CN103217562B - Alternating current and direct current voltage detection method and device for inhibiting optical voltage transducer nonlinear characteristic - Google Patents

Abstract

The invention discloses an alternating current and direct current voltage detection method and device for inhibiting an optical voltage transducer nonlinear characteristic. Considering that a closed loop error signal has a nonlinear characteristic and is easily influenced by disturbance of an external environment, an output of a photoelectric detector is pre-processed, square waves of the nonlinear closed loop error signal are modulated, and the frequency of the error signal is migrated to a high frequency region. The error signal is extracted through a band-pass filter in an undistorted mode, and white noise of the output of the photoelectric detector is filtered. An output signal of the band-pass filter is converted into a digital signal and is demodulated into low-pass filter. A system state equation is established, and the stability of the system state equation is controlled, so that the indicial response decay speed of the error signal is recovered to be a zero balance point, specified noise suppression level is met, the influence of the nonlinear characteristic to the closed loop performance of an optical voltage transducer system is inhibited, a dynamic measurement range of direct current voltage and the bandwidth width are widened, and a dynamic response characteristic of the system is improved.

Description

Suppress alterating and direct current pressure detection method and the device of optical voltage transformer nonlinear characteristic

Technical field

The invention belongs to optical voltage transformer technical field, be specifically related to a kind of the alterating and direct current pressure detection method and the pick-up unit that suppress optical voltage transformer nonlinear characteristic.

Background technology

Optical voltage transformer utilizes closed loop detect method and square-wave frequency modulation technology, makes system works in phase zero points, and its advantage is to obtain high sensitivity, good linear and wide dynamic range.

Closed loop optical voltage transformer have employed square-wave frequency modulation and staircase waveform feedback technique, inhibits the impact of optical power fluctuation to a great extent, and expands the dynamic range of system.But system is still a nonlinear system, its non-linear effects optical voltage transformer performance, and optical voltage transformer is subject to the disturbing influence of external environment condition.

Optical voltage transformer schematic diagram of the prior art as shown in Figure 1, optical voltage transformer closed-loop detection circuit comprises light source 1, circulator 2, polarizer 3, phase-modulator 4, protect off-delay optical cable 5, Faraday polarization apparatus 6, BGO crystal 7, photodetector 8 and signal processing circuit 9, described circulator 2 is three port devices, first port is light source 1 entrance, second port connects the input port of polarizer 3, 3rd port connects the input end of photodetector 8, the output connection signal treatment circuit 9 of photodetector 8, signal processing circuit 9 provides modulation voltage for phase-modulator 4.Described polarizer 3 connects phase-modulator 4, and tie point 45 ° of weldings; Be connected by protecting off-delay optical cable 5 between phase-modulator 4 with polarization apparatus 6, BGO crystal 7 end points in described polarization apparatus 6 has reflectance coating 10, in order to reflected light.

By the line polarisation of polarizer 3 through 45 ° of welding angles, be divided into the linearly polarized light that two bundles are orthogonal, the orthogonal polarized light of this two bundle is by integrated phase modulator 4, emergent light postpones 5 via polarization maintaining optical fibre, two-beam enters to inject Faraday polarization apparatus 6, pairwise orthogonal linear polarization pattern rotates 45 °, incide in BGO crystal 7, tested voltage is applied in the light of two polarized orthogonal patterns in the mode of Pockels phase shift, pairwise orthogonal polarized light is by the reflection of reflectance coating, return along incident light path, act on through phase-modulator 4, finally interfere at polarizer 3 place two-beam, the phase place of wherein interfering is the twice of Pockels phase shift.The light of two bundle orthogonal polarization modes is at every turn through nonreciprocal Faraday polarization apparatus 6, all can rotate 45 °, because faraday nonreciprocal in light path collimates the introducing of polarization apparatus, except BGO crystal 7, pairwise orthogonal polarization mode is through identical light path, form accurate reciprocity reflection type optical path, reduce the not enough metrical error caused of defect because of external disturbance and equipment.

The closed-loop error signal of optical voltage transformer is faint nonlinear properties, and is subject to system disturbance impact.Optical voltage transformer is in the practicality of measuring high pressure is measured, and the noise that is non-linear and that exist of its physical device is the principal element causing system performance degradation.

Summary of the invention

The present invention proposes a kind of the alterating and direct current pressure detection method and the pick-up unit that suppress optical voltage transformer nonlinear characteristic, with improve based on Pockels effect optical voltage transformer measure combined-voltage time precision and non-linear rejection ability.

The alterating and direct current pressure detection method of described suppression optical voltage transformer nonlinear characteristic, comprises the steps:

The first step, exports interference light intensity v to photodetector _outt () carries out pre-service, to nonlinear closed loop's error signal carry out square-wave frequency modulation, by the frequency shift of nonlinear closed loop's error signal to high frequency region, to avoid the adverse effect of 1/f noise Middle and low frequency noise; The guarantee of employing bandpass filter is distortionless extracts nonlinear closed loop's error signal and the white noise in the output interference light intensity of the photodetector of filtering simultaneously; F wherein represents frequency;

Second step, by the output signal v of bandpass filter _bft () converts digital signal v to _bf(k), and by one and described digital signal v _bfthe synchronous digital square-wave f of (k) same frequency _b(t) demodulation, the output signal v after demodulation _dcontaining nonlinear closed loop's error signal in (k) composition, but also contains unwanted high-frequency signal simultaneously;

3rd step, wave digital lowpass filter is to the output signal v after demodulation _dk () carries out low-pass filtering, with the output signal v after demodulation described in filtering _dk the HFS of (), improves signal to noise ratio (S/N ratio) simultaneously further; Nonlinear closed loop's error signal in the output signal v (k) of now wave digital lowpass filter is digital signal

4th step, according to the output signal v (k) of wave digital lowpass filter, sets up system state equation;

5th step, stability control is carried out to system state equation, when optical voltage transformer mission nonlinear closed-loop error signal is at (-π, π) in scope, described stability controls to make nonlinear closed loop's error return to zero balancing point with the rate of decay of indicial response, inhibit the non-linear impact on optical voltage transformer system closed-loop characteristic, expand the range of dynamic measurement of DC voltage and the frequency span of ac voltage measurement, improve the dynamic response characteristic of optical voltage transformer system.

The invention has the advantages that:

(1) when measuring combined-voltage, the pass band of bandpass filter of the present invention's design all can ensure distortionlessly to extract nonlinear closed loop's error signal, suppress most white noises simultaneously, improve the signal to noise ratio (S/N ratio) of expected frequency signal.

(2) method of suppression optical voltage transformer nonlinear characteristic provided by the invention is adopted, for optical voltage transformer nonlinear closed loop error signal, its scope is at (-π, time π), optical voltage transformer system can the squelch level of index access stability and regulation.

(3) method of suppression optical voltage transformer nonlinear characteristic provided by the invention is adopted, the combined-voltage measuring accuracy of optical voltage transformer is respectively ± and 0.2% and ± 0.5%, bandwidth reaches 24.5kHz, and maximum step direct current measurement voltage is 19.5kV.The results show system obtains good dynamic property response and high precision, demonstrates the method for suppression nonlinear characteristic and the validity of pick-up unit and correctness that propose in the present invention.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the optical voltage transformer based on Pockels effect;

Fig. 2 is closed-loop detection circuit nonlinear closed loop error signal processing procedure schematic diagram in the present invention;

Fig. 3 is the frequency response measurement result of system;

Fig. 4 is the tested voltage of step response of system is 476.07V;

Fig. 5 is the tested DC voltage of step response is 19.5kV;

Fig. 6 is ac voltage measurement result and relative measurement error distribution curve;

Fig. 7 is DC voltage measurement result and relative measurement error distribution curve.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail.

The invention provides a kind of detection method suppressing optical voltage transformer nonlinear characteristic to realize combined-voltage measurement, and a kind of pick-up unit realizing described method is provided, described method and pick-up unit high-precisionly can detect nonlinear closed loop's error signal, and suppress outside disturbing signal, obtain exponentially stable optical voltage transformer output signal.The present invention analyzes non-linear, disturbance and time delay to the impact of optical voltage transformer system, establishes closed loop optical voltage transformer model and carries out leak control and check, achieving the measurement of combined-voltage.Consider that meeting life period postpones in closed-loop detection circuit simultaneously, in order to the squelch level of the fast dynamic response and expectation that obtain system, consider the impact that non-linear, time delay and external disturbance cause, the present invention devises Robust Control Algorithm, stability control is carried out to optical voltage transformer Circuits System state equation, ensure that the exponential stability of closed loop optical voltage transformer, and make optical voltage transformer in practical engineering application, obtain good squelch level.

The invention provides a kind of method and the pick-up unit that suppress optical voltage transformer nonlinear characteristic, described pick-up unit high precision can obtain optical voltage transformer nonlinear closed loop error signal, in the method and pick-up unit, and nonlinear closed loop's error signal through square-wave frequency modulation, frequency shift to avoid the adverse effect of low noise in 1/f noise, utilizes Digital Signal Processing to nonlinear closed loop's error signal to high frequency region process, the output signal v of bandpass filter _bft () is first become digital signal v by A/D converter conversion _bf(k), this digital signal by one with described digital signal v _bfthe synchronous digital square-wave f of (k) same frequency _bt () demodulation, after demodulation, output signal is v _d(k); Output signal nonlinear closed loop's error signal after a wave digital lowpass filter after last demodulation to be reduced with the form of digital signal, obtain the stable output of optical voltage transformer.The method of suppression optical voltage transformer nonlinear characteristic provided by the invention, specifically comprises the steps:

The first step, exports interference light intensity v to photodetector _outt () carries out pre-service, to nonlinear closed loop's error signal , carry out square-wave frequency modulation, closed-loop error signal frequency is moved to high frequency region, to avoid the adverse effect of 1/f noise Middle and low frequency noise; Bandpass filter is utilized to ensure distortionlessly to extract nonlinear closed loop's error signal white noise in the output interference light intensity of the photodetector of filtering simultaneously.

The digital closed loop detection technique of optical voltage transformer system introduces square-wave frequency modulation and staircase waveform feedback technique, obtains the interference light intensity v of photodetector output terminal _out(t) expression formula as shown in the formula:

in above formula, α represents the loss of light path, and β is the gain of photodetector, and 2 δ represent the Pockels phase shift of twice, with be be added in square-wave frequency modulation phase place on phase-modulator and staircase waveform feedback phase respectively, what τ represented is that light passes through and returns the interval time of phase-modulator, I _inand v _outt () is the output interference light intensity of the light intensity that sends of superluminescent diode (light source) and photodetector respectively.Be added in the square-wave frequency modulation phase place on phase-modulator expression formula as shown in the formula:

In formula, m is positive integer.

Definition wherein be intended to offset Pockels phase shift 2 δ.Therefore the output interference light intensity of photodetector can be write as following formula:

F in above formula _brepresent amplitude be the modulated square wave of ± 1, modulation methods wave period and phase place all with identical, nonlinear closed loop's error signal through square-wave frequency modulation, frequency shift, to high frequency region, avoids the adverse effect of 1/f noise Middle and low frequency noise.Order be the phase place of nonlinear closed loop's error signal, its value is floated at zero crossings, and frequency is identical with 2 δ; And from (3) formula, the light intensity signal that photodetector exports is nonlinear function.

Containing a large amount of noise signals in the output intensity of photodetector, these noises cause primarily of light path, comprise photon shot noise, reflecting background, rayleigh scattering noise etc., and these noises all can process as white noise.Therefore want to export interference light intensity v at photodetector _outt, in (), the nonlinear closed loop's error signal that extracts of high s/n ratio is very difficult.

In the output interference light intensity of photodetector for nonlinear closed loop's error signal, order wherein ω ₁the angular frequency of measured signal, when measured signal is DC voltage, ω ₁be zero.Right carry out Taylor expansion, as shown in the formula:

In conjunction with (4) formula and (3) formula, the output interference light intensity v of photodetector _outt () can be expressed as following Fourier expansion formula:

Wherein ω ₀modulated square wave f _bangular frequency, its value is 1/2 τ.

Compared to modulated square wave f _b, nonlinear closed loop's error signal be a low frequency signal, and change along with the input and output of optical voltage transformer.Can be found out by (5) formula, v _outt the frequency content of () is (2n-1) ω ₀± ω ₁,

(2 _n-1) ω ₀± 3 ω ₁, n=1,2,3 ..., in several frequency contents of composition nonlinear closed loop error signal, frequency is ω ₀± ω ₁and ω ₀± 3 ω ₁part account for v _outthe great majority of (t) energy, and carry ω ₁all information.Therefore, the invention provides a kind of bandpass filter, its pass band is ω ₀-3 ω ₁~ ω ₀+ 3 ω ₁, passband contains angular frequency ₀± ω ₁and ω ₀± 3 ω ₁, so that system can distortionless extraction nonlinear closed loop error signal, suppress a large amount of white noises simultaneously, improve signal to noise ratio (S/N ratio).Adopt the output interference light intensity of above-mentioned bandpass filter to photodetector to carry out filtering, obtain the output signal v of bandpass filter _bf(t) be:

K in formula _bffor the magnification ratio coefficient of bandpass filter.

Like this, just distortionlessly from the output interference light intensity of photodetector nonlinear closed loop's error signal has been extracted can be found out by (6) formula, the noise of the overwhelming majority, the AC compounent of DC component and coefficient n>1, by after bandpass filter all by filtering, the signal simultaneously in passband amplifies k _bfdoubly.

Second step, by the output signal v of bandpass filter _bft () becomes digital signal v through A/D converter analog to digital conversion _bf(k), and by one and v _bfthe synchronous digital square-wave f of (k) same frequency _b(t) demodulation; The output signal v of demodulation _dcontaining nonlinear closed loop's error signal component in (k), but also contains unwanted high-frequency signal simultaneously; The output signal of note demodulation is v _dk (), then have:

T and k in formula _adsampling period and the gain of A/D converter respectively.

As can be seen from above formula (7), the output signal v of demodulation _dk the frequency spectrum of () comprises HFS 2n ω ₀± ω ₁, 2n ω ₀± 3 ω ₁, n=1,2,3 ... and low frequency part ω ₁with 3 ω ₁, low frequency part contains the full detail of nonlinear closed loop's error signal, therefore needs a wave digital lowpass filter filtering HFS.

3rd step, wave digital lowpass filter is to demodulated output signal v _dk () carries out low-pass filtering; With filtering v _dk the HFS of (), obtains nonlinear closed loop's error signal accurately digital signal improve signal to noise ratio (S/N ratio) further simultaneously.

The transport function designing wave digital lowpass filter in the present invention is:

H(z)＝1+z ^-1，

The bandwidth that its-3dB locates is ω ₀t/2.Therefore in detection signal frequency spectrum angular frequency higher than ω ₀the part of T/2 all by filtering, demodulated output signal v _dk (), by after wave digital lowpass filter, nonlinear closed loop's error signal is reduced to the pattern of digital signal the output signal v (k) of wave digital lowpass filter is as follows:

Wherein, k is integer.

By above step, can find out, extract nonlinear closed loop's error signal accurately, and the process extracting nonlinear closed loop's error signal can as a scale model, its scale-up factor is the delay factor that wave digital lowpass filter is introduced is z ^-1.

4th step, according to the output signal v (k) of wave digital lowpass filter, sets up optical voltage transformer system state equation.

As shown in Figure 2, comprise the output signal v (k) of the wave digital lowpass filter of nonlinear closed loop's error for controller input signal, the design of controller is in order to obtain the exponential stability of system and to reach the squelch level of regulation.The noise of note controller is input as w (k) ∈ R, belongs to L ₂0 ,+∞.Utilize the state variable relational expression of controlled standard form, the state equation setting up optical voltage transformer system is as follows:

x(k+1)=Ax(k)+Bv(k)+Bw(k) (9)

u(k)=K _cx(k)

Matrix in above formula $A=\left[\begin{array}{cccc}1& 1& 0& ...\\ 0& 1& 1& 0\\ ...& ...& ...& 1\\ 0& ...& 0& 0\end{array}\right],$ $B=\left[\begin{array}{c}0\\ 0\\ ...\\ 1\end{array}\right],$ X (k) ∈ R ⁿbe the state variable in a kth moment, n is the exponent number of state variable, and x (k+1) is the state variable in+1 moment of kth, K _c∈ R ^{1 × n}it is the feedback gain matrix that the present invention needs the Robust Control Algorithm of the optical voltage transformer system designed, v (k) is wave digital lowpass filter output signal, u (k) is the output signal of controller, is also the output signal of closed loop optical voltage transformer; Described feedback gain matrix K _cobtained by Robust Control Algorithm provided by the invention.

According to Fig. 2, utilize (8) formula, the state variable in+1 moment of kth has following difference equation through conversion:

X (k) ∈ R in formula ⁿbe state vector, the starting condition of the optical voltage transformer system that formula (10) represents is: wherein θ and k ₀-1, k ₀relevant, k ₀sampling zero moment, be the starting condition of system, w (k) ∈ R is the noise input of controller.

5th step, stability control is carried out to system state equation, when optical voltage transformer mission nonlinear closed-loop error signal is at (-π, time π) in scope, stability controls to make closed-loop error return to zero balancing point with the rate of decay of indicial response, inhibit the non-linear impact on optical voltage transformer system closed-loop characteristic, expand the range of dynamic measurement of DC voltage and the frequency span of ac voltage measurement, improve the dynamic response characteristic of optical voltage transformer system.

Nonlinear response can have influence on stability and the dynamic property of optical voltage transformer, and the interference of noise can affect the accuracy of detection of optical voltage transformer.Based on this, for optical voltage transformer, the present invention adopts Robust Control Algorithm to carry out stability control to optical voltage transformer system, with the squelch level of the exponential stability and regulation that obtain system.If feedback control unit is u (k)=K _cx (k), wherein K _c∈ R ^{1 × n}feedback gain matrix, note k ₂the gain between feedback control unit (described feedback control unit refers to the unit be made up of phase-modulator and driving circuit thereof, D/A converter in Fig. 2) and feedback phase, will u (k)=K _cx (k) brings formula (10) into, the dynamic equation obtaining optical voltage transformer control system as shown in the formula:

x(k+1)=Ax(k)+Bk ₁sin(-k ₂K _cx(k))+Bk ₁sin(-k ₂K _cx(k-1))+Bw(k) (11)

The design of feedback gain matrix K the following detailed description of how _c, first introduce some definition.

Define 1. given constant 0< α <1, if there is constant κ >=0, if state variable during noise w (k)=0 of controller meets:

${\left|\right|x\left(k\right)\left|\right|}^2<\mathrm{\&kappa;}{(1-\mathrm{\&alpha;})}^{k-k_0}{\left|\right|\mathrm{\&phi;}\left|\right|}_L^2,\&ForAll;k\&GreaterEqual;k_0---\left(12\right)$

We just say that system (10) is exponentially stable.In formula

Define 2. given constant γ >0, if system is exponentially stable, and to all non-zero noise w (k) ∈ L under zero initial condition ₂[0, ∞), meet wherein, w (s) and x (s) is respectively system noise and system state.Then optical voltage transformer system had both met the dynamic property of exponential stability and had had the H of γ degree of suppression _∞squelch performance.

First, ignore the impact of noise w (k), by CONTROLLER DESIGN feedback gain matrix K _censure that optical voltage transformer system has good quick performance of dynamic tracking.

If there is positive definite matrix P in theorem 1., R ∈ R ^{n × n}, feedback gain matrix K _c∈ R ^{1 × n}, and normal number α, ε ₁, ε ₂, following formula is set up:

Then there is nonlinear closed loop's error signal index access stability in (-π, π) scope of the optical voltage transformer system of nonlinear characteristic.Wherein ζ ₁=A 0 Bk ₁bk ₁, ζ ₂=[A-I 0 Bk ₁bk ₁],

Theorem 1 proves: the system represented for (10) formula, has following segmentation Lyapunov Equation,

V(k)＝x ^T(k)Px(k)+x ^T(k-1)Qx(k-1)+η ^T(k)Rη(k)

In above formula, the definition of P, Q is as defined in theorem 1, η (k)=x (k)-x (k-1).

Utilize the solution of formula (10) to calculate Δ V (k)=V (k+1)-V (k), have following equation:

ΔV(k)+αV(k)＝x ^T(k+1)Px(k+1)-(1-α)x ^T(k)Px(k)+x ^T(k)Qx(k)-(1-α)x ^T(k-1)Qx(k-1)

+η ^T(k+1)Rη(k+1)-(1-α)η ^T(k)Rη(k)

in, notice the function being a monotone increasing and can leading, Yi Zhi and sin (.) local meets Lipschitz condition during f (0) ≡ 0 therefore sin () should meet following condition:

Wherein

Can obtain:

ΔV(k)+αV(k)

To arbitrary constant ε ₁>0, ε ₂>0, in formula ζ ₁and ζ ₂as in theorem 1 define.

Can obtain be equal to the H<0 in the lemma of Schur benefit, therefore the adequate condition of Δ v (k)+α V (k) <0 is H<0, if Δ v (k)+α V (k) <0, then have along the arbitrary trajectory of system (9), optical voltage transformer is all exponentially stable.

In addition, following formula is had:

${\mathrm{\&lambda;}}_1{\left|\right|x\left(k\right)\left|\right|}^2\&le;V\left(k\right)\&le;{(1-\mathrm{\&alpha;})}^{k-k_0}V\left(k_0\right)\&le;{\mathrm{\&lambda;}}_2{(1-\mathrm{\&alpha;})}^{k-k_0}{\left|\right|\mathrm{\&phi;}\left|\right|}_L^2---\left(14\right)$

λ in formula ₁=min λ (P) is the minimal eigenvalue of matrix P, λ ₂=max λ (P)+max λ (Q)+4max λ (R), max λ () is eigenvalue of maximum.

Meaning is had by (14) finally can reach a conclusion for

(10) system that formula represents is exponentially stable.Theorem card is finished.

Nonlinear closed loop's error signal is bounded, and meets Lipschitz condition.For the optical voltage transformer system with nonlinear characteristic, theorem 1 is design of feedback gain matrix K _cprovide adequate condition, when nonlinear closed loop's error signal is in (-π, π) scope, ensure that the local exponential stability of system, and expand the measurement range of DC voltage.

In practical engineering application, optical voltage transformer system is inevitably subject to the disturbing influence of external environment condition, and design meets H _∞the controller of squelch has great importance to the antijamming capability improving system, and can improve optical voltage transformer non-linear rejection ability in actual applications.Following theorem 2 gives optical voltage transformer system index access stability and expects H _∞the adequate condition of performance.

If there is positive definite matrix P in theorem 2., Q, R ∈ R ^{n × n}, feedback gain matrix K _c∈ R ^{1 × n}, and normal number α, ε ₁, ε ₂, following formula is set up:

$M=\left[\begin{array}{ccc}\mathrm{\&phi;}& {\mathrm{\&delta;}}_1^{T}P& {\mathrm{\&delta;}}_2^{T}R\\ {\mathrm{\&delta;}}_{1}P& -P& 0\\ {\mathrm{\&delta;}}_{2}R& 0& -R\end{array}\right]<0---\left(15\right)$

Nonlinear closed loop's error signal then with the optical voltage transformer system of nonlinear characteristic has exponential stability in (-π, π) scope, and has the expectation H that noise suppressed degree is γ _∞performance index, wherein δ ₁=[A 0 Bk ₁bk ₁b],

δ ₂=[A-I 0 Bk ₁ Bk ₁ B]， $\mathrm{\&phi;}=\left[\begin{array}{ccccc}-(1-\mathrm{\&alpha;})P+Q-(1-\mathrm{\&alpha;})R+I& (1-\mathrm{\&alpha;})R& {\mathrm{\&epsiv;}}_1{k}_2{K}_c& 0& 0\\ (1-\mathrm{\&alpha;})R& -(1-\mathrm{\&alpha;})(Q+R)& 0& {\mathrm{\&epsiv;}}_2{k}_2{K}_c& 0\\ {\mathrm{\&epsiv;}}_1{k}_2{K}_c^T& 0& -{\mathrm{\&epsiv;}}_{1}I& 0& 0\\ 0& {\mathrm{\&epsiv;}}_2{k}_2{K}_c^T& 0& -{\mathrm{\&epsiv;}}_{2}I& 0\\ 0& 0& 0& 0& -{\mathrm{\&gamma;}}^{2}I\end{array}\right].$

Prove: method of proof is similar to theorem 1. to be had:

ΔV(k)+αV(k)+x ^T(k)x(k)-γ ²w ^T(k)w(k)

(16)

≤ξ ₂(k) ^T(φ+δ ₁ ^TPδ ₁+δ ₂ ^TRδ ₂)ξ ₂(k)

In above formula δ ₁and δ ₂as in theorem 2. define.

Lemma is mended, φ+δ by schur ₁ ^tp δ ₁+ δ ₂ ^tr δ ₂<0, means M<0.So have:

ΔV(k)<-αV(k)-(x ^T(k)x(k)-γ ²w ^T(k)w(k)) (17)。

Make Γ (t)=x ^t(k) x (k)-γ ²w ^tk () w (k), be then easy to get:

$V\left(k\right)<{(1-\mathrm{\&alpha;})}^{k-k_0}V\left(k_0\right)-\underset{s=k_0}{\overset{k-1}{\mathrm{\&Sigma;}}}{(1-\mathrm{\&alpha;})}^{k-s-1}\mathrm{\&Gamma;}\left(s\right)---\left(18\right).$

Have under zero initial condition:

$\underset{s=k_0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{(1-\mathrm{\&alpha;})}^s{x}^T\left(s\right)x\left(s\right)-{\mathrm{\&gamma;}}^2{w}^T\left(s\right)w\left(s\right)\&le;0---\left(19\right),$

So can draw, about the optical voltage transformer system with nonlinear characteristic, there is the expectation H that noise suppressed degree is γ _∞performance.

On the other hand, make w (k)=0, then φ+δ ₁ ^tp δ ₁+ δ ₂ ^tr δ ₂<0 ensure that Δ V (k) <0 when this condition makes w (k)=0.Known by theorem 1, closed-loop system also has exponential stability, and theorem card is finished.

Based on the method for above-mentioned suppression optical voltage transformer nonlinear characteristic, the output packet of digital signal processing unit involves modulated square wave containing accumulating by close-loop feedback error u (k) digital staircase obtained, and is amplified by driving circuit through D/A circuit conversion.Last digital staircase involves modulated square wave and is loaded on phase-modulator, obtains feedback phase and phase modulation because digital staircase needs a reset, D/A converter is worked as in order during output, corresponding phase is 2 π, wherein n _dAit is the conversion figure place of D/A converter.Consider the gain drift of the phase-modulator that the change of optical voltage transformer operating ambient temperature is introduced, phase modulation technique basis is introduced second closed loop configuration with the gain drift of compensation of phase modulator, Ke Yiling as modulation and the gain of feedback element.As shown in Figure 2, the present invention also provides a kind of pick-up unit suppressing optical voltage transformer mission nonlinear characteristic, described pick-up unit comprises photodetector, bandpass filter, A/D converter, demodulating unit, wave digital lowpass filter, controller, phase-modulator and driving circuit thereof and D/A converter, nonlinear closed loop's error signal of measured signal is contained in the output interference light intensity of described photodetector, white noise after bandpass filter in filtering interference light intensity, and distortionlessly extract nonlinear closed loop's error signal; The output signal of bandpass filter transfers digital signal to through A/D converter, and after demodulating unit carries out square wave demodulation, through wave digital lowpass filter; The output of wave digital lowpass filter and the interference noise of controller enter controller, and the controller that Robust Control Algorithm obtains in controller exports; Described controller exports and involves after feedback Staircase wave through modulation methods in phase-modulator, inputs photodetector together with the light of light source.

In order to the validity of control program proposed in proof theory result and literary composition, build the model machine of optical voltage transformer.To Bi ₄ge ₃o ₁₂crystal carries out transverse modulation, and it is of a size of 8x15x4 (Inm), and the Pockels phase shift of twice can be expressed as:

Emission wavelength λ=the 1310nm of superluminescent diode in formula.L=15mm and d=4mm is Bi ₄ge ₃o ₁₂the length of crystal and width, and be parallel to the transmission direction of light and the direction of extra electric field respectively.N ₀=2.0575 is initials index of refraction of crystal,

γ ₄₁=1.03 × 10 ^-12m/V is the electrooptical coefficient of crystal.Half-wave voltage is 19.5kV, corresponding to making Bi ₄ge ₃o ₁₂voltage when the Pockels phase shift of crystal twice is π.

The closed-loop detection circuit utilizing the present invention to propose and control method analyze the accuracy of detection of optical voltage transformer, and Fig. 6, Fig. 7 represent combined-voltage measurement result and relative measurement error curve respectively.As shown in Figure 6, when tested voltage is alternating voltage: linearly, demarcating factor (SF) is 1.1902 for numeral output and tested voltage.By δ=| (U _out/ SF-U)/U × 100%| can obtain relative measurement error and be better than ± and 0.2%.Shown in Fig. 7, when tested voltage is DC voltage: demarcating factor is 1.1969, relative measurement error is better than ± and 0.5%.And the optical voltage transformer combined-voltage relative measurement error of the closed-loop detection circuit not adopting the present invention to propose and control method be respectively ± 0.44%, ± 1%.Result demonstrates testing circuit and control algolithm to the validity of restraint speckle.

The frequency response of system is tested, the bandwidth of result display optical voltage transformer (VT) be 24.5kHz as shown in Figure 3.And when the closed-loop detection circuit not adopting the present invention to propose and control method, the bandwidth of optical voltage transformer system is 12.4kHz.So far to the checking that the feasibility of system, performance and high dynamic performance all respond.

In order to analyze the performance of dynamic tracking when measuring High Level DC Voltage, carry out step response test experiments.The measurement result voltage magnitude of step response is 476.07V, and overshoot is 16.5%, and the rise time is less than 20.5 μ s, as shown in Figure 4.The control algolithm that this result verification proposes improves the dynamic property of system and meets exponential stability simultaneously.Secondly, the maximum step DC voltage that the system of testing can detect, this voltage is by Bi ₄ge ₃o ₁₂the half-wave voltage of crystal determines.In the present system, this voltage max is 19.5kV, as shown in Figure 5.The testing circuit proposed in literary composition in sum can extract nonlinear closed loop's error signal accurately, and when the sine wave signal phase place of interfering is close to pi/2, control algolithm can overcome the non-linear impact caused system of this signal.If simultaneously tested voltage be gradual signal but not step signal time, systematic survey hands over the maximum magnitude of straight voltage only relevant with the high figure place that FPGA can process.Above-mentioned experimental result, as Fig. 3 ~ Fig. 7, proves the optical voltage transformer based on detection hardware circuit in this paper and control algolithm, has good measuring accuracy and exponential stability.And in other optical voltage transformers based on Pockels effect, its detection scheme all can not realize the measurement to DC voltage, and does linear process to closed-loop error signal, because which limit the measurement range of alternating voltage.

In engineering practice, the non-linear dynamic property that can affect optical voltage transformer.The accuracy of detection of optical voltage transformer is inevitably subject to the impact of external environment condition disturbance simultaneously.These factors limit the application of optical voltage transformer in high voltage measuring.The dynamic response of herein theoretical analysis experimental verification optical voltage transformer system and robust performance.Devise signal transacting hardware circuit to extract nonlinear closed-loop error signal accurately.Simultaneously for the non-linear of optical voltage transformer and interference, give the design criteria of novel robust control device, ensure that the index dynamic stability of system reduces the impact of noise on system performance simultaneously.Experimental result supports the feasibility of control method in this paper and corresponding performance, overcomes the impact of nonlinear interference sinusoidal signal.Especially the proposition of these schemes can be applied in Practical Project to meet the requirement that power industry improves day by day to optical voltage transformer performance.

Claims (6)

1. suppress an alterating and direct current pressure detection method for optical voltage transformer nonlinear characteristic, it is characterized in that comprising the steps:

The first step, exports interference light intensity v to photodetector _outt () carries out pre-service, to nonlinear closed loop's error signal carry out square-wave frequency modulation, by the frequency shift of nonlinear closed loop's error signal to high frequency region, to avoid the adverse effect of 1/f noise Middle and low frequency noise; The guarantee of employing bandpass filter is distortionless extracts nonlinear closed loop's error signal and the white noise in the output interference light intensity of the photodetector of filtering simultaneously; F wherein represents frequency;

Second step, by the output signal v of bandpass filter _bft () converts digital signal v to _bf(k), and by one and described digital signal v _bfthe synchronous digital square-wave f of (k) same frequency _b(t) demodulation, the output signal v after demodulation _dcontaining nonlinear closed loop's error signal in (k) composition, but also contains unwanted high-frequency signal simultaneously;

3rd step, wave digital lowpass filter is to the output signal v after demodulation _dk () carries out low-pass filtering, with the output signal v after demodulation described in filtering _dk the HFS of (), improves signal to noise ratio (S/N ratio) simultaneously further; Nonlinear closed loop's error signal in the output signal v (k) of now wave digital lowpass filter is digital signal

4th step, according to the output signal v (k) of wave digital lowpass filter, sets up system state equation;

5th step, carries out stability control to system state equation, when optical voltage transformer mission nonlinear closed-loop error signal exists in scope, described stability controls to make nonlinear closed loop's error return to zero balancing point with the rate of decay of indicial response, inhibit the non-linear impact on optical voltage transformer system closed-loop characteristic, expand the range of dynamic measurement of DC voltage and the frequency span of ac voltage measurement, improve the dynamic response characteristic of optical voltage transformer system.

2. a kind of alterating and direct current pressure detection method suppressing optical voltage transformer nonlinear characteristic according to claim 1, it is characterized in that: the bound cutoff frequency of described bandpass filter, drawn by the physical characteristics of nonlinear closed loop's error signal, the pass band of bandpass filter is: ω ₀-3 ω ₁~ ω ₀+ 3 ω ₁, passband contains angular frequency ₀=ω ₁and ω ₀± 3 ω ₁; Wherein, ω ₁the angular frequency of measured signal, when measured signal is DC voltage, ω ₁be zero, ω ₀it is the angular frequency of modulated square wave.

3. a kind of alterating and direct current pressure detection method suppressing optical voltage transformer nonlinear characteristic according to claim 1, is characterized in that: described wave digital lowpass filter, and the bandwidth that its-3dB locates is therefore in detection signal frequency spectrum angular frequency higher than part all by filtering, wherein ω ₀be the angular frequency of modulated square wave, T is the sampling period of A/D converter.

4. a kind of alterating and direct current pressure detection method suppressing optical voltage transformer nonlinear characteristic according to claim 1, is characterized in that:

System state equation described in 4th step is as follows:

x(k+1)＝Ax(k)+Bv(k)+Bw(k) (9)

u(k)＝K _cx(k)

Matrix in above formula $A=\left[\begin{array}{cccc}1& 1& 0& ...\\ 0& 1& 1& 0\\ ...& ...& ...& 1\\ 0& ...& 0& 0\end{array}\right],B=\left[\begin{array}{c}0\\ 0\\ ...\\ 1\end{array}\right],$ X (k) ∈ R ⁿbe the state variable in a kth moment, n is the exponent number of state variable, and x (k+1) is the state variable in+1 moment of kth, K _c∈ R ^{1 × n}be feedback gain matrix, v (k) is wave digital lowpass filter output signal, and w (k) is the interference noise of controller, and u (k) is the output signal of controller, is also the output signal of closed loop optical voltage transformer;

Staircase waveform feedback phase digital signal is u (k)=K _cthe output that x (k) is controller, wherein, k ₂the gain between feedback control unit and feedback phase, K _c∈ R ^{1 × n}it is feedback gain matrix;

By staircase waveform feedback phase digital signal bring system state equation into, the dynamic equation obtaining optical voltage transformer control system as shown in the formula:

x(k+1)＝Ax(k)+Bk ₁sin(-k ₂K _cx(k))+Bk ₁sin(-k ₂K _cx(k-1))+Bw(k) (11)

Wherein, α represents the loss of light path, and β is the gain of photodetector, I _inthe light intensity that superluminescent diode sends, k _bffor the magnification ratio coefficient of bandpass filter, k _adit is the gain of A/D converter.

5. a kind of alterating and direct current pressure detection method suppressing optical voltage transformer nonlinear characteristic according to claim 1 or 4, it is characterized in that: described stability controls to refer to by the feedback gain matrix in Robust Control Algorithm solving system state equation, ensure the squelch level of nonlinear closed loop's error signal index access stability and regulation in (-π, π) scope of optical voltage transformer system; Feedback gain matrix K _cobtain by the following method:

If there is positive definite matrix P, R ∈ R ^{n × n}, feedback gain matrix K _c∈ R ^{1 × n}, and normal number α, ε ₁, ε ₂, following formula is set up:

Wherein,

The K then solved _cnonlinear closed loop's error signal of the optical voltage transformer system with nonlinear characteristic index access stability in (-π, π) scope can be ensured;

If there is positive definite matrix P, Q, R ∈ R ^{n × n}, feedback gain matrix K _c∈ R ^{1 × n}, and normal number α, ε ₁, ε ₂, following formula is set up:

$M=\left[\begin{array}{ccc}\mathrm{\&phi;}& {\mathrm{\&delta;}}_1^{T}P& {\mathrm{\&delta;}}_2^{T}R\\ {\mathrm{\&delta;}}_{1}P& -P& 0\\ {\mathrm{\&delta;}}_{2}R& 0& -R\end{array}\right]<0---\left(15\right)$

Wherein δ ₁=[A 0 Bk ₁bk ₁b], δ ₂=[A-I 0 Bk ₁bk ₁b],

$\mathrm{\&phi;}=\left[\begin{array}{ccccc}-(1-\mathrm{\&alpha;})P+Q-(1-\mathrm{\&alpha;})R+I& (1-\mathrm{\&alpha;})R& {\mathrm{\&epsiv;}}_1{k}_2{K}_c& 0& 0\\ (1-\mathrm{\&alpha;})R& -(1-\mathrm{\&alpha;})(Q+R)& 0& {\mathrm{\&epsiv;}}_2{k}_2{K}_c& 0\\ {\mathrm{\&epsiv;}}_1{k}_2{K}_c^T& 0& -{\mathrm{\&epsiv;}}_{1}I& 0& 0\\ 0& {\mathrm{\&epsiv;}}_2{k}_2{K}_c^T& 0& -{\mathrm{\&epsiv;}}_{2}I& 0\\ 0& 0& 0& 0& {-\mathrm{\&gamma;}}^{2}I\end{array}\right]$

The K then solved _ccan ensure that nonlinear closed loop's error signal of the optical voltage transformer system with nonlinear characteristic has exponential stability in (-π, π) scope, ensure that optical voltage transformer system has the expectation H that noise suppressed degree is γ simultaneously _∞performance index; I in above-mentioned formula is unit matrix;

Because above-mentioned formula (13), (15) are LMIs, therefore the solver applied in LMI tool box solves this LMI, namely obtains feedback gain matrix K _c∈ R ^{1 × n}.

6. one kind is suppressed the combined-voltage pick-up unit of optical voltage transformer nonlinear characteristic, it is characterized in that: described pick-up unit comprises photodetector, bandpass filter, A/D converter, demodulating unit, wave digital lowpass filter, controller, phase-modulator and driving circuit thereof and D/A converter, nonlinear closed loop's error signal is contained in the output interference light intensity of described photodetector, white noise after bandpass filter in filtering interference light intensity, and distortionlessly extract nonlinear closed loop's error signal; The output signal of bandpass filter transfers digital signal to through A/D converter, and after demodulating unit carries out square wave demodulation, through wave digital lowpass filter; The output of wave digital lowpass filter and the interference noise of controller enter controller, and in controller, Robust Control Algorithm suppresses closed-loop error nonlinear characteristic and the impact of noise on closed-loop characteristic to obtain controller output; Described controller exports and involves after feedback Staircase wave through modulation methods in phase-modulator, inputs photodetector together with the light of light source.