CN108375697A - A kind of adaptive frequency estimator method of non-equilibrium electric system - Google Patents
A kind of adaptive frequency estimator method of non-equilibrium electric system Download PDFInfo
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Abstract
The invention discloses a kind of adaptive frequency estimator methods of non-equilibrium electric system.First, the three-phase voltage signal of non-equilibrium electric system is indicated using not rounded signal；Then, using improved modified covariance method algorithm, Pisarenko Harmonic Decompositions algorithm or improved Pisarenko Harmonic Decompositions algorithm, in conjunction with Least Square Recurrence, adaptive frequency estimator is carried out to not rounded signal.The present invention can inhibit the interference of noise and harmonic wave to obtain accurate Frequency Estimation, and adaptively track frequency changes.
Description
Technical field
The invention belongs to signal processing technology fields, more particularly to a kind of adaptive frequency of non-equilibrium electric system is estimated
Meter method.
Background technology
" intelligent grid " based on the transregional power transmission network of extra-high voltage is developing in high gear, and power grid is related to country's warp
Ji lifeblood.Frequency is to investigate a key factor of power quality.To make power supply and homeostasis of load, frequency can only be at one
It is fluctuated in the range of very little.It is the prerequisite item for maintaining the stabilization of power grids and ensureing electrical equipment normal operation to have kept nominal frequency
Part, it is therefore necessary to accurately measure frequency of supply.
In order to solve these problems, many scholars how fast and accurate estimate frequency studying.Characterize Frequency Estimation
Precision is mean square error, it is desirable to carat Metro lower bound.In order to approach carat Metro lower bound, Rife in 1974 and
Boorstyn proposes maximum likelihood estimator module to estimate the frequency of simple signal.It in next many years, is opened up by simple signal
The harmonic signal of plus noise is opened up, the related algorithm of Frequency Estimation has zero passage method, phaselocked loop, based on minimum two in electric system
The sef-adapting filter that multiplies, newton recursive estimation, the comprehensive Kalman filtering (ECKF) of extension, adaptive notch filter, detection
Method, method of characteristic, Fourier transformation, wavelet transformation and Hilbert-Huang transform, but most of method calculation amount is excessively high and difficult
To use.And modified covariance method algorithm (Modified Covariance, MC), Pisarenko Harmonic Decomposition algorithms
(Pisarenko harmonic decomposition, PHD), improved Pisarenko Harmonic Decompositions algorithm (Reformed
Pisarenko harmonic decomposition, RPHD) computation complexity is low, it can be used for three-phase electric frequency real-time estimation.
1973, V.Pisarenko proposed a kind of harmonic wave descriptor index method that linear prediction property is derived i.e. PHD methods, main
The auto-correlation that utilize sampling point 1 and 2 to postpone.1996, D.Tufts proposed one kind based on prony methods simply and effectively
Frequency Estimation, that is, MC methods.2008, H.SO improved PHD methods.2010, Rim etc. then estimated real value using high-order auto-correlation
The frequency of simple signal.Also with good grounds different autocorrelation lags type further corrects PHD methods by follow-up scholar.However these
Auto-correlation function method based on time-domain signal sampled point can only estimate simple signal mostly, and there are frequency ambiguity phenomenons.
Not rounded signal is the signal that oval covariance i.e. pseudocovariance is not zero, such as amplitude modulation AM, amplitude shift keying
ASK, binary phase shift keying BPSK and multi-system amplitude keying MASK etc..These not rounded signals are widely used in communication, thunder
Up to in biomedicine.Differentiation circle is whether statistical property has invariable rotary property with not rounded signal, what statistical property referred to
It is probability density function, matrix or the cumulant in probability theory, do not have invariable rotary property is not rounded signal.
Invention content
In order to solve the technical issues of above-mentioned background technology proposes, the present invention is intended to provide a kind of non-equilibrium electric system
Adaptive frequency estimator method realizes the adaptive accurate tracking of not rounded signal frequency by tri- kinds of algorithms of MC, PHD and RPHD.
In order to achieve the above technical purposes, the technical scheme is that：
A kind of adaptive frequency estimator method of non-equilibrium electric system, includes the following steps：
(1) three-phase voltage signal of non-equilibrium electric system is indicated using not rounded signal；
(2) using improved modified covariance method algorithm, Pisarenko Harmonic Decompositions algorithm or improved Pisarenko
Harmonic Decomposition algorithm carries out adaptive frequency estimator in conjunction with Least Square Recurrence to the not rounded signal in step (1).
Further, in step (1), the not rounded signal is as follows：
In above formula, v (n) is the not rounded signal of the three-phase voltage signal of non-equilibrium electric system, and n indicates n-th of sampled point,
ω0For the frequency of unknown signaling, φ is the phase of unknown signaling, and j is imaginary unit, Va、VbAnd VcIt is the amplitude of each phase voltage；
Establish not rounded signal frequency estimation model：
X (n)=v (n)+q (n)
In above formula, x (n) is to receive signal, and q (n) is noise signal.
Further, in step (2), using improved modified covariance method algorithm combination Least Square Recurrence, to not rounded
The process that signal carries out Frequency Estimation is as follows：
Wherein,
In above formula,For the Frequency Estimation obtained using improved modified covariance method algorithm, e (n) is prediction error letter
Number, e (n)=x (n) -2cos (ω0) x (n-1)+x (n-2), k is sampling number；
Using Least Square Recurrence Ak、Bk, adaptive correction Frequency Estimation
Ak=λ Ak-1+x(k-1)[x(k-2)+x(k)]
Bk=λ Bk-1+x2(k-1)
In above formula, λ is the forgetting factor of frequency tracking, 0 ＜ λ ＜ 1.
Further, in step (2), using Pisarenko Harmonic Decomposition algorithm combination Least Square Recurrences, to not rounded
The process that signal carries out Frequency Estimation is as follows：
Wherein,
In above formula,For the Frequency Estimation obtained using Pisarenko Harmonic Decomposition algorithms, ri,kFor sample covariance, k
For sampling number；
Using Least Square Recurrence r1,k、r2,k, adaptive correction Frequency Estimation
In above formula, λ is the forgetting factor of frequency tracking, 0 ＜ λ ＜ 1.
Further, in step (2), using improved Pisarenko Harmonic Decompositions algorithm combination Least Square Recurrence,
The process that Frequency Estimation is carried out to not rounded signal is as follows：
Wherein,
In above formula,For the Frequency Estimation obtained using improved Pisarenko Harmonic Decompositions algorithm, k is sampled point
Number；
Using Least Square Recurrence Ck、Ak, adaptive correction Frequency Estimation
Ck=λ Ck-1+x2(k-3)-2x2(k-2)+x2(k-1)+2x(k-3)x(k-1)
Ak=λ Ak-1+x(k-1)[x(k-2)+x(k)]
In above formula, λ is the forgetting factor of frequency tracking, 0 ＜ λ ＜ 1.
The advantageous effect brought using above-mentioned technical proposal：
The non-equilibrium electric voltage frequency algorithm for estimating of traditional Three-phase Power Systems is difficult with, the present invention because calculation amount is high
The method for devising three kinds of low calculation amounts based on adaptive least square recursion, be respectively improved modified covariance method algorithm,
Pisarenko Harmonic Decompositions algorithm and improvement Pisarenko Harmonic Decomposition algorithms, can inhibit the interference of noise and harmonic wave to obtain
Accurate Frequency Estimation, and adaptively track frequency changes.
Description of the drawings
Fig. 1 is the method for the present invention flow chart；
Fig. 2 is the frequency tracking trajectory diagram of three kinds of frequency estimation algorithms when signal-to-noise ratio is equal to 10dB in embodiment；
Fig. 3 is the mean square error comparison diagram of three kinds of frequency estimation algorithms when signal-to-noise ratio is equal to 10dB in embodiment；
Fig. 4 is the frequency tracking trajectory diagram of three kinds of frequency estimation algorithms when signal-to-noise ratio is equal to 0dB in embodiment；
Fig. 5 is the mean square error comparison diagram of three kinds of frequency estimation algorithms when signal-to-noise ratio is equal to 0dB in embodiment.
Specific implementation mode
Below with reference to attached drawing, technical scheme of the present invention is described in detail.
The present invention devises a kind of adaptive frequency estimator method of non-equilibrium electric system, as shown in Figure 1.
First, the signal model of uneven three-phase electrical power system is constructed
The three-phase voltage of electric system can be indicated with following discrete-time version under noise-free environment：
va(n)=Vacos(ΩnΔT+φ)
Wherein, Va, VbAnd VcIt is the amplitude of each phase voltage, Δ T=1/fsFor sampling period, fsFor sample frequency, φ is first
Phase, the π of Ω=2 f0For angular frequency, f0For system frequency.
The complex voltage of system is constructed with not rounded signal v (n)：
Wherein, ωO=Ω Δ T and φ ∈ [0,2 π) respectively indicate unknown signaling frequency and phase.
1, modified covariance method algorithm (MC methods)
The model of not rounded signal frequency estimation：
X (n)=v (n)+q (n) (4)
Noise q (n) is the white process of zero-mean of unknown parameter.The present invention will from receive estimation signal in signal x (n) when
Frequency.Linear prediction method has used the simple recursion of linear signal：
V (n)=2cos (ωO)v(n-1)-v(n-2) (5)
Following prediction error functions can be generated from (5) formula：
E (n)=x (n) -2cos (γ) x (n-1)+x (n-2) (6)
Wherein γ is parameter to be asked.The thinking of MC methods is to enable the quadratic sum of all moment e (n) minimum.Its corresponding frequency
Estimation is usedIt indicates：
Wherein
K indicates number of samples.Calculate A to sample-by-samplekAnd BkAdaptively to realize MC methods：
Ak=λ Ak-1+x(k-1)[x(k-2)+x(k)] (10)
Bk=λ Bk-1+x2(k-1) (11)
Wherein 0 ＜ λ ＜ 1 are the forgetting factor tracked for parameter.Obviously, as λ=1, recursive equation (8) and (9) will
It is identical respectively with batch processing formula (10) with (11).
2, Pisarenko Harmonic Decompositions method (PHD methods)
Pisarenko uses the feature structure of covariance matrix in Frequency Estimation for the first time.The PHD estimations of not rounded signal exist
Sample covariance uses (3) formula in measuring, and using unit norm constraint to provide unbiased Frequency Estimation：
Wherein sample covariance r1,kAnd r2,kIt is defined as：
The derivation of adaptive PHD methods is similar to MC algorithms.{ r is used firsti,k-1Represent { ri,k, then with forget because
Son is multiplied by the former, finallyIt is constantly corrected in iteration：
Each iteration needs to calculate 7 sub-additions, 16 multiplication, 3 divisions, 1 evolution and 1 inverse cosine function operation.
It should be noted that many RLS algorithms are for estimating multiple sinusoidal signal frequencies, but the adaptive algorithm that this patent proposes
It is simpler, it is only applicable to not rounded signal.
3, Pisarenko Harmonic Decompositions method (RPHD methods) is improved
Similar with PHD methods, RPHD methods are under another similar constraint so that the quadratic sum of e (n) is minimum, to obtain
Unbiased Frequency Estimation.Although there is different, PHD in the method that final algorithm only merges signal sampling point at the beginning and end of calculating
It is with the main distinction of RPHD, the former is related to the covariance of sample, and the latter directly acts on data record.WithIt indicates
Go out RPHD Frequency Estimations：
Wherein
AkIt is defined in (8) formula.In adaptive RPHD methods, AkIt is updated according to (10) formula, and CkWith such as similarly hereinafter
The mode of sample is iterated adaptively：
Ck=λ Ck-1+x2(k-3)-2x2(k-2)+x2(k-1)+2x(k-3)x(k-1) (18)
The frequency of not rounded signal can be estimated based on high order linear prediction error functions simultaneously.The line of the not rounded signal of 2k ranks
Property prediction property show：
S (n)=2cos (k ω) s (n-k)-s (n-2k) (19)
The RPHD methods based on high order linear prediction error functions can be obtained by similar iteration self-adapting update.
Using Computer Simulation, compare under white Gaussian noise environment, the adaptive realization pair of MC, PHD and RPHD method
In the performance of not rounded signal frequency tracking.Setting every time in experiment φ be one [0,2 π) equally distributed constant on section.
By controlling noise variance, we produce compared with high s/n ratio and medium SNR environment and study.λ in all methods
It is disposed as 0.95.All displaying results are all the average value of 1000 test results herein.
Fig. 2 is illustrated in signal-to-noise ratio 10dB, to the frequency tracking track of a frequency hopped signals.Repeatedly at first 200 times
Actual frequency is 1.0 in generation, and frequency jumps to 2.0 immediately later.It can be seen from the figure that the study of PHD and RPHD methods is bent
Line is almost the same, and in the about the 20th time and the 300th iteration, it (is 1.0 Hes respectively that their Frequency Estimations, which converge to actual frequency,
2.0).Moreover, MC algorithms also have similar convergence rate, but its Frequency Estimation converges to 1.05 and 1.95, and there are frequency shift (FS)s.
Fig. 3 shows the frequency mean square error (mean square frequency error, MSFE) of each algorithm.It can be found that RPHD
Algorithm all has minimum MSFE on both frequencies, and improves 2-3dB than PHD method performances.Further, since frequency is inclined
It moves, the MSFE of MC algorithms is apparently higher than other algorithms.
Emulation has also been made in the environment of signal-to-noise ratio 0dB, as a result shows in figures 4 and 5.It can be found that PHD and RPHD
The track of the frequency tracking of algorithm is closely similar, and does not have frequency deviation.But the Frequency Estimation result of MC algorithms is 1.3 and 1.8 (all
Have frequency deviation), which results in sizable MSFE.
Embodiment is merely illustrative of the invention's technical idea, and cannot limit protection scope of the present invention with this, it is every according to
Technological thought proposed by the present invention, any change done on the basis of technical solution, each falls within the scope of the present invention.
Claims (5)
1. a kind of adaptive frequency estimator method of non-equilibrium electric system, which is characterized in that include the following steps：
(1) three-phase voltage signal of non-equilibrium electric system is indicated using not rounded signal；
(2) using improved modified covariance method algorithm, Pisarenko Harmonic Decompositions algorithm or improved Pisarenko harmonic waves
Decomposition algorithm carries out adaptive frequency estimator in conjunction with Least Square Recurrence to the not rounded signal in step (1).
2. the adaptive frequency estimator method of non-equilibrium electric system according to claim 1, which is characterized in that in step
(1) in, the not rounded signal is as follows：
In above formula, v (n) is the not rounded signal of the three-phase voltage signal of non-equilibrium electric system, and n indicates n-th of sampled point, ω0For
The frequency of unknown signaling, φ are the phase of unknown signaling, and j is imaginary unit, Va、VbAnd VcIt is the amplitude of each phase voltage；
Establish not rounded signal frequency estimation model：
X (n)=v (n)+q (n)
In above formula, x (n) is to receive signal, and q (n) is noise signal.
3. the adaptive frequency estimator method of non-equilibrium electric system according to claim 2, which is characterized in that in step
(2) in, using improved modified covariance method algorithm combination Least Square Recurrence, the process of Frequency Estimation is carried out such as to not rounded signal
Under：
Wherein,
In above formula,For the Frequency Estimation obtained using improved modified covariance method algorithm, e (n) is prediction error functions, e (n)
=x (n) -2cos (ω0) x (n-1)+x (n-2), k is sampling number；
Using Least Square Recurrence Ak、Bk, adaptive correction Frequency Estimation
Ak=λ Ak-1+x(k-1)[x(k-2)+x(k)]
Bk=λ Bk-1+x2(k-1)
In above formula, λ is the forgetting factor of frequency tracking, 0 ＜ λ ＜ 1.
4. the adaptive frequency estimator method of non-equilibrium electric system according to claim 2, which is characterized in that in step
(2) in, using Pisarenko Harmonic Decomposition algorithm combination Least Square Recurrences, the process of Frequency Estimation is carried out to not rounded signal
It is as follows：
Wherein,
In above formula,For the Frequency Estimation obtained using Pisarenko Harmonic Decomposition algorithms, ri,kFor sample covariance, k is to adopt
Number of samples；
Using Least Square Recurrence r1,k、r2,k, adaptive correction Frequency Estimation
In above formula, λ is the forgetting factor of frequency tracking, 0 ＜ λ ＜ 1.
5. the adaptive frequency estimator method of non-equilibrium electric system according to claim 2, which is characterized in that in step
(2) in, using improved Pisarenko Harmonic Decompositions algorithm combination Least Square Recurrence, Frequency Estimation is carried out to not rounded signal
Process it is as follows：
Wherein,
In above formula,For the Frequency Estimation obtained using improved Pisarenko Harmonic Decompositions algorithm, k is sampling number；
Using Least Square Recurrence Ck、Ak, adaptive correction Frequency Estimation
Ck=λ Ck-1+x2(k-3)-2x2(k-2)+x2(k-1)+2x(k-3)x(k-1)
Ak=λ Ak-1+x(k-1)[x(k-2)+x(k)]
In above formula, λ is the forgetting factor of frequency tracking, 0 ＜ λ ＜ 1.
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| CN103983847A (en) * | 2014-06-12 | 2014-08-13 | 福州大学 | Self-adaptive frequency tracking measurement method based on RLS (Recursive Least Squares) in synchronized phasor measurement |
| CN106680583A (en) * | 2016-12-27 | 2017-05-17 | 东南大学 | Method for frequency estimation of non-equilibrium power system |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103983847A (en) * | 2014-06-12 | 2014-08-13 | 福州大学 | Self-adaptive frequency tracking measurement method based on RLS (Recursive Least Squares) in synchronized phasor measurement |
| CN106680583A (en) * | 2016-12-27 | 2017-05-17 | 东南大学 | Method for frequency estimation of non-equilibrium power system |
Non-Patent Citations (1)
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| 张贵生: "基于多相滤波器组的频谱感知技术的研究", 《中国优秀硕士学位论文全文数据库 信息科技辑》 * |
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