CN103166232B - Reactive compensation device state estimation method based on Kalman filtering - Google Patents

Abstract

The invention provides a reactive compensation device state estimation method based on Kalman filtering. The reactive compensation device state estimation method based on the Kalman filtering includes the following steps: according to a discrete state equation under the condition of white noise interference of a reactive compensation device, a process interference noise matrix and a measurement noise matrix of the reactive compensation device are converted into a parameter matrix Q and a parameter matrix R known by a Kalman filter; and an iterative operation is carried out by utilizing a time update equation and a state update equation to obtain a state estimation value of the current reactive compensation device. The reactive compensation device state estimation method based on the Kalman filtering can obtain state unbiased estimation of the reactive compensation device, can effectively filter noise interference to the reactive compensation device in the measuring process, has a better filtering effect compared with a traditional state observer, and is quite suitable for being applied to electrical equipment with complex electromagnetic interference, for example, the reactive compensation device.

Description

Based on the reactive compensation device state estimation method of Kalman filtering

Technical field

The present invention relates to reactive power compensator Control System Design field in iron and steel metallurgical industry, be specifically related to the reactive compensation device state estimation method based on Kalman filtering.

Background technology

TCR type reactive power compensator has important function for voltage fluctuation in solution iron and steel metallurgical industry, power factor regulation, and reactive power compensator want obtain good dynamic and static state performance just must adopt STATE FEEDBACK CONTROL, excellent state estimation ability can increase system robustness, and therefore reactive power compensator state estimation just becomes the core of design compensation apparatus control system.

Summary of the invention

The technical problem to be solved in the present invention is: provide a kind of reactive compensation device state estimation method based on Kalman filtering, can obtain the reactive power compensator state unbiased estimator under noise jamming environment.

The present invention for solving the problems of the technologies described above taked technical scheme is: based on the reactive compensation device state estimation method of Kalman filtering, it is characterized in that: it comprises the following steps:

According to the discrete state equations under reactive power compensator white noise disturbed condition, be Kalman filter known parameters matrix Q, R by reactive power compensator process interference noise matrix and measurement noises matrix conversion;

Utilize time update equation and state updating equation to carry out interative computation and obtain current reactive power compensator state estimation.

By such scheme, the acquisition step of Kalman filter known parameters matrix Q, R is specific as follows:

S1, according to identification Method obtain reactive power compensator white noise disturbed condition under discrete state equations $\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+\mathrm{Bu}\left(k\right)+\mathrm{Fe}\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\mathrm{Ge}\left(k\right)\end{array}\right.,$ Wherein x (k) the reactive power compensator state value that is the k moment, the reactive power compensator input value that u (k) obtains for k moment measurement, y (k) for k moment measurement obtain reactive power compensator output variable, the white noise interference value that e (k) is the k moment, wherein x (k) is n × 1 column vector, u (k) is 1 × 1 dimensional vector, y (k) is 1 dimensional vector, e (k) is 1 × 1 vector, then A is n × n matrix, and B is n × 1 matrix, C is 1 × n matrix, F is n × 1 matrix, and G is 1 × 1 matrix, and A, B, C, F, G are known;

S2, calculating parameter matrix Q=F*F ', the wherein transpose operation of F ' expression F; Calculating parameter matrix R=G*G ', the wherein transpose operation of G ' expression G.

By such scheme, the acquisition step obtaining current reactive power compensator state estimation is specific as follows:

S3, reactive power compensator state estimation initial value prior estimate covariance is set wherein I _nfor n × n unit matrix, ρ be greater than 0 arithmetic number; Reactive power compensator state estimation initial value is set ${\hat{x}}_0={\left[\begin{array}{ccc}0& 0& 0\end{array}\right]}^{\′};$

S4, calculating reactive power compensator k moment priori estimates with the covariance of k moment state x prior estimate error computing formula is ${\hat{x}}_k^{-}=A{\hat{x}}_{k-1}+{\mathrm{Bu}}_{k-1},$ $P_k^{-}={\mathrm{AP}}_{k-1}{A}^{\′}+Q,$ Wherein for the posterior estimate of k-1 moment state x, u _k-1the reactive power compensator input value obtained for k-1 moment measurement and u (k-1), P _k-1for the covariance of the Posterior estimator error of k-1 moment state x;

S5, calculating reactive power compensator k moment posterior estimate computing formula is wherein kalman gain $K_k=P_k^{-}{C}^{\′}{(C{P}_k^{-}{C}^{\′}+R)}^{-1},$ $P_k=(I-K_{k}C)P_k^{-},$ it is right to represent finding the inverse matrix, y _kbe y (k);

Make k be current time, then current reactive power compensator state estimation is k moment posterior estimate

Beneficial effect of the present invention is: adopt this method can not only obtain reactive power compensator state unbiased esti-mator, but also effective filtering can be carried out to the noise jamming be subject in reactive power compensator measuring process, more traditional state observer has better filter effect, is applicable to very much the power equipment being applied to this electromagnetic interference complexity of reactive power compensator.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of one embodiment of the invention.

Fig. 2 is the first state estimation curve of reactive power compensator.

Fig. 3 is reactive power compensator the second state estimation curve.

Fig. 4 is the third state estimation curve of reactive power compensator.

Embodiment

Fig. 1 is the schematic diagram of one embodiment of the invention, it comprises the following steps: according to the discrete state equations under reactive power compensator white noise disturbed condition, is Kalman filter known parameters matrix Q, R by reactive power compensator process interference noise matrix and measurement noises matrix conversion; Utilize time update equation and state updating equation to carry out interative computation and obtain current reactive power compensator state estimation.

The acquisition step of Kalman filter known parameters matrix Q, R is specific as follows:

S1, according to identification Method obtain reactive power compensator white noise disturbed condition under discrete state equations $\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+\mathrm{Bu}\left(k\right)+\mathrm{Fe}\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\mathrm{Ge}\left(k\right)\end{array}\right.,$ Wherein x (k) the reactive power compensator state value that is the k moment, the reactive power compensator input value that u (k) obtains for k moment measurement, y (k) for k moment measurement obtain reactive power compensator output variable, the white noise interference value that e (k) is the k moment, wherein x (k) is n × 1 column vector, u (k) is 1 × 1 dimensional vector, y (k) is 1 dimensional vector, e (k) is 1 × 1 vector, then A is n × n matrix, and B is n × 1 matrix, C is 1 × n matrix, F is n × 1 matrix, and G is 1 × 1 matrix, and A, B, C, F, G are known;

S2, calculating parameter matrix Q=F*F ', the wherein transpose operation of F ' expression F; Calculating parameter matrix R=G*G ', the wherein transpose operation of G ' expression G.

The acquisition step obtaining current reactive power compensator state estimation is specific as follows:

S3, reactive power compensator state estimation initial value prior estimate covariance is set wherein I _nfor n × n unit matrix, ρ be greater than 0 arithmetic number; Reactive power compensator state estimation initial value is set ${\hat{x}}_0={\left[\begin{array}{ccc}0& 0& 0\end{array}\right]}^{\′};$

S4, calculating reactive power compensator k moment priori estimates with the covariance of k moment state x prior estimate error computing formula is ${\hat{x}}_k^{-}=A{\hat{x}}_{k-1}+{\mathrm{Bu}}_{k-1},$ $P_k^{-}={\mathrm{AP}}_{k-1}{A}^{\′}+Q,$ Wherein for the posterior estimate of k-1 moment state x, u _k-1the reactive power compensator input value obtained for k-1 moment measurement and u (k-1), P _k-1for the covariance of the Posterior estimator error of k-1 moment state x;

S5, calculating reactive power compensator k moment posterior estimate computing formula is wherein kalman gain $K_k=P_k^{-}{C}^{\′}{(C{P}_k^{-}{C}^{\′}+R)}^{-1},$ $P_k=(I-K_{k}C)P_k^{-},$ it is right to represent finding the inverse matrix, y _kbe y (k);

Make k be current time, then current reactive power compensator state estimation is k moment posterior estimate

Certain steel mill's bus being connected to a TCR type reactive power compensator discrete state equations is $\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+\mathrm{Bu}\left(k\right)+\mathrm{Fe}\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\mathrm{Ge}\left(k\right)\end{array}\right.,$ Wherein

$A=\left[\begin{array}{cc}0.963976420066891& -3.273887032994955\\ 0.000098190586240& 0.999835304739285\end{array}\right],$

B＝1.0e-004×[0.981905862397848 0.000049395486275]′，

C＝1.0e+012×[-0.027032939065630 2.036072837661347]，

F＝1.0e-007×[0.074295000000000 0.101530000000000]′，

G＝1。

Parameter can be obtained according to step S2

$Q=1.0e-015\×\left[\begin{array}{cc}0.055197470250000& 0.075431713500000\\ 0.075431713500000& 0.103083409000000\end{array}\right],$

R＝1。

Arranging reactive-load compensator Initial state estimation value is ${\hat{x}}_0={\left[\begin{array}{cc}0& 0\end{array}\right]}^{\′},$ State error covariance initial value $P_0^{-}=\left[\begin{array}{cc}0.01& 0\\ 0& 0.01\end{array}\right],$ Calculate reactive power compensator prior state respectively according to step S4 and S5 to estimate with posteriority state estimation the reactive power compensator Kalman designed to check the present invention filters filter status observation dynamic property, reactive power compensator 2 kinds of state estimation and output estimation value when testing step response in embodiment.Wherein state estimated value as shown in Figure 2, state estimated value as shown in Figure 3, output estimation value as shown in Figure 4.

Comprehensive accompanying drawing 2-4 is known, when given reactive power generation Spline smoothing, and state estimation also change fast, and estimated state settles out very soon, the reactive compensation device state estimation method shown based on Kalman filter has good static and dynamic performance thereupon.In addition, in accompanying drawing 4 based on state estimation the reactive power predicted value obtained can be good at approaching real output value, also show science and the practicality of the reactive compensation device state estimation method based on Kalman filter that the present invention proposes.

Claims (1)

1. based on the reactive compensation device state estimation method of Kalman filtering, it is characterized in that: it comprises the following steps:

According to the discrete state equations under reactive power compensator white noise disturbed condition, be Kalman filter known parameters matrix Q, R by reactive power compensator process interference noise matrix and measurement noises matrix conversion;

Utilize time update equation and state updating equation to carry out interative computation and obtain current reactive power compensator state estimation;

The acquisition step of Kalman filter known parameters matrix Q, R is specific as follows:

S1, according to identification Method obtain reactive power compensator white noise disturbed condition under discrete state equations $\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+\mathrm{Bu}\left(k\right)+\mathrm{Fe}\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\mathrm{Ge}\left(k\right)\end{array}\right.,$ Wherein x (k) the reactive power compensator state value that is the k moment, the reactive power compensator input value that u (k) obtains for k moment measurement, y (k) for k moment measurement obtain reactive power compensator output variable, the white noise interference value that e (k) is the k moment, wherein x (k) is n × 1 column vector, u (k) is 1 × 1 dimensional vector, y (k) is 1 dimensional vector, e (k) is 1 × 1 vector, then A is n × n matrix, and B is n × 1 matrix, C is 1 × n matrix, F is n × 1 matrix, and G is 1 × 1 matrix, and A, B, C, F, G are known;

S2, calculating parameter matrix Q=F*F', wherein F' represents the transpose operation of F; Calculating parameter matrix R=G*G', wherein G' represents the transpose operation of G;

The acquisition step obtaining current reactive power compensator state estimation is specific as follows:

S3, reactive power compensator state estimation initial value prior estimate covariance is set wherein I _nfor n × n unit matrix, ρ be greater than 0 arithmetic number; Reactive power compensator state estimation initial value is set

S4, calculating reactive power compensator k moment priori estimates with the covariance of k moment state x prior estimate error computing formula is ${\hat{x}}_k^{-}=A{\hat{x}}_{k-1}+{\mathrm{Bu}}_{k-1},$ $P_k^{-}={\mathrm{AP}}_{k-1}{A}^{\text{'}}+Q,$ Wherein for the posterior estimate of k-1 moment state x, u _k-1the reactive power compensator input value obtained for k-1 moment measurement and u (k-1), P _k-1for the covariance of the Posterior estimator error of k-1 moment state x;

S5, calculating reactive power compensator k moment posterior estimate computing formula is wherein kalman gain $K_k=P_k^{-}{C}^{\text{'}}{({\mathrm{CP}}_k^{-}{C}^{\text{'}}+R)}^{-1}\text{,}$ $P_k=(I-K_{k}C)P_k^{-},$ it is right to represent finding the inverse matrix, y _kbe y (k);

Make k be current time, then current reactive power compensator state estimation is k moment posterior estimate