CN102353839B - Electric power system harmonics analysis method based on multilayered feedforward neural network - Google Patents

Abstract

The invention discloses an electric power system harmonics analysis method based on a multilayered feedforward neural network in the electric power system signal testing technology field. In the invention, an electric power system voltage or current signal is obtained through an optical fiber voltage sensor or an optical fiber current sensor, single hidden layer of the multilayered feedforward neural network is established; an excitation function is a sine and a cosine function and a variable parameter is a harmonic amplitude and an angular frequency; a Hanning window is performed to an obtained electric power system signal; and then discrete fourier transform (DFT) is performed; the sine and cosine component amplitude of each corrected subharmonic and the harmonic angular frequency are taken as an initial weight value of the neural network; an RPROP algorithm training is employed on the basis of the initial weight value; the amplitude and the frequency of the each subharmonic can be acquired according to the trained weight value. By using the method of the invention, accuracy of a calculating result is high and a speed is fast. The harmonic wave analysis accuracy at short sampling time can be greatly raised. A principle is simple and the method is easy to be realized.

Description

Harmonic analysis in power system method based on multilayer feedforward neural network

Technical field

The invention belongs to the power system signal technical field of measurement and test, relate in particular to a kind of harmonic analysis in power system method based on multilayer feedforward neural network.

Background technology

Along with the development of electronic technology, a lot of precise electronic industry have proposed high requirement to the quality of power supply.But along with the use of power electronic devices in the industry is increasing, problem for power system harmonics is on the rise, has had a strong impact on the quality of power supply.The accurate analysis of harmonic wave is the precondition of harmonic wave control.Therefore, frequency analysis is a hot issue of electric system research always.

After accurately obtaining power system voltage and current signal, just very crucial by each harmonic amplitude and the phase place of harmonic analysis method picked up signal.Artificial neural network is used comparatively extensive in harmonic analysis in power system owing to have self study and adaptive ability in recent years.Can adopt first the fundamental frequency of the improvement fourier transform algorithm picked up signal of windowed interpolation, then adopt the training of Adaline neuron to obtain more accurately amplitude, the phase angle (FFT-Adaline) of each harmonic; This algorithm can obtain comparatively accurately frequency analysis result, but also has following problem:

(1) signal is added Hanning window, then carry out discrete Fourier transform (DFT), obtain the amplitude of each harmonic and algorithm (referred to as adding Hanning window interpolation harmonic analysis method) the calculating gained frequency of frequency after proofreading and correct and have error, but the Adaline neuron does not obtain more accurate value to frequency adjustment;

(2) use Widrow-Hoff δ rule convergence speed relatively slow, it is not high to be difficult to reach high precision and real-time.Can will add Hanning window interpolation harmonic analysis method for the amplitude, phase place and the signal frequency that obtain each harmonic, they are used for frequency analysis as network initial value, the improvement linear neuron (FFT-ANN) that then adds momentum term BP (backpropagation) Algorithm for Training with variable step, can effectively detect non-integer harmonics, but training algorithm is subjected to the impact of step-length and momentum term larger.As a rule optimum step-length is relevant with the scale of network structure and sample with momentum term, needs repeatedly to attempt just obtaining than the figure of merit, if step-length and momentum term can not be selected suitable value, then the precision of frequency analysis and speed just are difficult to ensure.

Summary of the invention

The deficiencies such as existing frequency analysis precision is inadequate for mentioning in the above-mentioned background technology, calculating length consuming time the present invention proposes a kind of harmonic analysis in power system method based on multilayer feedforward neural network.

Technical scheme of the present invention is that the harmonic analysis in power system method based on multilayer feedforward neural network is characterized in that said method comprising the steps of:

Step 1: obtain power system signal, it is added Hanning window and carries out discrete Fourier transform (DFT);

Step 2: to the signal correction of carrying out obtaining after the discrete Fourier transform (DFT), obtain the amplitude of the sinusoidal component of each harmonic, amplitude and the angular frequency of cosine component;

Step 3: with the result of step 2 weights as neural network, and with the algorithm of appointment neural network is trained;

Step 4: after training finishes, according to final amplitude and the frequency of weights acquisition each harmonic of network.

Described system signal is voltage signal or current signal.

Described voltage signal is obtained by optical fibre voltage sensor.

Described current signal is obtained by fibre optic current sensor.

The algorithm of described appointment is the RPROP algorithm.

Described neural network contains excitation function and variable element.

Described excitation function is sine and cosine functions.

Described variable element is amplitude and the angular frequency of harmonic wave.

Beneficial effect of the present invention comprises:

1. accuracy is high

The present invention adopts neural metwork training to harmonic amplitude and the angular frequency that tentatively obtains, and has further improved the accuracy of frequency analysis.Therefore, can more accurately obtain frequency, amplitude and the phase place of each harmonic.

2. speed is fast

Add Hanning window interpolation harmonic analysis method, when short signal length, can obtain comparatively accurately frequency analysis result, this value can effectively be reduced number of times and the time of neural metwork training as the initial value of neural network weight.Therefore, the present invention has the characteristics of frequency analysis speed.

3. can analyze fractional harmoni

Because the present invention also trains the angular frequency of each harmonic as the neural network variable element, therefore, it can obtain according to actual conditions frequency, amplitude and the phase place of fractional harmoni.

Description of drawings

The multilayer feedforward neural network structural drawing that accompanying drawing 1 adopts for the present invention;

Accompanying drawing 2 is the process flow diagram of the inventive method.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that following explanation only is exemplary, rather than in order to limit the scope of the invention and to use.

Step of the present invention is: at first obtain power system signal, it is added Hanning window and carries out discrete Fourier transform (DFT); Then the signal correction to carrying out obtaining after the discrete Fourier transform (DFT) obtains the amplitude of the sinusoidal component of each harmonic, amplitude and the angular frequency of cosine component; With the weights of these data as neural network, and with the algorithm of appointment neural network is trained; After training finishes, according to final amplitude and the frequency of weights acquisition each harmonic of network.Be specially:

1. the acquisition of neural network initial weight

The initial weight of neural network is signal each harmonic angular frequency and sinusoidal, cosine component amplitude, and its computation process is as follows.

The Hanning window function that N is ordered is:

$w\left(n\right)=\frac{1}{2}-\frac{1}{2}\cos \left(\frac{2\mathrm{\π}}{N}n\right),n=\mathrm{0,1},L,N-1---\left(1\right)$

Wherein:

The Hanning window function that w (n) is ordered for N.

If the discrete Fourier transform (DFT) DFT of discrete signal x (n) (Discrete Fourier Transform) acquired results is X (n), then add signal discrete Fourier transform acquired results behind the Hanning window:

$X_w\left(n\right)=\frac{1}{2}\left(n\right)-\frac{1}{4}X(n-1)-\frac{1}{4}X(n+1)---\left(2\right)$

Wherein:

X _w(n) for adding the value of signal discrete Fourier transform behind the Hanning window;

X (n) is the value of discrete signal x (n) after discrete Fourier transform (DFT).

Fundamental frequency f:

f＝(k+Δk)Δf (3)

Wherein:

F is fundamental frequency;

K is integer;

Δ k is decimal;

Δ f is signal frequency resolution, Δ f=1/T, and T is the duration of sampling.

Following formula is set up when using Hanning window:

Δ k substitution formula (3) can be tried to achieve the signal fundamental frequency.

The amplitude rectification formula:

B _k＝B′ _k2πΔk(1-Δk ²)/sin(Δkπ) (5)

Wherein:

B _kBe the harmonic amplitude after proofreading and correct;

B ' _kBe the harmonic amplitude before proofreading and correct, B ' _kCalculate according to signal Fourier result.

The phase angle updating formula:

θ _k＝angle(X _w(k)e ^{-jΔk(1-1/N)π}) (6)

Wherein:

θ _kBe the harmonic wave phase angle after proofreading and correct.

J is imaginary unit;

Angle () is used for obtaining the phase angle of plural number.

The sine of k subharmonic, cosine component amplitude and angular frequency are respectively suc as formula shown in (7)～(9)

B _k1＝B _kcos(θ _k) (7)

B _k2＝B _ksin(θ _k) (8)

ω _k＝2πkf (9)

Wherein:

B _K1Sinusoidal component amplitude for the k subharmonic;

B _K2Cosine component amplitude for the k subharmonic;

ω _kAngular frequency for the k subharmonic.

The calculated amount that use increases when adding Hanning window interpolation harmonic analysis method is less, programming realizes easily, and can obtain comparatively accurately each harmonic amplitude, phase place and frequency values.

2. the multilayer feedforward neural network that is used for frequency analysis

The power system signal that contains fractional harmoni can be expressed as follows:

$s\left(t\right)=A_0+\underset{k=1}{\overset{N}{\mathrm{\Σ}}}(A_{2k-1}\sin \left({\mathrm{\ω}}_{k}t\right)+A_{2k}\cos \left({\mathrm{\ω}}_{k}t\right))---\left(10\right)$

In the formula:

S (t) is power system signal;

A ₀Be DC component;

A _2k-1It is the sinusoidal component amplitude of k (mark) subharmonic;

A _2kIt is the cosine component amplitude of k (mark) subharmonic;

ω _kIt is the angular frequency of k (mark) subharmonic.

If signal s (t) is the discrete S (i) that turns to, time t is discrete to turn to T (i), and neural network is output as X (i), i=1,2 ..., K is discrete point.Its network structure as shown in Figure 1.

Network output:

$X\left(i\right)=w_1+\underset{n=1}{\overset{N}{\mathrm{\Σ}}}(w_{3n}\sin \left(w_{3n-1}T\left(i\right)\right)+w_{3n+1}\cos \left(w_{3n-1}T\left(i\right)\right))---\left(11\right)$

In the formula:

X (i) is the output valve of network output;

w ₁Be DC component;

w _3nIt is the sinusoidal component amplitude of n (mark) subharmonic;

w _3n+1It is the cosine component amplitude of n (mark) subharmonic;

w _3n-1It is the angular frequency of n (mark) subharmonic.

T (i) is the value after the time t discretize.

The error E of network is defined as half of all point tolerance quadratic sums:

$E=\frac{1}{2}\underset{i=1}{\overset{K}{\mathrm{\Σ}}}{(X\left(i\right)-S\left(i\right))}^2---\left(12\right)$

Think during less than setting value when the error of network and can adopt the BP Algorithm for Training network that becomes learning rate and add momentum term by network convergence, its speed and constringency performance await further raising, and the present invention adopts the RPROP Algorithm for Training.

3.RPROP algorithm

For improving speed of convergence, the present invention uses the RPROP Algorithm for Training Multilayer Feedforward Neural Networks, and this network is called the RPROP neural network.If n is iterations; Δ _i(n) be the amplitude of network variable element adjustment amount; W is the matrix that the network variable element forms, w _iBe its i element; E is half of quadratic sum of all sample errors,

Be the single order partial derivative of network variable element to network error; Δ w _i(n) be the adjustment amount of network variable element.Δ _i(n) adjustment formula is as follows:

In the formula: η ⁺Get 1.2; η ^-Get 0.5.

Formula (14) calculates the adjustment amount of variable element:

The variable element of network is adjusted with formula (15):

w _i(n+1)＝w _i(n)+Δw _i(n) (15)

When network is in local minimum point or error curved surface flat region (

Amplitude is very little), the Δ w of improvement linear neuron _iBe subjected to

The impact and reduce, cause network to be difficult for jumping out local minimum point or flat region; The Δ w of RPROP neural network _iBe not subjected to

Impact still keeps relatively large value, and the possibility that converges on global minimum point so network hop goes out local minimum point increases.When network is in dullly when regional, the RPROP algorithm gradually reduces the adjustment amplitude that situation increases variable element according to network error automatically, accelerates network convergence speed.This algorithm has utilized didactic training mode, only utilizes

Symbolic information adjust variable element, avoided the interference of less important information, but the accelerating network convergence.

η in the RPROP algorithm ⁺And η ^-The selection default value gets final product, and network training is for Δ _Ij(0) insensitive, it is initialized as any greater than zero random number, such as 0.01, the normal conditions lower network also can be adjusted to optimal value rapidly.The height adaptive of network parameter has avoided the user to get the process of optimal value by continuous test, is the RPROP algorithm with respect to one of advantage of BP algorithm.

4. the acquisition of each harmonic amplitude, phase place and frequency

Directly obtain amplitude and the angular frequency of k subharmonic sine, cosine component after network training finishes, can obtain amplitude, phase place and the frequency of each harmonic according to them.The amplitude of k subharmonic is

The phase place of k subharmonic is α tan (w _3k/ w _3k+l), the frequency of k subharmonic is w _3k-1/ 2 π.

The experimental verification signal indication is $S\left(t\right)=\underset{k=1}{\overset{3}{\mathrm{\Σ}}}{A}_k\sin (2\mathrm{\π}{f}_{k}t+{\mathrm{\θ}}_k).$

Wherein: A ₁=100; A ₂=3.5; A ₃=5; θ ₁=30 °; θ ₂=135 °; θ ₃=60 °; f ₁=50.2Hz; f ₂=105.42Hz; f ₃=150.6Hz.

Sample frequency is 1kHz, and sampling number is 100, and it is as shown in table 1 to add Hanning window interpolation harmonic analysis method acquisition frequency analysis resultant error.Realize improvement linear neuron (FFT-ANN) and RPROP neural network, be not more than 0.1 and 10 with all point tolerance quadratic sums of signal respectively ^-8As the convergence target.Error and computing time are shown in table 2,3.

Table 1 adds Hanning window interpolation harmonic analysis method error

Two kinds of algorithms relatively during table 2 low accuracy

Two kinds of algorithms relatively during table 3 pinpoint accuracy

Annotate: error refers to half of error sum of squares in the table 2,3.

As shown in Table 1, it is not very little adding Hanning window interpolation harmonic analysis method error, and phase differential can reach-1.76 degree, obviously greater than the error behind table 2, the 3 process neural metwork trainings.As can be seen from Table 2, two kinds of algorithms are respectively through error convergence is in 0.1 after 5 and 89 training, and the frequency analysis result is also comparatively close, and the training time of RPROP neural network is about 1/17 of improvement linear neuron from the time.Therefore, neural network tool on real-time of the present invention's proposition has an enormous advantage.As can be seen from Table 3, the RPROP neural network has just satisfied less than 10 in 96 time error quadratic sums of training ^-8Target, maximum error appears on the phase place, only is 3.51 * 10 ^-4Degree; Improving linear neuron error sum of squares after training 200 times is 2.62 * 10 ^-4, not yet convergence, the error of each component also is greater than the former, and maximum error also appears on the phase place, is-1.95 * 10 ^-2Degree.When even the RPROP arithmetic accuracy is higher, its 58.0 milliseconds consuming time also will be much smaller than improving 125.3 milliseconds of linear neuron.The network parameter of RPROP neural network need not to select, and is by parameter constantly being attempted selecting optimal value and improve linear neuron, and then training has obtained above result, and as seen the former adaptability also is better than the latter.

Because the RPROP algorithm is relatively responsive to initial value, increase along with the minimizing error in sampling time and add Hanning window interpolation harmonic analysis method, algorithm maximum error of the present invention only is 4 * 10 when the sampling time is not less than 0.06 second ^-4As seen degree, and maximum error is-262.09 degree when sampling time length is 0.05 second, algorithm sampling time otherwise less than 0.06 second.

The present invention has more pinpoint accuracy than the improvement fourier transform algorithm of windowed interpolation, neural net method training speed as compared with the past is faster, what is more important has significantly improved short sampling time time-harmonic wave analytical precision, and principle is simple simultaneously, realization is easy.

The above; only for the better embodiment of the present invention, but protection scope of the present invention is not limited to this, anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (7)

1. based on the harmonic analysis in power system method of multilayer feedforward neural network, it is characterized in that said method comprising the steps of:

Step 1: obtain power system signal, it is added Hanning window and carries out discrete Fourier transform (DFT);

Step 2: to the signal correction of carrying out obtaining after the discrete Fourier transform (DFT), obtain the amplitude of the sinusoidal component of each harmonic, amplitude and the angular frequency of cosine component;

Step 3: with the result of step 2 weights as neural network, and with the algorithm of appointment neural network is trained; The algorithm of described appointment is the RPROP algorithm;

Step 4: after training finishes, according to final amplitude and the frequency of weights acquisition each harmonic of network.

2. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 1 is characterized in that described system signal is voltage signal or current signal.

3. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 2 is characterized in that described voltage signal is obtained by optical fibre voltage sensor.

4. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 2 is characterized in that described current signal is obtained by fibre optic current sensor.

5. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 1 is characterized in that described neural network contains excitation function and variable element.

6. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 5 is characterized in that described excitation function is sine and cosine functions.

7. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 5 is characterized in that described variable element is amplitude and the angular frequency of harmonic wave.

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