CN103217562A - Alternating current and direct current voltage detection method and device for inhibiting optical voltage transducer nonlinear characteristic - Google Patents

Abstract

The invention discloses an AC and DC voltage detection method and device for suppressing the nonlinear characteristics of an optical voltage transformer. In view of the nonlinear characteristics of the closed-loop error signal and are easily affected by external environment disturbances, the output of the photodetector is preprocessed, the nonlinear closed-loop error signal is square-wave modulated, and the frequency of the error signal is migrated to a high-frequency region; Use a band-pass filter to ensure that the error signal is extracted without distortion, and filter out the white noise in the output of the photodetector; convert the output signal of the band-pass filter into a digital signal and perform low-pass filtering after demodulation; establish a system The state equation and its stability control, so that the error signal returns to the zero balance point at an exponential decay rate and meets the specified noise suppression level, suppressing the impact of nonlinearity on the closed-loop performance of the optical voltage transformer system, and expanding The dynamic measurement range of DC voltage and the frequency bandwidth of AC voltage measurement are improved, and the dynamic response characteristics of the system are improved.

Description

The alterating and direct current pressure detection method and the device that suppress the optical voltage transformer nonlinear characteristic

Technical field

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

Background technology

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

The closed loop optical voltage transformer has adopted square-wave frequency modulation and staircase waveform feedback technique, has suppressed to a great extent the impact of luminous power fluctuation, and has enlarged 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, the 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, the first port is light source 1 entrance, the second port connects the input port of polarizer 3, the 3rd port connects the input end of photodetector 8, the output of photodetector 8 connects signal processing circuit 9, signal processing circuit 9 provides modulation voltage for phase-modulator 4.Described polarizer 3 connects phase-modulator 4, and 45 ° of weldings of tie point; Between phase-modulator 4 and polarization apparatus 6, by protecting off-delay optical cable 5, be connected, BGO crystal 7 end points in described polarization apparatus 6 have reflectance coating 10, in order to reflected light.

Line polarisation by polarizer 3 is through 45 ° of welding angles, the linearly polarized light that is divided into two bundle quadratures, the polarized light of this two bundles quadrature is by integrated phase modulator 4, emergent light postpones 5 via polarization maintaining optical fibre, two-beam enters to inject Faraday polarization apparatus 6, 45 ° of pairwise orthogonal linear polarization pattern rotations, incide in BGO crystal 7, tested voltage is applied in the light of two polarized orthogonal patterns in the mode of Pockels phase shift, the pairwise orthogonal polarized light is by the reflection of reflectance coating, light path along incident is returned, through phase-modulator 4 effects, finally at polarizer 3 place's two-beams, interfere, the phase place of wherein interfering is the twice of Pockels phase shift.The light of two bundle orthogonal polarization modes is each through nonreciprocal Faraday polarization apparatus 6, all can rotate 45 °, because nonreciprocal faraday in light path collimates the introducing of polarization apparatus, except BGO crystal 7, the pairwise orthogonal polarization mode is through identical light path, form the reflective light path of accurate reciprocity, reduced the detection error that the defect deficiency because of external disturbance and equipment causes.

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

Summary of the invention

The present invention proposes a kind of alterating and direct current pressure detection method and pick-up unit that suppresses the optical voltage transformer nonlinear characteristic, to improve precision and the non-linear inhibition ability of optical voltage transformer when measuring combined-voltage based on the Pockels effect.

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

The first step, to photodetector output interference light intensity v _out(t) carry out pre-service, to non-linear closed loop error signal

carry out square-wave frequency modulation, the frequency of non-linear closed loop error signal is moved to high frequency region, to avoid the adverse effect of 1/f noise Middle and low frequency noise; Adopt bandpass filter to guarantee the distortionless non-linear closed loop error signal that extracts

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 _bf(t) convert digital signal v to _bf(k), and by one with described digital signal v _bf(k) the synchronous digital square-wave f of same frequency _b(t) demodulation, the output signal v after demodulation _d(k) contain non-linear closed loop error signal in

composition, but also comprised unwanted high-frequency signal simultaneously;

The 3rd step, the output signal v of wave digital lowpass filter after to demodulation _d(k) carry out low-pass filtering, with the output signal v after the described demodulation of filtering _d(k) HFS further improves signal to noise ratio (S/N ratio) simultaneously; Now the non-linear closed loop error signal in the output signal v of wave digital lowpass filter (k) is digital signal

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

The 5th step, system state equation is carried out to stability control, when the non-linear closed loop error signal of optical voltage transformer system at (π, π) in the scope, described stability is controlled and can be made non-linear closed loop error return to the zero balancing point with the rate of decay of indicial response, suppressed 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, improved the dynamic response characteristic of optical voltage transformer system.

The invention has the advantages that:

(1) when combined-voltage is measured, the passband scope of the bandpass filter of the present invention's design all can guarantee the distortionless non-linear closed loop error signal that extracts, suppress most white noises simultaneously, improved the signal to noise ratio (S/N ratio) of expected frequency signal.

(2) adopt the method for inhibition optical voltage transformer nonlinear characteristic provided by the invention, for the non-linear closed loop error signal of optical voltage transformer, its scope is when (π, π), and the optical voltage transformer system can index access stability and the squelch level of regulation.

(3) adopt the method for inhibition optical voltage transformer nonlinear characteristic provided by the invention, the combined-voltage measuring accuracy of optical voltage transformer is respectively ± and 0.2% and ± 0.5%, bandwidth has reached 24.5kHz, and maximum step direct current measurement voltage is 19.5kV.The results show system obtain the response of good dynamic property and high precision, verified the method for the inhibition nonlinear characteristic proposed in the present invention and validity and the correctness of pick-up unit.

The accompanying drawing explanation

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

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

The frequency response measurement result that Fig. 3 is system;

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

Fig. 5 is that 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 that the optical voltage transformer nonlinear characteristic realizes that combined-voltage is measured that suppresses, and provide a kind of pick-up unit of realizing described method, described method and pick-up unit can high-precisionly detect non-linear closed loop error signal, and suppress outside disturbing signal, obtain exponentially stable optical voltage transformer output signal.That the present invention has analyzed is non-linear, disturbance and time postpones the impact on the optical voltage transformer system, has set up closed loop optical voltage transformer model and has controlled and detect, and has realized the measurement of combined-voltage.Consider simultaneously in closed-loop detection circuit and can life period postpone, for the fast dynamic response that obtains system and the squelch level of expectation, consider the impact that non-linear, time delay and external disturbance cause, the present invention has designed Robust Control Algorithm, optical voltage transformer Circuits System state equation is carried out to stability control, guarantee the exponential stability of closed loop optical voltage transformer, and made optical voltage transformer obtain good squelch level in practical engineering application.

The invention provides a kind of method and pick-up unit that suppresses the optical voltage transformer nonlinear characteristic, described pick-up unit can high precision obtain the non-linear closed loop error signal of optical voltage transformer, in the method and pick-up unit, and non-linear closed loop error signal

through the square wave modulation, frequency moves to high frequency region to avoid low noise adverse effect in 1/f noise, utilizes Digital Signal Processing to non-linear closed loop error signal processed the output signal v of bandpass filter _bf(t) at first by the A/D converter conversion, become digital signal v _bf(k), this digital signal is by one and described digital signal v _bf(k) the synchronous digital square-wave f of same frequency _b(t) demodulation, after demodulation, output signal is v _d(k); After last demodulation, output signal non-linear closed loop error signal after a wave digital lowpass filter is reduced with the form of digital signal, obtains the stable output of optical voltage transformer.The method of inhibition optical voltage transformer nonlinear characteristic provided by the invention, specifically comprise the steps:

The first step, to photodetector output interference light intensity v _out(t) carry out pre-service, to non-linear closed loop 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; Utilize bandpass filter to guarantee the distortionless non-linear closed loop error signal that extracts

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 is introduced 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 means the loss of light path, and β is the gain of photodetector, and 2 δ mean the Pockels phase shift of twice,

with

respectively square-wave frequency modulation phase place and the staircase waveform feedback phase be added on phase-modulator, τ means be light by and return to interval time of phase-modulator, I _inand v _out(t) be respectively the light intensity sent of superluminescent diode (light source) and the output interference light intensity of photodetector.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 _bmean the modulated square wave that amplitude is ± 1, modulation methods wave period and phase place all with identical, non-linear closed loop error signal

through the square wave modulation, frequency moves to high frequency region, has avoided the adverse effect of 1/f noise Middle and low frequency noise.Order

be the phase place of non-linear closed-loop error signal, its value is floated near zero point, and frequency is identical with 2 δ; And, from (3) formula, the light intensity signal of photodetector output is nonlinear function.

Contain a large amount of noise signals in the output intensity of photodetector, these noises are mainly caused by light path, comprise photon shot noise, reflecting background, rayleigh scattering noise etc., and these noises all can be processed as white noise.Therefore want at photodetector output interference light intensity v _out(t), in, the non-linear closed loop error signal that extracts of high s/n ratio is very difficult.

In the output interference light intensity of photodetector

for non-linear closed loop error signal, order

ω wherein ₁the angular frequency of measured signal, when measured signal is DC voltage, ω ₁be zero.Right

carry out the Taylor expansion, as shown in the formula:

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

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

Compared to modulated square wave f _b, non-linear closed loop error signal

be a low frequency signal, and change along with the input and output of optical voltage transformer.Can be found out v by (5) formula _out(t) frequency content is (2n-1) ω ₀± ω ₁,

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

K in formula _bfmagnification ratio coefficient for bandpass filter.

Like this, just distortionlessly from the output interference light intensity of photodetector extracted non-linear closed loop error signal

can find out the noise of the overwhelming majority, DC component and coefficient n by (6) formula>1 AC compounent, by after bandpass filter all by filtering, the signal in passband amplifies k simultaneously _bfdoubly.

Second step, by the output signal v of bandpass filter _bf(t) become digital signal v through the A/D converter analog to digital conversion _bf(k), and by one and v _bf(k) the synchronous digital square-wave f of same frequency _b(t) demodulation; The output signal v of demodulation _d(k) contain non-linear closed loop error signal composition in, but also comprised unwanted high-frequency signal simultaneously; The output signal of note demodulation is v _d(k), have:

T and k in formula _adrespectively sampling period and the gain of A/D converter.

Can be found out the output signal v of demodulation by above formula (7) _d(k) frequency spectrum 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, the full detail that low frequency part has comprised non-linear closed loop error signal, therefore need a wave digital lowpass filter filtering HFS.

The 3rd step, wave digital lowpass filter is to demodulated output signal v _d(k) carry out low-pass filtering; With filtering v _d(k) HFS, obtain non-linear closed loop error signal accurately

digital signal further improve signal to noise ratio (S/N ratio) simultaneously.

In the present invention, the transport function of design wave digital lowpass filter is:

H(z)＝1+z ^-1，

Its-bandwidth at 3dB place is ω ₀t/2.Therefore in the detection signal frequency spectrum angular frequency higher than ω ₀the part of T/2 is all by filtering, demodulated output signal v _d(k) by after wave digital lowpass filter, non-linear closed loop error signal is reduced to the pattern of digital signal

the output signal v of wave digital lowpass filter (k) is as follows:

Wherein, k is integer.

By above step, can find out, extracted accurately non-linear closed loop error signal, and the process of extracting non-linear closed loop error signal can be used as a scale model, its scale-up factor is

the delay factor that wave digital lowpass filter is introduced is z ^-1.

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

As shown in Figure 2, the output signal v of the wave digital lowpass filter that comprises non-linear closed loop error (k) is controller input signal, and the design of controller is in order to the exponential stability of obtaining system and the squelch level that reaches 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 of setting up the 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 ⁿk state variable constantly, the exponent number that n is state variable, x (k+1) is k+1 state variable constantly, K _c∈ R ^{1 * n}it is the feedback gain matrix of the Robust Control Algorithm of the present invention's optical voltage transformer system that need to design, v (k) is the 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 _cby Robust Control Algorithm provided by the invention, obtained.

Shown in Fig. 2, utilize (8) formula, k+1 state variable constantly has following difference equation through conversion:

X in formula (k) ∈ R ⁿbe state vector, the starting condition of the optical voltage transformer system that formula (10) means is:

wherein θ and k ₀-1, k ₀relevant, k ₀zero moment of sampling,

be the starting condition of system, w (k) ∈ R is the noise input of controller.

The 5th step, system state equation is carried out to stability control, when the non-linear closed loop error signal of optical voltage transformer system at (π, in the time of π) in scope, stability is controlled and can be made the closed loop error return to the zero balancing point with the rate of decay of indicial response, suppressed 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, improved the dynamic response characteristic of optical voltage transformer system.

The nonlinear response meeting has 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 the optical voltage transformer system, with the exponential stability of obtaining system and the squelch level of regulation.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 in Fig. 2 the unit be comprised of phase-modulator and driving circuit thereof, D/A converter) and feedback phase, will u (k)=K _cx (k) brings formula (10) into, the dynamic equation that obtains the 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)

How below to describe design of feedback gain matrix K in detail _c, at first introduce some definition.

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

${\left|\right|x\left(k\right)\left|\right|}^2<\mathrm{\&kappa;}{(1-\mathrm{\&alpha;})}^{k-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002879930700021.png,HDA00002879930700022.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}{\left|\right|\mathrm{\&phi;}\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA00002879930700021.png,HDA00002879930700031.png"\; state="\{\{state\}\}">L</figure-callout>}}^2,\&ForAll;k\&GreaterEqual;k_0---\left(12\right)$

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

Define 2. given constant γ>0, if system is exponentially stable, and under zero initial condition to all non-zero noise w (k) ∈ L ₂[0, ∞), meet

wherein, w (s) and x (s) are respectively system noise and system state.The optical voltage transformer system had both met the dynamic property of exponential stability and had had the H of γ inhibition degree _∞the squelch performance.

At first, ignore the impact of noise w (k), by CONTROLLER DESIGN feedback gain matrix K _cguarantee that the 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, make following formula set up:

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

Theorem 1 proof: the system meaned for (10) formula, following segmentation Lyapunov Equation is arranged,

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

P in above formula, the definition of 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), following equation arranged:

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

a monotone increasing and the function that can lead, Yi Zhi

and during f (0) ≡ 0, sin (.) part meets the Lipschitz condition

therefore sin () should meet following condition:

Wherein

Can obtain:

ΔV(k)+αV(k)

To constant ε arbitrarily ₁0, ε ₂0, in formula

ζ ₁and ζ ₂as defined in theorem 1.

Can obtain

be equal to Schur and mend H in lemma<0, so the adequate condition of Δ v (k)+α V (k)<0 is H<0, if Δ v (k)+α V (k)<0 has along any track of system (9), optical voltage transformer is all exponentially stable.

In addition, following formula is arranged:

${\mathrm{\&lambda;}}_1{\left|\right|x\left(k\right)\left|\right|}^2\&le;V\left(k\right)\&le;{(1-\mathrm{\&alpha;})}^{k-k_0}V\left(k_0\right)\&le;{\mathrm{\&lambda;}}_2{(1-\mathrm{\&alpha;})}^{k-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002879930700021.png,HDA00002879930700022.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}{\left|\right|\mathrm{\&phi;}\left|\right|}_L^2---\left(14\right)$

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.

Mean by (14) and have

finally can reach a conclusion for

(10) system that formula means is exponentially stable.The theorem card is finished.

Non-linear closed loop error signal is bounded, and meets the Lipschitz condition.For the optical voltage transformer system with nonlinear characteristic, theorem 1 is design of feedback gain matrix K _cadequate condition is provided, when non-linear closed loop error signal is in (π, π) scope, has guaranteed the local exponential stability of system, and enlarged the measurement range of DC voltage.

In practical engineering application, the optical voltage transformer system inevitably can be subject to the disturbing influence of external environment condition, and design meets H _∞the controller of squelch has great importance to the antijamming capability that improves system, and can improve optical voltage transformer non-linear inhibition ability in actual applications.Following theorem 2 has provided optical voltage transformer system index access stability and expectation 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, make following formula set up:

$M=\left[\begin{array}{ccc}\mathrm{\&phi;}& {\mathrm{\&delta;}}_1^{T}P& {\mathrm{\&delta;}}_2^{T}R\\ {\mathrm{\&delta;}}_{1}P& -\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="HDA00002879930700021.png,HDA00002879930700022.png"\; state="\{\{state\}\}">P</figure-callout>}& 0\\ {\mathrm{\&delta;}}_{2}R& 0& -R\end{array}\right]<0---\left(15\right)$

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

δ ₂=[A-I 0 Bk ₁ Bk ₁ B]， $\mathrm{\&phi;}=\left[\begin{array}{ccccc}-(1-\mathrm{\&alpha;})P+Q-(1-\mathrm{\&alpha;})R+I& (1-\mathrm{\&alpha;})R& {\mathrm{\&epsiv;}}_1{k}_2{\mathrm{<figure-callout\; id="0"\; label="K\; c"\; filenames="HDA00002879930700021.png,HDA00002879930700022.png"\; state="\{\{state\}\}">K</figure-callout>}}_c& 0& 0\\ (1-\mathrm{\&alpha;})R& -(1-\mathrm{\&alpha;})(Q+R)& 0& {\mathrm{\&epsiv;}}_2{k}_2{\mathrm{<figure-callout\; id="0"\; label="K\; c"\; filenames="HDA00002879930700021.png,HDA00002879930700022.png"\; state="\{\{state\}\}">K</figure-callout>}}_c& 0\\ {\mathrm{\&epsiv;}}_1{k}_2{K}_c^T& 0& -{\mathrm{\&epsiv;}}_{1}I& 0& 0\\ 0& {\mathrm{\&epsiv;}}_2{k}_2{K}_c^T& 0& -{\mathrm{\&epsiv;}}_{2}I& 0\\ 0& 0& 0& 0& -{\mathrm{\&gamma;}}^{2}I\end{array}\right].$

Proof: 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 defined in theorem 2..

Mend lemma by schur, φ+δ ₁ ^tp δ ₁+ δ ₂ ^tr δ ₂<0, mean 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 ^t(k) w (k) is easy to get:

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

Under zero initial condition, have:

$\underset{s={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002879930700021.png,HDA00002879930700022.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{(1-\mathrm{\&alpha;})}^s{x}^T\left(s\right)x\left(s\right)-{\mathrm{\&gamma;}}^2{w}^T\left(s\right)w\left(s\right)\&le;0---\left(19\right),$

So the optical voltage transformer system about having nonlinear characteristic that can draw has the expectation H that the squelch degree is γ _∞performance.

On the other hand, make w (k)=0, φ+δ ₁ ^tp δ ₁+ δ ₂ ^tr δ ₂<0 has guaranteed

this condition makes w (k)=0 o'clock Δ V (k)<0.Known by theorem 1, closed-loop system also has exponential stability, and the theorem card is finished.

Method based on above-mentioned inhibition optical voltage transformer nonlinear characteristic, the output packet of digital signal processing unit involves modulated square wave containing the digital ladder obtained by close-loop feedback error u (k) accumulation, through the D/A circuit conversion and by driving circuit, amplifies.Last digital ladder involves modulated square wave and is loaded on phase-modulator, obtains feedback phase

and phase modulation

because digital staircase waveform need to have one to 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 variation of optical voltage transformer operating ambient temperature is introduced, introduce the gain drift of second closed loop configuration with the compensation of phase modulator on the phase modulation technique basis, can make

gain as modulation and feedback element.As shown in Figure 2, the present invention also provides a kind of pick-up unit that suppresses optical voltage transformer system 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, the non-linear closed loop error signal that has comprised measured signal in the output interference light intensity of described photodetector, white noise after bandpass filter in the filtering interference light intensity, and distortionlessly extract non-linear closed loop error signal; The output signal of bandpass filter transfers digital signal to through A/D converter, and after demodulating unit carries out the square wave demodulation, through wave digital lowpass filter; The output of wave digital lowpass filter and the interference noise of controller enter controller, the controller output obtained through Robust Control Algorithm in controller; The output of described controller, involve the modulation of feedback staircase waveform in phase-modulator through modulation methods after, is inputted photodetector with together with the light of light source.

For the validity of the control program that proposes in proof theory result and literary composition, built the model machine of optical voltage transformer.To Bi ₄ge ₃o ₁₂crystal is laterally modulated, 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 are Bi ₄ge ₃o ₁₂the length of crystal and width, and be parallel to respectively the transmission direction of light and the direction of extra electric field.N ₀the=2.0575th, the initial 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 that utilizes the present invention to propose and control method are analyzed the accuracy of detection of optical voltage transformer, and Fig. 6, Fig. 7 mean respectively combined-voltage measurement result and relative measurement error curve.As shown in Figure 6, when tested voltage is alternating voltage: numeral output and the linear ratio of tested voltage, demarcating factor (SF) is 1.1902.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 that does not adopt the present invention to propose and control method is respectively ± 0.44%, ± 1%.Result has proved that testing circuit and control algolithm are to suppressing the validity of noise.

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

In order to analyze the performance of dynamic tracking when measuring High Level DC Voltage, carried out the 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.This result verification the control algolithm that proposes improved the dynamic property of system and met exponential stability simultaneously.Secondly, tested the maximum step DC voltage that system can detect, this voltage is by Bi ₄ge ₃o ₁₂the half-wave voltage of crystal determines.In native system, this voltage max is 19.5kV, as shown in Figure 5.The testing circuit proposed in literary composition in sum can extract non-linear closed loop error signal accurately, and when the sine wave signal phase place of interfering approaches pi/2, control algolithm can overcome the non-linear impact that system is caused of this signal.If, when simultaneously tested voltage is gradual signal but not step signal, the high figure place that systematic survey hands over the maximum magnitude of straight voltage only can process with FPGA is relevant.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 at other in optical voltage transformer based on the Pockels effect, its detection scheme all can not be realized the measurement to DC voltage, and the closed loop error signal is done to linear process, therefore limited 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 inevitably can be subject to the impact of external environment condition disturbance simultaneously.These effects limit the application of optical voltage transformer aspect high voltage measuring.This paper theoretical analysis experimental verification dynamic response and the robust performance of optical voltage transformer system.Designed the signal processing hardware circuit to extract accurately nonlinear closed loop error signal.For the non-linear of optical voltage transformer and interference, provided the design criteria of novel robust control device simultaneously, guaranteed that the index dynamic stability of system has reduced the impact of noise on system performance simultaneously.Experimental result has been supported feasibility and the corresponding performance of control method in this paper, has overcome the impact of nonlinear interference sinusoidal signal.Especially the proposition of these schemes can be applied to the requirement to meet power industry, the optical voltage transformer performance improved day by day in Practical Project.

Claims (6)

1. a kind of AC/DC voltage detection method that suppresses the non-linear characteristic of optical voltage transformer, it is characterized in that comprising the steps: The first step is to preprocess the output interference light intensity v _out (t) of the photodetector, and the nonlinear closed-loop error signal

Perform square wave modulation to shift the frequency of the nonlinear closed-loop error signal to the high-frequency region to avoid the adverse effects of low-frequency noise in 1/f noise; use a band-pass filter to ensure that the nonlinear closed-loop error signal is extracted without distortion

And filter out the white noise in the output interference light intensity of photodetector simultaneously; Wherein f represents frequency; In the second step, the output signal v _bf (t) of the band-pass filter is converted into a digital signal v _bf (k), and a digital square wave signal f with the same frequency and phase as the digital signal v _bf (k) _b (t) demodulation, the demodulated output signal v _d (k) contains nonlinear closed-loop error signal

components, but also contains unwanted high-frequency signals; In the third step, the digital low-pass filter performs low-pass filtering on the demodulated output signal v _d (k), to filter out the high-frequency part of the demodulated output signal v _d (k), and further improve Signal-to-noise ratio; at this time, the nonlinear closed-loop error signal in the output signal v(k) of the digital low-pass filter is a digital signal

The fourth step is to establish the system state equation according to the output signal v(k) of the digital low-pass filter; The fifth step is to perform stability control on the system state equation. When the nonlinear closed-loop error signal of the optical voltage transformer system is within the range of (-π, π), the stability control can make the nonlinear closed-loop error an exponential characteristic The attenuation speed returns to the zero balance point, which suppresses the influence of nonlinearity on the closed-loop performance of the optical voltage transformer system, expands the dynamic measurement range of DC voltage and the frequency bandwidth of AC voltage measurement, and improves the dynamic response characteristics of the optical voltage transformer system . 2. a kind of AC/DC voltage detection method that suppresses the non-linear characteristic of optical voltage transformer according to claim 1, is characterized in that: the upper and lower limit cut-off frequency of described band-pass filter, by the non-linear closed-loop error signal According to the physical characteristics, the passband range of the bandpass filter is: ω ₀ -3ω ₁ ~ω ₀ +3ω ₁ , the passband includes the angular frequencies ω ₀ ±ω ₁ and ω0±3ω ₁ ; where ω ₁ is the The angular frequency of the measured signal, when the measured signal is a DC voltage, ω ₁ is zero. 3. a kind of AC/DC voltage detection method that suppresses the non-linear characteristic of optical voltage transformer according to claim 1, is characterized in that: described digital low-pass filter, the bandwidth at its-3dB place is ω ₀ T/ 2. Therefore, the portion of the detection signal spectrum with an angular frequency higher than ω ₀ T/2 is filtered out, where ω ₀ is the angular frequency of the modulated square wave, and T is the sampling period of the A/D converter. 4. a kind of AC/DC voltage detection method that suppresses the non-linear characteristic of optical voltage transformer according to claim 1, is characterized in that: The system state equation described in the fourth step is as follows: x(k+1)＝Ax(k)+Bv(k)+Bw(k) (9) u(k)=K _c x(k) The matrix in the 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 ⁿ is the state variable at the kth moment, n is the order of the state variable, x(k+1) is the state variable at the k+1th moment, K _c ∈ R ^1×n is the feedback Gain matrix, v(k) is the output signal of the digital low-pass filter, w(k) is the interference noise of the controller, u(k) is the output signal of the controller, and is also the output signal of the closed-loop optical voltage transformer; The step wave feedback phase digital signal is

u(k)=K _C x(k) is the output of the controller, where k ₂ is the gain between the feedback control unit and the feedback phase, and K _c ∈ R ^1×n is the feedback gain matrix; Feed back the step wave to the phase digital signal Bringing it into the system state equation, the dynamic equation of the optical voltage transformer control system is obtained as follows: x(k+1)=A _x (k)+Bk ₁ sin(-k ₂ K _c x(k))+Bk ₁ sin(-k ₂ K _c x(kl))+Bw(k) (11) . 5. according to claim 1 or 4 described a kind of AC/DC voltage detection method that suppresses the non-linear characteristic of optical voltage transformer, it is characterized in that: described stability control refers to solving system state equation by robust control algorithm The feedback gain matrix of the optical voltage transformer system ensures that the nonlinear closed-loop error signal of the optical voltage transformer system obtains exponential stability and a specified noise suppression level in the range of (-π, π); the feedback gain matrix K _c is obtained by the following method: If there is a positive definite matrix P,R∈R ^n×n , a feedback gain matrix K _c ∈R ^1×n , and constants α, ε ₁ , ε ₂ , the following formula holds:

where ζ ₁ =A 0 Bk ₁ Bk ₁ , ζ ₂ =[AI 0 Bk ₁ Bk ₁ ],

Then the _Kc obtained from the solution can ensure that the nonlinear closed-loop error signal of the optical voltage transformer system with nonlinear characteristics obtains exponential stability in the range of (-π, π); If there are positive definite matrices P, Q, R∈Rn×n, feedback gain matrix K _c ∈R ^1×n , and positive constants α,ε ₁ ,ε ₂ , so that the following formula holds: $\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; \&phi;</span>}& {\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; P</span>}& {\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; R</span>}\\ {\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; P</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; P</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}\end{array}\right]<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$ where δ _I =[A 0 Bk ₁ Bk ₁ B], δ ₂ =[AI 0 Bk ₁ Bk ₁ B], $\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccccc}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; I</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; R</span>}& {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; R</span>}& <span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; I</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; I</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\end{array}\right]$ Then the _Kc obtained from the solution can ensure that the nonlinear closed-loop error signal of the optical voltage transformer system with nonlinear characteristics has exponential stability in the range of (-π, π), and at the same time guarantees that the optical voltage transformer system has noise suppression is the expected H∞ performance index of γ; Since the above formulas (13) and (15) are linear matrix inequalities, the solver in the linear matrix inequality toolbox is used to solve the linear matrix inequalities, that is, the feedback gain matrix K _c ∈ R ^1×n is obtained. 6. An AC/DC voltage detection device that suppresses the nonlinear characteristics of an optical voltage transformer, characterized in that: the detection device includes a photodetector, a bandpass filter, an A/D converter, a demodulation unit, a digital low A pass filter, a controller, a phase modulator and its drive circuit, and a D/A converter, the output interference light intensity of the photodetector includes a nonlinear closed-loop error signal, and the interference is filtered out after passing through the band-pass filter The white noise in the light intensity can extract the nonlinear closed-loop error signal without distortion; the output signal of the bandpass filter is converted into a digital signal through the A/D converter, and after square wave demodulation in the demodulation unit, it is passed through Digital low-pass filter; the output of the digital low-pass filter and the interference noise of the controller enter the controller, and the controller output is obtained by suppressing the nonlinear characteristics of the closed-loop error and the influence of noise on the closed-loop performance through the robust control algorithm in the controller; The output of the controller described above is modulated by the square wave and the feedback ladder wave in the phase modulator, and then input to the photodetector together with the light from the light source.

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