CN103166232A - 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

Reactive power compensator method for estimating state based on 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 power compensator method for estimating state based on Kalman filtering.

Background technology

TCR type reactive power compensator has important function for voltage fluctuation in the solution iron and steel metallurgical industry, power factor regulation, and reactive power compensator wants to obtain the just necessary STATE FEEDBACK CONTROL that adopts of good dynamic and static state performance, excellent state estimation ability can increase system robustness, so the 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: a kind of reactive power compensator method for estimating state based on Kalman filtering is provided, can obtains the reactive power compensator state unbiased estimator under the noise jamming environment.

The present invention solves the problems of the technologies described above the technical scheme of taking to be: based on the reactive power compensator method for estimating state 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, reactive power compensator process interference noise matrix and measurement noise matrix are converted to Kalman filter known parameters matrix Q, R;

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

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

Discrete state equations under S1, the reactive power compensator white noise disturbed condition that obtains according to identification Method $\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+\mathrm{Bu}\left(k\right)+\mathrm{Fe}\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\mathrm{Ge}\left(k\right)\end{array}\right.,$ Wherein x (k) is k reactive power compensator state value constantly, the reactive power compensator input value that u (k) measures constantly for k, y (k) constantly measure for k the reactive power compensator output variable, e (k) is k white noise interference value constantly, 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, and 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 the transposition computing of F ' expression F; Calculating parameter matrix R=G*G ', wherein the transposition computing of G ' expression G.

Press such scheme, the acquisition step that obtains current reactive power compensator state estimation value is specific as follows:

S3, reactive power compensator state estimation initial value prior estimate covariance is set

I wherein _nBe n * n unit matrix, ρ is the arithmetic number greater than 0; 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 be priori estimates constantly Covariance with k state x prior estimate constantly 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

Be the posterior estimate of k-1 moment state x, u _k-1The reactive power compensator input value that constantly measures for k-1 is u (k-1), P _k-1Posteriority estimation error covariance for k-1 moment state x;

S5, calculating reactive power compensator k be posterior estimate constantly Computing formula is

Kalman gain wherein $K_k=P_k^{-}{C}^{\′}{(C{P}_k^{-}{C}^{\′}+R)}^{-1},$ $P_k=(I-K_{k}C)P_k^{-},$

It is right to represent Finding the inverse matrix, y _kBe y (k);

Make that k is current time, current reactive power compensator state estimation value is k posterior estimate constantly

Beneficial effect of the present invention is: adopt this method not only can obtain the reactive power compensator state without inclined to one side estimation, but also can carry out effective filtering to the noise jamming that is subject in the reactive power compensator measuring process, more traditional state observer has better filter effect, is fit to very much be applied to the power equipment of this electromagnetic interference complexity of reactive power compensator.

Description of drawings

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

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

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

Fig. 4 is the third state estimation value 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, reactive power compensator process interference noise matrix and measurement noise matrix are converted to Kalman filter known parameters matrix Q, R; Utilize time update equation and state renewal equation to carry out interative computation and obtain current reactive power compensator state estimation value.

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

Discrete state equations under S1, the reactive power compensator white noise disturbed condition that obtains according to identification Method $\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+\mathrm{Bu}\left(k\right)+\mathrm{Fe}\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\mathrm{Ge}\left(k\right)\end{array}\right.,$ Wherein x (k) is k reactive power compensator state value constantly, the reactive power compensator input value that u (k) measures constantly for k, y (k) constantly measure for k the reactive power compensator output variable, e (k) is k white noise interference value constantly, 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, and 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 the transposition computing of F ' expression F; Calculating parameter matrix R=G*G ', wherein the transposition computing of G ' expression G.

The acquisition step that obtains current reactive power compensator state estimation value is specific as follows:

S3, reactive power compensator state estimation initial value prior estimate covariance is set I wherein _nBe n * n unit matrix, ρ is the arithmetic number greater than 0; 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 be priori estimates constantly

Covariance with k state x prior estimate constantly 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

Be the posterior estimate of k-1 moment state x, u _k-1The reactive power compensator input value that constantly measures for k-1 is u (k-1), P _k-1Posteriority estimation error covariance for k-1 moment state x;

S5, calculating reactive power compensator k be posterior estimate constantly

Computing formula is Kalman gain wherein $K_k=P_k^{-}{C}^{\′}{(C{P}_k^{-}{C}^{\′}+R)}^{-1},$ $P_k=(I-K_{k}C)P_k^{-},$

It is right to represent

Finding the inverse matrix, y _kBe y (k);

Make that k is current time, current reactive power compensator state estimation value is k posterior estimate constantly

Being connected to a TCR type reactive power compensator discrete state equations on certain steel mill's bus 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。

Can get parameter 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。

Reactive-load compensator Initial state estimation value is set 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 respectively reactive power compensator priori state estimation according to step S4 and S5

With the posteriority state estimation

In order to check the reactive power compensator Kalman that the present invention designs to filter filter status observation dynamic property, 2 kinds of state estimation values of reactive power compensator and output estimation value when having tested step response in embodiment.State wherein

Estimated value as shown in Figure 2, state

Estimated value as shown in Figure 3, the output estimation value

As shown in Figure 4.

Comprehensive accompanying drawing 2-4 as can be known, when given reactive power generation step changes, the state estimation value

Also change fast thereupon, and estimated state settles out very soon, has shown that the reactive power compensator method for estimating state based on Kalman filter has good static and dynamic performance.In addition, state-based estimated value in accompanying drawing 4

The reactive power predicted value that obtains can be good at approaching real output value, science and the practicality based on the reactive power compensator method for estimating state of Kalman filter that have shown also that the present invention proposes.

Claims (3)

1. based on the reactive power compensator method for estimating state 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, reactive power compensator process interference noise matrix and measurement noise matrix are converted to Kalman filter known parameters matrix Q, R;

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

2. the reactive power compensator method for estimating state based on Kalman filtering according to claim 1, it is characterized in that: the acquisition step of Kalman filter known parameters matrix Q, R is specific as follows:

Discrete state equations under S1, the reactive power compensator white noise disturbed condition that obtains according to identification Method $\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+\mathrm{Bu}\left(k\right)+\mathrm{Fe}\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\mathrm{Ge}\left(k\right)\end{array}\right.,$ Wherein x (k) is k reactive power compensator state value constantly, the reactive power compensator input value that u (k) measures constantly for k, y (k) constantly measure for k the reactive power compensator output variable, e (k) is k white noise interference value constantly, 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, and 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 the transposition computing of F ' expression F; Calculating parameter matrix R=G*G ', wherein the transposition computing of G ' expression G.

3. the reactive power compensator method for estimating state based on Kalman filtering according to claim 2, it is characterized in that: the acquisition step that obtains current reactive power compensator state estimation value is specific as follows:

S3, reactive power compensator state estimation initial value prior estimate covariance is set

I wherein _nBe n * n unit matrix, ρ is the arithmetic number greater than 0; 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 be priori estimates constantly

Covariance with k state x prior estimate constantly 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 Be the posterior estimate of k-1 moment state x, u _k-1The reactive power compensator input value that constantly measures for k-1 is u (k-1), P _k-1Posteriority estimation error covariance for k-1 moment state x;

S5, calculating reactive power compensator k be posterior estimate constantly

Computing formula is Kalman gain wherein $K_k=P_k^{-}{C}^{\′}{(C{P}_k^{-}{C}^{\′}+R)}^{-1},$ $P_k=(I-K_{k}C)P_k^{-},$

It is right to represent Finding the inverse matrix, y _kBe y (k);

Make that k is current time, current reactive power compensator state estimation value is k posterior estimate constantly

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