includes:

S11:分别向各同步发电机集群的调速器输入阶跃频率偏差,采集机械功率的阶跃响应数据,对所述阶跃响应数据进行离散积分得到斜坡响应;S11: input step frequency deviations to the speed governors of each synchronous generator cluster, collect step response data of mechanical power, and perform discrete integration on the step response data to obtain a ramp response;

S12:利用线性多项式拟合各调速器的斜坡响应,得到:S12: Use the linear polynomial to fit the slope response of each governor to get:

Figure BDA0003961571750000031
Figure BDA0003961571750000031

Cramp_i(t)为发电机i调速器的斜坡响应,

Figure BDA0003961571750000032
为发电机i调速器斜坡响应的多项式线性拟合参数;tfit为拟合时长;拟合时长应大于频率偏差极值到达时长tnadirCramp_i (t) is the ramp response of generator i governor,
Figure BDA0003961571750000032
is the polynomial linear fitting parameter of the slope response of the generator i speed governor; t fit is the fitting time length; the fitting time length should be greater than the frequency deviation extremum arrival time t nadir ;

S12:利用拉普拉斯变换推导所述近似统一结构传递函数模型为:S12: using Laplace transform to derive the approximate unified structure transfer function model as:

Figure BDA0003961571750000033
Figure BDA0003961571750000033

式中,G′i(s)是发电机i调速器的近似统一结构传递函数。In the formula, G′ i (s) is the approximate unified structure transfer function of the governor of generator i.

在其中一个实施例中,所述PMU实测数据包括:从各所述同步发电机各机端从受到有功扰动瞬间到频率偏差到达极值的暂态过程中电磁功率数据和各发电机调速器的机械功率数据;所述S2包括:In one of the embodiments, the PMU measured data includes: the electromagnetic power data and the speed controllers of each generator during the transient process from the moment when each machine end of each synchronous generator is disturbed by active power to when the frequency deviation reaches the extreme value. The mechanical power data; the S2 includes:

S21:利用最小二乘法拟合所述电磁功率数据获取所述第一电磁功率变化表达式:ΔPei(t)=ΔPei(t0)+li(t)t,t∈(t0,tnadir);t0和tnadir分别为受扰瞬间和频率偏差到达极值时刻;ΔPei(t0)为受扰瞬间发电机i的初始电磁功率缺额;li(t)为最小二乘法自适应线性拟合参数;S21: Fit the electromagnetic power data using the least squares method to obtain the first electromagnetic power change expression: ΔP ei (t)=ΔP ei (t 0 )+l i (t)t,t∈(t 0 , t nadir ); t 0 and t nadir are the instant of disturbance and the moment when the frequency deviation reaches the extreme value; ΔP ei (t 0 ) is the initial electromagnetic power deficit of generator i at the instant of disturbance; l i (t) is the least square method Adaptive linear fitting parameters;

S22:利用恒定斜率的线性函数对所述机械功率数据进行建模分析,确定发电机i的第一机械功率变化表达式:S22: Using a linear function with a constant slope to model and analyze the mechanical power data, and determine the first mechanical power change expression of the generator i:

Figure BDA0003961571750000034
Figure BDA0003961571750000034

ΔPmi(tnadir)为频率偏差到达极值时刻tnadir时发电机i的机械功率变化量。ΔP mi (t nadir ) is the change in mechanical power of generator i when the frequency deviation reaches the extreme time t nadir .

在其中一个实施例中,所述S3包括:将所述第一电磁功率变化表达式和所述第一机械功率变化表达式输入转子运动方程

Figure BDA0003961571750000041
得到所述频率偏差暂态表达式:
Figure BDA0003961571750000042
Figure BDA0003961571750000043
其中,tnadir为方程变量,Hi为t时刻发电集群i的实时惯性时间常数。In one of the embodiments, the S3 includes: inputting the first electromagnetic power change expression and the first mechanical power change expression into the rotor motion equation
Figure BDA0003961571750000041
Get the frequency deviation transient expression:
Figure BDA0003961571750000042
Figure BDA0003961571750000043
Among them, t nadir is the equation variable, and H i is the real-time inertial time constant of power generation cluster i at time t.

在其中一个实施例中,所述S4包括:In one of the embodiments, the S4 includes:

将所述频率偏差暂态表达式输入所述近似统一结构传递函数模型,推导出各同步发电机的频域上第一机械功率变化表达式:

Figure BDA0003961571750000044
其中,Cstep_i(t)和Cramp_i(t)分别为发电机i调速器传递函数的阶跃响应和斜坡响应,Gi(s)是发电机i等值调速器的传递函数;通过分析有功频率响应机理,根据开环传递函数推导得到的第二机械功率变化表达式
Figure BDA0003961571750000045
The frequency deviation transient expression is input into the approximate unified structure transfer function model, and the first mechanical power change expression on the frequency domain of each synchronous generator is derived:
Figure BDA0003961571750000044
Among them, C step_i (t) and Cramp_i (t) are the step response and ramp response of the governor transfer function of generator i respectively, and G i (s) is the transfer function of the equivalent governor of generator i; Analyze the active frequency response mechanism, and derive the second mechanical power change expression based on the open-loop transfer function
Figure BDA0003961571750000045

在其中一个实施例中,所述S5包括:In one of the embodiments, the S5 includes:

S51:当频率偏差达到极值时,各同步发电机的第二机械功率表达式的值与第一电磁功率变化表达式的值相等,则有: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, then:

Figure BDA0003961571750000046
Figure BDA0003961571750000046

式中tnadir是方程变量;ΔPei(t0)、Hi、li(t)基于PMU量测数据计算而来,并跟随预测时刻t实时动态更新;[ki_0,ki_1,…ki_n]由离线数据分析得出;In the formula, t nadir is the equation variable; ΔP ei (t 0 ), H i , l i (t) are calculated based on PMU measurement data, and are dynamically updated in real time following the prediction time t; [k i_0 ,k i_1 ,…k i_n ] obtained by offline data analysis;

S52:从tnadir=0开始逐渐增加直至S51中的方程两边的差值满足误差要求求解得到的tnadir,即为频率偏差极值的到达时间预测值。S52: gradually increase from t nadir =0 until the difference on both sides of the equation in S51 satisfies the error requirement. The t nadir obtained by solving is the predicted value of the arrival time of the frequency deviation extremum.

在其中一个实施例中,所述S7包括:将所述第三电磁功率变化表达式ΔP″ei(t)、所述第三机械功率变化表达式ΔP″mi(t)和所述到达时间预测值tnadir输入所述转子运动方程,得到:In one of the embodiments, the S7 includes: predicting the third electromagnetic power change expression ΔP″ ei (t), the third mechanical power change expression ΔP″ mi (t) and the arrival time The value t nadir is entered into the rotor motion equation to obtain:

Figure BDA0003961571750000051
对其进行积分求解得到tnadir_pre_i为t时刻发电集群i的频率偏差极值到达时间预测值。
Figure BDA0003961571750000051
Integrating and solving it, t nadir_pre_i is the predicted value of arrival time of frequency deviation extremum of power generation cluster i at time t.

在其中一个实施例中,所述S8包括:In one of the embodiments, the S8 includes:

计算多个时刻点所述频率偏差极值预测值对应的预测误差指标;Calculating prediction error indicators corresponding to the frequency deviation extremum prediction values at multiple time points;

当预测误差指标满足精度时,输出对应的频率偏差极值预测值;When the prediction error index meets the accuracy, output the corresponding frequency deviation extreme value prediction value;

当预测误差指标不满足所述精度时,更新PMU实测数据重复执行S2-S7直至对应预测误差指数满足所述精度,从而得到对应的频率偏差极值预测值。When the prediction error index does not meet the accuracy, update the PMU measured data and repeat S2-S7 until the corresponding prediction error index meets the accuracy, so as to obtain the corresponding frequency deviation extreme value prediction value.

在其中一个实施例中,所述S8包括:In one of the embodiments, the S8 includes:

S81:初始设置所述预测误差指数PEI为1,每次预测时取当下以及前n个PMU采样点对应的频率偏差极值预测值,计算其平均值fave_i(t);S81: Initially set the prediction error index PEI to 1, take the current and the frequency deviation extremum prediction value corresponding to the previous n PMU sampling points during each prediction, and calculate its average value f ave_i (t);

S82:将临近n+1个预测值进行标幺化:

Figure BDA0003961571750000052
S82: Scale the adjacent n+1 predicted values:
Figure BDA0003961571750000052

S83:计算标幺化之后预测值斜率:

Figure BDA0003961571750000053
S83: Calculate the slope of the predicted value after per unitization:
Figure BDA0003961571750000053

S84:计算标幺斜率平均值指标A1:

Figure BDA0003961571750000054
S84: Calculating the average value index A1 of the slope per unit:
Figure BDA0003961571750000054

S85:计算标幺斜率方差指标A2:S85: Calculate the per unit slope variance index A2:

Figure BDA0003961571750000055
Figure BDA0003961571750000055

S86:离散仿真确定A1和A2的上下限值,将实时计算的A1(tk)和A2(tk)分别与限值进行对比;当均小于上限值时PEI变为0;反之PEI仍维持1;S86: The discrete simulation determines the upper and lower limits of A1 and A2, and compares the real-time calculated A 1 (t k ) and A 2 (t k ) with the limit values; when both are less than the upper limit, the PEI becomes 0; otherwise PEI remains at 1;

S87:当预测误差指数PEI变为0时输出动态预测结果;当预测误差指数PEI仍为1,则更新PMU实测数据重复执行S2-S7直至预测误差指数PEI变为0,从而得到对应的频率偏差极值预测值。S87: When the prediction error index PEI becomes 0, output the dynamic prediction result; when 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, so as to obtain the corresponding frequency deviation Extremum predicted value.

按照本发明的另一方面,提供了一种基于广域量测信息的频率偏差极值在线预测装置,用于执行所述的频率偏差极值在线预测方法。According to another aspect of the present invention, there is provided an on-line frequency deviation extremum prediction device based on wide-area measurement information, which is used to implement the above-mentioned frequency deviation extremum online prediction method.

总体而言,通过本发明所构思的以上技术方案与现有技术相比,能够取得下列有益效果:Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

本发明在传统纯物理分析模型的基础上,利用广域量测信息对各区域联络线上电磁功率的暂态变化进行近似拟合,建立了能快速计算的物理-数据融合的简化预测模型,同时风电等新能源对频率响应过程的影响以及惯量时空分布特点均通过广域量测信息被考虑进频率分析模型,故预测模型精度得到提升。同时,提出“预测误差指数”这一指标,用以间接量化各频率偏差极值预测值的误差,指导在线预测模型快速、智能的输出精度满足要求的有效预测值。因此,本发明不仅具有一定的预测精度,预测速度也较快。On the basis of the traditional purely physical analysis model, the present invention uses the wide-area measurement information to approximate the transient changes of the electromagnetic power on the tie lines in each area, and establishes a simplified prediction model of physics-data fusion that can be quickly calculated. At the same time, the influence of new energy sources such as wind power on the frequency response process and the spatiotemporal distribution of inertia are taken into account in the frequency analysis model through wide-area measurement information, so the accuracy of the prediction model is improved. At the same time, the index of "prediction error index" is proposed to indirectly quantify the error of the extreme value prediction value of each frequency deviation, and guide the online prediction model to quickly and intelligently output an effective prediction value that meets the requirements. Therefore, the present invention not only has a certain prediction accuracy, but also has a faster prediction speed.

附图说明Description of drawings

图1是本发明一实施例中提供的基于广域量测信息的频率偏差极值在线预测方法的流程图;Fig. 1 is a flowchart of an online prediction method for frequency deviation extremum based on wide-area measurement information provided in an embodiment of the present invention;

图2是本发明一实施例中机端电磁功率一次线性函数拟合方法示意图;Fig. 2 is a schematic diagram of a method for fitting a linear function of the terminal electromagnetic power in an embodiment of the present invention;

图3是本发明一实施例中频率偏差极值动态预测过程示意图;Fig. 3 is a schematic diagram of the dynamic prediction process of frequency deviation extremum in an embodiment of the present invention;

图4是本发明一实施例中单一预测时刻点频率偏差极值在线预测流程图;Fig. 4 is a flow chart of online prediction of frequency deviation extremum at a single prediction time point in an embodiment of the present invention;

图5是本发明一实施例中频率偏差极值预测值与斜率量化指标A1随预测时长变化的曲线图;Fig. 5 is a graph showing the variation of frequency deviation extremum predicted value and slope quantization index A1 with the predicted duration in an embodiment of the present invention;

图6是本发明一实施例中频率偏差极值预测值与方差量化指标A2随预测时长变化的曲线图;Fig. 6 is a graph showing the variation of frequency deviation extremum predicted value and variance quantization index A2 with the predicted duration in an embodiment of the present invention;

图7是本发明一实施例中四机两区域系统4台同步发电机在不同风电渗透率下频率偏差极值的预测速度仿真图;Fig. 7 is a simulation diagram of the predicted speed of four synchronous generators in a four-machine two-region system under different wind power penetration rates of the extreme value of frequency deviation in an embodiment of the present invention;

图8是本发明一实施例中四机两区域系统4台同步发电机在不同风电渗透率下频率偏差极值的预测精度仿真图。Fig. 8 is a simulation diagram of prediction accuracy of frequency deviation extreme value of 4 synchronous generators in a four-machine two-zone system under different wind power penetration rates in an embodiment of the present invention.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。此外,下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.

为实现以上目的,本发明的技术方案如下:For realizing above object, technical scheme of the present invention is as follows:

S1:离线测试,建立系统各同步发电机调速器近似统一结构传递函数。S1: Off-line test, establish an approximate unified structure transfer function of each synchronous generator governor of the system.

S2:基于PMU实测数据,分别利用一次线性函数,近似描述系统中各同步发电机从受到有功扰动瞬间到频率偏差到达极值这一段暂态过程中的电磁功率和机械功率变化。S2: Based on the measured data of the PMU, a linear function is used to approximately describe the electromagnetic power and mechanical power changes of each synchronous generator in the system during the transient process from the moment when the active power disturbance is received to the frequency deviation reaches the extreme value.

S3:将步骤S2中计算得到的电磁功率和机械功率一次线性函数表达式作为输入,基于转子运动方程,推导出频率偏差表达式。S3: Taking the linear function expressions of the electromagnetic power and mechanical power calculated in step S2 as input, and deriving the frequency deviation expression based on the rotor motion equation.

S4:基于步骤S1中各同步发电机调速器的近似统一传递函数,进一步推导得到各台同步发电机的机械功率变化表达式。S4: Based on the approximate unified transfer function of each synchronous generator governor in step S1, further deduce the mechanical power change expression of each synchronous generator.

S5:建立关于频率偏差极值到达时间tnadir的线性方程并迭代求解。S5: Establish a linear equation about the arrival time t nadir of the frequency deviation extremum and solve it iteratively.

S6:基于PMU实测数据,分别利用高次线性函数,近似描述系统中各同步发电机从受到有功扰动瞬间到频率偏差到达极值这一段暂态过程中的电磁功率和机械功率变化。S6: Based on the measured data of the PMU, the high-order linear functions are used to approximately describe the electromagnetic power and mechanical power changes of each synchronous generator in the system during the transient process from the moment when the active power disturbance is received to the frequency deviation reaches the extreme value.

S7:基于转子运动方程,结合频率偏差极值到达时间预测值,积分求解频率偏差极值预测值。S7: Based on the rotor motion equation, combined with the predicted value of the arrival time of the frequency deviation extreme value, integrally solve the frequency deviation extreme value prediction value.

S8:计算当前频率偏差极值预测值的“预测误差指数”指标,分析当前预测精度。如果当前预测精度满足要求,则输出当前频率偏差极值预测值,指示后续的频率稳定分析过程。S8: Calculate the "prediction error index" index of the current frequency deviation extreme value prediction value, and analyze the current prediction accuracy. If the current prediction accuracy meets the requirements, the current frequency deviation extremum prediction value is output to indicate the subsequent frequency stability analysis process.

进一步的,步骤S1中离线测试,建立系统各同步发电机调速器近似简化结构的步骤为:Further, in the offline test in step S1, the steps for establishing an approximate simplified structure of each synchronous generator governor in the system are:

S11:分别向多机系统各同步发电机集群的调速器输入阶跃形式的频率偏差,采集对应机械功率变化量的输出数据,对实测的阶跃响应数据进行离散积分可以得到斜坡响应。S11: Input the frequency deviation in step form to the governors of each synchronous generator cluster in the multi-machine system, collect the output data corresponding to the mechanical power variation, and perform discrete integration on the measured step response data to obtain the slope response.

S12:利用线性多项式拟合各类结构调速器的斜坡响应:S12: Use linear polynomials to fit the slope response of various structural governors:

Cramp_i(t)=ki_0+ki_1t+…ki_ntn,t∈(0,tfit) Cramp_i (t)=k i_0 +k i_1 t+…k i_n t n ,t∈(0,t fit )

式中,Cramp_i(t)为发电机i调速器传递函数的斜坡响应,

Figure BDA0003961571750000081
为发电机i调速器斜坡响应的多项式线性拟合参数;(0,tfit)意味着选取对应时间区间内的斜坡响应数据进行多项式拟合。拟合时长应大于系统实际的频率偏差极值到达时长tnadir,建议范围为5~20s。线性拟合阶数选择2到6次比较合理。In the formula, Cramp_i (t) is the ramp response of the generator i governor transfer function,
Figure BDA0003961571750000081
is the polynomial linear fitting parameter of the slope response of generator i governor; (0,t fit ) means that the slope response data in the corresponding time interval is selected for polynomial fitting. The fitting time should be longer than the actual arrival time t nadir of the extreme frequency deviation of the system, and the recommended range is 5-20s. It is more reasonable to choose the order of linear fitting from 2 to 6 times.

S13:利用拉普拉斯变换,推导出各类型调速器传递函数的统一形式,即:S13: Using the Laplace transform, deduce the unified form of the transfer function of various types of governors, namely:

Figure BDA0003961571750000082
Figure BDA0003961571750000082

式中,G′i(s)是发电机i调速器的近似统一结构传递函数。In the formula, G′ i (s) is the approximate unified structure transfer function of the governor of generator i.

进一步的,所述步骤S2中基于PMU实测数据,分别利用一次线性函数,近似描述系统中各同步发电机从受到有功扰动瞬间到频率偏差到达极值这一段暂态过程中的电磁功率和机械功率变化的步骤为:Further, in the step S2, based on the measured data of the PMU, a linear function is used to approximately describe the electromagnetic power and mechanical power of each synchronous generator in the system during the transient process from the moment when the active power disturbance is received to when the frequency deviation reaches the extreme value The steps to change are:

S21:系统中各台同步发电机从受扰瞬间到当前预测时刻之间,PMU以固定采样频率采集多个机端电磁功率数据。基于这些实测数据,利用最小二乘法拟合获取各台同步发电机一次线性函数形式的电磁功率变化表达式:S21: From the moment when each synchronous generator in the system is disturbed to the current prediction time, the PMU collects electromagnetic power data of multiple machine terminals at a fixed sampling frequency. Based on these measured data, the expression of the electromagnetic power change in the form of a linear function of each synchronous generator is obtained by using the least square method:

ΔPei(t)=ΔPei(t0)+li(t)t,t∈(t0,tnadir)ΔP ei (t)=ΔP ei (t 0 )+l i (t)t,t∈(t 0 ,t nadir )

其中,t0和tnadir分别为受扰瞬间和频率偏差到达极值时刻;ΔPei(t0)为受扰瞬间发电机i的初始电磁功率缺额;li(t)为最小二乘法自适应线性拟合参数。Among them, t 0 and t nadir are the moment of disturbance and the moment when the frequency deviation reaches the extreme value; ΔP ei (t 0 ) is the initial electromagnetic power deficit of generator i at the moment of disturbance; l i (t) is the least square method adaptive Linear fit parameters.

S22:利用恒定斜率的线性函数对发电机i调速器机械功率的变化进行简化建模分析,确定发电机i机械功率的暂态变化表达式:S22: Use a linear function with a constant slope to perform a simplified modeling analysis on the change of the mechanical power of the generator i governor, and determine the transient change expression of the mechanical power of the generator i:

Figure BDA0003961571750000091
Figure BDA0003961571750000091

进一步的,步骤S3中将步骤S2中计算得到的电磁功率和机械功率一次线性函数表达式作为输入,基于转子运动方程,推导出频率偏差表达式的步骤为:Further, in step S3, the linear function expressions of electromagnetic power and mechanical power calculated in step S2 are used as input, and based on the rotor motion equation, the steps of deriving the frequency deviation expression are as follows:

S31:根据转子运动方程

Figure BDA0003961571750000092
可以得到频率偏差的暂态表达式:S31: According to the rotor motion equation
Figure BDA0003961571750000092
The transient expression of the frequency deviation can be obtained:

Figure BDA0003961571750000093
Figure BDA0003961571750000093

其中,tnadir是未知参数,需要后续计算求解。Among them, t nadir is an unknown parameter, which needs subsequent calculation and solution.

进一步的,步骤S4中基于步骤S1中各同步发电机调速器的近似统一传递函数,进一步推导得到各台同步发电机的机械功率变化表达式的步骤为:Further, in step S4, based on the approximate unified transfer function of each synchronous generator governor in step S1, the steps of further deriving the mechanical power change expression of each synchronous generator are:

S41:将S31中推导出的抛物线式的频率偏差变化式送入同步发电机i等值调速器传递函数,可以得到频域上的机械功率输出:S41: Send the parabolic frequency deviation change formula deduced in S31 into the transfer function of the synchronous generator i equivalent speed governor, and the mechanical power output in the frequency domain can be obtained:

Figure BDA0003961571750000094
Figure BDA0003961571750000094

Cstep_i(t)和Cramp_i(t)分别为发电机i调速器传递函数的阶跃响应和斜坡响应,Gi(s)是发电机i等值调速器的传递函数。C step_i (t) and Cramp_i (t) are the step response and ramp response of the governor transfer function of generator i respectively, and G i (s) is the transfer function of the equivalent governor of generator i.

S42:应用反拉普拉斯变化可以得到:S42: Applying the inverse Laplace change can get:

Figure BDA0003961571750000101
Figure BDA0003961571750000101

式中,ΔP′mi(t)是通过分析有功-频率响应机理,根据开环传递函数推导得到的机械功率变化量,与前述的基于PMU实测数据拟合得到的ΔPmi(t)不同。In the formula, ΔP′ mi (t) is the mechanical power variation derived from the open-loop transfer function by analyzing the active power-frequency response mechanism, which is different from the aforementioned ΔP mi (t) obtained by fitting based on the measured data of the PMU.

进一步的,步骤S5中建立关于频率偏差极值到达时间tnadir的线性方程并迭代求解的步骤为:Further, in step S5, the steps of establishing a linear equation about the frequency deviation extremum arrival time t nadir and iteratively solving it are:

S51:将发电机i等值调速器的近似统一结构代入物理-数据融合模型,频率偏差达到极值时,各同步发电机的机械功率变化量与电磁功率变化量相等,故有:S51: Substituting the approximate uniform structure of the generator i equivalent governor into the physical-data fusion model, when the frequency deviation reaches the extreme value, the mechanical power variation of each synchronous generator is equal to the electromagnetic power variation, so:

Figure BDA0003961571750000102
Figure BDA0003961571750000102

式中tnadir是未知参数;ΔPei(t0)、Hi、li(t)基于PMU量测数据计算而来,并跟随预测时刻t实时动态更新;[ki_0,ki_1,…ki_n]由离线数据分析计算得出,后存储于在线预测模型中。In the formula, t nadir is an unknown parameter; ΔP ei (t 0 ), H i , l i (t) are calculated based on PMU measurement data, and are dynamically updated in real time following the prediction time t; [k i_0 ,k i_1 ,…k i_n ] is calculated by offline data analysis and stored in the online prediction model.

S51:从tnadir=0开始逐渐增加未知参数tnadir的取值,直至S51中的方程两边的差值满足误差要求,此时求解得到的tnadir即为频率偏差极值到达时间预测值。S51: gradually increase the value of the unknown parameter t nadir from t nadir = 0, until the difference between the two sides of the equation in S51 meets the error requirement, and the t nadir obtained by solving at this time is the predicted value of the arrival time of the frequency deviation extremum.

进一步的,步骤S6中PMU采集从受扰瞬间到当前预测时刻各台同步发电机机端的电磁功率和频率偏差变化,基于转子运动方程间接计算出各台同步发电机的机械功率变化。基于以上PMU等时间间隔的众多采样数据,分别利用高阶多项式函数拟合电磁功率和机械功率给的变化曲线,拟合结束在3~5次比较合适。Further, in step S6, the PMU collects the electromagnetic power and frequency deviation changes of each synchronous generator from the moment of disturbance to the current prediction moment, and indirectly calculates the mechanical power change of each synchronous generator based on the rotor motion equation. Based on the numerous sampling data of the above PMU and other time intervals, high-order polynomial functions are used to fit the change curves of electromagnetic power and mechanical power respectively. It is more appropriate to end the fitting at 3 to 5 times.

进一步的,步骤S7中基于转子运动方程,结合前述计算得到的频率偏差极值到达时间预测值,积分求解频率偏差极值预测值:Further, in step S7, based on the equation of motion of the rotor, combined with the predicted value of arrival time of the frequency deviation extremum obtained from the aforementioned calculation, the integral solution is obtained for the predicted value of the frequency deviation extremum value:

Figure BDA0003961571750000111
Figure BDA0003961571750000111

Hi(t)和tnadir_pre_i分别为t时刻发电集群i的实时惯性时间常数和频率偏差极值到达时间预测值。H i (t) and t nadir_pre_i are the real-time inertial time constant and frequency deviation extremum arrival time prediction value of power generation cluster i at time t, respectively.

进一步的,步骤S8中计算当前频率偏差极值预测值的“预测误差指数”指标,分析当前预测精度。如果当前预测精度满足要求,则输出当前频率偏差极值预测值,指示后续的频率稳定分析过程的步骤为:Further, in step S8, the "prediction error index" index of the current frequency deviation extremum prediction value is calculated, and the current prediction accuracy is analyzed. If the current prediction accuracy meets the requirements, the current frequency deviation extremum prediction value is output, indicating that the steps of the subsequent frequency stability analysis process are:

S81:初始设置“预测误差指数”PEI为1,在PMU采样间隔为0.01s的前提下,从受扰后0.01*n秒开始,每次预测时取当下以及前n个采样点对应的频率偏差极值预测值,计算其平均值:S81: Initially set the "prediction error index" PEI to 1. On the premise that the PMU sampling interval is 0.01s, starting from 0.01*n seconds after being disturbed, the frequency deviation corresponding to the current and previous n sampling points is taken for each prediction Extremum predictors, whose mean is computed:

Figure BDA0003961571750000112
Figure BDA0003961571750000112

式中,[Δfmax_i(tk-n),Δfmax_i(tk-n+1),…Δfmax_i(tk)],(tk<t)为最近的n+1个频率偏差极值预测值;fave_i(t)为n+1个预测值的平均值。In the formula, [Δf max_i (t kn ),Δf max_i (t k-n+1 ),…Δf max_i (t k )], (t k <t) is the latest n+1 frequency deviation extremum prediction value ; f ave_i (t) is the average value of n+1 predicted values.

S82:将临近n+1个预测值进行“标幺化”:S82: Perform "per unitization" on the adjacent n+1 predicted values:

Figure BDA0003961571750000113
Figure BDA0003961571750000113

式中,Δfpu_i(tk-i),i∈[0,1,…n]分别是标幺化之后的n+1个频率偏差极值预测值。In the formula, Δf pu_i (t ki ), i∈[0,1,…n] are n+1 frequency deviation extremum predicted values after per unitization respectively.

S83:计算“标幺化”之后预测值斜率dfpu_i(tk):S83: Calculate the predicted value slope df pu_i (t k ) after "per unitization":

Figure BDA0003961571750000114
Figure BDA0003961571750000114

S84:计算标幺斜率平均值指标A1:S84: Calculating the average value index A1 of the slope per unit:

Figure BDA0003961571750000121
Figure BDA0003961571750000121

S85:计算标幺斜率方差指标A2:S85: Calculate the per unit slope variance index A2:

Figure BDA0003961571750000122
Figure BDA0003961571750000122

S86:离散仿真确定A1和A2的合理限值,将实时计算的A1(tk)和A2(tk)分别与限值进行对比,当其均小于上限值时,PEI由1变为0;反之,则PEI仍维持1。S86: Discrete simulation determines the reasonable limits of A1 and A2, compares the real-time calculated A 1 (t k ) and A 2 (t k ) with the limit values, and when they are both smaller than the upper limit, the PEI changes from 1 to is 0; otherwise, PEI remains 1.

S87:当“预测误差指数”PEI变为0,预测系统输出动态预测结果;当“预测误差指数”PEI仍为1,则继续返回步骤S2,等待PMU下一采样点数据上传,执行S2-S7,再一次计算频率偏差极值预测值。S87: When the "prediction error index" PEI becomes 0, the forecasting system outputs the dynamic forecast result; when the "prediction error index" PEI is still 1, continue to return to step S2, wait for the data upload of the next sampling point of the PMU, and execute S2-S7 , and calculate the frequency deviation extremum prediction value again.

将本发明应用于含风电的四机两区域系统中,在原系统的7号节点并入5台风机,每台风机由50台额定容量为2MW的双馈风力发电机等值,双馈风机采用忽略了定子暂态的三阶模型。为了充分分析不同新能源渗透率下的模型预测精度,本文分别在风电渗透率为12.98%、19.47%、25.96%、38.94%四种工况进行仿真验证,设置7号节点发生273.4MW的有功突减故障,依次进行频率偏差极值的在线预测。频率偏差极值在线预测方法流程图如图1所示,包括以下步骤:Applying the present invention to a four-machine two-area system with wind power, 5 wind turbines are incorporated into the No. 7 node of the original system, and each wind turbine is equivalent to 50 double-fed wind power generators with a rated capacity of 2MW, and the double-fed wind turbine adopts The third-order model of the stator transients is ignored. In order to fully analyze the prediction accuracy of the model under different new energy penetration rates, this paper conducts simulation verification under four working conditions with wind power penetration rates of 12.98%, 19.47%, 25.96%, and 38.94%. Subtracting faults, the online prediction of frequency deviation extremum is carried out sequentially. The flow chart of the online prediction method for frequency deviation extreme value is shown in Figure 1, including the following steps:

S1离线测试,建立系统各同步发电机调速器近似统一结构传递函数。S1 off-line test, establish the approximate uniform structure transfer function of each synchronous generator governor of the system.

S2基于PMU实测数据,分别利用一次线性函数,近似描述系统中各同步发电机从受到有功扰动瞬间到频率偏差到达极值这一段暂态过程中的电磁功率和机械功率变化。S2 is based on the measured data of the PMU, respectively using a linear function to approximately describe the electromagnetic power and mechanical power changes of each synchronous generator in the system during the transient process from the moment when the active power disturbance is received to the frequency deviation reaches the extreme value.

S3将步骤S2中计算得到的电磁功率和机械功率一次线性函数表达式作为输入,基于转子运动方程,推导出频率偏差表达式。S3 takes the linear function expressions of the electromagnetic power and mechanical power calculated in step S2 as input, and derives the frequency deviation expression based on the rotor motion equation.

S4基于步骤S1中各同步发电机调速器的近似统一传递函数,进一步推导得到各台同步发电机的机械功率变化表达式。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.

S5建立关于频率偏差极值到达时间tnadir的线性方程并迭代求解。S5 establishes a linear equation about the arrival time t nadir of the frequency deviation extremum and solves it iteratively.

S6基于PMU实测数据,分别利用高次线性函数,近似描述系统中各同步发电机从受到有功扰动瞬间到频率偏差到达极值这一段暂态过程中的电磁功率和机械功率变化。Based on the measured data of PMU, S6 uses high-order linear functions to approximately describe the electromagnetic power and mechanical power changes of each synchronous generator in the system during the transient process from the moment when the active power disturbance is received to the frequency deviation reaches the extreme value.

S7基于转子运动方程,结合频率偏差极值到达时间预测值,积分求解频率偏差极值预测值。S7 is based on the rotor motion equation, combined with the predicted value of the arrival time of the extreme value of the frequency deviation, and integrally solves the predicted value of the extreme value of the frequency deviation.

S8计算当前频率偏差极值预测值的“预测误差指数”指标,分析当前预测精度。如果当前预测精度满足要求,则输出当前频率偏差极值预测值,指示后续的频率稳定分析过程。S8 calculates the "prediction error index" index of the current frequency deviation extreme value prediction value, and analyzes the current prediction accuracy. If the current prediction accuracy meets the requirements, the current frequency deviation extremum prediction value is output to indicate the subsequent frequency stability analysis process.

如图2所示,随着预测时刻的推移,PMU采样数据的增加,系统中各台同步发电机机端的电磁功率一次线性函数拟合参数也随之不断更新。As shown in Figure 2, with the passage of prediction time and the increase of PMU sampling data, the fitting parameters of the electromagnetic power linear function of each synchronous generator in the system are also continuously updated.

如图3所示,基于PMU实测数据,对各台同步发电机的电磁功率和机械功率作更高阶次、更准确的高次函数拟合,并结合步骤S5中计算出的频率偏差极值到达时间预测值,基于转子运动方程积分求解频率偏差极值预测值。随着预测时刻的推移,PMU采样数据增多,频率偏差极值到达时间预测值不断更新,频率偏差极值预测值也随之不断更新。As shown in Figure 3, based on the PMU measured data, a higher-order and more accurate high-order function fitting is performed on the electromagnetic power and mechanical power of each synchronous generator, and combined with the frequency deviation extreme value calculated in step S5 The arrival time prediction value is based on the integral of the rotor motion equation to solve the frequency deviation extreme value prediction value. As the prediction time goes by, the PMU sampling data increases, the predicted value of the arrival time of the frequency deviation extreme value is continuously updated, and the predicted value of the frequency deviation extreme value is also continuously updated.

如图4所示,单一预测时刻频率偏差极值的预测流程主要包括三个阶段:数据输入、数据处理、融合模型分析求解预测值。数据输入阶段通过离线测试,确定系统中各台同步发电机调速器的统一近似简化结构参数;数据处理阶段,对PMU实测的系统受扰前后暂态量进行最小二乘法的函数拟合,包括机端电磁功率变化量、间接计算得到的各台同步发电机机械功率的变化量;融合模型分析求解预测值阶段,基于数据拟合的电磁功率和机械功率近似表达式输入有功-频率开环解耦模型中,建立关于频率偏差极值到达时间的方程,迭代求解之后,进一步积分求解频率偏差极值预测值。As shown in Figure 4, the prediction process of the frequency deviation extreme value at a single prediction time mainly includes three stages: data input, data processing, and fusion model analysis to solve the predicted value. In the data input stage, the unified and approximate simplified structural parameters of each synchronous generator governor in the system are determined through offline testing; in the data processing stage, the function fitting of the least squares method is performed on the transient quantities measured by the PMU before and after the system is disturbed, including The amount of electromagnetic power change at the machine end and the change amount of mechanical power of each synchronous generator obtained by indirect calculation; in the stage of fusion model analysis and solution prediction value, the approximate expression of electromagnetic power and mechanical power based on data fitting is input into the active power-frequency open-loop solution In the coupled model, an equation about the arrival time of the extreme value of the frequency deviation is established, and after iterative solution, the predicted value of the extreme value of the frequency deviation is further integrated to solve.

如图5所示,在经典四机两区域系统的7号节点并入双馈风机模型,在风电渗透率为19.47%的工况下,设置7号节点发生273.4MW的有功突减故障。同时设置PMU采样频率为100Hz,“预测误差指数”分析对象为临近0.3s内的所有频率偏差极值预测值,即n=29,对应“预测误差指数”指标的组成之一斜率量化指标A1随预测时长增加,采样数据增多而降低,与预测误差的变化趋势一致。As shown in Figure 5, the No. 7 node of the classic four-machine two-region system is incorporated into the double-fed wind turbine model. Under the working condition of the wind power penetration rate of 19.47%, the No. 7 node is set to have a 273.4MW active power sudden drop fault. At the same time, the PMU sampling frequency is set to 100Hz, and the analysis object of the "prediction error index" is all frequency deviation extreme value prediction values within 0.3s, that is, n=29, corresponding to one of the components of the "prediction error index" index. As the forecast time increases, the sampling data increases and decreases, which is consistent with the trend of forecast error.

如图6所示,“预测误差指数”指标的组成之一斜率量化指标A2同样随预测时长增加,采样数据增多而降低,与预测误差的变化趋势一致。综合图5,其共同体现了“预测误差指数”指标间接描述预测精度的有效性。As shown in Figure 6, the slope quantification index A2, one of the components of the "forecast error index", also decreases with the increase of the forecast time and the increase of sampled data, which is consistent with the trend of forecast error. Combining Figure 5, it collectively embodies the effectiveness of the "forecast error index" index to indirectly describe the forecast accuracy.

如图7所示,设置A1和A2的限值分别为4和0.05,不同新能源渗透率下预测各发电机的频率偏差极值,对在线预测模型的有效性进行分析。As shown in Figure 7, the limit values of A1 and A2 are set to 4 and 0.05, respectively, and the frequency deviation extreme value of each generator is predicted under different new energy penetration rates, and the effectiveness of the online prediction model is analyzed.

可以看出,4种风电渗透率下在线预测模型均能在频率偏差极值到达之前输出4台同步发电机机端的频率偏差极值预测值,预测提前时间为3~6s,模型预测速度较快。图8分析输出的频率偏差极值预测值的误差,本文所提在线预测模型因为考虑了受扰后机端电磁功率的暂态变化,故预测误差比SFR模型降低一半以上,4种风电渗透率下、4台同步机机端频率偏差极值的预测均位于20%的误差范围内。综上,本文所提在线预测模型能一定程度的兼顾预测速度和预测精度,满足实际系统要求。It can be seen that the online prediction models under the four wind power penetration rates can output the extreme frequency deviation prediction value of the four synchronous generators before the frequency deviation extreme value arrives. The prediction lead time is 3-6s, and the model prediction speed is relatively fast . Figure 8 analyzes the error of the output frequency deviation extreme value prediction value. The online prediction model proposed in this paper considers the transient change of the electromagnetic power at the terminal after being disturbed, so the prediction error is more than half lower than that of the SFR model. The four wind power penetration rates The predictions of extreme frequency deviations of the lower and four synchronous machines are all within the error range of 20%. To sum up, the online prediction model proposed in this paper can take into account the prediction speed and prediction accuracy to a certain extent, and meet the actual system requirements.

本领域的技术人员容易理解,以上所述仅为本发明的较佳实施例而已,并不用以限制本发明,凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等,均应包含在本发明的保护范围之内。It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

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 ei (t) the third mechanical power variation expression Δ P mi (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 Method and device for online prediction of frequency deviation extremum based on wide-area measurement information Pending CN115764928A (en)

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