CN109188078A - A kind of variable step- size LMS adaptive harmonic current detection method - Google Patents

A kind of variable step- size LMS adaptive harmonic current detection method Download PDF

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CN109188078A
CN109188078A CN201811206823.4A CN201811206823A CN109188078A CN 109188078 A CN109188078 A CN 109188078A CN 201811206823 A CN201811206823 A CN 201811206823A CN 109188078 A CN109188078 A CN 109188078A
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胡福年
朱娜
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Jiangsu Normal University
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Abstract

一种变步长LMS自适应谐波电流检测方法,属于电力技术,在低信噪比条件下,针对现有变步长最小均方(LMS)算法在谐波电流检测方面存在的不足,提出一种新的变步长LMS算法。该算法以误差信号e(n)在待检测信号中所占比率K(n)作为算法的回馈量,通过建立步长因子与回馈量的均值估计的类Sigmoid函数关系,实现动态控制其参数的变化,以保证在有较大噪声干扰的情况下,谐波检测过程也能保证既具有较快的动态响应速度,又保持较高的检测精度和较好的动态跟踪效果。通过对该谐波检测算法进行仿真,证明其具有良好的谐波检测性能。

A variable-step LMS adaptive harmonic current detection method belongs to the power technology. Under the condition of low signal-to-noise ratio, aiming at the shortcomings of the existing variable-step least mean square (LMS) algorithm in harmonic current detection, a method is proposed. A new variable-step LMS algorithm. The algorithm takes the ratio K(n) of the error signal e(n) in the signal to be detected as the feedback amount of the algorithm, and realizes the dynamic control of its parameters by establishing a sigmoid-like function relationship between the step size factor and the mean value of the feedback amount. In order to ensure that in the case of large noise interference, the harmonic detection process can also ensure that it has a fast dynamic response speed, and maintains a high detection accuracy and a better dynamic tracking effect. Through the simulation of the harmonic detection algorithm, it is proved that it has good harmonic detection performance.

Description

A kind of variable step- size LMS adaptive harmonic current detection method
Technical field
The present invention relates to power technologies, and in particular to a kind of variable step- size LMS adaptive harmonic current detection method.
Background technique
With more and more non-linear power electronic equipment investment applications, resulting a large amount of harmonic waves are directly affected The harmonic pollution problems of the power quality of power grid, power grid are extremely serious.Corresponding effective measures must be taken to come to harmonic problem Inhibited, with this come reduce or even avoid harmonic wave bring influence.Active Power Filter-APF can be compensated dynamically as one kind The device of harmonic wave has obtained extensive attention and application.Wherein as the core of active filter --- Harmonic currents detection Link will have a direct impact the effect of harmonics restraint using which kind of technology and methods, therefore the real-time inspection to harmonic current The research of method of determining and calculating seems particularly significant with improvement.
Current main Harmonic Detecting Algorithm includes being become based on instantaneous reactive power theory, Fast Fourier Transform (FFT), small echo It changes.Wherein made in active filter by the H.Akagi method based on instantaneous reactive power proposed and its improved method With more universal, but its detection system is open loop, and frequency is fixed, extremely sensitive for the variation of original part parameter and voltage on line side, And it is only applicable to three-phase system.Adaptive algorithm detection system is closed loop, and system has adaptivity, and detection effect is good;Not only Monophase system is also applied for suitable for three-phase system.Currently, lowest mean square (Least Mean Square, LMS) is most widely used General adaptive algorithm.In Measurement of Harmonics in Power System, what is proposed earliest is fixed step algorithm, because fixed step size can not be protected simultaneously The equilibrium problem of convergence rate and steady-state error is demonstrate,proved, so that the application of algorithm is by many limitations.In order to solve fixed step size institute band Problems, various Variable Step Algorithms propose that harmonic detecting effect also increasingly optimizes in succession.
Summary of the invention
Goal of the invention of the invention is to provide a kind of variable step- size LMS adaptive harmonic current detection method, humorous to improve Precision, convergence rate and the real-time of wave current detecting.
For achieving the above object, technical scheme is as follows:
A kind of variable step- size LMS adaptive harmonic current detection method, comprising steps of
S1: installing voltage sensor or current sensor in each phase of network system respectively, to monitor the load of every phase Electric current iL(t) and system voltage us(t), wherein L represents load, and S represents system, and variable t is the time;
S2: to periodically non-sinusoidal load current iL(t) and the active reference signal x of its fundamental current1, x1=sin (ω t), idle reference signal x2, x2=cos (ω t) synchronizes sampling, respectively obtains the load current of current sample time n Discrete value iL(n), the fundamental active discrete value x of reference signal1(n) and fundamental wave reactive power discrete value x2 (n), wherein x1For standard Fundamental voltage, x2For the value after 90 ° of its phase shift, ω is that fundamental wave hands over frequency;
S3: by the fundamental active discrete value x of current sample time1(n) and fundamental wave reactive power discrete value x2(n) composition is currently adopted The discrete value matrix X (n) of the fundamental wave at sample moment=[x1(n), x2(n)];
S4: by estimating for fundamental wave discrete matrix X (n) and the mutually multiplied sampled signal of weight coefficient matrix W (n) of current sample time Evaluation, filter export y (n), y (n)=X (n) WT(n), initial value 0, W (n)=[w1(n), w2(n)], x1(n) corresponding For fundamental active discrete value x1(n) weight, x2(n) fundamental wave reactive power discrete value x is corresponded to2(n) weight;
S5: the discrete value iL (n) of current time load current is subtracted to the estimated value and y of fundamental current current sample time (n), the harmonic current i of current sample time is obtainedh(n) error amount, error signal are e (n), e (n)=iL(n)-y(n);
S6: calculating the sef-adapting filter weight coefficient matrix W (n+1) of next sampling instant,
W (n+1)=+ 2 μ (n) e (n) X (n) of W (n)
Wherein μ is step-length of the sef-adapting filter in current sample time, and μ needs to meet certain condition of convergence, 0 < μ < 1/λmax, λmaxFor the maximum eigenvalue of input signal autocorrelation matrix, X (n) is the discrete value matrix of fundamental wave of current sample time Autocorrelation matrix characteristic value;
S7: the update of step-length
1) letter i is being originally inputted with signalL(n) the related averaged power spectrum of proportion is as feedback amount in,
μ (n+1)=α μ (n)+γ P2(n)
Wherein, P (n) is the related averaged power spectrum of proportion in original input signal;β is forgetting factor, 0 < β < 1;α is Fixed value;γ is preset parameter, γ > 0;
2) β (n)=γ β (n-1)+η is obtained by P (n) | P (n) |, γ and η are preset parameter, the change of common constraint beta (n) Change;
3) it replaces volume e (n) to be used as feedback amount by P (n), establishes the class sigmoid functional relation of step-length Yu feedback amount;
4) n=n+1 is enabled, repeating above step S3 to S7 can be realized real-time inspection to the harmonic current in load current It surveys.
Technical solution as a further improvement of that present invention, the step 3) in the step S7 specifically include:
It replaces volume e (n) to be used as feedback amount by P (n), establishes the class sigmoid functional relation of step-length Yu feedback amount,
μ (n)=β (n) (1-exp (- α (n) | P (n) |2)), whereinα (n) be currently with previous step System tracking error ratio.
The value range of technical solution as a further improvement of that present invention, the α (n) is
The clipping of technical solution as a further improvement of that present invention, the step-length is
Beneficial effects of the present invention:
1, be zero principle by steady state power harmonic wave mean value it is foundation, error is replaced by coherence average estimation P (n) of error Feedback amount of the e (n) as algorithm, eliminates influence of the harmonic component ξ (n) to step change;Secondly class Sigmoid function is utilized Compression Mappings, the functional relation for establishing step-length and feedback amount carrys out the variation of dynamic adjusting step, and by preset parameter α and β becomes variable α (n) and β (n) carrys out the variation of dynamic adjusting step so that algorithm has faster initial convergence speed, when transition compared with Higher convergence precision when the dynamically track effect and stable state got well;
2, α (n) is currently to be embodied in the system tracking error of previous step ratio for constraining step change speed When error becomes larger, α (n) becomes larger, and the increase of step-size factor obtains very fast convergence rate;When error becomes smaller, α (n) reduces, step Long coefficient value reduces available lesser steady-state error;γ and η is preset parameter, and the variation of common constraint beta (n) is different from β For caused by definite value when P (n) level off to zero when, brought suddenly to change, dynamic constraint beta (n) allows side length slow Variation, thus avoid algorithm stable state or when close to stable state because of β value it is fixed caused by larger steady-state error.
Detailed description of the invention
Fig. 1 is traditional fixed step size adaptive algorithm in the Real output waveform of asynchronous long time base wave and ideal output wave The comparison diagram of shape, it is u=0.1 that wherein a figure, which is step-length, and figure b is step-length u=0.04;
Fig. 2 is the fundamental current figure and sheet of the algorithm for the class Sigmoid functional relation established between step-length and mean square error The fundamental current figure of algorithm in inventive embodiments, wherein a figure is the algorithm of class Sigmoid functional relation, and b figure is of the invention real Apply the algorithm in example;
Fig. 3 is right value update change curve, and wherein a figure is the algorithm of class Sigmoid functional relation, and b figure is of the invention real Apply the algorithm in example;
Fig. 4 is fundamental current change curve when loading current jump, and wherein a figure is class Sigmoid functional relation Algorithm, b figure are the fundamental current figure of the algorithm in the embodiment of the present invention;
Fig. 5 is weight change curve when loading current jump, and wherein a figure is the algorithm of class Sigmoid functional relation, B figure is the algorithm in the embodiment of the present invention.
Specific embodiment:
Embodiment
A kind of variable step- size LMS adaptive harmonic current detection method, comprising the following steps:
Step 1: voltage sensor or current sensor are installed respectively in each phase of network system, to monitor every phase Load current iL(t) and system voltage us(t), subscript L represents load, and S represents system, and variable t is the time;
Step 2: to periodically non-sinusoidal load current iL(t) and the active reference signal x of its fundamental current1,x1= Sin (ω t), idle reference signal x2,x2=cos (ω t) synchronizes sampling, respectively obtains the load electricity of current sample time n The discrete value i of streamL(n), the fundamental active discrete value x of reference signal1(n) and fundamental wave reactive power discrete value x2 (n);Wherein x1For mark Quasi- fundamental voltage, x2For the value after 90 ° of its phase shift, ω is that fundamental wave hands over frequency;
Step 3: by the fundamental active discrete value x of current sample time1(n) and fundamental wave reactive power discrete value x2(n) composition is worked as The discrete value matrix X (n) of the fundamental wave of preceding sampling instant=[x1(n),x2(n)].
Step 4: by the mutually multiplied sampled signal of weight coefficient matrix W (n) of fundamental wave discrete matrix X (n) and current sample time Estimated value, i.e., filter output y (n), y (n)=X (n) WT(n), initial value 0, W (n)=[w1(n),w2(n)],x1 (n) fundamental active discrete value x is corresponded to1(n) weight, x2(n) fundamental wave reactive power discrete value x is corresponded to2(n) weight;
Step 5: the discrete value iL (n) of current time load current to be subtracted to the estimation of fundamental current current sample time Value and y (n), just obtain the harmonic current i of current sample timeh(n) error amount, that is, error signal e (n), e (n)=iL(n)-y (n);
Step 6: the sef-adapting filter weight coefficient matrix W (n+1) of next sampling instant is calculated,
W (n+1)=+ 2 μ (n) e (n) X (n) of W (n)
Wherein μ is step-length of the sef-adapting filter in current sample time, and μ needs to meet certain condition of convergence, 0 < μ < 1/λmaxmaxFor the maximum eigenvalue of input signal autocorrelation matrix), X (n) is the discrete value matrix of fundamental wave of current sample time Autocorrelation matrix characteristic value.
Step 7: the update of step-length
1, letter i is being originally inputted with signalL(n) the related averaged power spectrum of proportion is as feedback amount in, i.e.,
μ (n+1)=α μ (n)+γ P2(n),
P (n) is the related averaged power spectrum of proportion in original input signal, and harmonic carcellation electric current does step-length update It disturbs;β is forgetting factor, value range (0,1), influence of the past signal to present status, and value is determined by the width of time window, β is bigger, indicates that the forgetting degree of signal in the past is bigger, to present influence with regard to smaller;Conversely, β is smaller, the past, signal was to present It influences bigger.;α is fixed value, it determines step value when restraining known to formula;γ is the preset parameter close to 1, certainly Determine convergence rate (γ > 0).
2, β (n)=γ β (n-1)+η is obtained by P (n) | P (n) |, γ and η are preset parameter, the change of common constraint beta (n) Change, be different from β be definite value caused by when P (n) level off to zero when, brought suddenly to change, dynamic constraint beta (n) makes side Length can be slowly varying, thus avoid algorithm stable state or when close to stable state because of β value it is fixed caused by larger steady-state error.
3, it replaces volume e (n) to be used as feedback amount by P (n), establishes the class sigmoid functional relation of step-length Yu feedback amount, such as
μ (n)=β (n) (1-exp (- α (n) | P (n) |2)), whereinα (n) be currently with previous step System tracking error ratio is embodied in when error becomes larger, α (n) becomes larger, step-size factor for constraining step change speed Increase obtain very fast convergence rate, sayed by above-mentioned, the value range that can obtain α (n) is
It is simultaneously the stability for guaranteeing algorithm, does not generate biggish step value jump, algorithm is restrained, step-length Need clipping.
In formula: μmax、μminSelection should ensure that the stability of algorithm, usually enable μmaxIt is calculated close to fixed step size adaptive-filtering The neutrality step value of method.
4, n=n+1 is enabled, repeating the above steps three to seven can be realized real-time inspection to the harmonic current in load current It surveys.
Emulation experiment
In order to examine the superiority and accuracy of new algorithm, using simulation software, to verify new algorithm.To be calculated convenient for comparing The performance of method, the present embodiment use in emulation and penetrate load current are as follows:
iL=A (sin (ω t)+0.2sin (6 ω t)+0.1sin (10 ω t)+0.05sin (ω t)) fundamental frequency is 50HZ, sampling number define 32 sampled points of each period, reference input in emulation are as follows:
[x1, x2]=[sin ω t, cos ω t]
Tap input be w=[w1, w2], weight initial value zero, i.e.,
W (0)=[0,0].
The value of parameter is as shown in table 1 in algorithm, and by simulating, verifying, the present embodiment algorithm has selected more good ginseng Number setting, it is same to see the table below 1.
1 algorithm parameter value table of table
Emulation experiment one
Fig. 1 is traditional fixed step size adaptive algorithm in the Real output waveform of asynchronous long time base wave and ideal output wave The comparison diagram of shape, as shown in Figure 1 when guaranteeing that step-length can be in convergent situation, when the step-length taken takes smaller u=0.04, although can To keep lesser steady-state error, but obviously it can be seen that convergent speed is very slow;When taking biggish step-length u=0.1, step-length Convergence rate is obviously accelerated, but compared with the former, disadvantage is that steady-state error error is again very big.It is possible thereby to simple proof, Implacable relationship between convergence rate and steady-state error possessed by the fixed not long algorithm of tradition.
Emulation experiment two
Fig. 2 is the fundamental current figure of the algorithm based on class sigmoid function, the fundamental wave of the algorithm proposed with the present embodiment Current graph.
The present embodiment modified hydrothermal process is obviously faster than based on class sigmoid function in convergence rate it can be seen from figure b Algorithm, begin to restrain and tend towards stability in a cycle, there is lesser steady-state error.
Fig. 3 is weight with new change curve, by weight change curve can be seen that the present embodiment algorithm convergence rate with It will be better than the algorithm based on class sigmiod function on stable state accuracy.
Emulation experiment three
It can be seen from Fig. 4 and Fig. 5 when load current amplitude mutates, the present embodiment innovatory algorithm can be quickly The tracking ideal fundamental current variation of speed, and ideal fundamental current variation has just been kept up in a cycle, and by weight Change curve, which can be seen that the present embodiment innovatory algorithm not only, has fast convergence rate and lesser steady-state error, works as input When electric current mutates, the present embodiment algorithm also has faster dynamic responding speed.

Claims (4)

1.一种变步长LMS自适应谐波电流检测方法,其特征在于,包括步骤:1. a variable step length LMS adaptive harmonic current detection method, is characterized in that, comprises the steps: S1:在电网系统每一相上分别安装电压传感器或电流传感器,以监测每相的负载电流iL(t)和系统电压us(t),其中,L代表负载,S代表系统,变量t为时间;S1: Install a voltage sensor or a current sensor on each phase of the power grid system to monitor the load current i L (t) and system voltage u s (t) of each phase, where L represents the load, S represents the system, and the variable t for time; S2:对周期性非正弦的负载电流iL(t)和其基波电流的有功参考信号x1,x1=sin(ωt),无功参考信号x2,x2=cos(ωt)进行同步采样,分别得到当前采样时刻n的负载电流的离散值iL(n)、参考信号的基波有功离散值x1(n)和基波无功离散值x2(n),其中,x1为标准基波电压,x2为其移相90°后的值,ω为基波交频率;S2: For the periodic non-sinusoidal load current i L (t) and the active reference signal x 1 , x 1 =sin(ωt) and the reactive reference signal x 2 , x 2 =cos(ωt) of its fundamental current Synchronous sampling to obtain the discrete value i L (n) of the load current at the current sampling time n, the discrete value of the fundamental wave active power x 1 (n) of the reference signal, and the discrete value of the fundamental wave reactive power x2 (n), where x 1 is the standard fundamental wave voltage, x 2 is the value after the phase shift of 90°, ω is the fundamental wave crossover frequency; S3:将当前采样时刻的基波有功离散值x1(n)和基波无功离散值x2(n)组成当前采样时刻的基波离散值矩阵X(n)=[x1(n),x2(n)];S3: The fundamental wave active discrete value x 1 (n) and the fundamental wave reactive power discrete value x 2 (n) at the current sampling moment are formed into the fundamental wave discrete value matrix X(n)=[x 1 (n) at the current sampling moment , x 2 (n)]; S4:将基波离散矩阵X(n)与当前采样时刻的权系数矩阵W(n)相乘得采样信号的估计值,滤波器输出y(n),y(n)=X(n)WT(n),其初始值为0,W(n)=[w1(n),w2(n)],x1(n)对应为基波有功离散值x1(n)的权值,x2(n)对应为基波无功离散值x2(n)的权值;S4: Multiply the fundamental wave discrete matrix X(n) and the weight coefficient matrix W(n) at the current sampling moment to obtain the estimated value of the sampled signal, and the filter outputs y(n), y(n)=X(n)W T (n), its initial value is 0, W(n)=[w 1 (n), w 2 (n)], x 1 (n) corresponds to the weight of the fundamental active discrete value x 1 (n) , x 2 (n) corresponds to the weight of the fundamental wave reactive power discrete value x 2 (n); S5:将当前时刻负载电流的离散值iL(n)减去基波电流当前采样时刻的估计值与y(n),得到当前采样时刻的谐波电流ih(n)的误差值,误差信号为e(n),e(n)=iL(n)-y(n);S5: Subtract the estimated value of the fundamental wave current at the current sampling time and y(n) from the discrete value iL(n) of the load current at the current time to obtain the error value of the harmonic current i h (n) at the current sampling time, and the error signal is e(n), e(n)=i L (n)-y(n); S6:计算下一采样时刻的自适应滤波器权系数矩阵W(n+1),S6: Calculate the adaptive filter weight coefficient matrix W(n+1) at the next sampling time, W(n+1)=W(n)+2μ(n)e(n)X(n)W(n+1)=W(n)+2μ(n)e(n)X(n) 其中μ为自适应滤波器在当前采样时刻的步长,μ需要满足一定的收敛条件,0&lt;μ&lt;1/λmax,λmax为输入信号自相关矩阵的最大特征值,X(n)为当前采样时刻的基波离散值矩阵的自相关矩阵的特征值;where μ is the step size of the adaptive filter at the current sampling time, μ needs to satisfy certain convergence conditions, 0&lt;μ&lt;1/λ max , λ max is the maximum eigenvalue of the autocorrelation matrix of the input signal, X(n) is The eigenvalues of the autocorrelation matrix of the fundamental discrete value matrix at the current sampling time; S7:步长的更新S7: Update of step size 1)用信号在原始输入信iL(n)中所占比例的相关平均估计作为回馈量,1) Use the relative average estimate of the proportion of the signal in the original input signal i L (n) as the feedback amount, μ(n+1)=αμ(n)+γP2(n)μ(n+1)=αμ(n)+γP 2 (n) 其中,P(n)为原始输入信号中所占比例的相关平均估计;β为遗忘因子,0&lt;β&lt;1;α为固定值;γ为固定参数,γ>0;Among them, P(n) is the relative average estimate of the proportion of the original input signal; β is the forgetting factor, 0&lt;β&lt;1; α is a fixed value; γ is a fixed parameter, γ>0; 2)由P(n)得到β(n)=γβ(n-1)+η|P(n)|,γ和η为固定参数,共同约束β(n)的变化;2) β(n)=γβ(n-1)+η|P(n)| is obtained from P(n), γ and η are fixed parameters, which jointly constrain the change of β(n); 3)由P(n)代替额e(n)作为回馈量,建立步长与回馈量的类sigmoid函数关系;3) Use P(n) instead of e(n) as the feedback amount, and establish a sigmoid-like function relationship between the step size and the feedback amount; 4)令n=n+1,重复上述步骤S3至S7即可实现对负载电流中的谐波电流的实时检测。4) Let n=n+1, repeat the above steps S3 to S7 to realize real-time detection of the harmonic current in the load current. 2.根据权利要求1所述的一种变步长LMS自适应谐波电流检测方法,其特征在于,所述步骤S7中的步骤3)具体包括:2. a kind of variable step length LMS adaptive harmonic current detection method according to claim 1, is characterized in that, step 3 in described step S7) specifically comprises: 由P(n)代替额e(n)作为回馈量,建立步长与回馈量的类sigmoid函数关系,Use P(n) instead of e(n) as the feedback amount, and establish a sigmoid-like function relationship between the step size and the feedback amount, μ(n)=β(n)(1-exp(-α(n)|P(n)|2)),其中α(n)为当前与上一步的系统跟踪误差比。μ(n)=β(n)(1-exp(-α(n)|P(n)| 2 )), where α(n) is the system tracking error ratio between the current and the previous step. 3.根据权利要求2所述的一种变步长LMS自适应谐波电流检测方法,其特征在于,所述α(n)的取值范围为3 . A variable-step LMS adaptive harmonic current detection method according to claim 2 , wherein the value range of the α(n) is 4.根据权利要求2所述的一种变步长LMS自适应谐波电流检测方法,其特征在于,所述步长的限幅为4. a kind of variable step length LMS adaptive harmonic current detection method according to claim 2, is characterized in that, the amplitude limit of described step length is
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