CN104578115A - Electric system low frequency oscillation mode identification method based on correlation functions - Google Patents
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Abstract
本发明公开了一种基于相关函数的电力系统低频振荡模式辨识方法，包括以下步骤：步骤A：读取一段电力系统无大扰动情况下对低频振荡模式具有较高可观性的线路有功功率信号作为待分析信号并确定采样时间间隔T s ；步骤B：将所述读取的有功功率信号进行预处理获得相应的功率波动信号；步骤C：将所述功率波动信号求取自相关函数，获得系统自由振荡信号；步骤D：基于扩展Prony方法，对所述自由振荡信号进行模式辨识，得出低频振荡模式频率和阻尼比。本发明的有益效果是：实现了仅基于随机响应信号的电力系统低频振荡模式辨识方法，操作简单、计算量小，辨识准确性较好。
The invention discloses a method for identifying low-frequency oscillation modes of power systems based on correlation functions, which includes the following steps: Step A: Reading a section of line active power signals that have high observability for low-frequency oscillation modes without major disturbances in the power system as The signal to be analyzed and the sampling time interval T s are determined; Step B: Preprocess the read active power signal to obtain the corresponding power fluctuation signal; Step C: Calculate the autocorrelation function of the power fluctuation signal to obtain the system Free oscillation signal; Step D: Based on the extended Prony method, conduct mode identification on the free oscillation signal to obtain the low frequency oscillation mode frequency and damping ratio. The beneficial effects of the present invention are: realizing the low-frequency oscillation mode identification method of the electric power system based only on the random response signal, with simple operation, small calculation amount and good identification accuracy.
Description
技术领域 technical field
本发明涉电力系统分析控制技术领域，具体地，涉及一种基于相关函数的电力系统低频振荡模式辨识方法。 The present invention relates to the technical field of power system analysis and control, and in particular, relates to a method for identifying low-frequency oscillation modes of power systems based on correlation functions.
背景技术 Background technique
低频振荡是交流互联系统具有的固有现象，电力系统的互联程度的提高、互联规模的扩大、电力系统中快速励磁系统的大量使用都会使得低频振荡问题更加突出。目前低频振荡问题严重威胁着电力系统稳定和限制互联电网电能传输能力。准确掌握系统低频振荡模式对电力系统安全稳定运行具有重要意义。 Low-frequency oscillation is an inherent phenomenon of AC interconnection systems. The improvement of the interconnection degree of the power system, the expansion of the interconnection scale, and the extensive use of fast excitation systems in the power system will make the problem of low-frequency oscillation more prominent. At present, the low frequency oscillation problem seriously threatens the stability of the power system and limits the power transmission capacity of the interconnected grid. Accurately grasping the low-frequency oscillation mode of the system is of great significance to the safe and stable operation of the power system.
基于量测数据进行低频振荡模式分析能够克服基于模型分析不能跟随系统结构和参数变化的不足，更具有实用性。基于量测信号的低频振荡模式辨识方法按照输入信号类型分类，可分为基于暂态振荡信号的方法和基于随机响应信号的方法。暂态振荡信号指系统经受明显扰动后的自由振荡响应，可用一系列复指数函数的线性组合来拟合；随机响应信号指系统正常运行情况下由新能源发电和负荷的随机波动所激发的响应，为系统在随机激励下的全响应，一般不能直接由复指数函数的线性组合来拟合，因此基于暂态振荡信号的方法一般不能直接应用于随机响应信号辨识低频振荡模式。在实际电网中暂态振荡信号数据量小，而由发电和负荷波动引起的随机响应信号在系统中几乎时刻存在，容易获得，基于随机响应信号的低频振荡模式辨识结果能够更好地反映系统正常运行情况下系统的小扰动稳定性。 Analysis of low-frequency oscillation modes based on measurement data can overcome the shortcomings of model-based analysis that cannot follow changes in system structure and parameters, and is more practical. According to the type of input signal, the low-frequency oscillation mode identification method based on the measurement signal can be divided into the method based on the transient oscillation signal and the method based on the random response signal. The transient oscillation signal refers to the free oscillation response of the system after an obvious disturbance, which can be fitted by a linear combination of a series of complex exponential functions; the random response signal refers to the response excited by the random fluctuation of new energy power generation and load under the normal operation of the system , is the full response of the system under random excitation, and generally cannot be directly fitted by a linear combination of complex exponential functions, so methods based on transient oscillation signals generally cannot be directly applied to random response signals to identify low-frequency oscillation modes. In the actual power grid, the amount of transient oscillation signal data is small, but the random response signal caused by power generation and load fluctuations exists almost all the time in the system and is easy to obtain. The low-frequency oscillation mode identification result based on the random response signal can better reflect the normal state of the system. Small-perturbation stability of the system under operating conditions.
基于随机响应信号进行低频振荡模式辨识的方法中，子空间方法需要量测系统输入信号，而实际电力系统中输入信号不可量测限制了该方法的应用；随机子空间方法需要对一个庞大的矩阵进行奇异值分解，计算量较大、算法复杂；基于ARMA模型的方法难以准确辨识阻尼比；随机减量技术结合Prony的方法，由于随机减量技术对自由振荡信号的估计较为粗糙，使得Prony对阻尼比的辨识不够准确。 In the method of low-frequency oscillation mode identification based on random response signals, the subspace method needs to measure the input signal of the system, but the unmeasurable input signal in the actual power system limits the application of this method; the random subspace method requires a huge matrix Singular value decomposition requires a large amount of calculation and complex algorithms; the method based on the ARMA model is difficult to accurately identify the damping ratio; the random decrement technique combined with Prony’s method, because the random decrement technique estimates the free oscillation signal is relatively rough, making Prony’s The identification of the damping ratio is not accurate enough.
因此，在现有技术中，存在所需要的电力系统输入信号不可量测、计算量较大或者方法对阻尼比的辨识不够准确的技术问题。 Therefore, in the prior art, there are technical problems that the required power system input signal cannot be measured, the amount of calculation is large, or the identification of the damping ratio by the method is not accurate enough.
发明内容 Contents of the invention
本发明所要解决的技术问题是提供一种仅基于电力系统输出的随机响应信号、算法简单可靠、阻尼比辨识准确度较高的基于相关函数的电力系统低频振荡模式辨识方法。 The technical problem to be solved by the present invention is to provide a low-frequency oscillation mode identification method of a power system based on a correlation function, which is only based on the random response signal output by the power system, the algorithm is simple and reliable, and the damping ratio identification accuracy is high.
本发明解决上述问题所采用的技术方案是： The technical solution adopted by the present invention to solve the above problems is:
一种基于相关函数的电力系统低频振荡模式辨识方法，包括以下步骤： A method for identifying low-frequency oscillation modes of power systems based on correlation functions, comprising the following steps:
步骤A：读取一段电力系统无大扰动情况下对低频振荡模式具有较高可观性的线路有功功率信号作为待分析信号并确定采样时间间隔T s ； Step A: Read a section of line active power signal with high observability to the low-frequency oscillation mode under the condition of no major disturbance in the power system as the signal to be analyzed and determine the sampling time interval T s ;
步骤B：将所述读取的有功功率信号进行预处理获得相应的功率波动信号； Step B: Preprocessing the read active power signal to obtain a corresponding power fluctuation signal;
步骤C：将所述功率波动信号求取自相关函数，获得系统自由振荡信号； Step C: Calculating the autocorrelation function of the power fluctuation signal to obtain a system free oscillation signal;
步骤D：基于扩展Prony方法，对所述自由振荡信号进行模式辨识，得出低频振荡模式频率和阻尼比。 Step D: Based on the extended Prony method, conduct mode identification on the free oscillation signal to obtain the low-frequency oscillation mode frequency and damping ratio.
本发明直接利用电网正常运行情况下由发电和负荷波动激发的系统随机响应信号，不依赖于大扰动激发系统的自由振荡信号，本申请方法不需要量测电力系统输入信号、计算量较小、辨识准确性较好，有助于准确掌握电网正常运行状态下系统的阻尼特性，为抑制弱阻尼或负阻尼低频振荡发生、改善电网的功角稳定性奠定基础，有效解决了现有的基于随机响应信号的电力系统低频振荡模式辨识方法存在的需要量测系统输入信号、计算量较大或者阻尼比辨识准确性不好的技术问题。 The present invention directly utilizes the random response signal of the system stimulated by power generation and load fluctuations under normal operation of the power grid, and does not rely on the free oscillation signal of the large disturbance excitation system. The method of this application does not need to measure the input signal of the power system, and the calculation amount is small The identification accuracy is good, which helps to accurately grasp the damping characteristics of the system under normal operating conditions of the power grid, and lays the foundation for suppressing the occurrence of low-frequency oscillations with weak or negative damping and improving the power angle stability of the power grid. The low-frequency oscillation mode identification method of the power system based on the response signal has the technical problems of needing to measure the input signal of the system, a large amount of calculation, or poor identification accuracy of the damping ratio.
进一步的，所述步骤B：将所述读取的有功功率信号进行预处理获得相应的功率波动信号的具体操作步骤为： Further, the step B: the specific operation steps of preprocessing the read active power signal to obtain the corresponding power fluctuation signal are:
将所述读取的线路有功功率信号通过数据预处理剔除异常数据，当数据出现缺失时用前一个正常数据填补缺失数据，得到修正后的有功功率序列P，再利用减去最小二乘拟合多项式的方法去除趋势项，得到数据长度为N的功率波动信号ΔP。本发明以电力系统正常运行情况下的线路有功功率信号P作为待分析信号，因此信号P中没有较大的突变，而异常数据的特征在于远偏离正常值，可根据下式条件确定异常值。 The read active power signal of the line is eliminated by data preprocessing, and when the data is missing, the previous normal data is used to fill in the missing data, and the corrected active power sequence P is obtained, which is then fitted by subtracting the least squares The polynomial method removes the trend item and obtains the power fluctuation signal Δ P with a data length of N. The present invention uses the active power signal P of the line under the normal operation of the power system as the signal to be analyzed, so there is no large mutation in the signal P , and the characteristic of abnormal data is that it deviates far from the normal value, and the abnormal value can be determined according to the following conditions.
若该条件成立，则第i个点判定为异常数据点，用前一个正常数据填补；若该条件不成立，则认为该点为正常数据点。 If the condition is true, the i -th point is judged as an abnormal data point and filled with the previous normal data; if the condition is not true, the point is considered as a normal data point.
进一步的，得到修正后的有功功率序列P，再利用减去最小二乘拟合多项式的方法去除趋势项，得到数据长度为N的功率波动信号ΔP的具体操作步骤为： Further, the corrected active power sequence P is obtained, and then the trend item is removed by subtracting the least squares fitting polynomial method, and the specific operation steps to obtain the power fluctuation signal ΔP with a data length of N are as follows:
B1：构造长度为N，时间间隔为T s 的时间序列T； B1: Construct a time series T with a length of N and a time interval of T s ;
； ;
B2：构造矩阵A； B2: construct matrix A;
； ;
其中，m为拟合多项式的阶数； Among them, m is the order of the fitted polynomial;
B3：计算拟合多项式的系数b； B3: Calculate the coefficient b of the fitting polynomial;
； ;
其中，上标T表示求取矩阵的转置矩阵，系数； Among them, the superscript T means to find the transpose matrix of the matrix, and the coefficient ;
B4：求取功率波动信号ΔP， B4: Calculate the power fluctuation signal Δ P ,
。 .
进一步的，所述步骤C：将所述功率波动信号ΔP求取自相关函数，获得长度为L的自由振荡响应信号R(k)(k=0，1,……L-1)； Further, the step C: calculate the autocorrelation function of the power fluctuation signal ΔP to obtain a free oscillation response signal R ( k ) with a length of L ( k =0, 1,... L- 1);
其中：N为功率波动信号ΔP数据长度。 Where: N is the data length of the power fluctuation signal ΔP .
进一步的，所述步骤D：基于扩展Prony参数估计方法，对所述自由振荡响应信号进行模式辨识，辨识出低频振荡模式频率和阻尼比的具体操作步骤为： Further, the step D: based on the extended Prony parameter estimation method, performing mode identification on the free oscillation response signal, and identifying the low-frequency oscillation mode frequency and damping ratio. The specific operation steps are:
D1：利用所述自由振荡信号R中的数据R(0)，R(1)，……，R(L-1)计算样本函数r(i, j)： D1: Utilize the data R (0), R (1), ..., R ( L- 1) in the free oscillation signal R to calculate the sample function r ( i, j ):
其中，L为自由振荡响应数据长度，p e 为扩展阶数，p e 大小取为L/2； Among them, L is the free oscillation response data length, pe is the expansion order, and the size of pe is taken as L / 2 ;
D2：构造扩展矩阵R e ： D2: Construct the expansion matrix R e :
； ;
D3：对扩展矩阵R e 进行奇异值分解： D3: Perform singular value decomposition on the extended matrix R e :
其中，H表示共轭转置；U为矩阵R e 的左奇异向量组成的矩阵；V为矩阵R e 的右奇异向量组成的矩阵；∑为对角阵，对角元素为矩阵R e 的奇异值，，…，； Among them, H represents the conjugate transpose; U is a matrix composed of left singular vectors of matrix Re e ; V is a matrix composed of right singular vectors of matrix Re e ; ∑ is a diagonal matrix, and the diagonal elements are singular of matrix Re e value , ,..., ;
D4：根据矩阵R e 的奇异值确定阶数p，并构造矩阵V 1 、 V 2 ： D4: Determine the order p according to the singular value of the matrix Re , and construct the matrix V 1 , V 2 :
比较对角阵∑中的元素，找出满足的最小的整数i，取信号阶数p=i；并构造矩阵V 1 、 V 2 ： compares elements in the diagonal matrix Σ , to find the satisfying The smallest integer i of , take the signal order p = i ; and construct the matrix V 1 , V 2 :
， ,
； ;
D5：求取系数a 1 、a 2 、…、a p ： D5: Calculate the coefficients a 1 , a 2 , ..., a p :
其中，a = [a 1 , a 2 , …, a p ]T； where, a = [ a 1 , a 2 , …, a p ] T ;
D6：求取下列多项式的根 D6: Find the roots of the following polynomials
； ;
D7：计算低频振荡模式的频率f i 、阻尼比d i ，(i=1,2, …,p) D7: Calculate the frequency f i and damping ratio d i of the low-frequency oscillation mode, ( i =1,2, …, p )
； ;
其中：T s 为采样时间间隔，arctan为反正切函数，ln为取自然对数，Re表示取复数的实部，Im表示取复数的虚部。 Among them: T s is the sampling time interval, arctan is the arc tangent function, ln is the natural logarithm, Re means the real part of the complex number, and Im means the imaginary part of the complex number.
综上，本发明的有益效果是： In sum, the beneficial effects of the present invention are:
由于采用了首先读取一段电力系统无大扰动情况下对低频振荡模式具有较高可观性的线路有功功率信号作为待分析信号并确定采样时间间隔T s ；然后将所述读取的有功功率信号进行预处理获得相应的功率波动信号；然后将所述功率波动信号求取自相关函数，获得系统自由振荡信号；最后基于扩展Prony方法，对所述自由振荡响应信号进行模式辨识，辨识出低频振荡模式频率和阻尼比的技术方案，即，直接利用电网正常运行情况下由发电和负荷波动激发的系统随机响应信号，不依赖于大扰动激发系统的自由振荡信号，本申请方法不需要量测电力系统输入信号、计算量较小、辨识准确性较好，有助于准确掌握电网正常运行状态下系统的阻尼特性，为抑制弱阻尼或负阻尼低频振荡发生、改善电网的功角稳定性奠定基础，有效解决了现有的基于随机响应信号的电力系统低频振荡模式辨识方法存在的需要量测系统输入信号、计算量较大、算法复杂或者阻尼比辨识准确性较差的技术问题。实现了电力系统正常运行情况下低频振荡模式辨识方法仅基于电力系统输出的随机响应信号、算法简单可靠和阻尼比辨识准确度较高的技术效果。 Since the line active power signal with high observability to the low-frequency oscillation mode is first read as the signal to be analyzed and the sampling time interval T s is determined; then the read active power signal Perform preprocessing to obtain the corresponding power fluctuation signal; then obtain the autocorrelation function of the power fluctuation signal to obtain the system free oscillation signal; finally, based on the extended Prony method, perform mode identification on the free oscillation response signal to identify the low frequency oscillation The technical scheme of mode frequency and damping ratio, that is, directly using the random response signal of the system excited by power generation and load fluctuations under normal operation of the power grid, does not rely on the free oscillation signal of the system excited by large disturbances, and the method of this application does not need to measure power The input signal of the system, the calculation amount is small, and the identification accuracy is good, which is helpful to accurately grasp the damping characteristics of the system under the normal operation state of the power grid, and lay the foundation for suppressing the occurrence of low-frequency oscillations with weak damping or negative damping and improving the power angle stability of the power grid , which effectively solves the technical problems existing in the existing random response signal-based power system low-frequency oscillation mode identification methods that need to measure the system input signal, has a large amount of calculation, complex algorithms, or poor damping ratio identification accuracy. The low-frequency oscillation mode identification method under the normal operation of the power system is only based on the random response signal output by the power system, the algorithm is simple and reliable, and the technical effect of high damping ratio identification accuracy is achieved.
附图说明 Description of drawings
图1是本发明的流程图； Fig. 1 is a flow chart of the present invention;
图2是IEEE16机68节点测试系统的示意图。 Fig. 2 is a schematic diagram of an IEEE16-machine 68-node test system.
具体实施方式 Detailed ways
下面结合实施例及附图，对本发明作进一步地的详细说明，但本发明的实施方式不限于此。 The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.
实施例： Example:
如图1所示，一种基于相关函数的电力系统低频振荡模式辨识方法，包括以下步骤： As shown in Figure 1, a method for identifying low-frequency oscillation modes in power systems based on correlation functions includes the following steps:
步骤A：读取一段电力系统无大扰动情况下对低频振荡模式具有较高可观性的线路有功功率信号作为待分析信号并确定采样时间间隔T s ； Step A: Read a section of line active power signal with high observability to the low-frequency oscillation mode under the condition of no major disturbance in the power system as the signal to be analyzed and determine the sampling time interval T s ;
电网无大扰动是指电网中无短路故障发生或大容量机组运行状态切换。低频振荡本质是发电机功角之间的相对振荡，而明显表现于线路上有功功率的振荡，因此工程上习惯于从线路有功功率数据辨识低频振荡模式，选择对低频振荡模式具有较高可观性的线路有功功率信号作为待分析信号是能够准确辨识低频振荡模式的前提，而线路有功功率信号对模式的可观性是根据电力系统的模型分析或长期的运行经验得出的，是本领域公知常识。本实施例中仿真步长为0.01秒，因此T s 取为0.01秒。 No major disturbance in the power grid means that there is no short-circuit fault or large-capacity unit operating state switching in the power grid. The essence of low-frequency oscillation is the relative oscillation between generator power angles, and it is obviously manifested in the oscillation of active power on the line. Therefore, engineering is accustomed to identifying low-frequency oscillation modes from line active power data, and the selection of low-frequency oscillation modes has a high degree of observability. The active power signal of the line as the signal to be analyzed is the premise of being able to accurately identify the low-frequency oscillation mode, and the observability of the line active power signal to the mode is obtained based on the model analysis of the power system or long-term operating experience, which is common knowledge in the field . In this embodiment, the simulation step size is 0.01 second, so T s is taken as 0.01 second.
步骤B：将所述读取的有功功率信号进行预处理获得相应的功率波动信号； Step B: Preprocessing the read active power signal to obtain a corresponding power fluctuation signal;
步骤C：将所述功率波动信号求取自相关函数，获得系统自由振荡信号； Step C: Calculating the autocorrelation function of the power fluctuation signal to obtain a system free oscillation signal;
步骤D：基于扩展Prony方法，对所述自由振荡信号进行模式辨识，得出低频振荡模式频率和阻尼比。 Step D: Based on the extended Prony method, conduct mode identification on the free oscillation signal to obtain the low-frequency oscillation mode frequency and damping ratio.
所述步骤B：将所述读取的有功功率信号进行预处理获得相应的功率波动信号的具体操作步骤为： The step B: the specific operation steps of preprocessing the read active power signal to obtain the corresponding power fluctuation signal are:
将所述读取的线路有功功率信号通过数据预处理剔除异常数据，估计缺失数据，即当数据出现缺失时用前一个正常数据填补缺失数据，得到修正后的有功功率序列P，再利用减去最小二乘拟合多项式的方法去除趋势项，得到数据长度为N的功率波动信号ΔP。本发明以电力系统正常运行情况下的线路有功功率信号P作为待分析信号，因此信号P中没有较大的突变，而异常数据的特征在于远偏离正常值，可根据下式条件确定异常值。 The read active power signal of the line is eliminated by data preprocessing to eliminate abnormal data and estimate the missing data, that is, when the data is missing, the previous normal data is used to fill the missing data, and the corrected active power sequence P is obtained, and then subtracted The least squares fitting polynomial method removes the trend item and obtains the power fluctuation signal Δ P with data length N. The present invention uses the active power signal P of the line under the normal operation of the power system as the signal to be analyzed, so there is no large mutation in the signal P , and the characteristic of abnormal data is that it deviates far from the normal value, and the abnormal value can be determined according to the following conditions.
（1） (1)
若该条件成立，则第i个点判定为异常数据点，用前一个正常数据填补；若该条件不成立，则认为该点为正常数据点。 If the condition is true, the i -th point is judged as an abnormal data point and filled with the previous normal data; if the condition is not true, the point is considered as a normal data point.
得到修正后的有功功率序列P，确定采样时间间隔T s 后，再利用减去最小二乘拟合多项式的方法去除趋势项，得到数据长度为N的功率波动信号ΔP的具体操作步骤为： After obtaining the corrected active power sequence P , after determining the sampling time interval T s , the trend item is removed by subtracting the least squares fitting polynomial method, and the specific operation steps to obtain the power fluctuation signal ΔP with a data length of N are as follows:
B1：构造长度为N，时间间隔为T s 的时间序列T； B1: Construct a time series T with a length of N and a time interval of T s ;
；（2） ;(2)
B2：构造矩阵A； B2: Construct matrix A ;
；（3） ;(3)
其中，m为拟合多项式的阶数； Among them, m is the order of the fitted polynomial;
B3：计算拟合多项式的系数b； B3: Calculate the coefficient b of the fitting polynomial;
； ;
其中，上标T表示求取矩阵的转置矩阵，系数，理论上m的值越大趋势项去除得越彻底，但m越大计算量越大，实际应用中阶数m取为5即可； Among them, the superscript T means to find the transpose matrix of the matrix, and the coefficient , in theory, the larger the value of m is, the more thoroughly the trend items are removed, but the larger the value of m , the greater the amount of calculation. In practical applications, the order m can be set to 5;
B4：求取功率波动信号ΔP， B4: Calculate the power fluctuation signal Δ P ,
。 .
所述步骤C：将所述功率波动信号ΔP求取自相关函数，获得长度为L的自由振荡响应信号R(k)(k=0,1,……L-1)； The step C: calculating the autocorrelation function of the power fluctuation signal ΔP to obtain a free oscillation response signal R ( k ) of length L ( k =0,1,... L -1);
（4） (4)
其中：N为功率波动信号ΔP的数据长度，本实施例中N取10分钟内数据采样个数，L为自由振荡信号的长度，本实施例中L取为10秒内数据采样个数，即： Wherein: N is the data length of the power fluctuation signal ΔP . In this embodiment, N is the number of data samples within 10 minutes. L is the length of the free oscillation signal. In this embodiment, L is the number of data samples within 10 seconds. Right now:
（5） (5)
所述步骤D：基于扩展Prony参数估计方法，对所述自由振荡响应信号进行模式辨识，辨识出低频振荡模式频率和阻尼比的具体操作步骤为： The step D: based on the extended Prony parameter estimation method, the mode identification is carried out on the free oscillation response signal, and the specific operation steps for identifying the low-frequency oscillation mode frequency and damping ratio are as follows:
D1：利用所述自由振荡信号R中的数据R(0)，R(1)，……，R(L-1)计算样本函数r(i, j)： D1: use the data R (0), R (1), ..., R ( L -1) in the free oscillation signal R to calculate the sample function r ( i, j ):
（6） (6)
其中，L为自由振荡响应数据长度，p e 为扩展阶数，p e 大小取为L/2； Among them, L is the free oscillation response data length, pe is the expansion order, and the size of pe is taken as L / 2 ;
D2：构造扩展矩阵R e ： D2: Construct the expansion matrix R e :
（7） (7)
D3：对扩展矩阵R e 进行奇异值分解： D3: Perform singular value decomposition on the extended matrix R e :
（8） (8)
其中，H表示共轭转置；U为矩阵R e 的左奇异向量组成的矩阵；V为矩阵R e 的右奇异向量组成的矩阵；∑为对角阵，对角元素为矩阵R e 的奇异值，，…，； Among them, H represents the conjugate transpose; U is a matrix composed of left singular vectors of matrix Re e ; V is a matrix composed of right singular vectors of matrix Re e ; ∑ is a diagonal matrix, and the diagonal elements are singular of matrix Re e value , ,..., ;
D4：根据矩阵R e 的奇异值确定阶数p，并构造矩阵V 1 、 V 2 ： D4: Determine the order p according to the singular value of the matrix Re , and construct the matrix V 1 , V 2 :
比较对角阵∑中的元素，找出满足的最小的整数i，取信号阶数p=i；并构造矩阵V 1 、 V 2 ： compares the elements in the diagonal matrix Σ , to find the satisfying The smallest integer i of , take the signal order p = i ; and construct the matrix V 1 , V 2 :
（9） (9)
（10） (10)
D5：求取系数a 1 、a 2 、…、a p ： D5: Calculate the coefficients a 1 , a 2 , ..., a p :
（11） (11)
其中，a = [a 1 , a 2 , …, a p ]T。 where a = [ a 1 , a 2 , …, a p ] T .
D6：求取下列多项式的根 D6: Find the roots of the following polynomials
（12） (12)
D7：计算低频振荡模式的频率f i 、阻尼比d i ，(i=1,2, …,p) D7: Calculate the frequency f i and damping ratio d i of the low-frequency oscillation mode, ( i =1,2, …, p )
（13） (13)
其中：T s 为采样时间间隔，arctan为反正切函数，ln为取自然对数，Re表示取复数的实部，Im表示取复数的虚部。 Among them: T s is the sampling time interval, arctan is the arc tangent function, ln is the natural logarithm, Re means the real part of the complex number, and Im means the imaginary part of the complex number.
其中，基于自相关函数从系统全响应信号中提取自由振荡信号已在机械故障诊断和结构振动模式识别等方面得到应用。技术的核心是线性系统在白噪声激励下线性系统全响应的自相关函数与系统自由响应函数有相同形式的表达式，通过求解自相关函数以近似估计系统的自由振荡信号。 Among them, the free oscillation signal extracted from the system full response signal based on the autocorrelation function has been applied in mechanical fault diagnosis and structural vibration mode recognition. The core of the technology is that the autocorrelation function of the linear system's full response under the excitation of white noise has the same form of expression as the system's free response function, and the free oscillation signal of the system can be approximated by solving the autocorrelation function.
下面通过仿真实验对本申请实施例中的方案进行介绍： The scheme in the embodiment of the present application is introduced through the simulation experiment below:
采用IEEE16机68节点测试系统对本申请实施例中的方案进行仿真验证，如图2所示系统主要分为5个区域，区域1（G1-G9），区域2（G10-G13），区域3（G14），区域4（G15），区域5（G16）。通过对系统线性化后状态矩阵的特征值分析可知，系统中存在4个主导振荡模式，如表1所示，表1为16机68节点系统区域间低频振荡模式真实值，其中，模式的阻尼比可以通过调节发电机的PSS参数改变。模式1为区域1-2相对于区域3-5振荡，模式2为区域1-4相对于区域5振荡，模式3为区域1相对于区域2振荡，模式4为区域3和区域5相对于区域4振荡。选择线路1-47、线路68-50、线路8-9和线路67-42有功功率分别监测模式1、模式2、模式3和模式4。 The scheme in the embodiment of this application is simulated and verified by using the IEEE16 machine 68 node test system. As shown in Figure 2, the system is mainly divided into five areas, area 1 (G1-G9), area 2 (G10-G13), and area 3 ( G14), Region 4 (G15), Region 5 (G16). Through the analysis of the eigenvalues of the state matrix after system linearization, it can be seen that there are four dominant oscillation modes in the system, as shown in Table 1. Table 1 shows the real value of the inter-area low-frequency oscillation mode of the 16-machine 68-node system. Among them, the damping of the mode The ratio can be changed by adjusting the PSS parameters of the generator. Mode 1 is regions 1-2 oscillating relative to regions 3-5, mode 2 is regions 1-4 oscillating relative to region 5, mode 3 is region 1 oscillating relative to region 2, and mode 4 is region 3 and region 5 oscillating relative to 4 Oscillations. Select Line 1-47, Line 68-50, Line 8-9, and Line 67-42 to monitor the active power of Mode 1, Mode 2, Mode 3 and Mode 4 respectively.
为了模拟实际电力系统中的小幅随机扰动，在16机68节点系统主要负荷节点处注入该负荷点幅值0.5%的随机小幅扰动功率信号，该功率扰动信号服从高斯分布，仿真时长10分钟。为了排除单次功率波动导致辨识结果偶然性，采用蒙特卡洛思路仿真，进行100次仿真实验，从概率统计的角度对本申请中的方法进行检验，表2为本申请中的方法辨识结果。 In order to simulate the small random disturbance in the actual power system, a random small disturbance power signal with an amplitude of 0.5% of the load point is injected into the main load node of the 16-machine 68-node system. The power disturbance signal obeys the Gaussian distribution, and the simulation time is 10 minutes. In order to eliminate the contingency of the identification results caused by a single power fluctuation, Monte Carlo simulation was used to conduct 100 simulation experiments, and the method in this application was tested from the perspective of probability and statistics. Table 2 shows the identification results of the method in this application.
表1 Table 1
表2 Table 2
由此可知，将上述辨识结果与真实值进行比较可知，采用本申请中的方法对随机响应信号进行处理，多次实验所得到的频率和阻尼比均值与理论值接近，各模式频率均值误差小于1%、阻尼比均值误差小于10%，且频率和阻尼比的标准差较小，表明本申请中的方法可以从电力系统随机响应信号中较准确地辨识出低频振荡模式。 It can be seen from this that, comparing the above identification results with the real values, it can be seen that the random response signal is processed by the method in this application, and the average values of frequency and damping ratio obtained by multiple experiments are close to the theoretical values, and the average error of each mode frequency is less than 1%, the average error of damping ratio is less than 10%, and the standard deviation of frequency and damping ratio is small, indicating that the method in this application can more accurately identify low-frequency oscillation modes from random response signals of power systems.
综上，本发明由于采用了首先读取一段电力系统无大扰动情况下对低频振荡模式具有较高可观性的线路有功功率信号作为待分析信号并确定采样时间间隔T s ；然后将读取的有功功率信号进行预处理获得相应的功率波动信号；将所述功率波动信号求取自相关函数，获得系统自由振荡信号；最后基于扩展Prony方法，对所述自由振荡信号进行模式辨识，辨识出低频振荡模式频率和阻尼比的技术方案，即，直接利用电网正常运行情况下有负荷波动激发的系统随机响应信号，不依赖于大扰动激发系统的自由振荡信号，本申请方法操作简单、计算量小，辨识准确性较好，有助于准确掌握电网正常运行状态下系统的阻尼特性，为抑制弱阻尼或负阻尼低频振荡发生、改善电网的稳定性奠定基础，有效解决了现有的基于随机响应信号的电力系统低频振荡模式辨识方法存在的需要量测系统输入信号、操作复杂计算量大或者阻尼比辨识准确性不好的技术问题。 In summary, the present invention adopts firstly to read a section of line active power signal which has high observability to the low-frequency oscillation mode under the condition of no major disturbance in the power system as the signal to be analyzed and determine the sampling time interval T s ; then the read The active power signal is preprocessed to obtain the corresponding power fluctuation signal; the power fluctuation signal is obtained from the autocorrelation function to obtain the system free oscillation signal; finally, based on the extended Prony method, the free oscillation signal is pattern identified to identify the low frequency The technical scheme of oscillation mode frequency and damping ratio, that is, directly using the random response signal of the system excited by load fluctuations under the normal operation of the power grid, does not rely on the free oscillation signal of the system excited by large disturbances. The method of this application is simple to operate and has a small amount of calculation , the identification accuracy is better, it is helpful to accurately grasp the damping characteristics of the system under the normal operation state of the power grid, lay a foundation for suppressing the occurrence of low-frequency oscillations with weak damping or negative damping, and improving the stability of the power grid, effectively solving the existing problems based on random response There are technical problems in the low-frequency oscillation mode identification method of the power system based on signals, such as the need to measure the system input signal, complex operation and large amount of calculation, or poor damping ratio identification accuracy.
如上所述，可较好的实现本发明。 As described above, the present invention can be preferably carried out.
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| CN113158785A (en) * | 2021-03-11 | 2021-07-23 | 复旦大学 | Method for identifying modal parameters of oscillation signals |
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