WO2015172661A1 - 一种适用于微网谐波监测的压缩感知重构方法 - Google Patents

一种适用于微网谐波监测的压缩感知重构方法 Download PDF

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WO2015172661A1
WO2015172661A1 PCT/CN2015/077868 CN2015077868W WO2015172661A1 WO 2015172661 A1 WO2015172661 A1 WO 2015172661A1 CN 2015077868 W CN2015077868 W CN 2015077868W WO 2015172661 A1 WO2015172661 A1 WO 2015172661A1
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harmonic
sparse
signal
microgrid
compressed
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PCT/CN2015/077868
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French (fr)
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杨挺
袁博
冯瑛敏
盆海波
王洪涛
游金阔
徐明玉
祖玛亚艾伯特.Y.H.
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天津大学
悉尼大学
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/37—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35
    • H03M13/39—Sequence estimation, i.e. using statistical methods for the reconstruction of the original codes

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  • the invention relates to a reconstruction method of compressed sensing, in particular to a compressed sensing reconstruction method suitable for harmonic monitoring of a micro network.
  • Micro-grid also known as micro-grid, refers to a small-scale power distribution system that is a collection of distributed power sources, energy storage devices, energy conversion devices, related loads, monitoring and protection devices. It can be connected to the external distribution network. It can be operated in isolation and is an important part of the future smart grid. A large number of distributed power sources and power electronics exist in the microgrid, which complicates the power signal and also affects the power quality of the distribution network. The monitoring and governance of harmonics as the main aspect of power quality is a key issue for microgrids.
  • the compressed sensing technology has made up for the shortcomings of the traditional Nyquist sampling framework to consume and waste a lot of hardware resources and storage space when compressing data. It combines the compression process with the sampling process to complete the data in the sampling process. Compression, the collected data is compressed data. Therefore, compressed sensing technology has great practical value for microgrid harmonic monitoring.
  • Compressed sensing technology is to compress and measure the original signal (compressed sampling) with a small amount of linear random projection as the measurement method under the condition of satisfying sparsity, and reconstruct the original signal with extremely high probability by using the compressed sensing reconstruction method. It combines compression and sampling by compressing the data during the sampling process.
  • the specific implementation process of the compressed sensing is specifically: the sampling end realizes the compression measurement of the original signal x through the measurement matrix ( The compressed sampling value (compressed measurement signal) y is obtained, and the data analysis end realizes the signal reconstruction process through a certain reconstruction method to obtain the original reconstructed signal.
  • the sparse representation coefficient s (sparse vector) of the original signal under a sparse basis. Reconstruct the original signal estimate (original reconstructed signal) It can be seen that the sparse basis is also needed in the compressed sensing reconstruction method.
  • the sparse basis is also a precondition for the compressed sensing application, that is, the N ⁇ 1 dimensional original signal x must satisfy the N 2 -N under a sparse basis.
  • the vector s formed by the sparse representation coefficients is sparse, and s is called a sparse vector.
  • the compressed sensing technology sampling model and reconstruction model can be described as:
  • the measurement matrix ⁇ ⁇ R M ⁇ N (M ⁇ N) is M ⁇ 1 dimensional vector, since M ⁇ N, the number of sample values is greatly reduced, compared to the sampling under the Nyquist sampling frame to reduce big data Storage capacity.
  • Compressed sensing technology mainly involves three main contents: sparse representation of signals (selection of sparse basis), design of measurement matrix and signal reconstruction. Among them, signal reconstruction needs to be realized by a certain compressed sensing reconstruction method, which is the key and core of compressed sensing technology.
  • the compressed sensing reconstruction method suitable for microgrid harmonic monitoring of the invention fully utilizes the respective characteristics of the fundamental wave component and the harmonic component in the original signal of the microgrid, thereby improving the harmonic signal reconstruction effect.
  • the ideal voltage (or current) waveform of the microgrid is a cosine wave, but due to the existence of various nonlinear components in the microgrid, the voltage (or current) contains various harmonics, the waveform is distorted, and the original harmonic signal in the microgrid (Voltage or current waveforms containing harmonic components) can be described by a superposition of cosine functions:
  • a 1 , f 1 and ⁇ 1 represent the frequency, amplitude and phase of the fundamental component
  • a h , f h and ⁇ h ( h ⁇ 2) represent the frequency, amplitude and phase of the h-th harmonic component, including H-1 harmonic components.
  • the technical problem to be solved by the present invention is to provide a compressed sensing reconstruction method suitable for microgrid harmonic monitoring, which can effectively improve the harmonic signal reconstruction effect.
  • the technical solution adopted by the invention is: a compressed sensing reconstruction method suitable for micro-network harmonic monitoring, which comprises the following stages:
  • Parameter initialization of the spectral projection gradient method including: sparse vector estimation of the initial harmonic component
  • the harmonic component is used to compress the sampled value y harmonic as the input, and the sparse vector estimate of the harmonic component is reconstructed. Including the following steps:
  • the compressed sample value y described in the stage 1) is a measurement matrix of the collected N ⁇ 1 dimensional power system harmonic original signal x and the binary sparse random measurement matrix ⁇ as the power system harmonic data compression sampling.
  • the sparse basis ⁇ described in stage 1) is a sparse basis N of N x N dimensions.
  • Stage 3 includes the following steps:
  • Step (1) in stage 6) includes:
  • ⁇ t min ⁇ max ,max[ ⁇ min ,( ⁇ s T ⁇ s)/( ⁇ s T ⁇ g)] ⁇ .
  • the compressed sensing reconstruction method suitable for microgrid harmonic monitoring has the following features:
  • the compressed sensing technology is applied to further improve the signal reconstruction effect of the compressed sensing reconstruction method.
  • the reconstruction method is used to reconstruct the signal. The better this property is, the full digging of the amplitude of the fundamental component in the original harmonic signal of the microgrid is caused by the fact that its proportion in the sparsity is far greater than that of the harmonic component.
  • a harmonic suitable for the microgrid is proposed.
  • the harmonic sensing system based on compressed sensing includes signal sampling and signal reconstruction.
  • the signal sampling of the present invention adopts a random measurement method to obtain a compressed measurement signal, and mixes the analog value and the modulated wave sensed by the voltage or current transformer, and uses an integrator. The addition operation is performed to obtain a compressed measurement signal.
  • the present invention firstly performs basic wave sieving on the microgrid harmonic compression sample value to obtain the sparse vector estimation value of the fundamental wave component and the harmonic component compressed sample value after filtering the fundamental component (only harmonic Wave component), the signal reconstruction is performed by spectral projection gradient method to obtain the sparse vector estimation value of the harmonic component, and finally the original harmonic signal is reconstructed.
  • the above reconstruction process is performed in the calculation unit and the execution controller.
  • the harmonic signal K of the harmonic signal after filtering out the fundamental wave is greatly reduced, so the harmonic signal reconstruction effect is effectively improved.
  • the compressed sensing reconstruction method of the invention is suitable for micro-network harmonic monitoring, and makes up for the fact that the existing compressed sensing reconstruction method does not consider the characteristics of the micro-network harmonic signal, so that the reconstruction effect is not ideal, and the signal-to-noise ratio is low. Less than a low defect.
  • FIG. 1 is a schematic structural diagram of a compression sensing technology framework
  • FIG. 2 is a flow chart of a compressed sensing reconstruction method suitable for microgrid harmonic monitoring according to the present invention
  • FIG. 3 is a structural diagram of a hardware system of the present invention.
  • Figure 4 is a use diagram of a 0.4kV low-voltage micro-network Benchmark reference model
  • FIG. 5 is a diagram showing the effect of signal reconstruction signal to noise ratio obtained by different methods
  • Fig. 6 is a diagram showing the effect of signal reconstruction error obtained by different methods.
  • the invention provides a compressed sensing reconstruction method suitable for micro-grid harmonic monitoring, which acquires a compressed measurement signal by a binary-sparse random measurement method at a sampling end, that is, an analog value perceived by a voltage (or current) transformer.
  • the mixer is sent to the mixer, and the modulated signal is mixed, and then the mixed signal is sequentially sent to the integrator to obtain a compressed sample value y.
  • the compressed sampled value is transmitted to the signal reconstruction end, and the compressed sample value y is subjected to fundamental wave filtering in the early stage of the reconstruction end to obtain a sparse vector estimation value of the fundamental wave component.
  • the discrete Fourier transform base is determined as the N ⁇ N-dimensional sparse basis ⁇ , where N is the original The number of vector elements of the harmonic signal.
  • FIG. 2 A flow of a compressed sensing reconstruction method suitable for microgrid harmonic monitoring according to the present invention is shown in FIG. 2, and includes the following stages:
  • the collected N ⁇ 1 dimensional power system harmonic original signal x and the binary sparse random measurement matrix ⁇ are used as the measurement matrix for the power system harmonic data compression sampling, and simultaneously sent to the mixer for compression under the analog signal.
  • Sampling: y ⁇ x, and then performing A/D conversion on the analog signal y to obtain an M ⁇ 1 dimensional compressed sample value (compressed measurement signal) y.
  • the generation of the binary sparse random measurement matrix ⁇ is to first generate M ⁇ N.
  • the number of N the number of vector elements of the original harmonic signal.
  • the sensing matrix ⁇ and the compressed sample value y are sent to the signal reconstruction and data analysis end;
  • Parameter initialization of the spectral projection gradient method including: sparse vector estimation of the initial harmonic component
  • FIG. 3 A hardware structure diagram of a compressed sensing reconstruction method suitable for microgrid harmonic monitoring of the present invention is shown in FIG. 3:
  • the hardware components include: voltage (or current) transformer, mixer, modulation signal generator, integrator, A/D conversion circuit, waveform display device, calculation circuit, signal reconstruction execution controller, interface circuit, etc. .
  • System components include: signal sampling system and central monitoring system.
  • the signal acquisition system consists of a voltage (or current) transformer, a mixer, a modulation signal generator, an integrator, etc., to achieve signal sampling.
  • the voltage (or current) analog voltage obtained by the voltage (or current) transformer and the modulated signal output by the modulation signal generator are simultaneously sent to the mixer for mixing processing and outputting the mixed signal; the mixed signal is sequentially sent to the integrator
  • the compressed measurement signal is obtained as an output of the signal sampling system, and the output compressed measurement signal is connected to the central monitoring system.
  • the central monitoring system consists of a signal reconstruction execution controller and a calculation circuit to realize signal reconstruction.
  • the calculation circuit is responsible for the specific calculation of the reconstruction method, and the controller performs the control function of signal reconstruction calculation and waveform display, and also realizes the control function of interaction with other external systems.
  • the central monitoring system provides a set of interfaces, including a serial interface and an RJ45 network port, as a cascade interface with other external systems.
  • the front end of the monitoring system uses a voltage (or current) transformer to achieve voltage (or current) acquisition of the micro-grid monitoring position, and then input the analog value of voltage (or current) sensing into the mixer, and modulate the wave. Mixing, then sending the mixing signal to the integrator, obtaining the analog value of the compression measurement, and obtaining the final compressed measurement value y through the A/D conversion device.
  • the central monitoring system mainly completes the signal reconstruction function, which is realized by reconstructing the execution controller and the calculation circuit. The reconstructed signal can be used to display the final waveform through the display device, and can also be provided to other monitoring devices through the interface circuit.
  • the method of the present invention is applied to the original harmonic compression measurement signal for signal reconstruction effect analysis.
  • microgrid harmonic current signals are obtained as shown in Table 1.
  • the piconet model is a micro-network Benchmark 0.4kV reference model, and the grid-connected operation mode, the fundamental frequency of the distribution network varies within 50 ⁇ 0.2 Hz, the WT is a wind turbine in the micro-grid, the load adopts a constant power model, and the fan model A permanent magnet direct drive fan model based on a double pulse width modulated back-to-back converter is used.
  • the reconstruction process of the compressed sensing technology of the microgrid original harmonic signals in Table 1 is respectively performed.
  • the reconstructed signal-to-noise ratio effect of the original harmonic signal is shown in Fig. 5, and the signal reconstruction error effect is shown in Fig. 6.
  • the evaluation index in the reconstruction effect analysis uses the reconstructed signal to noise ratio (SNR) and signal reconstruction error (err), which are defined as follows:
  • the abscissa is the compression ratio of the sample, defined as M/N.
  • the reconstructed signal-to-noise ratio of the method of the present invention is significantly higher than the compressed sample matching pursuit (CoSaMP) algorithm, the sub-algorithm space tracking (SP) algorithm, The spectral projection gradient (SPG) algorithm and the fast iterative shrinkage threshold (FISTA) algorithm can achieve a signal-to-noise ratio of more than 90 dB even at a low compression ratio of 1/10.
  • CoSaMP compressed sample matching pursuit
  • SP sub-algorithm space tracking
  • SPG spectral projection gradient
  • FISTA fast iterative shrinkage threshold

Abstract

一种适用于微网谐波监测的压缩感知重构方法，包括：设感知矩阵（I）；进行基波滤除的初始化；进行基波滤除；滤除压缩采样值中的基波成分；对谱投影梯度法进行参数初始化；利用谱投影梯度法；以谐波分量压缩采样值yharmonic作为输入量，重构出谐波分量的稀疏向量估计值ŝharmonic；完成对微网谐波原始信号x的重构。本发明先对微网谐波压缩采样值进行基波滤除得到基波分量的稀疏向量估计值和滤除基波分量后的谐波分量压缩采样值（只含谐波分量），谐波信号重构效果得到有效提升，更适用于微网谐波监测。

Description

一种适用于微网谐波监测的压缩感知重构方法 技术领域
本发明涉及一种压缩感知的重构方法，特别涉及一种适用于微网谐波监测的压缩感知重构方法。
背景技术
在能源需求与环境保护的双重压力下，国际能源界已将更多目光投向了微网技术的相关研究领域。微网又称微电网，是指由分布式电源、储能装置、能量转换装置、相关负荷和监控、保护装置汇集而成的小型发配电系统，可以与外部配电网并网运行，也可以孤立运行，是未来智能电网的重要组成部分。微网中存在的大量分布式电源和电力电子装置，这使其电能信号变得复杂，同时也给配电网的电能质量带来影响。作为电能质量主要方面的谐波的监测和治理是微网面临的关键问题。随着谐波分析的实时化、智能化发展，微网中谐波监测海量数据的传输和存储问题日益凸显。数据采集和压缩技术越来越成为一项提高电力系统控制的实时性和电力系统运行管理水平的关键支撑技术。以傅里叶变换、离散余弦变换和小波变换等为代表的传统数据压缩方法均在Nyquist采样定理基础上，先对电能质量数据进行高采样率的采集和A/D转换，再对数据进行压缩。采样后期的数据压缩在一定程度上解决了采样数据量巨大带来传输压力的问题，但数据压缩前的一次高速采样需要消耗大量的硬件资源和存储空间。特别对于微网谐波信息采集，由于其谐波环境复杂，信号的采样频率较高，Nyquist采样得到的原始谐波信号数据存储量巨大。而近年来诞生的压缩感知技术弥补了传统Nyquist采样框架进行数据压缩时消耗和浪费大量的硬件资源和存储空间的缺陷，它是通过将压缩过程与采样过程相融合，在采样过程中完成对数据的压缩，采集的数据即是压缩数据。因此，压缩感知技术用于微网谐波监测具有重大实用价值。
压缩感知技术是原始信号在满足稀疏性的条件下采用少量线性随机投影作为测量方式对原始信号进行压缩测量(压缩采样)，并利用压缩感知重构方法以极高概率准确重构出原始信号。它通过在采样过程中对数据进行压缩实现压缩与采样相融合，结合图1所示的压缩感知技术框架，压缩感知具体实现过程具体是：采样端通过测量矩阵实现对原始信号x的压缩测量(压缩采样)得到压缩采样值(压缩测量信号)y，数据分析端通过一定的重构方法实现信号重构过程，得到原始重构信号
Figure PCTCN2015077868-appb-000001
在重构过程中，需要先求解原始信号在某个稀疏基下的稀疏表示系数s(稀疏向量)的估计值
Figure PCTCN2015077868-appb-000002
再重构出原始信号估计值(原始重构信号)
Figure PCTCN2015077868-appb-000003
可见，压缩感知重构方法中还需用到稀疏基，稀疏基也是压缩感知应用的一个前提条件，即是N×1维原始信号x必须为满足在某个稀疏基Ψ∈RN×N下的稀疏表示系数构成的向量s是稀疏的，称s为稀疏向量。压缩感知技术采样模型和重构模型可描述为：
Figure PCTCN2015077868-appb-000004
测量矩阵Φ∈RM×N(M<<N)，压缩采样值y为M×1维向量，由于M<<N，采样值个数大大 减少，相比Nyquist采样框架下的采样减少大数据存储量。压缩感知技术主要涉及三方面的主要内容：信号的稀疏表示(稀疏基的选取)、测量矩阵的设计和信号重构。其中，信号重构需要通过一定的压缩感知重构方法实现，是压缩感知技术的关键和核心。
目前压缩感知中的重构理论研究均未考虑微网谐波信号的特点，在实际微网谐波监测系统中的重构效果不十分理想。本发明的一种适用于微网谐波监测的压缩感知重构方法充分利用微网原始信号中基波分量和谐波分量各自特点，从而提升了谐波信号重构效果。
微网理想的电压(或电流)波形是余弦波，但由于微网中存在各种非线性元件，使电压(或电流)中含有多种谐波，波形发生畸变，微网中原始谐波信号(含有谐波成分的电压或电流波形)可用余弦函数的叠加形式描述：
Figure PCTCN2015077868-appb-000005
其中A1、f1和φ1表示基波分量的频率、幅值和相位，Ah、fh和φh(h≥2)表示h次谐波分量的频率、幅值和相位，共含H-1个谐波分量。根据电能质量谐波限值GB/T 14549-1993国家标准，公共电网的谐波总畸变率在5％以内，奇次和偶次谐波的幅值是基波幅值的4％以内和2％以内，即有Ah<0.04A0(h＝3,5,7,9···)或Ah<0.02A0(h＝2,4,6,8···)，基波分量的幅值远远大于谐波分量的幅值。
压缩感知技术的创始人之一的Cand□s指出，在压缩感知技术中，信号的重构精度和原始信号的稀疏度K密切相关，原始信号的稀疏度K越小重构算法的重构效果越好，信号自身特征和稀疏基是K的主要影响因素。
发明内容
本发明所要解决的技术问题是，提供能够使谐波信号重构效果得到有效提升的一种适用于微网谐波监测的压缩感知重构方法。
本发明所采用的技术方案是：一种适用于微网谐波监测的压缩感知重构方法，包括有如下阶段：
1)设感知矩阵Θ＝ΦΨ，将感知矩阵Θ和原始谐波信号的压缩采样值y送入信号重构端，其中所述的稀疏基Ψ为离散傅里叶变换基；
2)进行基波滤除的初始化，包括：初始迭代次数t＝1，初始残差r0＝y，初始基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000006
初始支撑集
Figure PCTCN2015077868-appb-000007
初始支撑矩阵Ω0＝[]，初始干扰集
Figure PCTCN2015077868-appb-000008
干扰集元素数量p＝0；
3)进行基波滤除，根据压缩采样值y重构出基波分量的稀疏向量估计值；
4)滤除压缩采样值中的基波成分，具体是计算基波分量的原始信号估计值
Figure PCTCN2015077868-appb-000009
进而计算滤除基波分量后的谐波分量压缩采样值
Figure PCTCN2015077868-appb-000010
5)对谱投影梯度法进行参数初始化，包括：初始谐波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000011
初始残差r0＝y；初始梯度g0＝-ΘTr0；初始谱步长α0∈[αmin,αmax]；初始迭代次数e＝1；
6)利用谱投影梯度法，以谐波分量压缩采样值yharmonic作为输入量，重构出谐波分量的 稀疏向量估计值
Figure PCTCN2015077868-appb-000012
包括如下步骤：
(1)更新本次迭代谐波分量的稀疏向量估计值和下次迭代的谱步长，
(2)若||rt||2-(yTrt-τ||gt||∞)/||rt||2≥δ，迭代次数e＝e+1，返回(1)；否则，则结束循环，得到谐波分量的稀疏估计值
Figure PCTCN2015077868-appb-000013
7)完成对微网谐波原始信号x的重构，包括：
(1)计算微网谐波原始信号的稀疏向量估计值
Figure PCTCN2015077868-appb-000014
(2)计算微网谐波原始信号的重构估计值
Figure PCTCN2015077868-appb-000015
阶段1)中所述的压缩采样值y，是将采集到的N×1维电力系统谐波原始信号x和由二进稀疏随机测量矩阵Φ作为电力系统谐波数据压缩采样的测量矩阵，同时送入混频器进行模拟信号下的压缩采样：y＝Φx，进而对模拟信号y进行A/D转换，得到M×1维压缩采样值y，所述二进稀疏随机测量矩阵Φ的生成是，首先生成M×N维零矩阵Φ，将Φ中每一列随机选取μN个位置，其中μ＝1/32，将所述μN个位置元素置1，生成二进稀疏随机测量矩阵Φ，其中M为压缩测量信号的向量元素的个数，N为原始谐波信号的向量元素的个数；
阶段1)中所述的稀疏基Ψ是N×N维的稀疏基Ψ。
阶段3)包括如下步骤：
(1)寻找索引λt＝arg max|ΘTrt-1|，其中ΘT是感知矩阵Θ的转置，rt-1是第t-1次循环迭代的残差；
(2)更新支撑集Λt＝Λt-1∪{λt}和支撑矩阵
Figure PCTCN2015077868-appb-000016
其中
Figure PCTCN2015077868-appb-000017
为感知矩阵Θ的第λt列向量；
(3)最小二乘更新基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000018
(4)更新残差
Figure PCTCN2015077868-appb-000019
(5)若基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000020
中所有非零元素位置相邻，则进入步骤(6)；否则，将不相邻元素位置索引μp放入干扰集Γp＝Γp-1∪{μp}，干扰集元素数量p＝p+1；
(6)若基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000021
中所有非零元素满足
Figure PCTCN2015077868-appb-000022
其中
Figure PCTCN2015077868-appb-000023
则返回步骤(1)，迭代次数t＝t+1；否则进入步骤(7)；
(7)将基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000024
中对应干扰集索引的位置元素置零
Figure PCTCN2015077868-appb-000025
其中，i＝1,2…p，得到基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000026
阶段6)中的步骤(1)包括：
(a)更新稀疏向量估计值
Figure PCTCN2015077868-appb-000027
和残差
Figure PCTCN2015077868-appb-000028
其中，Pτ是谱投影梯度法的投影算子
Figure PCTCN2015077868-appb-000029
(b)若
Figure PCTCN2015077868-appb-000030
则进行(c)；否则，αt-1＝αt-1/2，返回(a)；
(c)更新梯度：gt＝-ΘTrt；
(d)
Figure PCTCN2015077868-appb-000031
△g＝gt-gt-1；
(e)αt＝min{αmax,max[αmin,(△sT△s)/(△sT△g)]}。
本发明的一种适用于微网谐波监测的压缩感知重构方法，具有如下特点：
在微网谐波监测中应用压缩感知技术，以进一步提升压缩感知重构方法的信号重构效果为目的，结合压缩感知技术中原始信号稀疏度K越小、重构方法对信号的重构效果越好这一性质，充分挖掘微网原始谐波信号中基波分量幅值很高造成其在稀疏度中所占比例远远大于谐波分量的特点，提出了一种适用于微网谐波监测的压缩感知重构方法。基于压缩感知的谐波监测系统包括信号采样和信号重构，本发明的信号采样采用随机测量方式得到压缩测量信号，将电压或电流互感器感知的模拟值和调制波进行混频，采用积分器进行加法运算，得到压缩测量信号。在信号重构时，本发明前期先对微网谐波压缩采样值进行基波筛分得到基波分量的稀疏向量估计值和滤除基波分量后的谐波分量压缩采样值(只含谐波分量)，后期采用谱投影梯度法进行信号重构得到谐波分量的稀疏向量估计值，最终重构出原始谐波信号，上述重构过程在计算单元和执行控制器进行。滤除基波后的谐波信号稀疏度K大大降低，因此谐波信号重构效果得到有效提升。本发明的压缩感知重构方法适用于微网谐波监测，弥补了现有的压缩感知重构方法均未考虑微网谐波信号的特点而使重构效果不理想，低压缩比下信噪比低的缺陷。
附图说明
图1是压缩感知技术框架结构示意图；
图2是本发明的适用于微网谐波监测的压缩感知重构方法的流程图；
图3是本发明的硬件系统结构图；
图4是0.4kV低压微网Benchmark参考模型用例图；
图5是采用不同方法得到的信号重构信噪比效果图；
图6是采用不同方法得到的信号重构误差效果图。
具体实施方式
下面结合实施例和附图对本发明的一种适用于微网谐波监测的压缩感知重构方法做出详细说明。
本发明的一种适用于微网谐波监测的压缩感知重构方法，在采样端将原始信号x以二进稀疏随机测量方式获取压缩测量信号，即将电压(或电流)互感器感知的模拟值送入混频器，和调制信号进行混频，然后将混频后的信号依次送入积分器，得到压缩采样值y。将该压缩采样值传输至信号重构端，在重构端前期对压缩采样值y进行基波滤除得到基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000032
和只含谐波分量的压缩采样值yharmonic，接着对yharmonic用谱投影梯度法进行谐 波分量的信号重构过程，得到谐波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000033
最终重构出原始谐波信号
Figure PCTCN2015077868-appb-000034
在重构过程中需要用到稀疏基，由于微网谐波信号的傅里叶变换的系数具有良好的稀疏性，确定离散傅里叶变换基作为N×N维稀疏基Ψ，其中N为原始谐波信号的向量元素的个数。
本发明的一种适用于微网谐波监测的压缩感知重构方法流程如图2所示，包括有如下阶段：
1)将采集到的N×1维电力系统谐波原始信号x和由二进稀疏随机测量矩阵Φ作为电力系统谐波数据压缩采样的测量矩阵，同时送入混频器进行模拟信号下的压缩采样：y＝Φx，进而对模拟信号y进行A/D转换，得到M×1维压缩采样值(压缩测量信号)y，所述二进稀疏随机测量矩阵Φ的生成是，首先生成M×N维零矩阵Φ，将Φ中每一列随机选取μN(μ＝1/32)个位置，将该μN个位置元素置1，生成二进稀疏随机测量矩阵Φ；其中M为压缩测量信号的向量元素的个数，N为原始谐波信号的向量元素的个数。
2)由于微网谐波信号的傅里叶变换的系数具有良好的稀疏性，确定压缩感知N×N维稀疏基Ψ为离散傅里叶变换(DFT)基，设感知矩阵Θ＝ΦΨ，将感知矩阵Θ和压缩采样值y送入信号重构和数据分析端；
3)进行基波滤除的初始化，包括：初始迭代次数t＝1，初始残差r0＝y，初始基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000035
初始支撑集
Figure PCTCN2015077868-appb-000036
初始支撑矩阵Ω0＝[]，初始干扰集
Figure PCTCN2015077868-appb-000037
干扰集元素数量p＝0；
4)进行基波滤除，根据压缩采样值y重构出基波分量的稀疏向量估计值，包括如下步骤：
(1)寻找索引λt＝arg max|ΘTrt-1|，其中ΘT是感知矩阵Θ的转置，rt-1是第t-1次循环迭代的残差；
(2)更新支撑集Λt＝Λt-1∪{λt}和支撑矩阵
Figure PCTCN2015077868-appb-000038
其中
Figure PCTCN2015077868-appb-000039
为感知矩阵Θ的第λt列向量；
(3)最小二乘更新基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000040
(4)更新残差
Figure PCTCN2015077868-appb-000041
(5)若基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000042
中所有非零元素位置相邻，则进入步骤(6)；否则，将不相邻元素位置索引μp放入干扰集Γp＝Γp-1∪{μp}，干扰集元素数量p＝p+1；
(6)若基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000043
中所有非零元素满足
Figure PCTCN2015077868-appb-000044
其中
Figure PCTCN2015077868-appb-000045
则返回步骤(1)，迭代次数t＝t+1；否则进入步骤(7)；
(7)将基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000046
中对应干扰集索引的位置元素置零
Figure PCTCN2015077868-appb-000047
其中，i＝1,2…p，得到基波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000048
5)滤除压缩采样值中的基波成分，具体是计算基波分量的原始信号估计值
Figure PCTCN2015077868-appb-000049
进而计算滤除基波分量后的谐波分量压缩采样值
Figure PCTCN2015077868-appb-000050
6)对谱投影梯度法进行参数初始化，包括：初始谐波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000051
初始残差r0＝y；初始梯度g0＝-ΘTr0；初始谱步长α0∈[αmin,αmax]；初始迭代次数e＝1；
7)利用谱投影梯度法，以谐波分量压缩采样值yharmonic作为输入量，重构出谐波分量的稀疏向量估计值
Figure PCTCN2015077868-appb-000052
包括如下步骤：
(1)更新本次迭代谐波分量的稀疏向量估计值和下次迭代的谱步长，包括：
(a)更新稀疏向量估计值
Figure PCTCN2015077868-appb-000053
和残差
Figure PCTCN2015077868-appb-000054
其中，Pτ是谱投影梯度法的投影算子
Figure PCTCN2015077868-appb-000055
(b)若
Figure PCTCN2015077868-appb-000056
则进行(c)；否则，αt-1＝αt-1/2，返回(a)；
(c)更新梯度：gt＝-ΘTrt；
(d)
Figure PCTCN2015077868-appb-000057
△g＝gt-gt-1；
(e)αt＝min{αmax,max[αmin,(△sT△s)/(△sT△g)]}；
(2)若||rt||2-(yTrt-τ||gt||∞)/||rt||2≥δ，迭代次数e＝e+1，返回(a)；否则，结束循环，得到谐波分量的稀疏估计值
Figure PCTCN2015077868-appb-000058
8)完成对微网谐波原始信号x的重构，包括：
(1)计算微网谐波原始信号的稀疏向量估计值
Figure PCTCN2015077868-appb-000059
(2)计算微网谐波原始信号的重构估计值
Figure PCTCN2015077868-appb-000060
本发明的一种适用于微网谐波监测的压缩感知重构方法的硬件结构示意图如图3所示：
(1)硬件组成包括：电压(或电流)互感器、混频器、调制信号发生器、积分器、A/D转换电路、波形显示装置、计算电路、信号重构执行控制器、接口电路等。
(2)系统组成包括：信号采样系统和中心监控系统。信号采集系统由电压(或电流)互感器、混频器、调制信号发生器、积分器等组成，实现信号采样功能。电压(或电流)互感器得到的电压(或电流)模拟值和调制信号发生器输出的调制信号同时送入混频器，进行混频处理，输出混频信号；混频信号依次送入积分器，得到压缩测量信号作为信号采样系统的输出，其输出压缩测量信号接入中心监控系统。中心监控系统由信号重构执行控制器和计算电路组成，实现信号重构。其中，计算电路负责重构方法的具体计算，执行控制器实现信号重构计算和波形显示的控制功能，同时还实现与其他外部系统交互的控制功能。此外，中心监控系统还对外提供一组接口，包含串行接口和RJ45网口，作为与其他外部系统级联接口。
(3)该监测系统前端采用电压(或电流)互感器实现对微网监测位置的电压(或电流)采集，随后将电压(或电流)感知的模拟值输入混频器内，和调制波进行混频，然后将混频信号送至积分器，得到压缩测量的模拟值，并通过A/D转换装置得到最终的压缩测量值y。中心监控系统则主要完成信号重构功能，通过重构执行控制器和计算电路实现。重构的信号可通过显示装置实现最终的波形显示，同时也可通过接口电路提供给其他监测装置。
为验证本发明的一种适用于微网谐波监测的压缩感知重构方法的有效性，对原始谐波压缩测量信号应用本发明的方法进行信号重构效果分析。
利用如图4所示的微网模型，得到微网谐波电流信号如表1所示。该微网模型为微网Benchmark 0.4kV参考模型，并网运行模式，配电网基波频率在50±0.2Hz范围内变动，微网中WT为风力发电机，负荷采用恒功率模型，风机模型采用基于双脉宽调制背靠背变流器的永磁直驱式风机模型。
表1微网谐波原始信号
谐波次数 0.5 1 4.8 5 6.6 7
频率(Hz) 24.9000 49.8000 239.0400 249.0000 328.6800 348.6000
幅值(A) 0.2258 39.1554 0.1091 0.8147 0.0808 0.4330
相位(o) 17.9232 39.4610 25.7891 27.4878 51.3986 97.4573
利用本发明的一种适用于微网谐波监测的压缩感知重构方法和现有的典型压缩感知重构方法，分别对表1中的微网原始谐波信号进行压缩感知技术的重构过程，原始谐波信号的重构信噪比效果如图5所示，信号的重构误差效果如图6所示。重构效果分析中的评价指标采用重构信号信噪比(signal to noise ratio，SNR)和信号重构误差(err)，定义如下：
Figure PCTCN2015077868-appb-000061
Figure PCTCN2015077868-appb-000062
其中，
Figure PCTCN2015077868-appb-000063
为重构信号的均方误差。
图5和图6中横坐标为采样的压缩比，定义为M/N，本发明方法的重构信噪比明显高于压缩采样匹配追踪(CoSaMP)算法、子算法空间追踪(SP)算法、谱投影梯度(SPG)算法以及快速迭代收缩阈值(FISTA)算法，即使在1/10的低压缩比时，本发明重构方法的信噪比仍能达到90dB以上。

Claims (5)

  1. 一种适用于微网谐波监测的压缩感知重构方法，其特征在于，包括有如下阶段：
    1)设感知矩阵Θ＝ΦΨ，将感知矩阵Θ和原始谐波信号的压缩采样值y送入信号重构端，其中所述的稀疏基Ψ为离散傅里叶变换基；
    2)进行基波滤除的初始化，包括：初始迭代次数t＝1，初始残差r0＝y，初始基波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100001
    初始支撑集
    Figure PCTCN2015077868-appb-100002
    初始支撑矩阵Ω0＝[]，初始干扰集
    Figure PCTCN2015077868-appb-100003
    干扰集元素数量p＝0；
    3)进行基波滤除，根据压缩采样值y重构出基波分量的稀疏向量估计值；
    4)滤除压缩采样值中的基波成分，具体是计算基波分量的原始信号估计值
    Figure PCTCN2015077868-appb-100004
    进而计算滤除基波分量后的谐波分量压缩采样值
    Figure PCTCN2015077868-appb-100005
    5)对谱投影梯度法进行参数初始化，包括：初始谐波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100006
    初始残差r0＝y；初始梯度g0＝-ΘTr0；初始谱步长α0∈[αmin,αmax]；初始迭代次数e＝1；
    6)利用谱投影梯度法，以谐波分量压缩采样值yharmonic作为输入量，重构出谐波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100007
    包括如下步骤：
    (1)更新本次迭代谐波分量的稀疏向量估计值和下次迭代的谱步长，
    (2)若||rt||2-(yTrt-τ||gt||∞)/||rt||2≥δ，迭代次数e＝e+1，返回(1)；否则，则结束循环，得到谐波分量的稀疏估计值
    Figure PCTCN2015077868-appb-100008
    7)完成对微网谐波原始信号x的重构，包括：
    (1)计算微网谐波原始信号的稀疏向量估计值
    Figure PCTCN2015077868-appb-100009
    (2)计算微网谐波原始信号的重构估计值
    Figure PCTCN2015077868-appb-100010
  2. 根据权利要求1所述的一种适用于微网谐波监测的压缩感知重构方法，其特征在于，阶段1)中所述的压缩采样值y，是将采集到的N×1维电力系统谐波原始信号x和由二进稀疏随机测量矩阵Φ作为电力系统谐波数据压缩采样的测量矩阵，同时送入混频器进行模拟信号下的压缩采样：y＝Φx，进而对模拟信号y进行A/D转换，得到M×1维压缩采样值y，所述二进稀疏随机测量矩阵Φ的生成是，首先生成M×N维零矩阵Φ，将Φ中每一列随机选取μN个位置，其中μ＝1/32，将所述μN个位置元素置1，生成二进稀疏随机测量矩阵Φ，其中M为压缩测量信号的向量元素的个数，N为原始谐波信号的向量元素的个数；
  3. 根据权利要求1所述的一种适用于微网谐波监测的压缩感知重构方法，其特征在于，阶段1)中所述的稀疏基Ψ是N×N维的稀疏基Ψ。
  4. 根据权利要求1所述的一种适用于微网谐波监测的压缩感知重构方法，其特征在于，阶段3)包括如下步骤：
    (1)寻找索引λt＝arg max|ΘTrt-1|，其中ΘT是感知矩阵Θ的转置，rt-1是第t-1次循环迭代的残差；
    (2)更新支撑集Λt＝Λt-1∪{λt}和支撑矩阵其中
    Figure PCTCN2015077868-appb-100012
    为感知矩阵Θ的第λt列向量；
    (3)最小二乘更新基波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100013
    (4)更新残差
    Figure PCTCN2015077868-appb-100014
    (5)若基波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100015
    中所有非零元素位置相邻，则进入步骤(6)；否则，将不相邻元素位置索引μp放入干扰集Γp＝Γp-1∪{μp}，干扰集元素数量p＝p+1；
    (6)若基波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100016
    中所有非零元素满足
    Figure PCTCN2015077868-appb-100017
    其中
    Figure PCTCN2015077868-appb-100018
    则返回步骤(1)，迭代次数t＝t+1；否则进入步骤(7)；
    (7)将基波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100019
    中对应干扰集索引的位置元素置零
    Figure PCTCN2015077868-appb-100020
    其中，i＝1,2…p，得到基波分量的稀疏向量估计值
    Figure PCTCN2015077868-appb-100021
  5. 根据权利要求1所述的一种适用于微网谐波监测的压缩感知重构方法，其特征在于，阶段6)中的步骤(1)包括：
    (a)更新稀疏向量估计值
    Figure PCTCN2015077868-appb-100022
    和残差
    Figure PCTCN2015077868-appb-100023
    其中，Pτ是谱投影梯度法的投影算子
    Figure PCTCN2015077868-appb-100024
    (b)若
    Figure PCTCN2015077868-appb-100025
    则进行(c)；否则，αt-1＝αt-1/2，返回(a)；
    (c)更新梯度：gt＝-ΘTrt；
    (d)
    Figure PCTCN2015077868-appb-100026
    △g＝gt-gt-1；
    (e)αt＝min{αmax,max[αmin,(△sT△s)/(△sT△g)]}。
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