CN106405203A - Least square method-based single phase voltage drop detection method - Google Patents

Abstract

The invention relates to a least square method-based single phase voltage drop detection method. A periodic voltage signal comprising all harmonic waves is expressed as a Fourier series in a form of a trigonometric function, a voltage model is built and discretized, and then the voltage model is expressed in a matrix form; according to a least square principle, via continuous reduction of a sum of the squares of errors that are obtained after the voltage model is subtracted from actual voltage sampling values, all component parameters of the voltage model are corrected, and a voltage model that conforms with practical conditions is obtained; the least square principle is used again for detecting difference between the a real time sampling values of the voltage signals and the built model, parameter information of corresponding fundamental waves and all the harmonic waves is obtained via a covariance matrix, an obtained voltage fundamental wave amplitude value is compared with a set voltage drop compensation valve value, and that a voltage drop occurs is determined when the fundamental wave amplitude value is lower than the voltage drop compensation valve value. The least square method-based single phase voltage drop detection method is small in steady state error and high in sensitivity, and the voltage drop can be rapidly detected.

Description

Detection method is fallen based on the single-phase voltage of method of least square

Technical field

The invention belongs to POWER SYSTEM STATE monitoring field, more particularly, to a kind of fallen based on the single-phase voltage of method of least square Fall detection method.

Background technology

Dynamic electric voltage recovery device (Dynamic Voltage Restorer, DVR) is that one kind is used for ensureing that sensitive load supplies The stable effective series compensation device of piezoelectric voltage, can be to injection amplitude and the phase of connecting between system and load within the Millisecond time The adjustable voltage in position, offset voltage temporarily drops, thus ensure the voltage of sensitive load when by system voltage disturbance still in can In the range of acceptance.

In order to meet the requirement of real-time of detection, common three-phase sag detection method has dq conversion, α β conversion etc. to DVR, Although above-mentioned algorithm is simple, the speed influence from harmonic of detection is big.And single-phase detection method has based on Fourier transform Detection method, consider detection method etc. of phase hit, these methods also all cannot solve to be increased by the bandwidth that harmonic wave causes well, The problems such as detection time extends.

Content of the invention

It is an object of the invention to provide a kind of detection side of the quick detection grid voltage sags in the presence of solution harmonic wave Method, the harmonic content being related in system detects and falls quick detection.

The technical scheme realizing the object of the invention is：A kind of detection method is fallen based on the single-phase voltage of method of least square, Comprise the following steps：

Step 1, the periodic voltage signal containing each harmonic is expressed as the Fourier space of trigonometric function form, sets up Voltage model；

Step 2, by the voltage model obtaining in step 1 discretization, and is indicated with matrix form；

Step 3, according to the principle of least square, by constantly reducing the voltage-mode that virtual voltage sampled value is set up with step 2 Type subtracts each other the quadratic sum of the error obtaining, and revises each component parameters in voltage model, obtains the voltage model tallying with the actual situation；

Step 4, reuses principle of least square method and the real-time sampling value of voltage signal is entered with the difference setting up model Row detection, obtains the parameter information of corresponding fundamental wave and each harmonic, by the voltage fundamental obtaining amplitude using covariance matrix Compensate threshold values with the Voltage Drop of setting to be compared, be considered as falling when fundamental voltage amplitude is less than when Voltage Drop compensates threshold values Fall.

Compared with prior art, the remarkable advantage of the present invention is：

(1) present invention decreases harmonic-model and the difference of actual electric network voltage waveform, divided by the harmonic wave based on FFT Analysis, model parameter is modified, and obtains the model parameter of optimum；

(2) present invention, using the model parameter after optimizing, carries out drop-off voltage detection, steady-state error is less, and sensitivity is high, Voltage Drop can be quickly detected.

Brief description

Fig. 1 falls detection method flow chart for the present invention's based on the single-phase voltage of method of least square.

Fig. 2 (a) is fundamental detecting oscillogram during Voltage Drop 20%.

Fig. 2 (b) is triple-frequency harmonics detection waveform figure during Voltage Drop 20%.

Fig. 2 (c) is quintuple harmonics detection waveform figure during Voltage Drop 20%.

Fig. 2 (d) is the seventh harmonic detection waveform figure during Voltage Drop 20%.

Fig. 3 (a) is fundamental detecting oscillogram during Voltage Drop 60%.

Fig. 3 (b) is triple-frequency harmonics detection waveform figure during Voltage Drop 60%.

Fig. 3 (c) is quintuple harmonics detection waveform figure during Voltage Drop 60%.

Fig. 3 (d) is the seventh harmonic detection waveform figure during Voltage Drop 60%.

Specific embodiment

In conjunction with Fig. 1, a kind of method for detecting voltage drop based on least-squares algorithm of the present invention, comprise the following steps：

Step 1, the periodic voltage signal containing each harmonic is expressed as the Fourier space of trigonometric function form, sets up Voltage model：

Wherein, u (t) is periodic voltage signal, and the cycle is T₁, fundamental wave angular frequencyU_n,ω_n,Respectively single-phase The amplitude of corresponding fundamental wave and each harmonic component, angular frequency and initial phase angle in line voltage,N=1,2, ... N, N are highest overtone order；

Step 2, by the voltage model obtaining in step 1 discretization, and is indicated with matrix form：

u(t_i)=H (t_i)x(t_i)

H(t_i)=[cos ω₁t_i-sinω₁t_i…cosω_Nt_i-sinω_Nt_i] (2)

Wherein, u (t_i) represent discrete after voltage signal, H (t_i) and x (t_i) for the expansion matrix on the right of equation in (1) formula Expression-form；

Step 3, according to the principle of least square, by constantly reducing the voltage-mode that virtual voltage sampled value is set up with step 2 Type subtracts each other the quadratic sum of the error obtaining, and revises each component parameters in voltage model, obtains the voltage model tallying with the actual situation； It is specially：

Step 3-1, sampled data is divided into two groups of A (n) and B (n), length is respectively j₁And j-j₁, wherein j is hits According to total length, and j₁＞ j-j₁；

Step 3-2, the quadratic sum of the error of calculating A (n)：

Wherein, f is forgetting factor, f ∈ (0,1), X (t_i) it is x (t_i) estimated value, to E_AMinimized, obtained corresponding Estimated value X (t_i)；

Step 3-3, the X (t that step 3-2 is obtained_i) bring into group B (n) verified, corresponding error sum of squares is：

Define error threshold ε₁If, E_B≥ε₁Then estimated value error is big, readjusts overtone order N and j₁, then repeat to walk Rapid 3-2 and step 3-3, if E_B＜ ε₁, then estimated value is as the parameter of system voltage model；

Step 4, reuses principle of least square method and the real-time sampling value of voltage signal is entered with the difference setting up model Row detection, obtains the parameter information of corresponding fundamental wave and each harmonic, by the voltage fundamental obtaining amplitude using covariance matrix Compensate threshold values with the Voltage Drop of setting to be compared, be considered as falling when fundamental voltage amplitude is less than when Voltage Drop compensates threshold values Fall；It is specially：

Estimated value X (the t being obtained according to step 3_i), method of least square algorithm expression formula is：

Wherein, H_n(t_i)=[cos ω_nt_i-sinω_nt_i],X_n (t_i) it is state vector x_n(t_i) estimated value；P_n(t_i-1) be the i-th -1 time iteration two-dimentional covariance matrix, initial value is p_1...nI, p_1...n=(p₁, p₁, p₂, p₂..., p_n, p_n) it is initializaing variable, I is unit matrix；r_n(t_i) and k_n(t_i) it is a young waiter in a wineshop or an inn The intermediate variable of multiplication formula；

The fundamental voltage amplitude of single-phase mains voltage is：

Assuming that Voltage Drop compensates threshold values is U_sagIf, U_{amp_1}＞ U_sagThen show to fall, if U_{amp_1}≤U_sagThen Show to fall；

Error e (the t of method of least square_i) be：

e(t_i)=u (t_i)-H(t_i)X(t_i) (7)

Setting threshold epsilon₂, as error e (t_i) it is more than threshold epsilon₂When, judge that current electric grid voltage occurs temporarily dropping process, will enter State to be compensated, simultaneously by covariance matrix P_n(t_i-1) reset to initial value；As error e (t_i) it is less than or equal to threshold epsilon₂When, then Judge that line voltage, within normal range, does not compensate, covariance matrix need not be reset；

Half primitive period time delay is set, when error e (t is detected_i) it is more than threshold epsilon₂When reset covariance, simultaneously enter Delay procedure, shielding covariance reset terminates could reset covariance again until time delay.

With reference to specific embodiment, the invention will be further described.

Embodiment

Harmonic wave in industrial electrical network is typically various rectifying installations and causes, and such overtone order is odd number, and with Number of times is higher, and harmonic amplitude is less.If therefore by the harmonic detecting based on method of least square, obtaining humorous in real system Wave component, the harmonic wave recording in system is 3,5,7 times, and virtual value is respectively 20V, 10V, 5V.The equation containing harmonic voltage set up As follows：

In order to verify the accuracy of detection and rapidity in the case of difference is fallen, separately design and fallen 20% and 60% Experiment.

Fig. 2 is falling with tester simulating grid voltage 20%, that is, drop to original 80%, and solid line is sampling ripple Shape, dotted line is detection waveform, and Fig. 2 (a) is fundamental wave amount, and Fig. 2 (b) is triple-frequency harmonics amount, and Fig. 2 (c) is quintuple harmonics amount, Fig. 2 (d) For the seventh harmonic amount；In figure, label value represents transverse and longitudinal coordinate value, and abscissa represents sampled point, and vertical coordinate represents amplitude.

Fig. 3 is falling with tester simulating grid voltage 60%, that is, drop to original 40%, and solid line is sampling ripple Shape, dotted line is detection waveform, and Fig. 3 (a) is fundamental wave amount, and Fig. 3 (b) is triple-frequency harmonics amount, and Fig. 3 (c) is quintuple harmonics amount, Fig. 3 (d) For the seventh harmonic amount；In figure, label value represents transverse and longitudinal coordinate value, and abscissa represents sampled point, and vertical coordinate represents amplitude.

Above oscillogram is obtained using Matlab emulation, and the sampling interval of sampled point is 50us.Permissible from Fig. 2 and Fig. 3 Find out, accuracy of detection is 5-10ms in 0.1V, detection speed, the speed impact falling depth to detection is little.

Claims (5)

1. a kind of detection method is fallen it is characterised in that comprising the following steps based on the single-phase voltage of method of least square：

Step 1, the periodic voltage signal containing each harmonic is expressed as the Fourier space of trigonometric function form, sets up voltage Model；

Step 2, by the voltage model obtaining in step 1 discretization, and is indicated with matrix form；

Step 3, according to the principle of least square, by constantly reducing the voltage model phase that virtual voltage sampled value is set up with step 2 Subtract the quadratic sum of the error obtaining, revise each component parameters in voltage model, obtain the voltage model tallying with the actual situation；

Step 4, reuses principle of least square method and the real-time sampling value of voltage signal is examined with the difference setting up model Survey, obtain the parameter information of corresponding fundamental wave and each harmonic using covariance matrix, by the voltage fundamental obtaining amplitude with set The Voltage Drop put compensates threshold values and is compared, and is considered as falling when fundamental voltage amplitude is less than when Voltage Drop compensates threshold values.

2. according to claim 1 detection method is fallen based on the single-phase voltage of method of least square it is characterised in that step In 1, the periodic voltage signal containing each harmonic is expressed as the Fourier space of trigonometric function form：

Wherein, u (t) is periodic voltage signal, and the cycle is T₁, fundamental wave angular frequencyU_n,ω_n,It is respectively single-phase electrical network The amplitude of corresponding fundamental wave and each harmonic component, angular frequency and initial phase angle in voltage,N=1,2 ... N, N For highest overtone order.

3. according to claim 2 detection method is fallen based on the single-phase voltage of method of least square it is characterised in that step 2 are specially：Function discretization in formula (1) is changed into discrete form, is represented with matrix form：

Wherein, u (t_i) represent discrete after voltage signal, H (t_i) and x (t_i) for the expansion expression matrix on the right of equation in (1) formula Form.

4. according to claim 3 detection method is fallen based on the single-phase voltage of method of least square it is characterised in that step 3 specifically include following steps：

Step 3-1, sampled data is divided into two groups of A (n) and B (n), length is respectively j₁And j-j₁, wherein j is that sampled data is total Length, and j₁＞ j-j₁；

Step 3-2, the quadratic sum of the error of calculating A (n)：

$E_A=\underset{i=0}{\overset{j_1}{\Σ}}{f}^{j_1-i}{\left(u\right(t_i)-H(t_i\left)X\right(t_i\left)\right)}^2---\left(3\right)$

Wherein, f is forgetting factor, f ∈ (0,1), X (t_i) it is x (t_i) estimated value, to E_AMinimized, estimated accordingly Evaluation X (t_i)；

Step 3-3, the X (t that step 3-2 is obtained_i) bring into group B (n) verified, corresponding error sum of squares is：

$E_B=\underset{i=j_1+1}{\overset{j}{\Σ}}{f}^{j-i}{\left(u\right(t_i)-H(t_i\left)X\right(t_i\left)\right)}^2---\left(4\right)$

Define error threshold ε₁If, E_B≥ε₁Then estimated value error is big, readjusts overtone order N and j₁, then repeat step 3-2 With step 3-3, if E_B＜ ε₁, then estimated value is as the parameter of system voltage model.

5. according to claim 4 detection method is fallen based on the single-phase voltage of method of least square it is characterised in that step 4 are specially：

Estimated value X (the t being obtained according to step 3_i), method of least square algorithm expression formula is：

$\begin{array}{c}{r}_n\left(t_i\right)=f+H_n\left(t_i\right)P_n\left(t_{i-1}\right)H_n^T\left(t_i\right)\\ k_n\left(t_i\right)=P_n\left(t_{i-1}\right)H_n^T\left(t_i\right)r_n^{-1}\left(t_i\right)\\ P_n\left(t_i\right)=f^{-1}\left(P_n\right(t_{i-1})-k_n\left(t_i\right)H_n\left(t_i\right)P_n\left(t_{i-1}\right))\\ X_n\left(t_i\right)=X_n\left(t_{i-1}\right)+k_n\left(t_i\right)\left(u\right(t_i)-H_n\left(t_i\right)X_n\left(t_{i-1}\right))\end{array}---\left(5\right)$

Wherein, H_n(t_i)=[cos ω_nt_i-sinω_nt_i],X_n(t_i) be State vector x_n(t_i) estimated value；P_n(t_i-1) be the i-th -1 time iteration two-dimentional covariance matrix, initial value be p_1...nI, p_1...n=(p₁, p₁, p₂, p₂..., p_n, p_n) it is initializaing variable, I is unit matrix；r_n(t_i) and k_n(t_i) calculate for method of least square The intermediate variable of formula；

The fundamental voltage amplitude of single-phase mains voltage is：

Assuming that Voltage Drop compensates threshold values is U_sagIf, U_{amp_1}＞ U_sagThen show to fall, if U_{amp_1}≤U_sagThen show to send out Life is fallen；

Error e (the t of method of least square_i) be：

e(t_i)=u (t_i)-H(t_i)X(t_i) (7)

Setting threshold epsilon₂, when error is more than threshold epsilon₂When, judge that current electric grid voltage occurs temporarily dropping process, shape to be compensated will be entered State, simultaneously by covariance matrix P_n(t_i-1) reset to initial value；When error is less than or equal to threshold epsilon₂When, then judge that line voltage exists In normal range, do not compensate, covariance matrix need not be reset；

Half primitive period time delay is set, when error e (t is detected_i) it is more than threshold epsilon₂When reset covariance, simultaneously enter time delay Program, shielding covariance reset terminates could reset covariance again until time delay.