基于小波变换的电力系统无功功率测量研究
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摘要
随着现代信息技术及电力工业的飞速发展,电力系统中的电源及负荷种类变得越来越多,新能源的利用如风力发电、太阳能发电等新的能源系统和一些新型的智能化的电力变换设备的大量使用,以及系统中的一些变流和补偿调节装置越来越复杂,电力系统中的非线性特征变得越来越明显,大量的非线性负荷在电力系统中的使用使得电力网络所提供的电压电流波形的畸变越来越严重。电力网络的不对称和负荷非线性特征及电力网络的谐波污染变得越来越明显,同时电力网络还可能会受到一些随机信号的干扰,如电磁辐射和一些电力设备在运行中所产生的随机性、非平稳性的一些干扰信号,这样一些随机信号和频率分布很广的谐波信号在实际系统中要对其进行准确测量难度很大。
很多的科技人员在随机信号检测及谐波分析中进行了大量研究,出现了很多关于信号检测及谐波处理的文献。解决电力系统中各种新型的电力设备和非线性负荷对电网的污染及电力网络电能质量分析成了当前电力系统研究的热点。如电力系统中电能质量分析、谐波分析补偿装置的研制、无功功率检测与补偿、电力滤波器的设计等研究方向在当前获得了很大发展。如以瞬时无功功率理论为基础的电力系统无功功率的检测和补偿作为当前的研究热点之一在电网谐波电流检测中获得了广泛应用。目前电力系统关于无功功率的检测的精度不是很高,这种现状特别是对电力系统的检测控制造成了很大影响,在电力系统中有功功率和无功功率准确检测是进行无功调节的基础,检测精度的高低直接影响着控制的效果,同时随着电力市场的发展,电价的高低不仅仅只是考虑有功功率,现在很多系统开始把无功功率考虑在内,所以有功功率和无功功率准确检测也是电力系统电能计量和计费的基础。
电力系统信号处理中涌现了大量的理论,传统的信号处理及分析方法表现出了很大的局限性。随着信号处理技术的发展,傅里叶变换开始获得了广泛应用,采用傅里叶变换分析信号所得的频谱特性成为了目前电力谐波检测和功率测量的基本理论依据,在很大程度上解决了检测精度的问题。但傅里叶变换在实际工程应用中也存在很大的问题,由于在电力系统中可能会遇到复杂的随机信号,采用傅里叶变换对信号进行分解时在一定条件下会产生频谱泄露、频谱混叠和栅栏效应等现象。同时采用傅里叶变换对信号分解时,是将信号按基波频率分解成为基频整数倍的谐波,而实际信号中可能存在频率不为基波整数倍的间谐波,这会导致分析计算的结果与实际不相吻合。同时傅里叶变换将一个周期信号分解成为正弦和余弦函数的叠加,这种算法的运算量很大,实际信号分析中会占用大量的处理器时间,导致实时性变差。信号处理中较优秀的时频分析方法一般是按照频带分割的思想来处理的,通过算法和滤波器将信号分解成几个不同的频带,这样不仅满足了信号频率分割的要求,还可以根据信号分解的时频要求调整算法复杂度,和傅里叶变换相比计算量也不大,能够适应信号处理的精度要求和实时性的要求。
以傅里叶变换为基础的信号处理方式及传统的有功无功功率理论在仪器仪表及检测领域得到了广泛应用,在目前日益复杂的电力负载和电力新能源设备的系统中,这些理论方法和基于这些理论的测量仪表逐渐变得捉襟见肘,对电力系统中出现的大量随机非平稳信号,它们的分析结论可能和实际相差很远,信号的检测精度越来越差,不能应对目前越来越复杂的电力系统信号,有时甚至会得出错误的结论。因此必须要寻找更优秀的时频分析理论来对电力系统的信号进行分析。
小波变换作为一种较新的时频分析方法受到了很多学者的重视,开始在很多领域表现出了它的生命力,除了在语音图像处理领域获得应用以外,它还在电力系统暂态信号的分析中获得了应用。利用小波变换可以准确地分析随机信号的特征,如暂态谐波信号的突变时刻,突变时段及暂态信号的幅度和频率成分,能够非常精确地分析暂态信号的局部特征,同时还能分析计算随机信号的统计特征,在信号分解中具有优良的分频特性,可以将信号中的稳态分量和暂态分量有效地分离出来。
小波变换作为基于频域功率信号和按频带分解信号的理论,在电力网络信号分析及处理中具有很大的意义,利用它进行谐波分析及无功功率检测不仅是电力系统中及电能计量的需要,而且分析和计算的结果也是无功检测与无功补偿的基础。本文在研究电力系统无功功率测量理论和小波变换理论及算法的基础上进行了以下的一些研究工作：
(1)分析了目前广泛使用的各种无功功率理论和几种常用的无功功率测量算法,并根据信号处理及滤波器设计理论对目前使用的各种功率理论和算法的优势和不足进行了对比研究。对傅里叶变换在信号分解中存在的优缺点进行论述,指出了其具有的实用范围及不足,对于非平稳信号等信号变化剧烈的情况时,傅里叶变换固定的时频窗函数不能适应此类信号的分析和计算,并提出了改进的方向。在对无功功率的时域和频域分析方法进行探讨的过程中,重点分析了国内外几个专家学者对无功功率不同的定义及具体的在平稳周期信号下的功率分解和测量的理论,同时也分析了在信号为畸变条件下实用的各种功率理论并论述了各种功率理论和算法的实际物理意义及其适用范围。
(2)研究了含有多频谐波信号的非正弦电路的无功功率理论及其无功功率测量算法,在对各种无功功率测量算法进行研究的基础上,根据Budeanu关于非正弦电路的无功功率定义提出了基于希尔伯特变换的无功功率测量算法,该算法通过设计一个希尔伯特数字滤波器来实现数字信号的相移,就可以采用有功功率的计算理论来计算无功功率。这种通过采用移相滤波和功率计算的无功检测算法适合于含有谐波信号分析计算,对于含有多频谐波的非正弦电路是非常实用的。本文结合滤波器设计理论所设计的希尔伯特数字滤波器具有优秀的相移特性,能够在很大的频率范围内实现精确的相移并且具有优越的频率响应特性,这样高精度的相移能够大幅提高信号谐波分解能力和功率测量准确度。
(3)重点研究了时频信号处理中经常运用的连续小波变换、离散小波变换等几种高性能的信号处理变换方法,分析了连续小波变换、离散小波变换的时频分解特性。指出了傅里叶变换方法在信号时频分解方面的局限,论述了小波变换相对于傅里叶变换性能方面的提升。在对各种小波分析方法进行研究的基础上,根据实际系统中信号的特点提出了小波函数的构造方法。同时对各种不同类型的小波函数滤波器进行了对比研究,如Dmeyer小波、不同阶次的DB小波等对信号进行处理时的不同特点。对分解的结果进行了对比,论述了不同的小波函数分解信号的误差及产生的原因,同时给出了提高信号分解精度的方法。并采用构造的小波滤波器把信号分解到各个不同频率的子频带中,重构则恰好为一个逆过程,然后在各个不同的子频带中分别对信号进行分析和计算,由此得到信号的有效值、功率等相关参数。针对目前电力系统中存在的非线性、非平稳暂态信号等也提出了分析检测方法,提取信号的特征,并推导了几种基于小波滤波器理论的电力系统无功功率测量算法。
(4)分析研究了离散小波函数的构造及其正交镜像滤波器组的选取对信号分解、谐波分析及无功功率检测的影响,在对电力系统实际信号分析的基础上,结合已有的小波函数和小波滤波器设计理论,构造了全新的频域局部性好的正交小波函数,该正交小波函数能够实现信号的高精度分频和测量,能提高各个子频带的测量准确度,同时系统地研究了离散小波变换多相滤波器组测量有功及无功的整体结构和方案,并验证了小波分析所具有时域和频域双重分辨率,所设计的正交小波函数在信号分解时的无功测量算法有很好的频带谐波提取效果及功率检测精度。
(5)对基于小波变换的异步电机转矩测试仪进行了研究设计,采用构造的小波滤波器对异步电机的输入电压电流进行分解计算,由此计算出电机的有功和无功。采用红外测速装置测试出电机的转速,再结合异步电机的动态方程推导出了转矩的观测公式,在此基础上测量出异步电机的转矩。
(6)对离散小波变换及构造的正交镜像滤波器组存在的混叠问题进行了研究,对小波变换中导致小波混叠的实质原因进行了分析,重点探讨了小波滤波器组的幅频特性和由幅频特性所导致的小波分解幅度相位方面的误差。并采用具体的小波函数的幅频特性图说明了小波混叠现象及混叠对检测的影响,并结合正交镜像滤波器理论分析计算了混叠分量的大小,在此基础上提出了具体的混叠抑制方法,采用计算出的混叠分量去补偿实际的分解结果。在对小波变换的频率特性及能量泄漏问题了研究的基础上提出了解决泄露及保证检测精度的小波函数选用原则,在构造小波函数时分析了小波分解滤波器序列长度和能量泄漏之间的关系,并结合滤波器的幅频特性提出了消除小波混叠及提高检测精度的小波滤波器选取方法,消除了采用传统小波滤波器可能带来的混叠现象和检测误差。
With the rapid development of modern information technology and electric power industry, power system, power supply and load types have become more and more. New energy sources such as wind power, solar power and other new energy systems and some new intelligent equipment are used in power system. The extensive use of conversion device, as well as the system flow and compensate for some of the variable adjustment device is become more complex, nonlinear characteristics of power system has become increasingly clearly, a large number of non-linear loads in power system and the use of electric power network provided by the voltage and current waveform distortion are getting worse. Asymmetry of power network and load characteristics and power networks, non-linear harmonic pollution has become increasingly serious, while the power network also may be subject to some random signal interference, such as electromagnetic radiation, and some electrical equipment in operation generated stochastic, non-stationary nature of some of the interference signal, and the random signal and the frequency distribution of a wide harmonic signal in the system are very difficult to be measured accurately.
Many scientist and technician have undertaken extensive research in the random signal detection and harmonic analysis, there has been a lot of literature about signal detection and harmonic processing. Solving the power quality pollution in a variety of new electrical equipment, non-linear load on the grid power system and power network analysis has become hot in the current power system research. Such as the power quality analysis, harmonic analysis of compensation device research and development, testing and compensation of reactive power, power filter design, research has achieved great development. As in the instantaneous reactive power theory-based power system reactive power detection and compensation as one of the current research focus harmonic detection gained wider application. The reactive power detection of power system is not accurate currently, this situation especially for the detection and control of power system had a significant impact in the power system, The accurate detection of active power and reactive power is not only the base of reactive power regulation, but also has a direct impact on the level of precision of detection control. At the same time with the electricity market development, electricity prices not only take into account the level of active power, but also the reactive power is taken into account in the system, so the accurate detection active and reactive power of power system is the base of energy metering and billing.
A large number of theories have emerged in power system signal processing, the traditional signal processing and analysis methods have significant limitations. With the development of signal processing, Fourier transform have began to gain a wide range of applications, Fourier transform spectral characteristics analysis obtained the fundamental theoretical basis of the current electricity power harmonics detection and measurement, and solved the detection accuracy problems. But the applications of the Fourier transform in practical engineering have also encountered problems, because the power system may experience a complex random signals, using Fourier transform signal decomposition under certain conditions, will produce spectral leakage, spectrum aliasing and phenomena such as fence effect. At the same time Fourier transform is to decompose the signal according to fundamental frequency as an integer multiple of fundamental frequency harmonics, while the actual signal may exist the fundamental frequency is not an integer multiple of the inter-harmonics, which will lead to analysis results of the calculation does not correspond with reality. At the same time Fourier transform decompose signal into the superposition of sine and cosine functions and this algorithm has a large computational complexity, the actual signal analysis will occupy a lot of processor time, resulting in real-time variation. The more excellent time-frequency signal processing and analysis methods are generally decompose signal according to band division, through algorithms and filters decompose the signal into several different frequency bands, so that not only meets the requirements of the signal frequency division and also be according to the signal decomposition of time-frequency and revise the complexity of the algorithm, Compared with Fourier transform, it can adapt to the accuracy of signal processing requirements and real-time requirements and has little computation.
Signal processing method based on Fourier transform and the traditional active, reactive power theory have been widely applied in the field of instrumentation and testing. In the system of increasingly complex power load and new energy power equipment, these theoretical approaches and measuring instruments based on these theories have become increasingly stretched, due to a lot of random non-stationary signals appeared in power system, the analysis and practical conclusion may be far from actuality, the signal detection accuracy is getting worse and can not cope with increasing complexity of the power system signals currently, and sometimes even come to the wrong conclusions. So it must find better time-frequency analysis theory for power system signal analysis.
Wavelet transform as a relatively new method of time-frequency analysis is received attention by many scholars and it began to show its vitality in many areas. In addition to the field of image and voice access processing, it is also applied in the transient signal analysis of power system, with Wavelet transform, we can accurately analyze the characteristics of random signals, such as the transient moment of harmonic signal mutations, mutation moment and transient signal amplitude and frequency components, it also can analyze the local transient signal characteristics and calculate the statistical characteristics of random signals very precisely. It has excellent characteristics of sub frequency signal decomposition, and can separate the steady-state signal and transient signal effectively.
Wavelet transform is a theory based on frequency domain of power signal and on band decomposition of signal, it is of great significance in signal analysis and processing in power grid. Using it for harmonic analysis and reactive power detection is not only the needs of power system and the electric energy metering, but its analysis and calculation results will also be the basis of reactive detection and reactive power compensation. This paper studies power system reactive power measurement theory, wavelet transform theory and algorithm based on the following research work:
(1) Analyzed the widely used reactive power theory currently and several commonly used in reactive power measurement algorithm, comparatively studied the advantages and disadvantages of the power theories and algorithms based on signal processing and filter design theory. Discussed the advantages and disadvantages of Fourier transform in signal decomposition, pointed out its application scope and practical lack, In the situation of signals such as non-stationary signals and rapid change signals, Fourier transform has a fixed time-frequency window function and can not meet the demand of such signal analysis and calculation, at the same time proposed directions for improvement. In the explore process of time domain and frequency domain analysis methods of reactive power mearsurement, focused on analyzing several domestic, foreign experts, scholars on the different definitions of reactive power and the specified the stable periodic signal power decomposition and measurement theory. Analyzed the practical power theories under the conditions of the signal distortion and discussed a variety of power theory, algorithms, real physical significance and specified the scope of application.
(2) Studied reactive power theory and reactive power measurement algorithm of non-sinusoidal circuit containing multi-frequency harmonic signal, through the analysis of the variety of reactive power measurement algorithm, proposed the reactive power measurement algorithm based on the reactive power definition of Budeanu non-sinusoidal circuit and based on Hilbert transform, which achieved the digital signals phase shift through a Hilbert digital filter, So it can calculate the reactive power with the active power theoretical calculation. This phase shift through the use of filtering and calculation of reactive power detection algorithm is suitable to the signal analysis and calculation which containing the harmonic signal, it is very practical for the non-sinusoidal circuit containing the multi-frequency harmonics. In this paper, filter design theory, digital filter designed by Hilbert phase shift with excellent features, have a large frequency range to achieve accurate phase shift and has a superior frequency response characteristics, such high-precision phase-shifting can substantially increase the capacity of signal harmonics decomposition and power measurement accuracy.
(3) Focused on continuous wavelet transform, discrete wavelet transform and several high-performance signal processing method in the time-frequency signal processing. Analyzed the continuous wavelet transform, discrete wavelet transform time-frequency decomposition characteristics. Pointed out the limitations of Fourier transform method in time-frequency decomposition and the performance improvement is discussed about wavelet transform Compare to the Fourier transform. based on the analysis of a variety of wavelet transform and the signal characteristics of actual system we constructed the wavelet function. At the same time we researched various types of wavelet function filters compatively, such as Dmeyer wavelet, DB wavelet of different levels such as the signal processing of the different characteristics. The decomposition results were compared, and the errors and their causes are discussed by different wavelet decomposition, at the same time found the way to improve the accuracy of signal decomposition. And using the constructed wavelet filter to decompose the signal into different frequency sub-bands, the reconstruction is just a reverse process, and then the signal analysis and calculation is performed in different sub-bands respectively, got the effective value, power and other related parameters of the signal. Made an analysis of detection methods to extract signal features in the current power system by presence of non-linear, non-stationary transient signals, and derived several reactive power measurement algorithm of power system based on wavelet filter.
(4) Analysis of the construction of discrete wavelet functions and their selection of quadrature mirror filter banks for signal decomposition, harmonic analysis and detection of reactive power impact on power system based on the actual signal analysis, combined with the existing wavelet function and wavelet filter design theory, constructed a new frequency-domain partial good orthogonal wavelet function, the orthogonal wavelet function is able to achieve high-precision sub-band signals and measurement of various sub-bands, which can improve measurement accuracy. At the same time systematically studied the overall structure and programs of the active and reactive power measurement based on discrete wavelet transform polyphase filter, and verified that the wavelet analysis has a dual time-domain and frequency domain resolution, the orthogonal wavelet function algorithm designed has a very good band harmonic extraction and power detection accuracy in the signal decomposition at the reactive power measurement.
(5) Studied and designed the induction motor torque tester based on Wavelet transform, Analyzed and calculated the input voltage and current of induction motors by the constructed wavelet filter, therefore calculated the motor active and reactive power. Tested the motor rotate speed by infrared gun device, derived motor torque observations formula combined with the dynamic equations of induction motor, and measured the induction motor's torque.
(6) Studied the existing aliasing of the discrete wavelet transform and the quadrature mirror filter bank structure conducted a, analyzed the real causes of the wavelet aliasing caused in wavelet transform, focused discused the wavelet filter amplitude-frequency characteristics and amplitude, phase errors caused by amplitude-frequency characteristics of the wavelet decomposition. Used specific wavelet function of the amplitude-frequency characteristic diagram to illustrate the wavelet-aliasing, and aliasing effects on the detection, calculated the aliasing component combined with theoretical analysis of quadrature mirror filters, and promoted the specific aliasing suppression method, using the calculated result to compensate the aliasing of the actual decomposition. Promote the wavelet function selection principle to solve detection leaks and to ensure the accuracy by the frequency characteristics of wavelet transform and the energy leakage. Analyzed the relationship between the wavelet decomposition filter sequence length and the energy leakage suggested at the wavelet function construction, promoted the wavelet filter selection method of the elimination of wavelet-aliasing and to improve detection accuracy combined with the filter amplitude-frequency characteristic, eliminated the aliasing and testing errors of traditional wavelet filter.
很多的科技人员在随机信号检测及谐波分析中进行了大量研究,出现了很多关于信号检测及谐波处理的文献。解决电力系统中各种新型的电力设备和非线性负荷对电网的污染及电力网络电能质量分析成了当前电力系统研究的热点。如电力系统中电能质量分析、谐波分析补偿装置的研制、无功功率检测与补偿、电力滤波器的设计等研究方向在当前获得了很大发展。如以瞬时无功功率理论为基础的电力系统无功功率的检测和补偿作为当前的研究热点之一在电网谐波电流检测中获得了广泛应用。目前电力系统关于无功功率的检测的精度不是很高,这种现状特别是对电力系统的检测控制造成了很大影响,在电力系统中有功功率和无功功率准确检测是进行无功调节的基础,检测精度的高低直接影响着控制的效果,同时随着电力市场的发展,电价的高低不仅仅只是考虑有功功率,现在很多系统开始把无功功率考虑在内,所以有功功率和无功功率准确检测也是电力系统电能计量和计费的基础。
电力系统信号处理中涌现了大量的理论,传统的信号处理及分析方法表现出了很大的局限性。随着信号处理技术的发展,傅里叶变换开始获得了广泛应用,采用傅里叶变换分析信号所得的频谱特性成为了目前电力谐波检测和功率测量的基本理论依据,在很大程度上解决了检测精度的问题。但傅里叶变换在实际工程应用中也存在很大的问题,由于在电力系统中可能会遇到复杂的随机信号,采用傅里叶变换对信号进行分解时在一定条件下会产生频谱泄露、频谱混叠和栅栏效应等现象。同时采用傅里叶变换对信号分解时,是将信号按基波频率分解成为基频整数倍的谐波,而实际信号中可能存在频率不为基波整数倍的间谐波,这会导致分析计算的结果与实际不相吻合。同时傅里叶变换将一个周期信号分解成为正弦和余弦函数的叠加,这种算法的运算量很大,实际信号分析中会占用大量的处理器时间,导致实时性变差。信号处理中较优秀的时频分析方法一般是按照频带分割的思想来处理的,通过算法和滤波器将信号分解成几个不同的频带,这样不仅满足了信号频率分割的要求,还可以根据信号分解的时频要求调整算法复杂度,和傅里叶变换相比计算量也不大,能够适应信号处理的精度要求和实时性的要求。
以傅里叶变换为基础的信号处理方式及传统的有功无功功率理论在仪器仪表及检测领域得到了广泛应用,在目前日益复杂的电力负载和电力新能源设备的系统中,这些理论方法和基于这些理论的测量仪表逐渐变得捉襟见肘,对电力系统中出现的大量随机非平稳信号,它们的分析结论可能和实际相差很远,信号的检测精度越来越差,不能应对目前越来越复杂的电力系统信号,有时甚至会得出错误的结论。因此必须要寻找更优秀的时频分析理论来对电力系统的信号进行分析。
小波变换作为一种较新的时频分析方法受到了很多学者的重视,开始在很多领域表现出了它的生命力,除了在语音图像处理领域获得应用以外,它还在电力系统暂态信号的分析中获得了应用。利用小波变换可以准确地分析随机信号的特征,如暂态谐波信号的突变时刻,突变时段及暂态信号的幅度和频率成分,能够非常精确地分析暂态信号的局部特征,同时还能分析计算随机信号的统计特征,在信号分解中具有优良的分频特性,可以将信号中的稳态分量和暂态分量有效地分离出来。
小波变换作为基于频域功率信号和按频带分解信号的理论,在电力网络信号分析及处理中具有很大的意义,利用它进行谐波分析及无功功率检测不仅是电力系统中及电能计量的需要,而且分析和计算的结果也是无功检测与无功补偿的基础。本文在研究电力系统无功功率测量理论和小波变换理论及算法的基础上进行了以下的一些研究工作：
(1)分析了目前广泛使用的各种无功功率理论和几种常用的无功功率测量算法,并根据信号处理及滤波器设计理论对目前使用的各种功率理论和算法的优势和不足进行了对比研究。对傅里叶变换在信号分解中存在的优缺点进行论述,指出了其具有的实用范围及不足,对于非平稳信号等信号变化剧烈的情况时,傅里叶变换固定的时频窗函数不能适应此类信号的分析和计算,并提出了改进的方向。在对无功功率的时域和频域分析方法进行探讨的过程中,重点分析了国内外几个专家学者对无功功率不同的定义及具体的在平稳周期信号下的功率分解和测量的理论,同时也分析了在信号为畸变条件下实用的各种功率理论并论述了各种功率理论和算法的实际物理意义及其适用范围。
(2)研究了含有多频谐波信号的非正弦电路的无功功率理论及其无功功率测量算法,在对各种无功功率测量算法进行研究的基础上,根据Budeanu关于非正弦电路的无功功率定义提出了基于希尔伯特变换的无功功率测量算法,该算法通过设计一个希尔伯特数字滤波器来实现数字信号的相移,就可以采用有功功率的计算理论来计算无功功率。这种通过采用移相滤波和功率计算的无功检测算法适合于含有谐波信号分析计算,对于含有多频谐波的非正弦电路是非常实用的。本文结合滤波器设计理论所设计的希尔伯特数字滤波器具有优秀的相移特性,能够在很大的频率范围内实现精确的相移并且具有优越的频率响应特性,这样高精度的相移能够大幅提高信号谐波分解能力和功率测量准确度。
(3)重点研究了时频信号处理中经常运用的连续小波变换、离散小波变换等几种高性能的信号处理变换方法,分析了连续小波变换、离散小波变换的时频分解特性。指出了傅里叶变换方法在信号时频分解方面的局限,论述了小波变换相对于傅里叶变换性能方面的提升。在对各种小波分析方法进行研究的基础上,根据实际系统中信号的特点提出了小波函数的构造方法。同时对各种不同类型的小波函数滤波器进行了对比研究,如Dmeyer小波、不同阶次的DB小波等对信号进行处理时的不同特点。对分解的结果进行了对比,论述了不同的小波函数分解信号的误差及产生的原因,同时给出了提高信号分解精度的方法。并采用构造的小波滤波器把信号分解到各个不同频率的子频带中,重构则恰好为一个逆过程,然后在各个不同的子频带中分别对信号进行分析和计算,由此得到信号的有效值、功率等相关参数。针对目前电力系统中存在的非线性、非平稳暂态信号等也提出了分析检测方法,提取信号的特征,并推导了几种基于小波滤波器理论的电力系统无功功率测量算法。
(4)分析研究了离散小波函数的构造及其正交镜像滤波器组的选取对信号分解、谐波分析及无功功率检测的影响,在对电力系统实际信号分析的基础上,结合已有的小波函数和小波滤波器设计理论,构造了全新的频域局部性好的正交小波函数,该正交小波函数能够实现信号的高精度分频和测量,能提高各个子频带的测量准确度,同时系统地研究了离散小波变换多相滤波器组测量有功及无功的整体结构和方案,并验证了小波分析所具有时域和频域双重分辨率,所设计的正交小波函数在信号分解时的无功测量算法有很好的频带谐波提取效果及功率检测精度。
(5)对基于小波变换的异步电机转矩测试仪进行了研究设计,采用构造的小波滤波器对异步电机的输入电压电流进行分解计算,由此计算出电机的有功和无功。采用红外测速装置测试出电机的转速,再结合异步电机的动态方程推导出了转矩的观测公式,在此基础上测量出异步电机的转矩。
(6)对离散小波变换及构造的正交镜像滤波器组存在的混叠问题进行了研究,对小波变换中导致小波混叠的实质原因进行了分析,重点探讨了小波滤波器组的幅频特性和由幅频特性所导致的小波分解幅度相位方面的误差。并采用具体的小波函数的幅频特性图说明了小波混叠现象及混叠对检测的影响,并结合正交镜像滤波器理论分析计算了混叠分量的大小,在此基础上提出了具体的混叠抑制方法,采用计算出的混叠分量去补偿实际的分解结果。在对小波变换的频率特性及能量泄漏问题了研究的基础上提出了解决泄露及保证检测精度的小波函数选用原则,在构造小波函数时分析了小波分解滤波器序列长度和能量泄漏之间的关系,并结合滤波器的幅频特性提出了消除小波混叠及提高检测精度的小波滤波器选取方法,消除了采用传统小波滤波器可能带来的混叠现象和检测误差。
With the rapid development of modern information technology and electric power industry, power system, power supply and load types have become more and more. New energy sources such as wind power, solar power and other new energy systems and some new intelligent equipment are used in power system. The extensive use of conversion device, as well as the system flow and compensate for some of the variable adjustment device is become more complex, nonlinear characteristics of power system has become increasingly clearly, a large number of non-linear loads in power system and the use of electric power network provided by the voltage and current waveform distortion are getting worse. Asymmetry of power network and load characteristics and power networks, non-linear harmonic pollution has become increasingly serious, while the power network also may be subject to some random signal interference, such as electromagnetic radiation, and some electrical equipment in operation generated stochastic, non-stationary nature of some of the interference signal, and the random signal and the frequency distribution of a wide harmonic signal in the system are very difficult to be measured accurately.
Many scientist and technician have undertaken extensive research in the random signal detection and harmonic analysis, there has been a lot of literature about signal detection and harmonic processing. Solving the power quality pollution in a variety of new electrical equipment, non-linear load on the grid power system and power network analysis has become hot in the current power system research. Such as the power quality analysis, harmonic analysis of compensation device research and development, testing and compensation of reactive power, power filter design, research has achieved great development. As in the instantaneous reactive power theory-based power system reactive power detection and compensation as one of the current research focus harmonic detection gained wider application. The reactive power detection of power system is not accurate currently, this situation especially for the detection and control of power system had a significant impact in the power system, The accurate detection of active power and reactive power is not only the base of reactive power regulation, but also has a direct impact on the level of precision of detection control. At the same time with the electricity market development, electricity prices not only take into account the level of active power, but also the reactive power is taken into account in the system, so the accurate detection active and reactive power of power system is the base of energy metering and billing.
A large number of theories have emerged in power system signal processing, the traditional signal processing and analysis methods have significant limitations. With the development of signal processing, Fourier transform have began to gain a wide range of applications, Fourier transform spectral characteristics analysis obtained the fundamental theoretical basis of the current electricity power harmonics detection and measurement, and solved the detection accuracy problems. But the applications of the Fourier transform in practical engineering have also encountered problems, because the power system may experience a complex random signals, using Fourier transform signal decomposition under certain conditions, will produce spectral leakage, spectrum aliasing and phenomena such as fence effect. At the same time Fourier transform is to decompose the signal according to fundamental frequency as an integer multiple of fundamental frequency harmonics, while the actual signal may exist the fundamental frequency is not an integer multiple of the inter-harmonics, which will lead to analysis results of the calculation does not correspond with reality. At the same time Fourier transform decompose signal into the superposition of sine and cosine functions and this algorithm has a large computational complexity, the actual signal analysis will occupy a lot of processor time, resulting in real-time variation. The more excellent time-frequency signal processing and analysis methods are generally decompose signal according to band division, through algorithms and filters decompose the signal into several different frequency bands, so that not only meets the requirements of the signal frequency division and also be according to the signal decomposition of time-frequency and revise the complexity of the algorithm, Compared with Fourier transform, it can adapt to the accuracy of signal processing requirements and real-time requirements and has little computation.
Signal processing method based on Fourier transform and the traditional active, reactive power theory have been widely applied in the field of instrumentation and testing. In the system of increasingly complex power load and new energy power equipment, these theoretical approaches and measuring instruments based on these theories have become increasingly stretched, due to a lot of random non-stationary signals appeared in power system, the analysis and practical conclusion may be far from actuality, the signal detection accuracy is getting worse and can not cope with increasing complexity of the power system signals currently, and sometimes even come to the wrong conclusions. So it must find better time-frequency analysis theory for power system signal analysis.
Wavelet transform as a relatively new method of time-frequency analysis is received attention by many scholars and it began to show its vitality in many areas. In addition to the field of image and voice access processing, it is also applied in the transient signal analysis of power system, with Wavelet transform, we can accurately analyze the characteristics of random signals, such as the transient moment of harmonic signal mutations, mutation moment and transient signal amplitude and frequency components, it also can analyze the local transient signal characteristics and calculate the statistical characteristics of random signals very precisely. It has excellent characteristics of sub frequency signal decomposition, and can separate the steady-state signal and transient signal effectively.
Wavelet transform is a theory based on frequency domain of power signal and on band decomposition of signal, it is of great significance in signal analysis and processing in power grid. Using it for harmonic analysis and reactive power detection is not only the needs of power system and the electric energy metering, but its analysis and calculation results will also be the basis of reactive detection and reactive power compensation. This paper studies power system reactive power measurement theory, wavelet transform theory and algorithm based on the following research work:
(1) Analyzed the widely used reactive power theory currently and several commonly used in reactive power measurement algorithm, comparatively studied the advantages and disadvantages of the power theories and algorithms based on signal processing and filter design theory. Discussed the advantages and disadvantages of Fourier transform in signal decomposition, pointed out its application scope and practical lack, In the situation of signals such as non-stationary signals and rapid change signals, Fourier transform has a fixed time-frequency window function and can not meet the demand of such signal analysis and calculation, at the same time proposed directions for improvement. In the explore process of time domain and frequency domain analysis methods of reactive power mearsurement, focused on analyzing several domestic, foreign experts, scholars on the different definitions of reactive power and the specified the stable periodic signal power decomposition and measurement theory. Analyzed the practical power theories under the conditions of the signal distortion and discussed a variety of power theory, algorithms, real physical significance and specified the scope of application.
(2) Studied reactive power theory and reactive power measurement algorithm of non-sinusoidal circuit containing multi-frequency harmonic signal, through the analysis of the variety of reactive power measurement algorithm, proposed the reactive power measurement algorithm based on the reactive power definition of Budeanu non-sinusoidal circuit and based on Hilbert transform, which achieved the digital signals phase shift through a Hilbert digital filter, So it can calculate the reactive power with the active power theoretical calculation. This phase shift through the use of filtering and calculation of reactive power detection algorithm is suitable to the signal analysis and calculation which containing the harmonic signal, it is very practical for the non-sinusoidal circuit containing the multi-frequency harmonics. In this paper, filter design theory, digital filter designed by Hilbert phase shift with excellent features, have a large frequency range to achieve accurate phase shift and has a superior frequency response characteristics, such high-precision phase-shifting can substantially increase the capacity of signal harmonics decomposition and power measurement accuracy.
(3) Focused on continuous wavelet transform, discrete wavelet transform and several high-performance signal processing method in the time-frequency signal processing. Analyzed the continuous wavelet transform, discrete wavelet transform time-frequency decomposition characteristics. Pointed out the limitations of Fourier transform method in time-frequency decomposition and the performance improvement is discussed about wavelet transform Compare to the Fourier transform. based on the analysis of a variety of wavelet transform and the signal characteristics of actual system we constructed the wavelet function. At the same time we researched various types of wavelet function filters compatively, such as Dmeyer wavelet, DB wavelet of different levels such as the signal processing of the different characteristics. The decomposition results were compared, and the errors and their causes are discussed by different wavelet decomposition, at the same time found the way to improve the accuracy of signal decomposition. And using the constructed wavelet filter to decompose the signal into different frequency sub-bands, the reconstruction is just a reverse process, and then the signal analysis and calculation is performed in different sub-bands respectively, got the effective value, power and other related parameters of the signal. Made an analysis of detection methods to extract signal features in the current power system by presence of non-linear, non-stationary transient signals, and derived several reactive power measurement algorithm of power system based on wavelet filter.
(4) Analysis of the construction of discrete wavelet functions and their selection of quadrature mirror filter banks for signal decomposition, harmonic analysis and detection of reactive power impact on power system based on the actual signal analysis, combined with the existing wavelet function and wavelet filter design theory, constructed a new frequency-domain partial good orthogonal wavelet function, the orthogonal wavelet function is able to achieve high-precision sub-band signals and measurement of various sub-bands, which can improve measurement accuracy. At the same time systematically studied the overall structure and programs of the active and reactive power measurement based on discrete wavelet transform polyphase filter, and verified that the wavelet analysis has a dual time-domain and frequency domain resolution, the orthogonal wavelet function algorithm designed has a very good band harmonic extraction and power detection accuracy in the signal decomposition at the reactive power measurement.
(5) Studied and designed the induction motor torque tester based on Wavelet transform, Analyzed and calculated the input voltage and current of induction motors by the constructed wavelet filter, therefore calculated the motor active and reactive power. Tested the motor rotate speed by infrared gun device, derived motor torque observations formula combined with the dynamic equations of induction motor, and measured the induction motor's torque.
(6) Studied the existing aliasing of the discrete wavelet transform and the quadrature mirror filter bank structure conducted a, analyzed the real causes of the wavelet aliasing caused in wavelet transform, focused discused the wavelet filter amplitude-frequency characteristics and amplitude, phase errors caused by amplitude-frequency characteristics of the wavelet decomposition. Used specific wavelet function of the amplitude-frequency characteristic diagram to illustrate the wavelet-aliasing, and aliasing effects on the detection, calculated the aliasing component combined with theoretical analysis of quadrature mirror filters, and promoted the specific aliasing suppression method, using the calculated result to compensate the aliasing of the actual decomposition. Promote the wavelet function selection principle to solve detection leaks and to ensure the accuracy by the frequency characteristics of wavelet transform and the energy leakage. Analyzed the relationship between the wavelet decomposition filter sequence length and the energy leakage suggested at the wavelet function construction, promoted the wavelet filter selection method of the elimination of wavelet-aliasing and to improve detection accuracy combined with the filter amplitude-frequency characteristic, eliminated the aliasing and testing errors of traditional wavelet filter.
引文
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