CN108872777A - Winding in Power Transformer state evaluating method based on improved system delay Order- reduction - Google Patents
Winding in Power Transformer state evaluating method based on improved system delay Order- reduction Download PDFInfo
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Abstract
Description
技术领域technical field
本发明属于电力变压器安全故障检测技术领域,具体涉及一种基于改进型系统延迟阶数估计的电力变压器绕组状态评估方法。The invention belongs to the technical field of power transformer safety fault detection, and in particular relates to a power transformer winding state evaluation method based on an improved system delay order estimation.
背景技术Background technique
大型电力变压器作为电力系统中十分重要的一环,其安全运行对保证电网安全、可靠供电举足轻重。在电力变压器故障中,绕组的故障比例高达46.4%,为变压器故障的最主要部件,且在电动力作用下绕组发生机械变形而导致的严重故障占绕组总故障的70%。即便是绕组的轻微变形,也会引发绕组机械性能恶化、绝缘强度与抗短路能力降低等问题,带来极大的安全隐患。因此,在变压器带电监测中实现对其主要故障部件绕组的状态监测与评估,是十分必要且重要的。As a very important part of the power system, large power transformers play an important role in ensuring the safe and reliable power supply of the power grid. In power transformer faults, the proportion of winding faults is as high as 46.4%, which is the most important part of transformer faults, and the serious faults caused by mechanical deformation of windings under the action of electrodynamic force account for 70% of the total faults of windings. Even a slight deformation of the winding will cause deterioration of the mechanical properties of the winding, reduction of insulation strength and short-circuit resistance, and other problems, which will bring great safety hazards. Therefore, it is very necessary and important to realize the state monitoring and evaluation of the main faulty component winding in the transformer live monitoring.
振动分析法通过对采集到的油箱壁振动信号进行分析,获取变压器内部部件状态信息,当变压器内部机械结构发生改变时,势必导致振动系统的系统响应发生改变。因此,可构建输入电磁力与输出绕组振动响应的关系模型,并通过提取该模型的系统特性反映变压器绕组的机械结构状态。The vibration analysis method analyzes the collected vibration signals of the oil tank wall to obtain the status information of the internal components of the transformer. When the internal mechanical structure of the transformer changes, it will inevitably lead to changes in the system response of the vibration system. Therefore, the relationship model between the input electromagnetic force and the vibration response of the output winding can be constructed, and the mechanical structure state of the transformer winding can be reflected by extracting the system characteristics of the model.
申请号为201310047702.0的中国专利提了一种基于电-振动模型的电力变压器故障诊断方法,其通过采集变压器的电压信号、电流信号、油温信号以及多个振动测点,建立了振动各频率成分与电流、电压及油温间的回归模型,并利用振动的实测数据与通过模型得到的预测数据进行比较,以对变压器进行故障诊断;该方法虽一定程度上考虑了变压器振动中的非线性,但仍存在由磁滞效应等强非线性引入的部分频率成分无法建模或模型误差较大等问题,因此该方法在准确性和有效性上还有一定的局限性。The Chinese patent with the application number 201310047702.0 proposes a power transformer fault diagnosis method based on the electric-vibration model, which establishes the vibration frequency components by collecting the voltage signal, current signal, oil temperature signal and multiple vibration measuring points of the transformer. and the regression model between current, voltage and oil temperature, and compare the measured data of vibration with the predicted data obtained through the model to diagnose the fault of the transformer; although this method considers the nonlinearity in the vibration of the transformer to a certain extent, However, there are still some problems that some frequency components introduced by strong nonlinearity such as hysteresis effect cannot be modeled or the model error is large, so this method still has certain limitations in accuracy and effectiveness.
申请号为201710867458.0的中国专利则在变压器绕组振动原理的基础上,提出并构建了电流-绕组振动间的Hammerstein非线性模型,并通过提取该模型的系统特性——系统延迟阶数,反映变压器绕组的机械结构状态;该方法考虑了机械故障对模型系统特性的影响的物理机制,仅提取模型中与故障相关的部分信息作为诊断依据,可有效避免直接由模型误差引入的误判,然而其系统延迟阶数提取算法在系统输入输出阶数相差较大时会出现估计误差较大甚至估计错误的问题,影响绕组状态评估结果的准确性。The Chinese patent with the application number 201710867458.0 proposes and constructs a Hammerstein nonlinear model between current and winding vibration based on the principle of transformer winding vibration, and extracts the system characteristics of the model - the system delay order, reflecting the transformer winding The state of the mechanical structure; this method takes into account the physical mechanism of the influence of mechanical faults on the characteristics of the model system, and only extracts part of the fault-related information in the model as a basis for diagnosis, which can effectively avoid misjudgments directly caused by model errors. When the delay order extraction algorithm has a large difference between the input and output orders of the system, the estimation error will be large or even wrong, which will affect the accuracy of the winding state evaluation results.
发明内容Contents of the invention
鉴于上述,本发明提供了一种基于改进型系统延迟阶数估计的电力变压器绕组状态评估方法,能够在线检测出电力变压器绕组机械结构状态,改善了当输入输出阶数差异较大时阶数估计不准的问题,使提取参数能更准确的反映绕组的实际状态。In view of the above, the present invention provides a power transformer winding state evaluation method based on the improved system delay order estimation, which can detect the mechanical structure state of the power transformer winding online, and improves the order estimation when the input and output order differences are large. Inaccurate problems, so that the extracted parameters can more accurately reflect the actual state of the winding.
一种基于改进型系统延迟阶数估计的电力变压器绕组状态评估方法,包括如下步骤:A method for evaluating the state of a power transformer winding based on an improved system delay order estimation, comprising the following steps:
(1)在电力变压器油箱表面对应绕组位置分散地布置多个振动传感器,记录电力变压器在低电压负载运行条件下各振动传感器的振动信号,并同步采集电力变压器的一次侧电流;(1) Dispersively arrange multiple vibration sensors at the positions corresponding to the windings on the surface of the power transformer oil tank, record the vibration signals of each vibration sensor of the power transformer under low-voltage load operating conditions, and collect the primary side current of the power transformer synchronously;
(2)对所述振动信号以及电流信号进行预处理,其中包括对电流信号的去磁滞化处理;(2) Preprocessing the vibration signal and the current signal, including demagnetization of the current signal;
(3)对于任一振动传感器,通过构建电流与绕组振动的关系模型,并根据该振动传感器预处理后的振动信号以及电流信号估算出模型的延迟阶数n作为系统特性的特征量,n=Na+Nb,Na和Nb分别为系统输出和输入的实际线性延迟阶数,Na和Nb均为自然数;进而依据n、Na和Nb判断基于该振动传感器数据情况下电力变压器绕组的机械结构状态;(3) For any vibration sensor, the relationship model between current and winding vibration is constructed, and the delay order n of the model is estimated as the characteristic quantity of the system characteristic according to the preprocessed vibration signal and current signal of the vibration sensor, n= Na + N b , Na and N b are the actual linear delay orders of the system output and input respectively, and both Na and N b are natural numbers; and then judge based on the vibration sensor data based on n, Na and N b The state of mechanical structure of power transformer windings;
(4)根据步骤(3)遍历所有振动传感器,当基于一定比例的振动传感器判断出绕组机械结构状态为正常,则最终判定电力变压器绕组正常,否则判定电力变压器绕组异常。(4) Traverse all vibration sensors according to step (3). When the mechanical structure state of the winding is determined to be normal based on a certain proportion of the vibration sensors, it is finally determined that the power transformer winding is normal, otherwise it is determined that the power transformer winding is abnormal.
进一步地,所述步骤(2)中对振动信号以及电流信号进行预处理的具体过程为:首先,对振动信号和电流信号进行归一化处理;然后,根据以下公式对归一化后的电流信号进行非线性变换:Further, the specific process of preprocessing the vibration signal and the current signal in the step (2) is: first, normalize the vibration signal and the current signal; then, according to the following formula, normalize the current The signal is transformed nonlinearly:
其中:i(t)为归一化后的电流信号,t为时刻,ip(t)为非线性变换后的电流信号。Among them: i(t) is the current signal after normalization, t is the time, ip (t) is the current signal after nonlinear transformation.
进一步地,所述步骤(3)中估算模型延迟阶数n的具体过程如下:Further, the specific process of estimating the model delay order n in the step (3) is as follows:
3.1根据以下公式计算延迟阶数为n情况下关系模型中所有采样点组合的Lipschitz系数:3.1 Calculate the Lipschitz coefficients of all sampling point combinations in the relational model according to the following formula:
其中:lij (n)表示延迟阶数为n情况下关系模型中第i采样点与第j采样点组合的Lipschitz系数,i和j均为采样点序号;当n为偶数时,γ1(i)~γn(i)对应等于y(i-1),x(i-1),y(i-2),x(i-2),...,y(i-Na),x(i-Nb),γ1(j)~γn(j)对应等于y(j-1),x(j-1),y(j-2),x(j-2),...,y(j-Na),x(j-Nb);当n为奇数时,γ1(i)~γn(i)对应等于y(i-1),x(i-1),y(i-2),x(i-2),...,y(i-Nb),x(i-Nb),y(i-Na),γ1(j)~γn(j)对应等于y(j-1),x(j-1),y(j-2),x(j-2),...,y(j-Nb),x(j-Nb),y(j-Na);y(i)和y(j)分别为振动传感器预处理后的振动信号中对应第i采样点和第j采样点的信号值,y(i-1)和y(j-1)分别为振动传感器预处理后的振动信号中对应第i-1采样点和第j-1采样点的信号值,y(i-2)和y(j-2)分别为振动传感器预处理后的振动信号中对应第i-2采样点和第j-2采样点的信号值,y(i-Na)和y(j-Na)分别为振动传感器预处理后的振动信号中对应第i-Na采样点和第j-Na采样点的信号值,y(i-Nb)和y(j-Nb)分别为振动传感器预处理后的振动信号中对应第i-Nb采样点和第j-Nb采样点的信号值,x(i-1)和x(j-1)分别为处理后的电流信号中对应第i-1采样点和第j-1采样点的信号值,x(i-2)和x(j-2)分别为处理后的电流信号中对应第i-2采样点和第j-2采样点的信号值,x(i-Nb)和x(j-Nb)分别为处理后的电流信号中对应第i-Nb采样点和第j-Nb采样点的信号值;Among them: l ij (n) represents the Lipschitz coefficient of the i-th sampling point and the j-th sampling point combination in the relationship model when the delay order is n, i and j are the serial numbers of the sampling points; when n is an even number, γ 1 ( i)~γ n (i) corresponds to y(i-1),x(i-1),y(i-2),x(i-2),...,y(iN a ),x( iN b ), γ 1 (j)~γ n (j) corresponds to y(j-1),x(j-1),y(j-2),x(j-2),...,y (jN a ),x(jN b ); when n is an odd number, γ 1 (i)~γ n (i) corresponds to y(i-1),x(i-1),y(i-2) ,x(i-2),...,y(iN b ),x(iN b ),y(iN a ), γ 1 (j)~γ n (j) correspond to y(j-1), x(j-1),y(j-2),x(j-2),...,y(jN b ),x(jN b ),y(jN a ); y(i) and y( j) are the signal values corresponding to the i-th sampling point and the j-th sampling point in the vibration signal preprocessed by the vibration sensor respectively, and y(i-1) and y(j-1) are the vibration signal preprocessed by the vibration sensor y(i-2) and y(j-2) are the signal values corresponding to the i-1th sampling point and the j-1th sampling point in the vibration sensor, respectively, corresponding to the i-2th sampling point in the vibration signal preprocessed by the vibration sensor and the signal value of the j-2th sampling point, y(iN a ) and y(jN a ) are the signal values corresponding to the iN a -th sampling point and the jN a -th sampling point in the vibration signal preprocessed by the vibration sensor respectively, y (iN b ) and y(jN b ) are the signal values corresponding to the iN b sampling point and the jN b sampling point in the vibration signal preprocessed by the vibration sensor, x(i-1) and x(j-1) are the signal values corresponding to the i-1th sampling point and the j-1th sampling point in the processed current signal respectively, and x(i-2) and x(j-2) are the signal values corresponding to the i-th sampling point in the processed current signal respectively. -2 sampling point and the signal value of the j-2th sampling point, x(iN b ) and x(jN b ) are respectively the signal values corresponding to the iN b sampling point and the jN b sampling point in the processed current signal;
3.2将步骤3.1中计算得到的所有Lipschitz系数从大到小排序并截取前m个Lipschitz系数,进而根据以下公式计算延迟阶数为n情况下关系模型的Lipschitz平均系数:3.2 Sort all the Lipschitz coefficients calculated in step 3.1 from large to small and intercept the first m Lipschitz coefficients, and then calculate the average Lipschitz coefficient of the relational model when the delay order is n according to the following formula:
其中:l(n)表示延迟阶数为n情况下关系模型的Lipschitz平均系数,l(n)(z)为从大到小排序后的第z个Lipschitz系数,m通常取0.01Nset,Nset为采样点总数;Among them: l (n) represents the Lipschitz average coefficient of the relationship model when the delay order is n, l (n) (z) is the zth Lipschitz coefficient sorted from large to small, m usually takes 0.01N set , N set is the total number of sampling points;
3.3初始化延迟阶数n=2且Na=Nb=1;3.3 Initialize delay order n=2 and N a =N b =1;
3.4使Na累加上1,然后根据步骤3.1~3.2计算n=Na+Nb和n=Na-1+Nb情况下对应的Lipschitz平均系数l(Na+Nb)和l(Na-1+Nb)并进行以下判断:3.4 Add 1 to Na, and then calculate the corresponding Lipschitz average coefficient l (Na + Nb) and l ( Na- 1+Nb) and make the following judgments:
若l(Na+Nb)-l(Na-1+Nb)≤ε×l(Na-1+Nb)且Nb未确定,则确定Na为本次累加前的值并执行步骤3.5;If l (Na+Nb) -l (Na-1+Nb) ≤ε×l (Na-1 + Nb) and N b is not determined, determine that Na is the value before this accumulation and perform step 3.5;
若l(Na+Nb)-l(Na-1+Nb)≤ε×l(Na-1+Nb)且Nb已确定,则确定Na为本次累加前的值并使确定的Na和Nb相加即为延迟阶数n;If l (Na+Nb) -l (Na-1+Nb )≤ε×l (Na-1 + Nb) and N b has been determined, then determine Na as the value before this accumulation and make the determined Na The addition of N b is the delay order n;
若l(Na+Nb)-l(Na-1+Nb)>ε×l(Na-1+Nb)且Nb未确定,则执行步骤3.5;If l (Na+Nb) -l (Na-1+Nb )>ε×l (Na-1+Nb) and N b is not determined, then perform step 3.5;
若l(Na+Nb)-l(Na-1+Nb)>ε×l(Na-1+Nb)且Nb已确定,则反复执行步骤3.4直至Na确定并使确定的Na和Nb相加即为延迟阶数n;If l (Na+Nb) -l (Na-1+Nb) >ε× l (Na-1 + Nb) and N b has been determined, repeat step 3.4 until Na is determined and the determined Na and N The addition of b is the delay order n;
3.5使Nb累加上1,然后根据步骤3.1~3.2计算n=Na+Nb和n=Na+Nb-1情况下对应的Lipschitz平均系数l(Na+Nb)和l(Na+Nb-1)并进行以下判断:3.5 Add 1 to N b , and then calculate the corresponding Lipschitz average coefficient l ( Na + Nb) and l ( Na+ Nb-1) and make the following judgments:
若l(Na+Nb)-l(Na+Nb-1)≤ε×l(Na+Nb-1)且Na未确定,则确定Nb为本次累加前的值并返回执行步骤3.4;If l (Na+Nb) -l (Na+Nb-1) ≤ε×l (Na+Nb-1) and N a is not determined, then determine N b as the value before this accumulation and return to step 3.4;
若l(Na+Nb)-l(Na+Nb-1)≤ε×l(Na+Nb-1)且Na已确定,则确定Nb为本次累加前的值并使确定的Na和Nb相加即为延迟阶数n;If l (Na+Nb) -l (Na+Nb-1) ≤ε×l (Na+Nb-1) and N a has been determined, then determine N b as the value before this accumulation and make the determined N a The addition of N b is the delay order n;
若l(Na+Nb)-l(Na+Nb-1)>ε×l(Na+Nb-1)且Na未确定,则返回执行步骤3.4;If l (Na+Nb) -l (Na+Nb-1) >ε× l (Na+Nb-1) and Na is not determined, return to step 3.4;
若l(Na+Nb)-l(Na+Nb-1)>ε×l(Na+Nb-1)且Na已确定,则反复执行步骤3.5直至Nb确定并使确定的Na和Nb相加即为延迟阶数n;If l (Na+Nb) -l (Na+Nb-1) >ε× l (Na+Nb-1) and Na has been determined, then repeat step 3.5 until N b is determined and the determined Na and N The addition of b is the delay order n;
其中:ε为收敛系数。Where: ε is the convergence coefficient.
进一步地,当Na和Nb均未确定时,收敛系数ε=ε1;当Na和Nb其中一个确定时,收敛系数ε=ε2;其中,ε1和ε2分别为设定的两个不同的常数。Further, when neither N a nor N b is determined, the convergence coefficient ε=ε 1 ; when one of N a and N b is determined, the convergence coefficient ε=ε 2 ; where ε 1 and ε 2 are set respectively two different constants.
进一步地,所述步骤(3)中判断电力变压器绕组机械结构状态的具体过程为:首先,在确保电力变压器绕组正常情况下根据步骤(1)至(3)过程计算出模型的延迟阶数n以及Na和Nb;然后,使步骤(3)中基于当前振动传感器数据情况下实际测算得到的n、Na和Nb与电力变压器绕组正常情况下的n、Na和Nb进行比对,若两者数据吻合,则判定基于当前振动传感器数据情况下电力变压器绕组的机械结构状态为正常;若两者数据不吻合,则判定基于当前振动传感器数据情况下电力变压器绕组的机械结构状态为异常。Further, the specific process of judging the state of the mechanical structure of the power transformer winding in the step (3) is as follows: first, the delay order n of the model is calculated according to the steps (1) to (3) under the condition that the power transformer winding is normal And Na and N b ; Then, make n, Na and N b obtained under the actual measurement and calculation based on the current vibration sensor data situation in step (3) and n, Na and N b under normal conditions of the power transformer winding Yes, if the two data match, it is determined that the mechanical structure state of the power transformer winding based on the current vibration sensor data is normal; if the two data do not match, then it is determined that the mechanical structure state of the power transformer winding is based on the current vibration sensor data is abnormal.
基于上述技术方案,本发明的有益技术效果如下:Based on the above technical scheme, the beneficial technical effects of the present invention are as follows:
1.本发明具体实现与变压器无任何电气连接,且无需对变压器进行断电,对整个电力系统的运行影响很小。1. The present invention does not have any electrical connection with the transformer, and does not need to cut off the power of the transformer, which has little impact on the operation of the entire power system.
2.本发明方法基于绕组振动产生机理,更好地反映了绕组的机械结构状态,将绕组故障与特征量直接进行关联,为故障诊断的有效性与科学性提供依据。2. The method of the present invention is based on the winding vibration generation mechanism, better reflects the mechanical structure state of the winding, directly associates the winding fault with the characteristic quantity, and provides a basis for the validity and scientificity of the fault diagnosis.
3.本发明方法相较于改进之前,所提取特征量与系统实际阶数更为接近,能更准确的反映系统特性与绕组机械结构状态。3. Compared with the method before the improvement, the extracted feature quantity is closer to the actual order of the system, and can more accurately reflect the characteristics of the system and the state of the mechanical structure of the winding.
附图说明Description of drawings
图1为本发明方法的步骤流程示意图。Fig. 1 is a schematic flow chart of the steps of the method of the present invention.
图2为电力变压器油箱表面测点布置图。Figure 2 is a layout diagram of measuring points on the surface of the power transformer oil tank.
图3为输入电流i(t)与振动分量的关系曲线图。Figure 3 shows the input current i(t) and the vibration component relationship graph.
图4为经去磁滞变换后的输入电流ip(t)与振动分量的关系曲线图。Figure 4 shows the input current i p (t) and the vibration component after demagnetization transformation relationship graph.
图5为本发明改进后延迟阶数估计算法的流程示意图。FIG. 5 is a schematic flow chart of the improved delay order estimation algorithm of the present invention.
图6(a)为原始算法的阶数估计过程及结果示意图。Figure 6(a) is a schematic diagram of the order estimation process and results of the original algorithm.
图6(b)为本发明改进后算法的阶数估计过程及结果示意图。Fig. 6(b) is a schematic diagram of the order estimation process and results of the improved algorithm of the present invention.
具体实施方式Detailed ways
为了更为具体地描述本发明,下面结合附图及具体实施方式对本发明的技术方案进行详细说明。In order to describe the present invention more specifically, the technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.
本实施方式的具体实验对象为一台110kV三相油浸式电力变压器,为了验证本发明方法的有效性,特意对比了同一个绕组在正常情况下和故障情况下的振动特征。故障绕组是正常绕组通过短路冲击人为损坏实现,变压器短路实验是一种专门针对绕组的测试方法,通过低压端短路,在高压端施加电压,能够让变压器绕组电流达到额定值。The specific experimental object of this embodiment is a 110kV three-phase oil-immersed power transformer. In order to verify the effectiveness of the method of the present invention, the vibration characteristics of the same winding under normal conditions and fault conditions were deliberately compared. Faulty windings are caused by man-made damage to normal windings through short-circuit impact. Transformer short-circuit test is a special test method for windings. By short-circuiting the low-voltage end and applying voltage on the high-voltage end, the current of the transformer winding can reach the rated value.
在进行诊断时,为了便于不失真的获取不同幅值的振动信号,须选用灵敏度较高的振动传感器;为了保证传感器在采样滤波频带之内的振动响应,将振动传感器固定在油箱侧壁上应采用磁座吸附或胶水粘接的方式。振动采样装置包括前置放大、抗混叠滤波、AD采样等主要模块,其中AD采样位数至少12位,抗混叠滤波器截止频率为2000Hz;进行振动信号采样时,采样频率至少为4000Hz。在本实施例中,采集振动信号的采样频率设置为10000Hz,AD模块采样位数为16位,并采用连续采样模式来记录下实验的全过程。In diagnosis, in order to obtain vibration signals of different amplitudes without distortion, a vibration sensor with high sensitivity must be selected; in order to ensure the vibration response of the sensor within the sampling filter frequency band, the vibration sensor should be fixed on the side wall of the fuel tank. It adopts the method of magnetic seat adsorption or glue bonding. The vibration sampling device includes main modules such as preamplification, anti-aliasing filter, and AD sampling. The number of AD sampling bits is at least 12, and the cut-off frequency of the anti-aliasing filter is 2000 Hz; when sampling vibration signals, the sampling frequency is at least 4000 Hz. In this embodiment, the sampling frequency for collecting vibration signals is set to 10000 Hz, the number of sampling bits of the AD module is 16 bits, and the continuous sampling mode is used to record the whole process of the experiment.
如图1所示,本发明基于改进型系统延迟阶数估计的电力变压器绕组状态评估方法,包括如下步骤:As shown in Figure 1, the present invention is based on the power transformer winding state evaluation method of improved system delay order estimation, comprises the following steps:
(1)布置振动测点。(1) Arrange vibration measuring points.
在电力变压器油箱表面布置5个测点,如图2所示,因为A相绕组会在实验被人为损坏,所以5个测点布置在A相绕组对应的油箱壁上。Five measuring points are arranged on the surface of the oil tank of the power transformer, as shown in Figure 2, because the A-phase winding will be artificially damaged in the experiment, so the five measuring points are arranged on the oil tank wall corresponding to the A-phase winding.
(2)采集正常情况和异常情况下的振动信号及电流信号。(2) Collect vibration signals and current signals under normal and abnormal conditions.
首先对一台新的变压器进行短路实验,逐步提高高压侧上的电压来增加绕组上的电流,按照每次10%比例增大电流,逐步达到额定值;电流增加10%后,保持30秒稳定不变,利用连续采样模式,记录下所有测点所有时间的振动。First conduct a short-circuit test on a new transformer, gradually increase the voltage on the high-voltage side to increase the current on the winding, increase the current by 10% each time, and gradually reach the rated value; after the current increases by 10%, keep it stable for 30 seconds Change, use the continuous sampling mode to record the vibration of all measuring points at all times.
然后利用短路冲击电流对A相绕组进行人为破坏,确认A相绕组在中间位置发生了较大程度的变形,再对变压器进行同样的短路实验,同样记录下所有测点在整个过程中的振动。Then use the short-circuit impact current to artificially destroy the A-phase winding, confirm that the A-phase winding has a large degree of deformation in the middle, and then conduct the same short-circuit experiment on the transformer, and also record the vibration of all measuring points during the whole process.
(3)对信号进行预处理。(3) Preprocess the signal.
当以输入电流i(t)为自变量,以绕组振动在测点所贡献的振动分量为因变量绘制两者间关系曲线时(以测点为例,如图3所示),可见输出输入关系曲线呈现明显的磁滞特性,这是由于绕组所处磁场所引入的强非线性特性,在对输入信号进行如下非线性变换后:When the input current i(t) is taken as the independent variable, the winding vibration is at the measuring point Contributed vibration component When plotting the relationship curve between the two for the dependent variable (measured by point For example, as shown in Figure 3), it can be seen that the output-input relationship curve presents obvious hysteresis characteristics, which is due to the strong nonlinear characteristics introduced by the magnetic field where the winding is located. After the following nonlinear transformation is performed on the input signal:
其中:i'(t)为输入信号i(t)的微分形式,ip(t)为经过变换后的输入信号。该非线性变化将原输入信号从其所在的低纬空间映射到高维空间中,去除了系统中原非线性模块中带有的磁滞特性,图4则显示了在经过上述变换后的输入电流ip(t)与振动分量的关系曲线。Among them: i'(t) is the differential form of the input signal i(t), and i p (t) is the transformed input signal. This nonlinear change maps the original input signal from its low-latitude space to a high-dimensional space, and removes the hysteresis characteristic of the original nonlinear module in the system. Figure 4 shows the input current after the above transformation i p (t) and vibration components relationship curve.
(4)利用改进后阶数估计算法提取关系模型延迟阶数,判断绕组机械结构状态。(4) Use the improved order estimation algorithm to extract the delay order of the relational model to judge the state of the winding mechanical structure.
由变压器的振动机理可知,绕组的单位电动分布力主要是由流过绕组线圈的电流产生,且与绕组附近的漏磁场有关,漏磁场的大小与电流直接相关,但又与绕组本身结构与绕组线圈高度有关;从而可将单位电动分布力视为仅与电流i(t)相关的非线性函数F1(i(t))以及仅与线圈位置相关的非线性函数的组合。因此,绕组振动与输入电流的关系公式可写为:It can be seen from the vibration mechanism of the transformer that the unit electrodynamic distribution force of the winding is mainly generated by the current flowing through the winding coil, and it is related to the leakage magnetic field near the winding. The height of the coil is related; thus the unit electromotive force distribution can be Treated as a nonlinear function F 1 (i(t)) that depends only on the current i(t) and a nonlinear function that depends only on the coil position The combination. Therefore, the relationship formula between winding vibration and input current can be written as:
其中:表示绕组振动激励力到油箱壁响应点处的总体等效单位脉冲响应。in: Indicates the winding vibration excitation force to the tank wall response point The overall equivalent unit impulse response at .
观察上式可知,电流-绕组振动关系模型由一个静态非线性模块F1()和动态线性模块组成的非线性系统,与经典非线性Hammerstein模型结构相符,即由一输入端非线性静态模块与一线性动态模块串联组成。Observing the above formula, we can see that the current-winding vibration relationship model consists of a static nonlinear module F 1 () and a dynamic linear module The composed nonlinear system is consistent with the structure of the classical nonlinear Hammerstein model, that is, it consists of a nonlinear static module at the input end and a linear dynamic module connected in series.
由上述模型可知,绕组的机械结构特征将直接影响与位置相关的非线性函数特性以及传递特性,从而将直接影响该模型中的线性模块特性,因此可提取该线性模块系统特性作为绕组机械结构状态特征量。From the above model, it can be seen that the mechanical structure characteristics of the winding will directly affect the nonlinear function related to the position The characteristics and transfer characteristics will directly affect the characteristics of the linear module in the model, so the system characteristics of the linear module can be extracted as the characteristic quantity of the mechanical structure state of the winding.
对于线性系统而言,其延迟阶数变化将直接影响其系统响应,因此若能根据输入输出信号特征对该系统的延迟阶数进行直接估计,则可利用该延迟阶数的变化对变压器绕组机械结构特征进行评估。For a linear system, the change of its delay order will directly affect its system response. Therefore, if the delay order of the system can be directly estimated according to the characteristics of the input and output signals, the change of the delay order can be used to analyze the mechanical properties of the transformer winding. Structural features are evaluated.
对于一个非线性系统,输出y(t)可描述为与延迟输入、输出有关的函数,即:For a nonlinear system, the output y(t) can be described as a function related to the delayed input and output, namely:
y(t)=g(y(t-1),…,y(t-Na),x(t-1),…,x(t-Nb))y(t)=g(y(t-1),...,y(tN a ),x(t-1),...,x(tN b ))
=g(γ1,γ2,…,γn)=g(γ 1 ,γ 2 ,…,γ n )
其中:x(t)和y(t)分别为非线性系统的输入和输出,而Na和Nb分别为系统输出和输入的实际线性延迟阶数,g()为一非线性函数,且假设该函数具有连续性特征,满足Lipschitz连续性条件。这里使用γi,i=1,…,n作为该非线性函数自变量的标记,并令n=Na+Nb为自变量数目。Where: x(t) and y(t) are the input and output of the nonlinear system respectively, and N a and N b are the actual linear delay orders of the system output and input respectively, g() is a nonlinear function, and Assume that the function has continuous characteristics and satisfies the Lipschitz continuity condition. Here, γ i , i=1,...,n are used as the labels of the independent variables of the nonlinear function, and n=N a +N b is the number of independent variables.
定义Lipschitz系数lij (n)来表征非线性函数g(γ1,γ2,…,γn)的连续性:Define the Lipschitz coefficient l ij (n) to characterize the continuity of the nonlinear function g(γ 1 ,γ 2 ,…,γ n ):
当函数自变量中缺失必要变量γh时,则缺少该变量时的Lipschitz系数lij (h-1)值将远远大于存在该必要变量γh时的系数值lij (h),即此时lij (h-1)>>lij (h);与之相对的,若变量γh+1为一冗余或非必要自变量,则其对应Lipschitz系数lij (h+1)与缺失该变量时的系数lij (h)值近似相等,即lij (h+1)≈lij (h)。When the necessary variable γ h is missing in the independent variable of the function, the Lipschitz coefficient l ij (h-1) value when the variable is absent will be much larger than the coefficient value l ij (h) when the necessary variable γ h exists, that is, when l ij (h-1) >>l ij (h) ; in contrast, if the variable γ h+1 is a redundant or unnecessary independent variable, then its corresponding Lipschitz coefficient l ij (h+1) and When this variable is missing, the values of the coefficient l ij (h) are approximately equal, that is, l ij (h+1) ≈ l ij (h) .
为了避免测量时引入的噪声对上述结果的影响,使用Lipschitz平均系数l(n)替代系数lij (n):In order to avoid the influence of the noise introduced during the measurement on the above results, the Lipschitz average coefficient l (n) is used to replace the coefficient l ij (n) :
其中:l(n)(z)为lij (n)按递减规则重新排序后的第z个系数值,m通常使用0.01Nset,Nset为用于阶数估计的输入-输出对个数。Among them: l (n) (z) is the zth coefficient value of l ij (n) reordered according to the decreasing rule, m usually uses 0.01N set , and N set is the number of input-output pairs used for order estimation .
改进前阶数提取算法的主要思路是找到最小自变量个数n(n=Na+Nb),且令其对应的Lipschitz平均系数满足以下条件:The main idea of improving the pre-order extraction algorithm is to find the minimum number of independent variables n(n=N a +N b ), and make its corresponding Lipschitz average coefficient meet the following conditions:
其中:ε为一由经验阈值,一般令ε=0.1。然而,不难看出利用上述方法获得的阶数,阶数Na和Nb在寻找最优阶数的过程中呈交替阶梯递增,因此,在最终确定最优阶数n时,当阶数n为偶数时,当阶数n为偶数时,Na=Nb+1。而对于实际系统而言,其实际阶数Na及Nb往往并不相等。以Na<<Nb的情况为例,在阶数估计过程,阶数Na和Nb以阶梯形式交替递增,直到Na逼近实际值时,阶数估计过程满足中止条件而提前中止过程,而此时阶数Nb远小于实际值,并不准确。Among them: ε is an empirical threshold value, generally ε=0.1. However, it is not difficult to see that the order obtained by the above method, the order N a and N b are alternately stepped up in the process of finding the optimal order. Therefore, when the optimal order n is finally determined, when the order n is an even number, When the order n is an even number, Na a =N b +1. However, for an actual system, its actual order Na and N b are often not equal. Taking the case of N a << N b as an example, in the order estimation process, the order Na and N b are alternately increased in steps until N a approaches the actual value, the order estimation process meets the termination condition and the process is terminated early , and the order N b is far smaller than the actual value at this time, which is not accurate.
因此,为了能对延迟阶数进行准确估计,从而能更为准确的对系统状态进行评估,本发明方法采用改进后阶数估计算法,其步骤如图5所示:Therefore, in order to accurately estimate the delay order, thereby more accurately evaluating the system state, the method of the present invention adopts an improved order estimation algorithm, and its steps are shown in Figure 5:
①首先使延迟阶数n初始化为2,即令Na=1,Nb=1,记录并计算当前的Lipschitz系数l(2)。① Firstly, the delay order n is initialized to 2, that is, Na = 1, N b = 1, and the current Lipschitz coefficient l (2) is recorded and calculated.
②当阶数Na未确定时,递增待定阶数,令Na=Na+1,记录并计算当前的Lipschitz平均系数若最优阶数Na已经确定,则执行步骤④。②When the order N a is not determined, increment the undetermined order, set N a =N a +1, record and calculate the current Lipschitz average coefficient If the optimal order N a has been determined, go to step ④.
③对比及若两者间差值满足条件 则最优阶数Na估算结束,令其值Na=Na-1;不满足则执行下一步骤。③ comparison and If the difference between the two satisfies the condition Then the estimation of the optimal order N a ends, and its value N a =N a -1; if not satisfied, execute the next step.
④当阶数Nb未确定时,递增待定阶数,令Nb=Nb+1,记录并计算当前的Lipschitz平均系数若最优阶数Nb已经确定,算法中止,阶数估算结束。④ When the order N b is not determined, increment the undetermined order, set N b = N b +1, record and calculate the current Lipschitz average coefficient If the optimal order N b has been determined, the algorithm stops and the order estimation ends.
⑤对比及若两者间差值满足条件 则最优阶数Nb估算结束,令其值Nb=Nb-1;若不满足条件,重新执行步骤②。⑤ Contrast and If the difference between the two satisfies the condition Then the estimation of the optimal order N b ends, and its value N b =N b -1 is set; if the condition is not met, step ② is performed again.
在上述算法中,ε为设定的收敛阈值,且其中ε1=0.1,ε2=0.04。In the above algorithm, ε is the set convergence threshold, and Where ε 1 =0.1, ε 2 =0.04.
为了验证上述算法的准确性及有效性,且说明相较于改进前原算法的先进性,首先通过数学仿真的方法对一非线性系统的延迟阶数进行估计,比较实际阶数与估计阶数。该非线性系统由非线性模块和线性模块串联组成,其中非线性模块的关系式表征为:In order to verify the accuracy and effectiveness of the above algorithm, and to illustrate its advancement compared with the improved original algorithm, firstly, the delay order of a nonlinear system is estimated by mathematical simulation, and the actual order is compared with the estimated order. The nonlinear system is composed of a nonlinear module and a linear module connected in series, where the relational expression of the nonlinear module is expressed as:
v(t)=sin(0.6πx(t))+0.1 cos(1.5πx(t))v(t)=sin(0.6πx(t))+0.1 cos(1.5πx(t))
且表征线性模块的差分方程则为:And the difference equation characterizing the linear module is:
y(t)=-0.28y(t-1)+0.47y(t-6)+0.11v(t-1)+0.08v(t-3)y(t)=-0.28y(t-1)+0.47y(t-6)+0.11v(t-1)+0.08v(t-3)
由上式可知,该系统实际时延阶数为Na=6,Nb=3,且该系统输入x(t)定义为分布在(-1,1)的随机序列。It can be seen from the above formula that the actual delay order of the system is N a =6, N b =3, and the system input x(t) is defined as a random sequence distributed in (-1,1).
使用500个数据对进行阶数估计,并按γ1=y(t-1),γ2=x(t-1),γ3=y(t-2),γ4=x(t-2),…定义潜在输入变量,并根据算法中的步骤依次添加变量单元并计算相应的Lipschitz系数。图6(a)和图6(b)分别显示了使用原始阶数估计算法及改进后算法所得到的Lipschitz系数差值比从图中不难发现原始算法中Δl(3+3)≤0.1l(3+3),即在阶数(3,3)处满足算法中止条件,提前中止算法跳出,并以(3,3)作为最后的阶数估计值,显然与实际阶数不符。分析阶数估计过程可知,在阶数(3,3)处,由于实际阶数Nb=3,与实际值相等,因此,满足中止条件,而此时另一阶数Na=3仍远小于实际阶数6。而在使用改进后的算法进行阶数估计时,该过程首先在阶数(3,3)处第一次满足中止条件,并选择Na=3作为最终估计值,其后算法继续进行,并逐步递增Nb阶数值,直到在阶数(6,3)处再次满足中止条件,结束算法,并最终选取Na=3及Nb=3作为阶数最优估计值,且与实际阶数值相符,算法结果正确。上述仿真结果显示了改进后算法在Na和Nb与实际阶数相差较大的情况下仍可准确、有效的对非线性系统的延迟阶数进行估计。因此,该阶数估计算法可用于评估绕组振动系统的线性模块的系统特性变化,从而可进一步应用于对变压器绕组的机械结构状态进行评估和诊断中。Use 500 data pairs for order estimation, and follow γ 1 =y(t-1), γ 2 =x(t-1), γ 3 =y(t-2), γ 4 =x(t-2 ), ... define potential input variables, and add variable units sequentially according to the steps in the algorithm and calculate the corresponding Lipschitz coefficients. Figure 6(a) and Figure 6(b) show the difference ratio of Lipschitz coefficients obtained by using the original order estimation algorithm and the improved algorithm respectively It is not difficult to find from the figure that Δl (3+3) ≤ 0.1l (3+3) in the original algorithm, that is, the algorithm termination condition is satisfied at the order (3,3), the algorithm is terminated early, and the algorithm is terminated with (3,3 ) as the final order estimate, which obviously does not match the actual order. Analyzing the order estimation process shows that at the order (3,3), since the actual order N b = 3 is equal to the actual value, the termination condition is satisfied, while another order N a = 3 is still far away. less than the actual order of 6. However, when using the improved algorithm for order estimation, the process first satisfies the termination condition at the order (3,3) for the first time, and selects Na = 3 as the final estimated value, and then the algorithm continues, and Gradually increase the N b order value until the stop condition is met again at the order (6,3), and end the algorithm, and finally select N a =3 and N b =3 as the optimal estimated value of the order, and the actual order value match, the algorithm result is correct. The above simulation results show that the improved algorithm can still accurately and effectively estimate the delay order of the nonlinear system when Na and N b are quite different from the actual order. Therefore, the order estimation algorithm can be used to evaluate the system characteristic change of the linear module of the winding vibration system, so it can be further applied to the evaluation and diagnosis of the mechanical structure state of the transformer winding.
在绕组故障检测实验中选取0.5s时间长度的输入和输出数据进行延迟阶数估计,对正常绕组及异常绕组状态下所有测点振动与电流关系模型的延迟阶数进行估计,得到如表1所示结果:In the winding fault detection experiment, the input and output data with a time length of 0.5s are selected to estimate the delay order, and the delay order of the vibration-current relationship model of all measuring points under normal winding and abnormal winding state is estimated, as shown in Table 1. Show the result:
表1.绕组不同状态下所有测点的阶数估计结果(100%负载)Table 1. Order estimation results of all measuring points in different winding states (100% load)
从表1可知,当绕组机械结构出现异常(变形)时,大部分测点所对应的电流-振动关系模型的延迟阶数会发现显著变化,因此可通过监测模型延迟阶数的变化对绕组机械结构状态进行状态监测。It can be seen from Table 1 that when the mechanical structure of the winding is abnormal (deformed), the delay order of the current-vibration relationship model corresponding to most of the measuring points will be found to change significantly. Condition monitoring of the structural state.
上述对实施例的描述是为便于本技术领域的普通技术人员能理解和应用本发明。熟悉本领域技术的人员显然可以容易地对上述实施例做出各种修改,并把在此说明的一般原理应用到其他实施例中而不必经过创造性的劳动。因此,本发明不限于上述实施例,本领域技术人员根据本发明的揭示,对于本发明做出的改进和修改都应该在本发明的保护范围之内。The above description of the embodiments is for those of ordinary skill in the art to understand and apply the present invention. It is obvious that those skilled in the art can easily make various modifications to the above-mentioned embodiments, and apply the general principles described here to other embodiments without creative efforts. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art according to the disclosure of the present invention should fall within the protection scope of the present invention.
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