CN101102048A - A harmonic current prediction method for compensating control delay - Google Patents

Abstract

The invention is concerned with the harmonic current prediction method for compensating the controlling time-lapse, belongs to the harmonic current compensation technique field. Firstly, it measures the loading current instantaneous value in real time and low passes the filtering, and gets the phase corner of the electric-net voltage by phase-locked loop at the same time; predicts the current volume of the sampling time currently according to the electricity-net current phase corner and the fitting parameter vector; adjusts the fitting parameter vector according to the predicted error; then, according to the adjusted fitting parameter vector, the electricity-net voltage phase corner and the requested compensatory controlling time-lapse, it can predict the loading current volume of the tk+DeltaT time; and predicts the request compensatory harmonic current signal of the tk+DeltaT at last.

Description

A kind of harmonic current prediction method that is used to compensate the control time-delay

Technical field

The present invention relates to a kind of harmonic current prediction method that is used to compensate the control time-delay, be particularly useful for prediction, belong to the harmonic current compensation technical field the dynamic impact load electric current.

Background technology

The digitlization current controller of pwm voltage type current transformer is one of focus of research at present, but links such as A/D sampling in digital control, controlled quentity controlled variable calculating and PWM output are all introduced time-delay inevitably, thereby cause no matter taking what current Control Algorithm, the output current of current transformer always can lag behind instruction current.When controller adopted the dead beat control algolithm, state observer can be used for the calculating time-delay of compensating controller, makes controlled quentity controlled variable to export without delay, even but like this, the output current of current transformer still can lag behind sampling period of instruction current.

Solving above-mentioned latency issue best bet is that load current is predicted, according to predicted value load is compensated.With the example that is controlled to be of Active Power Filter-APF (hereinafter to be referred as APF), as long as can be at t _kConstantly dope t in advance _{K+ Δ T}(Δ T lags behind the time of instruction current for the current transformer output current) needs the harmonic current of compensation constantly, and with this predicted current as APF at t _kInstruction current constantly, then APF can be just at t _{K+ Δ T}The electric current that output loading constantly need compensate, although APF control algolithm inherent delay still exists like this, its compensation effect to nonlinear load has obtained tangible improvement.

It is the most direct a kind of thinking that the method for employing curve fit is carried out signal estimation.For example: linear interpolation method, parabolic interpolation etc. just is commonly used to predict the system voltage signal of sinusoidal variations.The thinking of another prediction sinusoidal current and voltage is to be converted into DC component in the rotating coordinate system by the park conversion, only need correct electric current and the magnitude of voltage that a leading angle can accurately dope any time on the phase angle when its park inverse transformation then.Signal for the cycle changes also can directly utilize the sampled data in previous or preceding several cycles to predict.

The all fairly simple easy realization of above current forecasting algorithm, but they only are applicable to the load current that prediction slowly changes.In general, the load current variation has the basis that certain rule is all prediction algorithms.Usually, slowly the load current rule ratio that changes is easier to grasp, and therefore also is easy to design corresponding predicted current algorithm; And for the dynamic impulsion load, the current instantaneous value that obtains owing to sampling before and after it changes very greatly, usually can't set up the feature priori that load current changes, and this feasible harmonic prediction to the dynamic impulsion load becomes very difficult.

In recent years, the harmonic prediction algorithm based on auto-adaptive filtering technique has obtained increasing research.Auto-adaptive filtering technique is a kind of any priori that need not signal and noise, and iteration filtering parameter automatically satisfying the requirement of certain criterion, thereby is realized the technology of optimal filter, and it is fit to be applied to the occasion of dynamic impulsion load very much.

The principle of auto-adaptive filtering technique as shown in Figure 1, it mainly is made up of two parts: the one, the filtering algorithm structure; The 2nd, be used for adjusting the adaptive algorithm of filtering parameter.The filtering algorithm structure of auto-adaptive filtering technique adopt finite impulse response (FIR) (hereinafter to be referred as FIR) or infinite impulse response (hereinafter to be referred as IIR) structure all can because there is stability problem in the IIR structure, the therefore general FIR structure that adopts.The purpose of adaptive algorithm is to adjust filtering parameter, makes last error signal reach minimum according to certain criterion.Criterion commonly used has two kinds of LMS least mean square (hereinafter to be referred as LMS) and recursion LMS least mean squares (hereinafter to be referred as RLS).

The target function of LMS algorithm is defined as: $J=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{[y_i-d_i]}^2$ , often adopt the iterative formula of the steepest descent method of widrow and Hoff proposition, that is: as filtering parameter

A(n+1)＝A(n)+2μe(n)X(n)

Wherein, X (n) expression is the input signal vector of n constantly, X (n)=[x (n), x (n-1) ..., x (n-L)], A (n) is the filtering parameter of moment n auto-adaptive filtering technique, A (n)=[a ₁(n), a ₂(n) ..., a _L(n)], e (n) is an error, and μ is the parameter (step factor) of control stability and convergence rate.

The target function of RLS algorithm is defined as: $J=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\λ}}^{L-i}{[y_i-d_i]}^2$ , iterative formula commonly used is:

$A(k+1)=A\left(k\right)+\mathrm{\γ}(k+1)P\left(k\right)X(k+1)(I_{\mathrm{tk}}-{\stackrel{\mathrm{\Λ}}{I}}_{\mathrm{tk}})$

In the formula: $P(k+1)=\frac{1}{\mathrm{\λ}}[P\left(k\right)-\mathrm{\γ}(k+1)P\left(k\right)X(k+1)X^T(k+1)P\left(k\right)]$

γ(k+1)＝1/λ+X ^T(k+1)P(k)X(k+1)

Wherein, λ is a forgetting factor, and the span of λ is 0～1, and concrete size can be selected according to experimental technique; The initial value of the filtering parameter A and the second intermediate variable P can adopt an initial L data point to find the solution or set arbitrarily A (0) and P (0)=ρ I, and wherein ρ is a very large positive scalar.

Auto-adaptive filtering technique has been widely used in System Discrimination and signal processing fields such as communication, automatic control, radar, can be summed up as adaptive noise cancellation techniques and automatic adaptation FIR predictive filtering algorithm in the main application of harmonic wave context of detection.

Fig. 2 is an adaptive noise opposition method schematic diagram.The adaptive noise opposition method is a kind of signal detecting method based on auto-adaptive filtering technique that Widrow proposes, and it can be a signal s from additive noise n ₀In separate.Detection system has two inputs, original input s+n ₀With reference input n _{0 '}Wherein, s and n ₀Be incoherent, s and n _{0 '}Also uncorrelated, but n ₀With n _{0 '}Be that correlated noise disturbs.Original input signal s+n ₀Output signal n with sef-adapting filter ₀ ^*Subtracting each other the system that obtains and export y, also is error signal e.By e the parameter of sef-adapting filter is adjusted, made its output n ₀ ^*Under the least mean-square error meaning, disturb n near the main channel ₀Thereby, make system's output approach signal, interference noise obtains offsetting.

When adopting the adaptive noise opposition method to carry out the harmonic current detection, get i _LAs original input, make its fundamental current i _LfAs " noise jamming " electric current, and harmonic current I _LhAs " signal " that needs detect, then desirable first-harmonic sine and cosine signal sinwt, coswt know easily that as with reference to input they are relevant with fundamental current, and uncorrelated with harmonic current.Therefore, can obtain " noise jamming " i by adaptive filter algorithm _LfAnd " signal " i _LhThe value of approaching under the least mean-square error meaning.But this method can only detect harmonic current in real time, does not possess the ability of prediction in advance.

Fig. 3 is automatic adaptation FIR predictive filtering algorithm principle figure.Among the figure, the input data sequence of adaptive filter algorithm be X (n)=[x (n), x (n-1) ..., x (n-L+1)], z ^-1Be the unit delay factor, y (n) is a desired output,

With

Be prediction

Result of calculation, and have: $\hat{y}(n+1)=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}{a}_k\left(n\right)x(n+1-k)=A\left(n\right)X(n+1)$ , A in the formula (n) is a filtering parameter, is adjusted automatically according to the predicated error in previous sampling period by adaptive filter algorithm.Adopt this automatic adaptation FIR predictive filtering algorithm can carry previous sampling period prediction harmonic current signal, but the existed algorithms amount of calculation is all too big at present, is difficult to realize under existing controller hardware condition.

Summary of the invention

The purpose of this invention is to provide a kind of harmonic current prediction method that is used to compensate the control time-delay, with the prediction dynamic impact load harmonic current of any time, thereby the time-delay that the compensating digits controller exists improves its compensation effect to the mains by harmonics electric current.

The harmonic current prediction method that is used to compensate the control time-delay that the present invention proposes may further comprise the steps:

(1) measures the instantaneous value It of electrical network load current in real time _k, obtain current sampling instant t by phase-locked loop simultaneously _kThe phase angle wt of line voltage _k

(2) sampled value of above-mentioned current instantaneous value is carried out low-pass filtering;

(3) according to above-mentioned current sampling instant electric network voltage phase angle wt _kGenerate the first list entries X (k):

X (k)=[cosh ₁Wt _k, sinh ₁Wt _k, cosh ₂Wt _k, sinh ₂Wt _k..., cosh _nWt _k, sinh _nWt _k] in the formula, h ₁, h ₂..., h _nBe respectively the characteristic harmonics number of times of electrical network load current;

(4) current time load current sampled value in the prediction electrical network

$\stackrel{\mathrm{\Λ}}{I_{t_k}}=A\left(k\right)\·X{\left(k\right)}^T$

In the formula, A (k) is the current sampling instant t of electrical network _kThe fitting parameter vector, A (k)=[a ₁, a ₂..., a _n], a ₁, a ₂..., a _nFor with the above-mentioned first list entries X (k) in the corresponding fitting coefficient of each component;

(5) with the current time current sampling data of above-mentioned prediction

Compare with above-mentioned real-time sampling current instantaneous value, obtain predicated error e (k) through low-pass filtering:

$e\left(k\right)=I_{t_k}-{\stackrel{\mathrm{\Λ}}{I}}_{t_k};$

(6) adjust above-mentioned fitting parameter vector A (k) according to above-mentioned predicated error e (k), its iterative formula is as follows:

$A(k+1)=A\left(k\right)+\mathrm{\γ}\left(k\right)P\left(k\right)X\left(k\right)(I_{t_k}-{\stackrel{\mathrm{\Λ}}{I}}_{t_k})$

In the formula: γ (k) is first intermediate variable in the iterative process, γ (k)=1/  λ+X ^T(k) P (k) X (k)  P (k) is second intermediate variable in the iterative process, P (k+1)= P (k)-γ (k) P (k) X (k) X ^T(k) P (k) /λ

Wherein, λ is a forgetting factor, and the span of λ is 0～1;

(7) according to above-mentioned current sampling instant electric network voltage phase angle wt _kCompensation control time-delay Δ T with setting generates the second list entries X (k+1):

X (k+1)=[cosh ₁W (t _k+ Δ T), sinh ₁W (t _k+ Δ T) ..., cosh _nW (t _k+ Δ T), sinh _nW (t _k+ Δ T)]; (8) with above-mentioned adjusted fitting parameter vector A (k+1), the prediction electrical network is at t _k+ Δ T load current constantly

${\stackrel{\mathrm{\Λ}}{I}}_{\mathrm{tk}+\mathrm{\ΔT}}=A(k+1)\·X{(k+1)}^T;$

(9) according to above-mentioned prediction electrical network at t _k+ Δ T load current constantly

, prediction needs the mains by harmonics electric current of compensation.

The harmonic current prediction method that is used to compensate the control time-delay that the present invention proposes is compared with traditional automatic adaptation FIR predictive filtering algorithm, has following effect and advantage:

(1) the needed input data sequence of the iterative process of the inventive method is according to current sampling instant electric network voltage phase angle wt _kBy just looking into, cosine table generated, and the instantaneous value It of the electrical network load current that real-time sampling obtains _kOnly proofread and correct the fitting parameter vector as the desired output of prediction algorithm.In fact, the method that adopts of the generating mode of this input data sequence and adaptive cancellation technology is on all four.The benefit of doing like this is to avoid sampling error to bring the disturbance of fitting parameter, and prediction algorithm is more flexible simultaneously, can predict the electric current of any time, and is not only electric current constantly of whole sampling period.

(2) in order to predict the dynamic impact load electric current, the inventive method has adopted the iterative algorithm of band forgetting factor when adjusting the fitting parameter vector, make its precision of prediction to the mains by harmonics electric current be greatly improved.

(3) amount of calculation of the inventive method is moderate, is convenient to Digital Realization.The amount of calculation of this method mainly concentrates on the iterative process, and according to iterative formula of the present invention as can be known, every iteration once needs to carry out 5L ²+ 6L+1 multiplication, 3L ²+ 4L+2 sub-addition needs storage L ²+ L intermediate variable, wherein L is the dimension of input data sequence, also is the number that needs the fitting parameter of identification.Because the prediction algorithm that this paper proposes needs the fitting parameter of identification fewer, generally be no more than 6, so the amount of calculation of whole algorithm is very little, much smaller than traditional automatic adaptation FIR predictive filtering algorithm, they need the fitting parameter of identification to reach 200.

In sum, the harmonic current prediction method that the present invention proposes is used to compensate the control time-delay has very high precision of prediction to the prediction of electrical network load harmonic current, can compensate the control time-delay effectively, thereby obviously improve its compensation effect to electrical network load harmonic current, amount of calculation is moderate simultaneously, is convenient to Digital Realization.

Description of drawings

Fig. 1 is existing auto-adaptive filtering technique schematic diagram.

Fig. 2 is existing adaptive noise opposition method schematic diagram.

Fig. 3 is existing automatic adaptation FIR predictive filtering algorithm principle figure.

Fig. 4 is the theory diagram of the inventive method.

Fig. 5 is the antijamming capability simulation result figure of the inventive method, and wherein Fig. 5 (a) is a nonlinear load electric current when containing higher harmonic components, and Fig. 5 (b) is that the nonlinear load electric current is when containing higher harmonic components and white noise and disturbing.

Fig. 6 is the rolling mill load current waveform that is adopted in the simulation example of the present invention.

Fig. 7 is the total percent harmonic distortion that adopts the inventive method front and back power network current.

Fig. 8 is the harmonic spectrum analysis of adopting the inventive method front and back power network current.

Embodiment

Thereby the present invention comes the prediction of match nonlinear load electric current realization to harmonic current with the multinomial that a series of harmonic current signal stacks are formed, and its theory diagram is measured the instantaneous value I of electrical network load current as shown in Figure 4 at first in real time _Tk, obtain current sampling instant t by phase-locked loop simultaneously _kThe phase angle wt of line voltage _kSampled value to current instantaneous value is carried out low-pass filtering; According to current sampling instant electric network voltage phase angle wt _kGenerate the first list entries X (k):

X(k)＝[cosh ₁wt _k，sinh ₁wt _k，cosh ₂wt _k，sinh ₂wt _k，…，cosh _nwt _k，sinh _nwt _k]

In the formula, h ₁, h ₂..., h _nBe respectively the characteristic harmonics number of times of electrical network load current; Current time load current sampled value in the prediction electrical network ${\stackrel{\mathrm{\Λ}}{I}}_{t_k}:\stackrel{\mathrm{\Λ}}{I_{t_k}}=A\left(k\right)\·X{\left(k\right)}^T$

In the formula, A (k) is the current sampling instant t of electrical network _kThe fitting parameter vector, A (k)=[a ₁, a ₂..., a _n], a ₁, a ₂..., a _nFor with the above-mentioned first list entries X (k) in the corresponding fitting coefficient of each component; Current time current sampling data with above-mentioned prediction Compare with above-mentioned real-time sampling current instantaneous value, obtain predicated error e (k) through low-pass filtering: $e\left(k\right)=I_{t_k}-{\stackrel{\mathrm{\Λ}}{I}}_{t_k};$

Adjust above-mentioned fitting parameter vector A (k) according to above-mentioned predicated error e (k), its iterative formula is as follows:

$A(k+1)=A\left(k\right)+\mathrm{\γ}\left(k\right)P\left(k\right)X\left(k\right)(I_{t_k}-{\stackrel{\mathrm{\Λ}}{I}}_{t_k})$

In the formula: γ (k) is first intermediate variable in the iterative process, γ (k)=1/  λ+X ^T(k) P (k) X (k)  P (k) is second intermediate variable in the iterative process, P (k+1)= P (k)-γ (k) P (k) X (k) X ^T(k) P (k) /λ

Wherein, λ is a forgetting factor, and the span of λ is 0～1, and concrete size can be selected according to experimental technique; The initial value of the fitting parameter A and the second intermediate variable P can adopt the individual data point of initial L (L=2n) to find the solution or set arbitrarily A (0) and P (0)=ρ I, and wherein ρ is a very large positive scalar;

According to above-mentioned current sampling instant electric network voltage phase angle wt _kCompensation control time-delay Δ T with setting generates the second list entries X (k+1):

X(k+1)＝[cosh ₁w(t _k+ΔT)，sinh ₁w(t _k+ΔT)，…，cosh _nw(t _k+ΔT)，sinh _nw(t _k+ΔT)]；

With above-mentioned adjusted fitting parameter vector A (k+1), the prediction electrical network is at t _k+ Δ T load current constantly

${\stackrel{\mathrm{\Λ}}{I}}_{\mathrm{tk}+\mathrm{\ΔT}}=A(k+1)\·X{(k+1)}^T;$

According to above-mentioned prediction electrical network at t _k+ Δ T load current constantly

, prediction needs the mains by harmonics electric current of compensation, and concrete grammar can adopt Ip-Iq harmonic wave detection algorithm.

In the said method, the sampled value of current instantaneous value is carried out low-pass filtering, main purpose is to filter out the high-frequency interferencing signal that exists in the sampled signal.In order to reduce the influence that phase place time-delay that this link certainly exists and amplitude attenuation cause the precision of prediction algorithm, its cut-off frequency is higher, generally is made as 10kHz.This module can constitute with hardware device, also can be realized by software program.If realize, can adopt following algorithm with software program:

${I^{\′}}_{\mathrm{tk}}=\frac{T_S}{T_S+2T}(I_{\mathrm{tk}}+I_{t(k-1)})+\frac{2T-T_S}{T_S+2T}{I^{\′}}_{t(k-1)}$

In the formula, Ts is the sampling period; T=1/f _C, f _CCut-off frequency for low pass filter, Itk and I ' tk are respectively before the tk filtering constantly and filtered load current instantaneous value, and it is before t (k-1) filtering constantly and filtered load current instantaneous value that It (k-1) and I ' t (k-1) are respectively the previous sampling period.

In the said method, according to current sampling instant electric network voltage phase angle wt _kGenerate the first list entries X (k):

X(k)＝[cosh ₁wt _k，sinh ₁wt _k，cosh ₂wt _k，sinh ₂wt _k，…，cosh _nwt _k，sinh _nwt _k]

In the formula, h ₁, h ₂..., h _nBe respectively the characteristic harmonics number of times of electrical network load current, can not integer, the dimension that increases input data sequence can improve the precision of algorithm predicts, but also can increase amount of calculation simultaneously, therefore in the general input data sequence except adopt first-harmonic just, the cosine signal, only need comprise with the harmonic wave of the main harmonic current same frequency of load just, cosine signal, its dimension generally is no more than 6.

In the said method, in order to predict the dynamic impact load electric current, when adjusting the fitting parameter vector, adopted the iterative algorithm of band forgetting factor, to accelerate the convergence rate of fitting parameter vector, thereby improve the precision of prediction of algorithm to a certain extent, bigger the time, can suitably increase the iterations of fitting parameter vector in the sampling period.The span of forgetting factor λ is 0～1, and concrete size can be selected according to experimental technique; The initial value of the fitting parameter A and the second intermediate variable P can adopt the individual data point of initial L (L=2n) to find the solution or set arbitrarily A (0) and P (0)=ρ I, and wherein ρ is a very large positive scalar.

Figure 5 shows that and introduce antijamming capability simulation result figure behind the forgetting factor λ.Input data sequence is only got first-harmonic sine and cosine signal in the emulation, and forgetting factor is taken as 0.7, predicts with the different nonlinear load electric currents of two classes that also contain the white noise interference simultaneously only containing harmonic current respectively.A) can see from the simulation result of Fig. 5, even only adopt independent first-harmonic sine and cosine signal as input data sequence, when in nonlinear load, except fundamental current, also containing very large higher harmonic current interference signal, the result that prediction at last obtains remains very accurately, and error is almost 0.Certainly, from the simulation result b of Fig. 5) can see that white noise interference meeting causes very large influence to the precision of prediction algorithm.It may be that the error of A/D sampling or the interference of inverter switching device action bring that white noise disturbs, and for fear of its influence to the prediction algorithm precision, can adopt low pass filter that sampled signal is carried out preliminary treatment.Certainly, low pass filter can bring the certain time-delay and the decay of amplitude, so its cut-off frequency should not select too lowly, otherwise can cause bigger influence to the precision of prediction algorithm.

In the said method, according to predicting that electrical network is at t _k+ Δ T load current constantly

, calculate the mains by harmonics electric current that needs compensation.Concrete grammar can adopt Ip-Iq harmonic wave detection algorithm.The Ip-Iq algorithm is because its superior performance, become the central widely used a kind of harmonic wave detection algorithm of Active Power Filter-APF, it can not have time-delay ground and detect the harmonic current signal that needs compensation in the middle of the predicted current signal, and, can also comprise the active current of fundamental reactive component and direct voltage control ring output in the last compensating instruction signal according to the difference of compensation purpose.

Below be an embodiment of the inventive method:

Adopt the PSCAD/EMTDC simulation software that prediction algorithm proposed by the invention is verified.The cut-off frequency of low-pass filtering is made as 10kHz in the emulation, sampling period is made as 80us, the iterations of fitting parameter is made as 4 times in per sampling period, and input data sequence adopts 4 dimension groups, be respectively first-harmonic just, cosine signal and 5 subharmonic just, cosine signal.

In the emulation instruction current signal is come the analog compensation device through time delay process (be used for the time-delay that exists in the analog current control algolithm, be made as 160us in the emulation) back controlled current source of control; As load, its typical waveform as shown in Figure 7 with the on-the-spot recorder data of another one controlled current source reproduction rolling mill.Theory analysis shows that the principal character harmonic component that the rolling mill that adopts AC-AC frequency converter to drive produces is (6k ± 1) F1 ± 6nfm, and wherein F1 is the electrical network fundamental frequency, and fm is the motor-driven frequency.As seen rolling mill is a dynamic impulsion load, and its harmonic spectrum is very abundant, and it not only can produce the integral frequency harmonizing wave electric current in whole rolling process, also can produce a large amount of mark subharmonic currents, even is lower than the subharmonic and the DC component of power frequency.Just because of this, can there be very large predicated error in general harmonic prediction algorithm when being used to predict this dynamic load, to the improvement of compensation effect and not obvious, also can cause the deterioration of compensation effect when serious.

Fig. 8 and Fig. 9 are the simulation results that adopts behind the harmonic wave prediction algorithm that the present invention proposes.After adopting the harmonic wave prediction algorithm as can see from Figure 8, in the whole rolling process, total percent harmonic distortion of system power reduces greatly, and about 5% when never adopting the harmonic prediction algorithm dropped to about 1%, satisfied the requirement of GB fully.Fig. 9 is the harmonic spectrum analysis of system power in the rolling mill course of work, can see when not adopting the harmonic prediction algorithm, because current controller time-delay, cause compensator to the higher harmonic current more than 11 times do not have compensation effect substantially, also not ideal enough to the compensation of low-order harmonic electric current.And after adopting the predicted current algorithm, improved the compensation effect of compensator greatly to these low-frequency range harmonic currents, the background harmonics (not displaying among the figure) that only has some superfrequencies (more than the 1kHz), and the harmonic wave of these superfrequencies be easy to can be by passive high pass filter filtering.

Claims (1)

1, a kind of harmonic current prediction method that is used to compensate the control time-delay is characterized in that the method comprising the steps of:

(1) measures the instantaneous value I of electrical network load current in real time _Tk, obtain current sampling instant t by phase-locked loop simultaneously _kThe phase angle wt of line voltage _k

(2) sampled value of above-mentioned current instantaneous value is carried out low-pass filtering;

(3) according to above-mentioned current sampling instant electric network voltage phase angle wt _kGenerate the first list entries X (k):

X(k)＝[cosh ₁wt _k，sinh ₁wt _k，cosh ₂wt _k，sinh ₂wt _k，…，cosh _nwt _k，sinh _nwt _k]

In the formula, h ₁, h ₂..., h _nBe respectively the characteristic harmonics number of times of electrical network load current;

(4) current time load current sampled value in the prediction electrical network

${\stackrel{\mathrm{\Λ}}{I}}_{t_k}=A\left(k\right)\·X{\left(k\right)}^T$

In the formula, A (k) is the current sampling instant t of electrical network _kThe fitting parameter vector, A (k)=[a ₁, a ₂..., a _n], a ₁, a ₂..., a _nFor with the above-mentioned first list entries X (k) in the corresponding fitting coefficient of each component;

(5) with the current time current sampling data of above-mentioned prediction

Compare with above-mentioned real-time sampling current instantaneous value, obtain predicated error e (k) through low-pass filtering:

$e\left(k\right)=I_{t_k}-{\stackrel{\mathrm{\Λ}}{I}}_{t_k};$

(6) adjust above-mentioned fitting parameter vector A (k) according to above-mentioned predicated error e (k), its iterative formula is as follows:

$A(k+1)=A\left(k\right)+\mathrm{\γ}\left(k\right)P\left(k\right)X\left(k\right)(I_{t_k}-{\stackrel{\mathrm{\Λ}}{I}}_{t_k})$

In the formula: γ (k) is first intermediate variable in the iterative process, γ (k)=1/  λ+X ^T(k) P (k) X (k)  P (k) is second intermediate variable in the iterative process, P (k+1)= P (k)-γ (k) P (k) X (k) X ^T(k) P (k) /λ

Wherein, λ is a forgetting factor, and the span of λ is 0～1;

(7) according to above-mentioned current sampling instant electric network voltage phase angle wt _kCompensation control time-delay Δ T with setting generates the second list entries X (k+1):

X(k+1)＝[cosh ₁w(t _k+ΔT)，sinh ₁w(t _k+ΔT)，…，cosh _nw(t _k+ΔT)，sinh _nw(t _k+ΔT)]；

(8) with above-mentioned adjusted fitting parameter vector A (k+1), the prediction electrical network is at t _k+ Δ T load current constantly

${\stackrel{\mathrm{\Λ}}{I}}_{\mathrm{tk}+\mathrm{\ΔT}}=A(k+1)\·X{(k+1)}^T;$

(9) according to above-mentioned prediction electrical network at t _k+ Δ T load current constantly

Prediction needs the mains by harmonics electric current of compensation.

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