CN102353839A - 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 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, the Harmonious Waves in Power Systems problem 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 through the 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 the fundamental frequency of the improvement fourier transform algorithm picked up signal of windowed interpolation earlier, adopt the training of Adaline neuron to obtain amplitude, the phase angle (FFT-Adaline) of each harmonic more accurately then; This algorithm can obtain frequency analysis result comparatively accurately, but also has following problem:

(1) signal is added Hanning window; Carry out discrete Fourier transform (DFT) then; Proofread and correct the amplitude of back acquisition each harmonic and algorithm (abbreviate as and add Hanning window interpolation harmonic analysis method) the calculating gained frequency of frequency and have error, but the Adaline neuron is not adjusted to obtain value more accurately frequency;

(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 amplitude, phase place and the signal frequency that Hanning window interpolation harmonic analysis method is used to obtain each harmonic will be added; They are used for frequency analysis as network initial value, the improvement linear neuron (FFT-ANN) that adds momentum term BP (backpropagation) algorithm training with variable step then; Can effectively detect non-integer harmonics, but training algorithm is subjected to the influence of step-length and momentum term bigger.As a rule Zui You 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

Deficiencies such as existing frequency analysis precision is not enough to 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:, obtain the amplitude of the sinusoidal component of each harmonic, the amplitude and the angular frequency of cosine component to the signal correction of carrying out obtaining after the discrete Fourier transform (DFT);

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

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

Said system signal is voltage signal or current signal.

Said voltage signal is obtained by optical fibre voltage sensor.

Said current signal is obtained by fibre optic current sensor.

The algorithm of said appointment is the RPROP algorithm.

Said neural network contains excitation function and variable element.

Said excitation function is a sine and cosine functions.

Said variable element is the 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 humorous wave 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 frequency analysis result comparatively accurately, this value can effectively be reduced the 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 rapid speed.

3. can analyze the mark subharmonic

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

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 scope of the present invention and application thereof.

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

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) gained result is X (n), then add signal discrete Fourier transform gained result 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 a fundamental frequency;

K is an integer;

Δ k is a decimal;

Δ f is a 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 humorous wave amplitude after proofreading and correct;

B ' _kBe the humorous wave 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 an imaginary unit;

Angle () is used to obtain 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 each harmonic amplitude, phase place and frequency values comparatively accurately.

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

The power system signal that contains the mark subharmonic can be represented 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 a 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 a discrete point.Its network structure is shown in accompanying drawing 1.

Network output:

$X\left(i\right)={\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA0000076434040000011.png"\; state="\{\{state\}\}">w</figure-callout>}}_1+\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_{3n}\sin \left(w_{3n-1}T\left(i\right)\right)+w_{3n+1}\cos \left(w_{3n-1}T\left(i\right)\right))---\left(11\right)$

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:

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

Think during less than setting value when the error of network and can adopt network convergence to become learning rate and the BP algorithm training network that adds momentum term, its speed and constringency performance await further raising, and the present invention adopts the RPROP algorithm training.

3.RPROP algorithm

For improving speed of convergence, the present invention uses RPROP algorithm training multilayer feedforward neural network, and this network is called the RPROP neural network.If n is an iterations; Δ _i(n) be the amplitude of network variable element adjustment amount; The matrix that W forms for the network variable element, 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 following:

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 influence 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

Influence still keeps relatively large value, and the possibility that converges on global minimum point so network hop goes out local minimum point heightens.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.The algorithm uses a heuristic training mode, using only

symbolic information to adjust the variable parameters, to avoid the interference of secondary information, can accelerate 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, as 0.01, the normal conditions lower network also can be adjusted to optimal value apace.The height adaptive of network parameter has avoided the user to get the process of optimal value through 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 the 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 does

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 does $S\left(t\right)=\underset{k=1}{\overset{3}{\mathrm{\&Sigma;}}}{A}_k\sin (2\mathrm{\&pi;}{f}_{k}t+{\mathrm{\&theta;}}_k).$

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 like table 2, shown in 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 is meant half of error sum of squares in the table 2,3.

Can be known that by table 1 it is not very little adding Hanning window interpolation harmonic analysis method error, phase differential can reach-1.76 degree, obviously greater than the error behind table 2, the 3 process neural metwork trainings.Can find out that from table 2 two kinds of algorithms are respectively through error convergences are in 0.1 after 5 and 89 training, 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, the neural network of the present invention's proposition has very big superiority on real-time.Can find out that 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, convergence not yet, 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 through parameter constantly being attempted selecting optimal value, training then to have obtained above result and improve linear neuron, it is thus clear that 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 ^-4Degree, and maximum error is-262.09 degree when sampling time length is 0.05 second, it is thus clear that 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 preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and any technician who is familiar with the present technique field is 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 (8)

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

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

Step 4: after training finishes, according to the 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 said 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 said 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 said 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, the algorithm that it is characterized in that said appointment is the RPROP algorithm.

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

7. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 1 is characterized in that said excitation function is a sine and cosine functions.

8. the harmonic analysis in power system method based on multilayer feedforward neural network according to claim 1 is characterized in that said variable element is the amplitude and the angular frequency of harmonic wave.

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