CN107102189B - Variable step- size LMS harmonic current detecting method based on S function - Google Patents
Variable step- size LMS harmonic current detecting method based on S function Download PDFInfo
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Abstract
Variable step- size LMS harmonic current detecting method based on S function, step is mainly: A, signal sampling: the discrete value matrix x (n) of fundamental wave B, being obtained the estimated value y (n) of fundamental current moment n, y (n)=x (n) w by LMS sef-adapting filterT(n)；C, the harmonic current i of sampling instant n is obtainedh(n) estimated value e (n), i.e. error signal e (n)；D, it calculates the LMS sef-adapting filter weight coefficient matrix w (n+1): the update of E, step-length of moment n+1: calculating error time cross-correlation mean value k (n), k (n)=ρ k (n-1)+K (1- ρ) e (n) e (n-1)；Obtain controlling elements β (n), β (n)=γ β (n-1)+η | k (n) |, obtain the step size mu (n+1) of moment n+1, μ (n+1)=β (n) (1-exp (- α (n) | k (n) |2))；F, the step of enabling n=n+1, repeating B, C, D, E realizes the Real-time and Dynamic Detection to the harmonic current in load current.This method is high to the detection accuracy of harmonic current, fast convergence rate, and real-time is good；There is stronger tracking performance to the system containing mutation load.
Description
Technical field
The invention belongs to the Harmonic currents detection technical fields of electric system.
Background technique
In recent years, the application with a large amount of power electronic devices in electric power network is so that electric power network harmonic pollution is asked
Topic becomes increasingly conspicuous, and drastically influences the safe operation of power grid quality and user equipment.Harmonic wave is thus effectively administered, to raising electric energy
Quality is particularly significant.Active Power Filter-APF (APF) accordingly injects one to power grid based on the real-time detection to mains by harmonics
The harmonic current of reverse phase, to realize the harmonic pollution compensation to power grid, inhibit.The quality of its performance is heavily dependent on
Harmonic current detecting method in detection real-time to harmonic current, accurate namely Active Power Filter-APF is most important.With
The development of sef-adapting filter is applied to Harmonic currents detection and achieves good effect.It the advantage is that as one
A closed loop detection system has adaptivity to the variation of electrical network parameter and algorithm is simple, has to single-phase, three-phase system general
Property.
Assuming that supply voltage is sinusoidal signal u (t)=Usin (ω t) of standard, wherein ω is angular frequency, and t is time, U
The amplitude of supply voltage.Power supply is added on nonlinear load L, the load current i that will be obtainedLIt is sampled, the sampling period is
T, then the discrete value i (n) of load current i (t) can be indicated are as follows:
In formula (1), n is sampling instant, IkAnd θkIt is the amplitude and phase of kth subharmonic current in load current, i respectively1
(n) what is indicated is the fundamental current in load current, and wherein fundamental current is again by fundamental active current i1p(n)=I1sin(ωnT)cos
θ1With fundamental reactive current i1q(n)=I1cos(ωnT)sinθ1Two parts composition,It is corresponding
Be higher harmonic current summation.
LMS (lowest mean square) algorithm in adaptive filtering theory is simple with it, is easily achieved, and is studied both at home and abroad
The extensive concern of person, therefore the Harmonic currents detection principle based on LMS (lowest mean square) is: filter weight coefficient w (n) is in cost
Function J (n)=| e (n) |2That is error mean square | e (n) |2Under the conditions of the smallest, according to load current iL(n) to the output of filter
The size of the error e (n) of y (n) automatically adjusts, so that the output y (n) of filter approaches fundamental current i1(n), it and then detects defeated
The harmonic current of approaching to reality out.Therefore, the formula of the Harmonic currents detection based on LMS algorithm is as follows:
Y (n)=x (n) wT(n) (2)
E (n)=iL(n)-y(n) (3)
W (n+1)=w (n)+μ e (n) x (n) (4)
Wherein: w (n) is the filter weight coefficient at n moment.μ is referred to as step factor, and size affects the convergence of algorithm
Speed and steady-state error, that is, excessive then fast convergence rate but steady-state error is big, too small then steady-state error is small but convergence rate
Slowly.
Meanwhile guaranteeing the adequate condition of algorithmic stability are as follows: the λ of 0 < μ < 1/max.Wherein, λmaxFor reference-input signal x (n) phase
Close the maximum eigenvalue of matrix.
There is the intrinsic contradictions of convergence rate and steady-state error for above-mentioned fixed step size LMS algorithm, therefore in order to effectively solve
Certainly this problem is a kind of preferable selection using New variable step-size LMS.In existing document, New variable step-size LMS is adopted mostly
It is certain functional relation for establishing step-length and feedback error.Wherein, the algorithm of better performances has following two:
(1) based on the harmonic current detection of SVS-LMS
Bibliography " a kind of new variable step size adaptive filtering algorithm " (Qin Jingfan, Ou Yangjingzheng, data acquisition and procession [J])
This method is to propose step-length directly to be regarded as the Sigmoid function as error e (n), i.e.,
This method is referred to as the harmonic current detecting method of SVS-LMS (S function variable-step least mean square algorithm).Although the method improve
The shortcomings that fixed step size method, combines steady-state error and convergence rate, and under different grid power grades algorithm have it is logical
With property, but the algorithm there are the problem of have:
When error leveled off to for 0 moment, step-length is still larger, can not obtain higher stable state accuracy, cause error
It is larger.
(2) based on the harmonic current detection of VSS-LMS
Bibliography " A variable step size LMS algorithm " (R.H.Kwong and
E.W.Johnston, IEEE Trans.Signal processing [J]) this method is by instantaneous error square adjusting step
It updates, in algorithm initial stage, error is big, causes step-length to increase and obtains very fast convergence rate, in algorithm steady-state process, error
Small, step-length, which accordingly reduces, obtains higher stable state accuracy.But the algorithm can generate biggish error in the environment of low signal-to-noise ratio,
Anti-interference ability is not strong.
In conclusion existing variable step- size LMS harmonic detecting method can not be in convergence rate, steady-state error and tracing property
It can go up while meet the requirements.
Summary of the invention
Goal of the invention of the invention is just to provide a kind of variable step- size LMS harmonic current detecting method based on S function, the party
Method is high to the detection accuracy of harmonic current, fast convergence rate, and real-time is good；To containing mutation load system have it is stronger with
Track performance.
The technical scheme adopted by the invention for realizing the object of the invention is a kind of variable step- size LMS harmonic wave electricity based on S function
Detection method is flowed, its step are as follows:
A, signal sampling:
To the active reference signal x of periodically non-sinusoidal load current i (t) and its fundamental current1, x1=sin (ω t),
Idle reference signal x2, x2=cos (ω t) synchronizes sampling, respectively obtains the load current i's (t) of current sample time n
The fundamental active discrete value x of discrete value i (n), reference signal1(n) and fundamental wave reactive power discrete value x2(n)；Wherein, ω is fundamental wave
Angular frequency, t are the time；
B, by the fundamental active discrete value x of the reference signal of obtained current sample time n1(n) and fundamental wave reactive power is discrete
Value x2(n), the discrete value matrix x (n) of fundamental wave of current sample time n, x (n)=[x are formed1(n), x2(n)], then fundamental wave is discrete
Value matrix x (n) obtains the estimated value y (n) of fundamental current current sample time n, y (n)=x after passing through LMS sef-adapting filter
(n)wT(n)；Wherein, w (n) is weight coefficient matrix w (n) of the LMS sef-adapting filter in current sample time n, w (n)=[w1
(n), w2(n)], initial value 0；w1(n) for corresponding to fundamental active discrete value x1(n) weight coefficient；w2(n) fundamental wave is corresponded to
Idle discrete value x2(n) weight coefficient；T represents the transposition of matrix；
C, by A walk in the discrete value i (n) of load current of current sample time n subtract fundamental current current sample time n
Estimated value y (n), obtain the harmonic current i of current sample time nh(n) estimated value e's (n) namely current sample time n
Error signal e (n), it may be assumed that
E (n)=i (n)-y (n)
D, the LMS sef-adapting filter weight coefficient matrix w (n+1) of next sampling instant n+1 is calculated:
W (n+1)=w (n)+μ (n) e (n) x (n)
Wherein: μ (n) be LMS sef-adapting filter current sample time n step-length, value range be 0 <μ<2/
λmax, and λmaxFor the autocorrelation matrix x of the discrete value matrix x (n) of fundamental wave of current sample time nT(n) characteristic value of x (n)；
E, the update of step-length:
E1, error e (n) and the error e (n-1) of previous sampling instant n-1 according to current sample time n, obtain error
Time cross-correlation mean value k (n), k (n)=ρ k (n-1)+K (1- ρ) e (n) e (n-1)；Wherein, ρ is forgetting factor, value range
Are as follows:M is the number of sampling points of load current in one cycle；K is accelerated factor, value range
Between 1 to 2；It is k (1)=0 that the initial value of error time cross-correlation mean value k (n), which is 0,；
E2, the controlling elements β (n) that control S function shape is obtained according to error time cross-correlation mean value k (n),
β (n)=γ β (n-1)+η | k (n) |, and
Wherein, γ is active factors parameter, and value range is 0.98~0.99；η is stable factor parameter, and value range is
0.01~0.1；Wherein βmaxFor controlling elements maximum value, βmax* 2/ λ of=(0.1-0.3)max, βminFor controlling elements minimum value,
βmin=βmax/100；
E3, LMS sef-adapting filter is obtained by S function below in the step size mu (n+1) of next sampling instant n+1,
μ (n+1)=β (n) (1-exp (- a (n) | k (n) |2))
Wherein α (n) be error rate square, α (n)=| e (n-1)/e (n) |2, exp expression exponential function operation；
F, the step of enabling n=n+1, repeating B, C, D, E, can be realized the real-time dynamic to the harmonic current in load current
Detection.
Compared with prior art, the beneficial effects of the present invention are:
One, adaptive feedback amount is used as using error time cross-correlation mean value k (n) in the present invention, k (n) is equivalent to accidentally
Poor e (n) and previous moment error e (n-1), constantly carry out Estimation of Mean, due to steady in the time window of the two moment width
Feature of the interference signal with zero-mean when state, therefore the method for using Estimation of Mean in the time window at front and back moment, can remove
Interference signal has stronger anti-interference, can make to exclude the influence that most of harmonic wave interference updates step-length.To its inspection
Precision height is surveyed, there is stronger tracking performance to the system containing mutation load.
Two, accelerated factor K is when step-length is in iteration and updates, for increasing error signal auto-correlation to the shadow of algorithm
It rings, value is typically greater than 1 positive number, when the error of sampling instant becomes larger, so that error time cross-correlation mean value k (n) increases
Greatly, make algorithm to the tracking performance improved to abruptly-changing system.In the initial stage of algorithm, systematic error is larger, corresponding to generate
Biggish error rate square α (n) and controlling elements β (n), controlling elements β (n) and error time cross-correlation mean value k (n) at
Direct ratio, and step-length is positively correlated with controlling elements β (n), when so that error increasing, step-size factor is also increased therewith and is obtained faster
Convergence rate.On the contrary, error current e (n) and previous moment error e (n-1) are gradually reduced and tend to be equal, error rate is flat
Square α (n) also gradually becomes smaller with controlling elements β (n), and step-length reduces to obtain higher stable state accuracy at this time.
Present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.
Detailed description of the invention
Fig. 1 a is the harmonic current curve of emulation experiment one of the present invention,
Fig. 1 b be the method for the present invention and SVS-LMS method emulation experiment once, Harmonic currents detection value and its theoretical value
Error curve.
Fig. 1 c be the method for the present invention and VSS-LMS method emulation experiment once, Harmonic currents detection value and its theoretical value
Error curve.
Fig. 2 a is the harmonic current curve of emulation experiment two of the present invention,
Fig. 2 b is the method for the present invention and SVS-LMS method under emulation experiment two, Harmonic currents detection value and its theoretical value
Error curve.
Fig. 2 c is the method for the present invention and VSS-LMS method under emulation experiment two, Harmonic currents detection value and its theoretical value
Error curve.
Specific embodiment
Embodiment
A kind of specific embodiment of the invention is a kind of variable step- size LMS harmonic current detecting method based on S function,
Its step are as follows:
A kind of variable step- size LMS harmonic current detecting method based on S function, its step are as follows:
A, signal sampling:
To the active reference signal x of periodically non-sinusoidal load current i (t) and its fundamental current1, x1=sin (ω t),
Idle reference signal x2, x2=cos (ω t) synchronizes sampling, respectively obtains the load current i's (t) of current sample time n
The fundamental active discrete value x of discrete value i (n), reference signal1(n) and fundamental wave reactive power discrete value x2(n)；Wherein, ω is fundamental wave
Angular frequency, t are the time；
B, by the fundamental active discrete value x of the reference signal of obtained current sample time n1(n) and fundamental wave reactive power is discrete
Value x2(n), the discrete value matrix x (n) of fundamental wave of current sample time n, x (n)=[x are formed1(n), x2(n)], then fundamental wave is discrete
Value matrix x (n) obtains the estimated value y (n) of fundamental current current sample time n, y (n)=x after passing through LMS sef-adapting filter
(n)wT(n)；Wherein, w (n) is weight coefficient matrix w (n) of the LMS sef-adapting filter in current sample time n, w (n)=[w1
(n), w2(n)], initial value 0；w1(n) for corresponding to fundamental active discrete value x1(n) weight coefficient；w2(n) fundamental wave is corresponded to
Idle discrete value x2(n) weight coefficient；T represents the transposition of matrix；
C, by A walk in the discrete value i (n) of load current of current sample time n subtract fundamental current current sample time n
Estimated value y (n), obtain the harmonic current i of current sample time nh(n) estimated value e's (n) namely current sample time n
Error signal e (n), it may be assumed that
E (n)=i (n)-y (n)
D, the LMS sef-adapting filter weight coefficient matrix w (n+1) of next sampling instant n+1 is calculated:
W (n+1)=w (n)+μ (n) e (n) x (n)
Wherein: μ (n) is step-length of the LMS sef-adapting filter in current sample time n, and value range is 0 < μ < 2/
λmax, and λmaxFor the autocorrelation matrix x of the discrete value matrix x (n) of fundamental wave of current sample time nT(n) characteristic value of x (n)；
E, the update of step-length:
E1, error e (n) and the error e (n-1) of previous sampling instant n-1 according to current sample time n, obtain error
Time cross-correlation mean value k (n), k (n)=ρ k (n-1)+K (1- ρ) e (n) e (n-1)；Wherein, ρ is forgetting factor, value range
Are as follows:M is the number of sampling points of load current in one cycle；K is accelerated factor, value range
Between 1 to 2；It is k (1)=0 that the initial value of error time cross-correlation mean value k (n), which is 0,；
E2, the controlling elements β (n) that control S function shape is obtained according to error time cross-correlation mean value k (n),
β (n)=γ β (n-1)+η | k (n) |, and
Wherein, γ is active factors parameter, and value range is 0.98~0.99；η is stable factor parameter, and value range is
0.01~0.1；Wherein βmaxFor controlling elements maximum value, βmax* 2/ λ of=(0.1-0.3)max, βminFor controlling elements minimum value,
βmin=βmax/100；
E3, LMS sef-adapting filter is obtained by S function below in the step size mu (n+1) of next sampling instant n+1,
μ (n+1)=β (n) (1-exp (- a (n) | k (n) |2))
Wherein α (n) be error rate square, α (n)=| e (n-1)/e (n) |2, exp expression exponential function operation；
F, the step of enabling n=n+1, repeating B, C, D, E, can be realized the real-time dynamic to the harmonic current in load current
Detection.
Emulation experiment
In order to verify the validity of the variable step- size LMS harmonic current detecting method based on S function, emulation experiment has been carried out,
And compared with having been done with the Harmonic currents detection of SVS-LMS and VSS-LMS Harmonic currents detection.In emulation experiment below, ginseng
The sinusoidal signal that input is power frequency is examined, sample frequency sets 10KHz.
The specific value of the parameter of each algorithm is as follows: in experiment
The parameter of each algorithm simulating of table 1 experiment
| SVS-LMS | β=0.03, α=50 |
| VSS-LMS | β=0.99, α=0.96, η=0.0003 |
| The present invention | γ=0.99, ρ=0.997, η=0.0008 |
Emulation experiment one
Experiment condition: power supply u (t) is the AC power frequency voltage of 220V, is loaded as band three-phase bridge uncontrollable rectifier circuit sense
Property load, wherein load resistance R=25 Ω, inductance L=2mH.Remaining parameter setting such as table 1 shows.
Fig. 1 a is the harmonic current curve that the present invention detects, Fig. 1 b is the method for the present invention and is obtained based on SVS-LMS method
The error curve of Harmonic currents detection value and its theoretical value out.Fig. 1 c is the method for the present invention and the harmonic wave electricity based on VSS-LMS
Flow the error curve of detected value and its theoretical value.
The error current fluctuation range that can be seen that SVS-LMS algorithm from Fig. 1 b is -0.488~0.488A, of the invention
Error current fluctuation range is -0.106~0.068A；SVS-LMS algorithm is respectively with dynamic response time of the invention
0.054s,0.032s；As it can be seen that the present invention is better than SVS-LMS algorithm on dynamic response time and steady-state error；
It can be seen that the error current fluctuation range of VSS-LMS algorithm from Fig. 1 c are as follows: -0.268~0.271A, the present invention
Error current fluctuation range only are as follows: -0.106~0.068A；VSS-LMS algorithm is respectively with dynamic response time of the invention
0.042s,0.032s；The present invention is also better than VSS-LMS algorithm on dynamic response time and steady-state error；
Experiment two
Experiment parameter: power supply u (t) is the AC power frequency voltage of 220V, is loaded as band three-phase bridge uncontrollable rectifier circuit sense
Property load, wherein load resistance R=25 Ω, inductance L=2mH, and the t=0.1s moment load mutation.Remaining parameter setting
As table 1 shows.
Fig. 2 a is the harmonic current curve detected under the present invention, and Fig. 2 b is the method for the present invention and based on SVS-LMS method
The error curve of Harmonic currents detection value and its theoretical value., Fig. 2 c be the method for the present invention and based on VSS-LMS method harmonic wave electricity
Flow detected value and its theoretical value error curve.
From Fig. 2 b it can be seen that before load sudden change SVS-LMS algorithm error current fluctuation range be -0.483~
0.484A, error current fluctuation range of the invention are -0.09~0.07A；SVS-LMS algorithm and of the invention before load sudden change
Dynamic response time is respectively as follows: 0.051s, 0.035s；The error current fluctuation range of SVS-LMS algorithm after load sudden change are as follows:-
0.973~0.972A, error current fluctuation range of the invention are respectively as follows: -0.216~0.205A；SVS-LMS after load sudden change
Algorithm and dynamic response time of the invention are respectively as follows: 0.05s, 0.039s.Whether mutate as it can be seen that no matter loading, this hair
It is bright to be all better than SVS-LMS algorithm on dynamic response time and steady-state error.
From Fig. 2 c it can be seen that before load sudden change VSS-LMS algorithm error current fluctuation range are as follows: -0.277~
0.267A, error current fluctuation range of the invention are as follows: -0.09~0.07A；VSS-LMS algorithm and the present invention before load sudden change
Dynamic response time be respectively as follows: 0.044s, 0.035s；The error current fluctuation range of VSS-LMS algorithm after load sudden change
Are as follows: -0.938~0.781A, error current fluctuation range of the invention are respectively as follows: -0.216~0.205A；After load sudden change
VSS-LMS algorithm and dynamic response time of the invention are respectively as follows: 0.042s, 0.039s；Whether dash forward as it can be seen that no matter loading
Become the present invention and is all better than VSS-LMS algorithm on dynamic response time and steady-state error.
Claims (1)
1. a kind of variable step- size LMS harmonic current detecting method based on S function, its step are as follows:
A, signal sampling:
To the active reference signal x of periodically non-sinusoidal load current i (t) and its fundamental current1, x1=sin (ω t), it is idle
Reference signal x2, x2=cos (ω t) synchronizes sampling, respectively obtains the discrete of the load current i (t) of current sample time n
The fundamental active discrete value x of value i (n), reference signal1(n) and fundamental wave reactive power discrete value x2(n)；Wherein, ω is the angular frequency of fundamental wave
Rate, t are the time；
B, by the fundamental active discrete value x of the reference signal of obtained current sample time n1(n) and fundamental wave reactive power discrete value x2
(n), the discrete value matrix x (n) of fundamental wave of current sample time n, x (n)=[x are formed1(n), x2(n)], then by fundamental wave discrete value square
Battle array x (n) is by obtaining the estimated value y (n) of fundamental current current sample time n, y (n)=x (n) w after LMS sef-adapting filterT
(n)；Wherein, w (n) is weight coefficient matrix w (n) of the LMS sef-adapting filter in current sample time n, w (n)=[w1(n), w2
(n)], initial value 0；w1(n) for corresponding to fundamental active discrete value x1(n) weight coefficient；w2(n) correspond to fundamental wave reactive power from
Dissipate value x2(n) weight coefficient；T represents the transposition of matrix；
C, by A walk in the discrete value i (n) of load current of current sample time n subtract estimating for fundamental current current sample time n
Evaluation y (n) obtains the harmonic current i of current sample time nh(n) error of estimated value e (n) namely current sample time n
Signal e (n), it may be assumed that
E (n)=i (n)-y (n)
D, the LMS sef-adapting filter weight coefficient matrix w (n+1) of next sampling instant n+1 is calculated:
W (n+1)=w (n)+μ (n) e (n) x (n)
Wherein: μ (n) is step-length of the LMS sef-adapting filter in current sample time n, and value range is the λ of 0 < μ < 2/max, and
λmaxFor the autocorrelation matrix x of the discrete value matrix x (n) of fundamental wave of current sample time nT(n) characteristic value of x (n)；
E, the update of step-length:
E1, error e (n) and the error e (n-1) of previous sampling instant n-1 according to current sample time n, obtain error time
Cross-correlation mean value k (n), k (n)=ρ k (n-1)+K (1- ρ) e (n) e (n-1)；Wherein, ρ is forgetting factor, value range are as follows:M is the number of sampling points of load current in one cycle；K is accelerated factor, value range 1
To between 2；It is k (1)=0 that the initial value of error time cross-correlation mean value k (n), which is 0,；
E2, the controlling elements β (n) that control S function shape is obtained according to error time cross-correlation mean value k (n),
β (n)=γ β (n-1)+η | k (n) |, and
Wherein, γ is active factors parameter, and value range is 0.98~0.99；η is stable factor parameter, value range 0.01
~0.1；Wherein βmaxFor controlling elements maximum value, βmax* 2/ λ of=(0.1-0.3)max, βminFor controlling elements minimum value, βmin=
βmax/100；
E3, LMS sef-adapting filter is obtained by S function below in the step size mu (n+1) of next sampling instant n+1,
μ (n+1)=β (n) (1-exp (- α (n) | k (n) |2))
Wherein α (n) be error rate square, α (n)=| e (n-1)/e (n) |2, exp expression exponential function operation；
F, the step of enabling n=n+1, repeating B, C, D, E, can be realized the Real-time and Dynamic Detection to the harmonic current in load current.
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| CN110133425A (en) * | 2019-06-10 | 2019-08-16 | 集美大学 | A kind of submarine cable fault-signal filtering method, terminal device and storage medium |
| CN110531138A (en) * | 2019-07-08 | 2019-12-03 | 江苏科技大学 | A kind of Active Power Filter Harmonic Currents detection method |
| CN111181462B (en) * | 2020-03-11 | 2023-03-14 | 天津工业大学 | Surface-mounted permanent magnet synchronous motor parameter identification method based on variable step size neural network |
| CN112748682B (en) * | 2020-12-07 | 2021-12-14 | 珠海格力电器股份有限公司 | Signal sampling processing method, device, equipment and storage medium |
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