电力系统间谐波检测算法及电动机间谐波源研究
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摘要
随着各种非线性负荷、电力电子装置和波动性负荷大量接入电网,电网中的间谐波含量逐渐增大。间谐波不仅会像谐波一样引起负荷功率因数的降低、增加各种能量的损耗、引发与供电系统的谐振,还会产生电压闪变、无源滤波器过载、电压过零点偏移等一系列新的问题,导致电能质量的恶化并影响到电网的安全经济运行。与传统的谐波相比,间谐波造成危害的范围更广,因此,必须对其进行治理。而治理的前提在于对间谐波参数进行准确估计及对间谐波产生机理的深入认识。间谐波具有一定时变性和随机性,其幅值通常较小且频率可能出现在任意频点上,因此,传统的谐波分析方法在分析间谐波时存在较大不足。针对间谐波的特点和目前的研究现状,论文主要从间谐波检测算法、电压闪变包络线提取方法、电动机间谐波源建模几个方面开展研究,主要工作如下：
(1)在间谐波检测方面,提出基于最优窗Burg算法的间谐波谱估计新方法。首先系统阐述了基于AR模型的间谐波分析原理,并对AR模型具有的高分辨率特性进行了深入分析。Burg算法为AR模型中较常用的方法,但Burg算法在递推AR模型参数的过程中,会产生误差项,造成AR模型参数与实际值不符,导致谱峰偏移和谱线分裂现象。针对Burg算法的这一缺点,提出加窗的方式来对误差项进行抑制,通过在平均频率误差方差最小的意义下来获得最优窗,然后利用加窗后的反射系数进行Levinson递推运算。由于该算法能保证获得一个稳定的AR模型,因此,其谱估计性能优于AR模型中的Marple算法。将该方法与目前间谐波检测中最常用的特征值法进行计算量和谱估计性能两方面比较,两者均具有较高的频率分辨率,并不受非同步采样的影响,但最优窗Burg算法由于利用了Levinson递推,其计算量远小于特征值法。在利用最优窗Burg算法获得间谐波信号的功率谱后,进一步采用最小二乘法求取各次谐波和间谐波的幅值和初相位。
(2)在电压闪变包络线提取方面,提出基于时频原子方法的电压闪变检测新方法。该方法将经同步检波后的电压闪变信号通过匹配追踪的方式分解成一系列时频原子,其中每一个原子都来自于冗余的时频原子库,选择的原子可以最好地匹配信号结构。通过对所选原子的频率参数进行取舍,从而达到低通滤波的目的。由于该方法中不含有卷积运算,因此避免了边界效应。其不仅能够对电压闪变信号进行不失真地包络检波,而且能避免FIR滤波器、IIR滤波器和小波变换等传统滤波方法带来的边界效应。
(3)负载转矩波动会导致感应电动机定子电流波动,该波动的电流中包含有间谐波。根据这一现象,建立了机械负荷波动时的感应电动机间谐波源模型。相比前人的工作,该模型考虑到感应电动机更多的参数,模型更为详细,具有更高的精度。针对感应电动机在负载转矩波动时的非线性模型,论文首先对其进行线形化处理,在此基础上推导出定子间谐波电流表达式。Matlab仿真结果验证了该表达式的正确性。进一步地,利用该表达式对负载转矩波动和定子间谐波电流频谱之间的关系进行分析,并分析了电动机稳态输出功率的变化对定子间谐波电流频谱的影响。
(4)建立了计及机械负荷波动且通过变频调速驱动的感应电动机间谐波源模型。首先对电动机输入电压频谱特征进行分析,在此基础上给出定子间谐波电流的频率预测公式,利用瞬时功率守恒理论和开关函数调制理论来分析定子间谐波电流穿越电压源型变频调速装置的过程,然后推导出供电系统侧间谐波电流的表达式,利用该表达式可对系统侧间谐波电流的频率及频谱特性进行分析,最后仿真研究了负载转矩波动对系统侧间谐波电流频谱的影响。
With extensive applications of nonlinear loads, power electronic devices and fluctuating loads in power system, it causes an increase of interharmonic content in the grid, and the interharmonic of the grid leads to a series of problems, besides the typical problems caused by harmonics such as the load power factor reductions, the variety of energy loss increase, and the excitation of various resonance modes with supply system, it creates some new problems, such as voltage flicker, the passive filter overload, zero offset of the voltage waveform. So it causes power quality deterioration and affects the safe and economic operation of the power grid. Comparing with the traditional harmonics, the interharmonics have a more extensive damage for the power system, so it must be suppressed. The accurate estimation of interharmonics parameters and the deep understanding of their origins are a premise of the suppression of them. The interharmonics have the time variability and randomness characteristics, and their amplitudes are usually very small, and their frequencies can appear any point of the spectrum, so the traditional harmonic analysis methods have a serious deficiency to the interharmonic analysis. According to the interharmonic characteristics and the research status at present, this paper researches on the interharmonic detection algorithm, the voltage flicker envelope extraction method and the motor interharmonic source. The main work is as follows:
(1) About interharmonic detection, a new method of interharmonic spectral estimation based on the optimal window Burg algorithm is presented. Firstly, the principle of the interharmonic analysis based on the AR model is elaborated, and the high resolution characteristic of AR model is analyzed. The Burg algorithm of AR model is often used, but the error will appears in the process of AR model parameter recursion. It causes that the AR model parameters don't consistent with the actual values, leading the shortcoming of the peak bias and spectral line splitting. Aiming at this shortcoming of the Burg algorithm, a windowed method is present to suppress the error. Firstly, the optimal window can be obtained by minimizing the variance of average frequency error, and then the Levinson recursion is operated by windowed reflection coefficient. Since the method can guarantee to obtain a stable AR model, its spectral estimation performance is better than the Marple algorithm of AR model. By comparing the optimal window Burg algorithm with the eigenvalue methods from the points of the view of computational complexity and spectrum estimation performance, we can find that they both have the high frequency resolution and aren't affected by the asynchronous sampling, but the computational complexity of the optimal window Burg algorithm is far less than the eigenvalue methods. According to the acquired power spectrum by using the optimal window Burg algorithm, the amplitudes and initial phases of every harmonic and interharmonic are computed further by least square method in this paper.
(2) About the voltage flicker envelope extraction, a new time-frequency atom-based method to detect voltage flicker is proposed. By means of matching pursuit, the voltage flicker signal after the synchronous detection is divided into a series of time-frequency atoms in which each atom is from redundant time-frequency atom dictionary and the chosen atoms can match to the signal structure. The frequency parameters of the chosen atoms are accepted or rejected to achieve the purpose of low-pass filtering. There is no convolution operation in the proposed method, so the boundary effect can be avoided. The results show that by use of the proposed method, not only undistorted envelope detection can be implemented, but also the boundary effect brought about by the traditional filtering methods, FIR filter, IIR filter and wavelet transform, can be avoided.
(3) The oscillating load torque leads to the induction motor stator current oscillations, and the oscillating current contains interharmonics. According to this phenomenon, the interharmonic source model of the induction motor with oscillation mechanical load is established. Compared to previous work, this model takes into account the more parameters of the induction motor, so the model is more detailed and has a higher accuracy. The mathematical model of the induction motor, which is nonlinear when the load torque oscillates, is linearized firstly. On this basis, the expression of the stator interharmonic currents is derived. The matlab simulation results verify the correctness of the proposed expression. Furthermore, the relationship between load torque oscillations and the spectrum of the stator interharmonic currents is analyzed by the proposed expression, and the effect of the various motor steady output powers on the spectrum of the interharmonics is investigated.
(4) The interharmonic source model of the induction motor driven by the voltage source inverters (VSI) considering mechanical load oscillation is established. Firstly the motor input voltage spectral characteristics is analyzed, on this basis, the formula to forecast the frequencies of the stator interharmonic currents is presented, and the process that the stator interharmonic currents pass through VSIs is analyzed using the modulation theory and instantaneous power conservation theory, and then, the expression of the interharmonic currents on supply system side is derived, and the frequencies and spectrum characteristics of interharmonic currents on supply system side can be analyzed by this expression, and finally, the effect of the load torque oscillation on the spectrum of the interharmonic currents on supply system side is investigated by simulation.
(1)在间谐波检测方面,提出基于最优窗Burg算法的间谐波谱估计新方法。首先系统阐述了基于AR模型的间谐波分析原理,并对AR模型具有的高分辨率特性进行了深入分析。Burg算法为AR模型中较常用的方法,但Burg算法在递推AR模型参数的过程中,会产生误差项,造成AR模型参数与实际值不符,导致谱峰偏移和谱线分裂现象。针对Burg算法的这一缺点,提出加窗的方式来对误差项进行抑制,通过在平均频率误差方差最小的意义下来获得最优窗,然后利用加窗后的反射系数进行Levinson递推运算。由于该算法能保证获得一个稳定的AR模型,因此,其谱估计性能优于AR模型中的Marple算法。将该方法与目前间谐波检测中最常用的特征值法进行计算量和谱估计性能两方面比较,两者均具有较高的频率分辨率,并不受非同步采样的影响,但最优窗Burg算法由于利用了Levinson递推,其计算量远小于特征值法。在利用最优窗Burg算法获得间谐波信号的功率谱后,进一步采用最小二乘法求取各次谐波和间谐波的幅值和初相位。
(2)在电压闪变包络线提取方面,提出基于时频原子方法的电压闪变检测新方法。该方法将经同步检波后的电压闪变信号通过匹配追踪的方式分解成一系列时频原子,其中每一个原子都来自于冗余的时频原子库,选择的原子可以最好地匹配信号结构。通过对所选原子的频率参数进行取舍,从而达到低通滤波的目的。由于该方法中不含有卷积运算,因此避免了边界效应。其不仅能够对电压闪变信号进行不失真地包络检波,而且能避免FIR滤波器、IIR滤波器和小波变换等传统滤波方法带来的边界效应。
(3)负载转矩波动会导致感应电动机定子电流波动,该波动的电流中包含有间谐波。根据这一现象,建立了机械负荷波动时的感应电动机间谐波源模型。相比前人的工作,该模型考虑到感应电动机更多的参数,模型更为详细,具有更高的精度。针对感应电动机在负载转矩波动时的非线性模型,论文首先对其进行线形化处理,在此基础上推导出定子间谐波电流表达式。Matlab仿真结果验证了该表达式的正确性。进一步地,利用该表达式对负载转矩波动和定子间谐波电流频谱之间的关系进行分析,并分析了电动机稳态输出功率的变化对定子间谐波电流频谱的影响。
(4)建立了计及机械负荷波动且通过变频调速驱动的感应电动机间谐波源模型。首先对电动机输入电压频谱特征进行分析,在此基础上给出定子间谐波电流的频率预测公式,利用瞬时功率守恒理论和开关函数调制理论来分析定子间谐波电流穿越电压源型变频调速装置的过程,然后推导出供电系统侧间谐波电流的表达式,利用该表达式可对系统侧间谐波电流的频率及频谱特性进行分析,最后仿真研究了负载转矩波动对系统侧间谐波电流频谱的影响。
With extensive applications of nonlinear loads, power electronic devices and fluctuating loads in power system, it causes an increase of interharmonic content in the grid, and the interharmonic of the grid leads to a series of problems, besides the typical problems caused by harmonics such as the load power factor reductions, the variety of energy loss increase, and the excitation of various resonance modes with supply system, it creates some new problems, such as voltage flicker, the passive filter overload, zero offset of the voltage waveform. So it causes power quality deterioration and affects the safe and economic operation of the power grid. Comparing with the traditional harmonics, the interharmonics have a more extensive damage for the power system, so it must be suppressed. The accurate estimation of interharmonics parameters and the deep understanding of their origins are a premise of the suppression of them. The interharmonics have the time variability and randomness characteristics, and their amplitudes are usually very small, and their frequencies can appear any point of the spectrum, so the traditional harmonic analysis methods have a serious deficiency to the interharmonic analysis. According to the interharmonic characteristics and the research status at present, this paper researches on the interharmonic detection algorithm, the voltage flicker envelope extraction method and the motor interharmonic source. The main work is as follows:
(1) About interharmonic detection, a new method of interharmonic spectral estimation based on the optimal window Burg algorithm is presented. Firstly, the principle of the interharmonic analysis based on the AR model is elaborated, and the high resolution characteristic of AR model is analyzed. The Burg algorithm of AR model is often used, but the error will appears in the process of AR model parameter recursion. It causes that the AR model parameters don't consistent with the actual values, leading the shortcoming of the peak bias and spectral line splitting. Aiming at this shortcoming of the Burg algorithm, a windowed method is present to suppress the error. Firstly, the optimal window can be obtained by minimizing the variance of average frequency error, and then the Levinson recursion is operated by windowed reflection coefficient. Since the method can guarantee to obtain a stable AR model, its spectral estimation performance is better than the Marple algorithm of AR model. By comparing the optimal window Burg algorithm with the eigenvalue methods from the points of the view of computational complexity and spectrum estimation performance, we can find that they both have the high frequency resolution and aren't affected by the asynchronous sampling, but the computational complexity of the optimal window Burg algorithm is far less than the eigenvalue methods. According to the acquired power spectrum by using the optimal window Burg algorithm, the amplitudes and initial phases of every harmonic and interharmonic are computed further by least square method in this paper.
(2) About the voltage flicker envelope extraction, a new time-frequency atom-based method to detect voltage flicker is proposed. By means of matching pursuit, the voltage flicker signal after the synchronous detection is divided into a series of time-frequency atoms in which each atom is from redundant time-frequency atom dictionary and the chosen atoms can match to the signal structure. The frequency parameters of the chosen atoms are accepted or rejected to achieve the purpose of low-pass filtering. There is no convolution operation in the proposed method, so the boundary effect can be avoided. The results show that by use of the proposed method, not only undistorted envelope detection can be implemented, but also the boundary effect brought about by the traditional filtering methods, FIR filter, IIR filter and wavelet transform, can be avoided.
(3) The oscillating load torque leads to the induction motor stator current oscillations, and the oscillating current contains interharmonics. According to this phenomenon, the interharmonic source model of the induction motor with oscillation mechanical load is established. Compared to previous work, this model takes into account the more parameters of the induction motor, so the model is more detailed and has a higher accuracy. The mathematical model of the induction motor, which is nonlinear when the load torque oscillates, is linearized firstly. On this basis, the expression of the stator interharmonic currents is derived. The matlab simulation results verify the correctness of the proposed expression. Furthermore, the relationship between load torque oscillations and the spectrum of the stator interharmonic currents is analyzed by the proposed expression, and the effect of the various motor steady output powers on the spectrum of the interharmonics is investigated.
(4) The interharmonic source model of the induction motor driven by the voltage source inverters (VSI) considering mechanical load oscillation is established. Firstly the motor input voltage spectral characteristics is analyzed, on this basis, the formula to forecast the frequencies of the stator interharmonic currents is presented, and the process that the stator interharmonic currents pass through VSIs is analyzed using the modulation theory and instantaneous power conservation theory, and then, the expression of the interharmonic currents on supply system side is derived, and the frequencies and spectrum characteristics of interharmonic currents on supply system side can be analyzed by this expression, and finally, the effect of the load torque oscillation on the spectrum of the interharmonic currents on supply system side is investigated by simulation.
引文
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