FRA interpretation using numerical indices: State-of-the-art

Frequency Response Analysis (FRA) is an effective diagnostic technique for detection of mechanical deformations inside a power transformer. The results of previous studies have led to the standardization of the FRA measurement procedure, but the interpretation process is still a subject of study. The numerical indices are one of the algorithms proposed for the interpretation, where the amount of an index extracted from two FRA traces can indicate a mechanical fault. Different indices are proposed in the literature, and this paper tries to survey and to compare these indices from different aspects to expand the knowledge about their characteristics. First, the numerical indices proposed in the literature are formulized, and proper references are introduced for each index. Then, the indices are categorized into two main groups. The first group of the indices is derived using exact calculations whereas the second group is calculated based on the estimation of the transfer function. The advantages and disadvantages of each group are addressed based on previous studies. Afterwards, the experiences of working with indices are reported and, finally, the vital steps which are needed to standardize the indices are discussed. The survey provided here is beneficial for the standardization process of these indices.     

Detection of transformer mechanical deformations by comparing different FRA connections

Frequency response analysis (FRA) is an effective technique to detect mechanical faults inside a power transformer. The FRA interpretation is normally carried out by comparing an FRA trace corresponding to a specific connection scheme with a fingerprint of its type. This paper, by contrast, proposes a novel method based on comparing FRA traces of different connection schemes recorded from the same winding to detect the mechanical deformations. In this contribution, the theoretical background is explained, and the experimental results are addressed to support the functionality of the proposed algorithm. Furthermore, a circuit model of the windings is created, and the simulation results are also used to validate the experimental measurements. Finally, two case studies describe the application of the new method in the condition assessment of transformers to achieve a more reliable decision. Although more research is needed to support the new applications, the early potential of the method is shown in this contribution.     

A probabilistic feature to determine type and extent of winding mechanical defects in power transformers

Frequency response analysis (FRA) is a widely-used method to detect axial displacement (AD) and radial deformation (RD) in windings of power transformers, because of its high sensitivity to small amount of mechanical defects. Interpretation of frequency response curves has been the most intricate problem of FRA method. To solve it, different numerical indices have been introduced by researchers to evaluate the frequency response of power transformers, but (1) the researchers have not discussed on genesis origin of the proposed indices and (2) most of these indices can not present a regular and linear behavior. In this paper, a probabilistic feature has been utilized to demonstrate how an efficient index originates, to diagnosis axial displacement and radial deformation in windings of power transformers. The resulted index presents a nearly linear mapping between frequency response curves and their related defect extent. To verify usefulness of this index, it has been applied to several sets of measured frequency response curves. It is illustrated that the extracted index is able to determine extent of the defects. To discriminate between axial displacement and radial deformation, local behavior of TF curves has been used.     

Improved modelling of power transformer winding using bacterial swarming algorithm and frequency response analysis

The paper discusses an improved modelling of transformer windings based on bacterial swarming algorithm (BSA) and frequency response analysis (FRA). With the purpose to accurately identify transformer windings parameters a model-based identification approach is introduced using a well-known lumped parameter model. It includes search space estimation using analytical calculations, which is used for the subsequent model parameters identification with a novel BSA. The newly introduced BSA, being developed upon a bacterial foraging behavior, is described in detail. Simulations and discussions are presented to explore the potential of the proposed approach using simulated and experimentally measured FRA responses taken from two transformers. The BSA identification results are compared with those using genetic algorithm. It is shown that the proposed BSA delivers satisfactory parameter identification and improved modelling can be used for FRA results interpretation.     

Power quality evaluation in smart grids considering modern distortion in electric power systems

High power quality level is required in smart grids especially for non-stationary situations due to increased use of nonlinear loads and PQ disturbances such as dips, swells, transients and interruptions. Many power quality indices (PQIs) are available. In this paper a new fuzzy-wavelet packet transform-based power quality Index (FWPTPQI) is developed to amalgamate existing power quality indices as the output of a fuzzy based module based on fuzzy inference systems, knowledge base and existing PQI as input. Fuzzy systems allow handling the uncertainties associated with the electric power quality evaluation. The proposed approach has been applied to two case studies; stationary balanced and non-stationary unbalanced three-phase systems. The results are compatible with prevalent situations. The new index gives significant sense of the quality of transmitted electrical power. A comparative study of using different wavelet basis functions is considered and results indicate that Daubechies 10 and Daubechies 15 could be considered as the overall best wavelet basis functions. Since the new index represents an amalgamation of the PQ indices with less number of wavelet coefficients, it helps reduce the size of data processed which is required in smart grid applications.     

Diagnosis Criterion of Abnormality of Transformer Winding by Frequency Response Analysis (FRA)

Frequency response analysis (FRA) is a powerful technique to detect internal abnormalities within power transformers. However, diagnosis criteria of power transformers by FRA have not been fully established yet. In this paper, a new evaluation method of degree of identification between two transfer functions is proposed. In the proposed method, a frequency window is employed and cross‐correlation factor is calculated with moving the window. Furthermore, the proposed method is applied to transfer functions of real transformers with or without some abnormalities. Based on this discussion, objective criteria for diagnosis of abnormalities of transformer windings by FRA are proposed. The proposed criteria are based on a few data of transformers with some abnormalities. Therefore, the proposed criteria are tentative and they would be improved by accumulation of further data.     

变压器绕组变形的频率响应分析法综述

目前对绕组频率响应的分析方法主要是基于幅频响应曲线的分析,因此从频段划分、幅频曲线特征的分析及曲线相似指数3方面综述了幅频响应曲线的研究现状,介绍了频率响应分析法的原理,从扫频范围的选择和影响测量的因素2方面讨论了绕组频率响应的测量,认为应建立原始的绕组频率响应数据库,在反映绕组变形程度的曲线相似指数研究方面有待于提出切实有效的量化标准。     

基于灵活性矩阵与优劣解距离的新能源功率预测评价方法

鉴于功率预测评价对电力系统运行和调度的重要性,文章充分考虑电网调度实际需求,从不同时期下机组的出力大小和不同时段下电网调度对预测精度的需求2个方面分析现有功率预测评价指标的不合理之处,并提出了新的准确率指标.首先,对不同时期下系统灵活性进行计算得到灵活性矩阵并对其进行预处理;其次,将处理后的灵活性矩阵输入到优劣解距离法...     

计及源荷双边性能指标的市场交易模型

高比例可再生能源电网内,为促进优质可控电源与可控负荷的发展,提高系统供需平衡的调节能力,考虑电源和负荷响应性能进行电力市场交易模式设计。在电源侧引入机组的调节性能指标;在负荷侧设置负荷聚合商参与市场的场景,并考虑负荷响应偏差的随机性进而提出负荷响应性能指标,以区分不同响应特性带来的运行成本差异。为合理协调计及性能指标的源荷双边资源,设计了两阶段的差异化出清机制。以系统总运行成本最小化为目标,构建有负荷聚合商参与的日前市场出清模型。通过算例结果表明,计及源荷双边性能指标的交易模型,可以引导资源的优化配置,降低市场的风险和损失。     

电力变压器绕组变形诊断分析

应用频率响应分析法判断变压器绕组在遭受短路冲击后是否发生严重变形具有重要的意义。介绍了频率响应法的基本原理并在大量实例的基础上,提出了横向比较分析法,即通过比较变压器三相绕组频率响应特性曲线的一致性及与同厂同型变压器绕组频率响应曲线对比来分析判断绕组变形程度;提出了定量表示2条曲线一致性的相关系数的概念,得出相关系数大小与曲线一致性的关系;提出了测试接线方法及测试过程中应注意的主要事项。     

Simple and efficient method for steady-state voltage stability assessment of radial distribution systems

A new static voltage stability index of a radial distribution system is proposed to faithfully evaluate the severity of the loading situation, thereby predicting for voltage instability at definite load value. The proposed index includes different parameters which affect the steady-state voltage stability of distribution systems, therefore it gives accurate results. The maximum value of 1 of that index denotes the point where the system reaches the point of collapse whereas a minimum value of 0 shows the state of no load. The performance of the new index was tested on two radial distribution systems consisting of 33 and 85 buses. Comparison between the results of the new index and those of previous indices showed that the new index yielded reliable results in predicting voltage stability condition of the system. The new index overcomes the problem which faces many previous indices especially as the load approaches the critical point. Analysis of the two-bus equivalents of the test systems under different scenarios is also presented. A new P–Q plane of stability is introduced based on the equation of the proposed index. The active, reactive and apparent power margins are then directly determined from the voltage stability boundary.     

A coherency based rescheduling method for dynamic security

For on-line dynamic security analysis, the preventive control or remedial action should be an integral part of the function if instability for a contingency is detected. Research done so far in on-line remedial action has been in rescheduling generation and most of the suggested methods for determining such preventive control use the sensitivities of the stability energy margin to the generator power injections. In this paper, a new coherency based sensitivity method is proposed for generation rescheduling. Different coherency indices have been defined and then compared by ranking the contingencies according to these indices as well as the energy margin index. Since the coherency indices are always functions of the rotor angles, the sensitivity trajectories of a coherency index, such as the most critical rotor angle, with respect to changes of generation can be calculated at every time step of the integration process. This paper suggests that these sensitivities calculated shortly after fault clearing be used for rescheduling the generation. The calculation of these sensitivities are obviously faster than the calculation of the energy margin sensitivities. This paper also shows, with test results using several different systems, that the rescheduling achieved by this method provides the necessary remedial action. It is also noted that this method is intuitively more direct as it uses the sensitivities of the worst affected generator angles for rescheduling     

考虑综合需求响应混合不确定性的综合能源系统优化调度策略

综合需求响应(integrated demand response,IDR)是挖掘综合能源系统(integrated energy system,IES)负荷侧调节潜力的主要手段。然而,IDR用户的用能行为具有随机性、模糊性相耦合的混合不确定性特征,由此产生的IDR不确定性不仅会给调度策略的制定带来挑战,而且会对系统的可靠性产生影响,甚至可能引起负荷断供。针对上述问题,首先提出了基于改进PMV-PPD(predicted mean vote-predicted percentage of dissatisfied)指标的用户参与意愿评估模型;其次,基于云模型理论,建立了考虑混合不确定性的价格型IDR模型;在此基础上,综合考虑各类能源响应量边界和价格弹性系数等因素的不确定性,提出了IES优化调度策略。算例结果表明所提的IES优化调度策略可以更好地应对IDR不确定性带来的负荷波动,有效提升系统可靠性。     

考虑综合需求响应混合不确定性的综合能源系统优化调度策略

综合需求响应(integrated demand response,IDR)是挖掘综合能源系统(integrated energy system,IES)负荷侧调节潜力的主要手段。然而,IDR用户的用能行为具有随机性、模糊性相耦合的混合不确定性特征,由此产生的IDR不确定性不仅会给调度策略的制定带来挑战,而且会对系统的可靠性产生影响,甚至可能引起负荷断供。针对上述问题,首先提出了基于改进PMV-PPD(predicted mean vote-predicted percentage of dissatisfied)指标的用户参与意愿评估模型;其次,基于云模型理论,建立了考虑混合不确定性的价格型IDR模型;在此基础上,综合考虑各类能源响应量边界和价格弹性系数等因素的不确定性,提出了IES优化调度策略。算例结果表明所提的IES优化调度策略可以更好地应对IDR不确定性带来的负荷波动,有效提升系统可靠性。     

基于希尔伯特变换的暂态信号正弦表示分析方法

为了分析电力系统暂态信号特性和计算暂态信号导数,依据采样信号拟合暂态信号函数表达式是一种可行方法,但现有的暂态信号拟合方法还存在拟合函数确定性和可导性方面的不足.针对这一问题,提出了一种基于希尔伯特变换的电力系统暂态信号正弦表示分析方法,采用暂态信号的正弦表示构成拟合基函数,利用希尔伯特变换以满足拟合函数的确定性.与现...     

电网大面积停电应急评价指标体系及其应用

根据电网大面积停电的特点,遵循应急的一般理论,应用系统论和方法论的思想,建立了大面积停电应急评价指标体系,指标体系包括4项一级指标、12项二级指标和38项指标属性。引入了模糊层次分析法进行多指标的综合量化分析,首先使用层次分析法确定各指标的权重,然后分层次进行模糊综合评价,最后,以一家省级电网企业为例对其应急能力进行综合评价,得出科学合理的分析结果,说明了该指标体系及其综合评价方法的有效性和实用性,可以为电力行业的大面积停电应急工作提供有效的参考和决策支持。     

一种基于电网特征差异的线损水平评价方法

线损水平与电网类型密切相关,单纯以实际线损率作为考核标准来评价不同电网的线损水平有失科学性。为了建立科学合理的线损水平评价方法,构建了考虑电网结构、设备参数、电网运行和用电结构等电网特征的线损评价指标体系,建立了所有指标的数学模型。在各个底层指标评价值的基础上采用层次分析法分析得到线损评价综合值。对电网线损评价值与实际线损率分别进行排序,通过分析排序的差异客观评价地区电网的线损水平。通过IEEE-14算例仿真分析了典型指标对线损率的影响;以江苏电网为例进行了线损水平评价。结果表明：所提出的典型指标能够反映不同电网特征对地区电网线损的影响,该方法为电网线损水平评估提供了量化计算依据,可广泛应用于评估各省、市或县级电网的线损现状,解决评估降损空间这一难题。     

A comparison of trans-admittance and characteristic impedance as metrics for detection of winding displacements in power transformers

Transfer function signatures are commonly used in condition monitoring analysis to give early indications of winding movement in power transformers. This paper presents a comparison of the use of trans-admittance (frequency response analysis, FRA), presently the industry standard, and characteristic impedance (transmission line diagnostics, TLD), a new method, as signatures for the detection of winding displacements in power transformers. To facilitate the comparison, a computer based winding model based on a multi-phase transmission line system was developed and different winding deformations were analyzed. The results show that TLD has a higher degree of sensitivity and can be used to augment the ability to classify different types of distortions currently diagnosed by FRA.     

基于长期运行模拟的独立型微网规划方案动态评估

为了评估独立型微网对于运行条件逐年动态变化的适应度,提出一种基于长期运行模拟的微网规划方案动态评估方法。首先建立动态评估的多时间尺度理论框架,并从可靠性、经济性、高效性、环保性等多个方面构建方案评估的指标体系。然后提出适应动态评估的长期运行模拟方法,在全寿命周期层面通过动态模型模拟外部环境与内部结构因素的逐年变化,在年运行层面通过序贯蒙特卡洛法模拟短期不确定性因素的随机变化。针对独立型风光柴储微网算例,通过与国际常用微网规划软件HOMER的结果对比,验证所提方法的正确性和有效性。算例结果表明,所提动态评估方法可以在不同场景下得到规划方案的综合指标结果和时序指标集,比静态评估更加全面、灵活,能够为微网规划及其扩展方案的制定提供科学合理的依据。     

500 kV/220 kV混压同塔四回路最优相序研究

同塔多回线路相序的选择需对多项电气与电磁指标进行综合考虑和协同优化。以电网安全稳定运行为出发点,首先梳理了电气不平衡度控制指标,建立了一套以输电网络电能传输效率最高为优化目标,以各项电压和电流不平衡指标必须满足安全限值为约束条件的数学模型,并采用数值方法对混压四回路1 296种相序进行遍历求解,得到电气不平衡最优及次优的若干个相序方案;然后对电气不平衡优化相序的电磁环境指标、感应电压和感应电流指标进行了协同分析和评估;最终确定优化相序方案综合可行性和合理性。通过典型500 kV/220 kV混压四回路案例验证了模型和算法的有效性。