CN103199545B - Optimal secondary Gauss controller of dynamic reactive power compensation device and design method thereof - Google Patents

Abstract

The invention provides an optimal secondary Gauss controller of a dynamic reactive power compensation device. A thyristor control angle of the reactive power compensation device is sampled and serves as an input quantity, a reactive power of the reactive power compensation device is sampled and serves as an output quantity, model orders of the reactive power compensation device are selected, and a continuous time state equation of the reactive power compensation device is obtained by utilizing a model identification algorithm according to input data and output data, a Kalman filter is designed according to the obtained continuous time state equation of the reactive power compensation device, and an estimated value of a state variable of the reactive power compensation device is obtained by utilizing the Kalman filter; an indicator function is established and optimized, an emphasis matrix of state energy and an emphasis matrix of control energy are set according to empirical and actual dynamic and static requirements; a Riccati equation is solved to obtain a positive definite symmetric matrix; a gain matrix of the optimal secondary Gauss controller of the reactive power compensation device is calculated according to the positive definite symmetric matrix; a given gain matrix of the reactive power is calculated; and the optimal secondary Gauss controller of the reactive power compensation device is constructed to obtain the input of the thyristor control angle.

Description

The optimum secondary Gauss's controller of dynamic reactive compensation device and method for designing thereof

Technical field

The present invention relates to the design of dynamic reactive compensation device control system in power supply system, be specifically related to the optimum secondary Gauss's controller of a kind of dynamic reactive compensation device and method for designing thereof.

Background technology

In the industrial electrical systems such as iron and steel, metallurgy, need due to the change of load to carry out dynamic passive compensation to system, control method conventional at present utilizes pid control algorithm to carry out double-closed-loop control to system, and the change due to load causes control system comparatively complicated in pid parameter is adjusted.The reactive power compensator applied in engineering reality adopts the control strategy of several forms such as power factor controlling, Control of Voltage, Reactive Power Control usually, these control strategies have a common ground to be exactly control system inner ring adjusts reactive power compensator output reactive power by adjustment thyristor control angle, can find that reactive power compensator is when busbar voltage is certain by analyzing, the functional relation that the reactive power of output is corresponding with between thyristor control angle remains unchanged.In order to reduce on-the-spot debugging in engineer applied, corresponding relation between reactive power and IGCT can be designed to a stable closed-loop control system, when the control mode adopting voltage, power factor etc. different, only need to adjust the stable operation that outer shroud controller parameter can realize reactive power compensator.

Summary of the invention

The technical problem to be solved in the present invention is: provide the optimum secondary Gauss's controller of a kind of dynamic reactive compensation device and method for designing thereof, the system of guarantee has optimum control performance.

The present invention for solving the problems of the technologies described above taked technical scheme is: a kind of dynamic reactive compensation device optimum secondary Gauss controller design method, is characterized in that: it comprises the following steps:

S1, sampling reactive power compensator thyristor control angle u are as input quantity, sampling reactive power compensator reactive power y is as output quantity, select reactive power compensation device model order n, utilize Model Distinguish algorithm according to input, export data acquisition reactive power compensator state equation continuous time, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) measures the t system state variables value obtained, represent the differential of x (t), w (t) is process random noise, and v (t) is for measuring random noise, and u (t) is t thyristor control angle, y (t) is t reactive power compensator reactive power, A, B, C, B _ωfor coefficient matrix, and A is n × n matrix, and B is n × 1 matrix, and C is 1 × n matrix, B _ωfor n × 1 matrix, w (t) is l × l matrix;

S2, the reactive power compensator state equation continuous time design Kalman filter obtained according to step S1, utilize Kalman filter to obtain reactive power compensator state variable estimate

S3, set up optimizing index function wherein r is given reactive power, N be system mode energy lay particular stress on matrix, R be Systematical control energy lay particular stress on matrix, and N be greater than zero real number, R be greater than zero real number, the transpose operation of subscript T representing matrix; Described N and R all empirically needs setting with the sound state of reality;

S4, solve Riccati equation A ^tp+PA-PBR ^-1b ^tp+C ^tnC=0, obtains positive definite symmetric matrices P; And calculate reactive power compensator optimum secondary Gauss controller gain matrix K=R according to positive definite symmetric matrices P ^-1b ^tp; Calculate the given gain matrix G=R of reactive power ^-1b ^t[PBR ^-1b ^t-A ^t] ^-1c ^tn;

S5, structure reactive power compensator optimum secondary Gauss controller, obtain the input at thyristor control angle:

$u=\mathrm{Gr}-K\hat{x}\left(t\right).$

By such scheme, also comprise step S6, constantly value is attempted to N and R, by the reactive power tracking response curve obtained under more different value, determine the preferred value of N and R.

Based on a dynamic reactive compensation device optimum secondary Gauss controller for above-mentioned dynamic reactive compensation device optimum secondary Gauss controller design method, it is characterized in that: it comprises:

Reactive power compensator continuous time model, for the reactive power compensator thyristor control angle u that samples as input quantity, sampling reactive power compensator reactive power y is as output quantity, select reactive power compensation device model order n, utilize Model Distinguish algorithm according to input, export data acquisition reactive power compensator state equation continuous time, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) measures the t system state variables value obtained, represent the differential of x (t), w (t) is process random noise, and v (t) is for measuring random noise, and u (t) is t thyristor control angle, y (t) is t reactive power compensator reactive power, A, B, C, B _ωfor coefficient matrix, and A is n × n matrix, and B is n × 1 matrix, and C is 1 × n matrix, B _ωfor n × 1 matrix, w (t) is l × l matrix;

Kalman filter, for what obtain according to reactive power compensator continuous time model reactive power compensator state variable estimate is obtained with y (t)

Optimizing index device, for setting up optimizing index function wherein r is given reactive power, N be system mode energy lay particular stress on matrix, R be Systematical control energy lay particular stress on matrix, and N be greater than zero real number, R be greater than zero real number, the transpose operation of subscript T representing matrix; Described N and R all empirically needs setting with the sound state of reality;

Optimum secondary Gauss controller gain device, for obtaining reactive power compensator optimum secondary Gauss controller gain matrix K=R ^-1b ^tp, and to the reactive power compensator state variable estimate that Kalman filter obtains carry out gain calculating, obtain gain reactive power compensator state variable estimate; Wherein P is positive definite symmetric matrices, by solving Riccati equation A ^tp+PA-PBR ^-1b ^tp+C ^tnC=0 obtains;

The given gain apparatus of reactive power, for obtaining the given gain matrix G=R of reactive power ^-1b ^t[PBR ^-1b ^t-A ^t] ^-1c ^tn, and gain calculating is carried out to given reactive power, obtain gain reactive power;

Subtracter, the gain reactive power for being obtained by given for reactive power gain apparatus deducts the gain reactive power compensator state variable estimate that excellent secondary Gauss controller gain device obtains, and its result is as reactive power compensator thyristor control angle u.

Beneficial effect of the present invention is: the present invention utilizes Kalman filter to obtain reactive power compensator state variable estimate, break away from system state variables physically measurable restriction, carry out feeding back again according to the dynamic and static state performance that designer requires based on this estimate, controller parameter is obtained by solving Riccati equation, thus the system that ensures has optimum control performance, realize the reactive power Output Tracking Control of fast and stable.

Accompanying drawing explanation

Fig. 1 is the structural representation of one embodiment of the invention.

Fig. 2 is the System Reactive Power aircraft pursuit course that optimum secondary Gauss controller 1 obtains.

Fig. 3 is the System Reactive Power aircraft pursuit course that optimum secondary Gauss controller 2 obtains.

Detailed description of the invention

Fig. 1 is the structural representation of one embodiment of the invention, dynamic reactive compensation device optimum secondary Gauss controller comprises: reactive power compensator continuous time model, for the reactive power compensator thyristor control angle u that samples as input quantity, sampling reactive power compensator reactive power y is as output quantity, select reactive power compensation device model order n, utilize Model Distinguish algorithm according to input, export data acquisition reactive power compensator state equation continuous time, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) measures the t system state variables value obtained, represent the differential of x (t), w (t) is process random noise, and v (t) is for measuring random noise, and u (t) is t thyristor control angle, y (t) is t reactive power compensator reactive power, A, B, C, B _ωfor coefficient matrix, and A is n × n matrix, and B is n × 1 matrix, and C is 1 × n matrix, B _ωfor n × 1 matrix, w (t) is l × l matrix; Kalman filter, for what obtain according to reactive power compensator continuous time model reactive power compensator state variable estimate is obtained with y (t) optimizing index device, for setting up optimizing index function wherein r is given reactive power, N be system mode energy lay particular stress on matrix, R be Systematical control energy lay particular stress on matrix, and N be greater than zero real number, R be greater than zero real number, the transpose operation of subscript T representing matrix; Described N and R all empirically needs setting with the sound state of reality; Optimum secondary Gauss controller gain device, for obtaining reactive power compensator optimum secondary Gauss controller gain matrix K=R ^-1b ^tp, and to the reactive power compensator state variable estimate that Kalman filter obtains carry out gain calculating, obtain gain reactive power compensator state variable estimate; Wherein P is positive definite symmetric matrices, by solving Riccati equation A ^tp+PA-PBR ^-1b ^tp+C ^tnC=0 obtains; The given gain apparatus of reactive power, for obtaining the given gain matrix G=R of reactive power ^-1b ^t[PBR ^-1b ^t-A ^t] ^-1c ^tn, and gain calculating is carried out to given reactive power, obtain gain reactive power; Subtracter, the gain reactive power for being obtained by given for reactive power gain apparatus deducts the gain reactive power compensator state variable estimate that excellent secondary Gauss controller gain device obtains, and its result is as reactive power compensator thyristor control angle u.

The method for designing of above-mentioned dynamic reactive compensation device optimum secondary Gauss controller comprises the following steps:

S1, sampling reactive power compensator thyristor control angle u are as input quantity, sampling reactive power compensator reactive power y is as output quantity, select reactive power compensation device model order n, utilize Model Distinguish algorithm according to input, export data acquisition reactive power compensator state equation continuous time, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) measures the t system state variables value obtained, represent the differential of x (t), w (t) is process random noise, and v (t) is for measuring random noise, and u (t) is t thyristor control angle, y (t) is t reactive power compensator reactive power, A, B, C, B _ωfor coefficient matrix, and A is n × n matrix, and B is n × 1 matrix, and C is 1 × n matrix, B _ωfor n × 1 matrix, w (t) is l × l matrix;

S2, the reactive power compensator state equation continuous time design Kalman filter obtained according to step S1, utilize Kalman filter to obtain reactive power compensator state variable estimate

S3, set up optimizing index function wherein r is given reactive power, N be system mode energy lay particular stress on matrix, R be Systematical control energy lay particular stress on matrix, and N be greater than zero real number, R be greater than zero real number, the transpose operation of subscript T representing matrix; Described N and R all empirically needs setting with the sound state of reality;

S4, solve Riccati equation A ^tp+PA-PBR ^-1b ^tp+C ^tnC=0, obtains positive definite symmetric matrices P; And calculate reactive power compensator optimum secondary Gauss controller gain matrix K=R according to positive definite symmetric matrices P ^-1b ^tp; Calculate the given gain matrix G=R of reactive power ^-1b ^t[PBR ^-1b ^t-A ^t] ^-1c ^tn;

S5, structure reactive power compensator optimum secondary Gauss controller, obtain the input at thyristor control angle:

$u=\mathrm{Gr}-K\hat{x}\left(t\right).$

The design's method also can comprise step S6, constantly attempt value to N and R, by the reactive power tracking response curve obtained under more different value, determines the preferred value of N and R.

Below in conjunction with instantiation, the present invention is further elaborated.

Certain steel mill 6.5kV bus is connected to a TCR type reactive power compensator, opened loop control is utilized to carry out Model Distinguish experiment to compensation arrangement according to step S1, sample the reactive power y that IGCT amplification coefficient u and system export in 1 second, selective system order is n=2, utilizes continuous time state equation discrimination method to obtain reactive power compensator system model and be:

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\left[\begin{array}{cc}-10.9025531534668& -188.7790221402286\\ 148.7801599579912& 2.4037216595325\end{array}\right]x\left(t\right)+\left[\begin{array}{c}-1856.51\\ -115.25\end{array}\right]u\left(t\right)+\left[\begin{array}{c}-0.0017876\\ -0.0117144\end{array}\right]w\left(t\right)\\ y\left(t\right)=\left[\begin{array}{cc}21765000& -4458700\end{array}\right]x\left(t\right)+v\left(t\right)\end{array}\right.---\left(1\right),$

For the reactive power compensation device model in formula (1), require to utilize Design on Kalman Filter method to obtain Kalman filter gain matrix according to step S2 $L=\left[\begin{array}{c}-0.001638768022482\\ -0.011733290026127\end{array}\right],$ Then reactive power compensator state estimation computing formula be $\stackrel{\stackrel{\·}{^}}{x}\left(t\right)=A\hat{x}\left(t\right)+\mathrm{Bu}\left(t\right)+L(y\left(t\right)-C\hat{x}\left(t\right)),$ for differential.

On the basis having designed Kalman filter, according to after reactive power compensator state equation continuous time as shown in formula (1) that step S1 obtains, empirically need to determine matrix N and R with the sound state of reality, in the present embodiment, N, R are arithmetic number.First can select N=1, R=1, solving Riccati equation according to step S4 can obtain:

$P={10}^{23}\left[\begin{array}{cc}0.000000000000270& 0.000000000020361\\ 0.000000000020361& 1.100820660606938\end{array}\right],$

Then optimum secondary Gauss controller gain matrix can be obtained:

K＝10 ¹²×[0.027032938775752 2.036072804326626]，

Calculate the given gain matrix of reactive power:

G＝0.999999999996362。

The Kalman filter of above-mentioned acquisition, controller gain K and given gain are substituted in the reactive power compensator control system shown in accompanying drawing 1, reactive power aircraft pursuit course as shown in Figure 2 can be obtained.N and R selected from the known designer of accompanying drawing 2 causes control system unstable, and reactive power is followed the tracks of and occurred larger fluctuation, therefore must reselect suitable N and R value.

By test, select N=10 ^-13, R=1, can obtain controller gain matrix according to above-mentioned design:

K＝10 ⁵×[0.090779207062918 6.727617988870169]，

Given reactive power gain matrix:

G＝3.460237471250594×10 ^-7。

In like manner, the controller parameter of second time design is substituted into system and carries out testing the reactive power aircraft pursuit course obtained as shown in Figure 3, comparative drawings figs 2 and accompanying drawing 3 can find to design for the second time the control system that obtains comparatively designed system has better control performance first time, and this is mainly owing to selecting different N and R to cause.

Claims (3)

1. a dynamic reactive compensation device optimum secondary Gauss controller design method, is characterized in that: it comprises the following steps:

S1, sampling reactive power compensator thyristor control angle u are as input quantity, sampling reactive power compensator reactive power y is as output quantity, select reactive power compensation device model order n, utilize Model Distinguish algorithm according to input, export data acquisition reactive power compensator state equation continuous time, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) measures the t system state variables value obtained, represent the differential of x (t), w (t) is process random noise, and v (t) is for measuring random noise, and u (t) is t thyristor control angle, y (t) is t reactive power compensator reactive power, A, B, C, B _ωfor coefficient matrix, and A is n × n matrix, and B is n × 1 matrix, and C is 1 × n matrix, B _ωfor n × 1 matrix, w (t) is l × l matrix;

S2, the reactive power compensator state equation continuous time design Kalman filter obtained according to step S1, utilize Kalman filter to obtain reactive power compensator state variable estimate

S3, set up optimizing index function wherein r is given reactive power, N be system mode energy lay particular stress on matrix, R be Systematical control energy lay particular stress on matrix, and N be greater than zero real number, R be greater than zero real number, the transpose operation of subscript T representing matrix; Described N and R all empirically needs setting with the sound state of reality;

S4, solve Riccati equation A ^tp+PA-PBR ^-1b ^tp+C ^tnC=0, obtains positive definite symmetric matrices P; And calculate reactive power compensator optimum secondary Gauss controller gain matrix K=R according to positive definite symmetric matrices P ^-1b ^tp; Calculate the given gain matrix G=R of reactive power ^-1b ^t[PBR ^-1b ^t-A ^t] ^-1c ^tn;

S5, structure reactive power compensator optimum secondary Gauss controller, obtain the input at thyristor control angle:

$u=\mathrm{Gr}-K\hat{x}\left(t\right).$

2. dynamic reactive compensation device according to claim 1 optimum secondary Gauss controller design method, it is characterized in that: also comprise step S6, constantly value is attempted to N and R, by the reactive power tracking response curve obtained under more different value, determine the preferred value of N and R.

3., based on a dynamic reactive compensation device optimum secondary Gauss controller for the optimum secondary Gauss of the dynamic reactive compensation device described in claim 1 or 2 controller design method, it is characterized in that: it comprises:

Reactive power compensator continuous time model, for the reactive power compensator thyristor control angle u that samples as input quantity, sampling reactive power compensator reactive power y is as output quantity, select reactive power compensation device model order n, utilize Model Distinguish algorithm according to input, export data acquisition reactive power compensator state equation continuous time, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) measures the t system state variables value obtained, represent the differential of x (t), w (t) is process random noise, and v (t) is for measuring random noise, and u (t) is t thyristor control angle, y (t) is t reactive power compensator reactive power, A, B, C, B _ωfor coefficient matrix, and A is n × n matrix, and B is n × 1 matrix, and C is 1 × n matrix, B _ωfor n × 1 matrix, w (t) is l × l matrix;

Kalman filter, for what obtain according to reactive power compensator continuous time model reactive power compensator state variable estimate is obtained with y (t)

Optimizing index device, for setting up optimizing index function wherein r is given reactive power, N be system mode energy lay particular stress on matrix, R be Systematical control energy lay particular stress on matrix, and N be greater than zero real number, R be greater than zero real number, the transpose operation of subscript T representing matrix; Described N and R all empirically needs setting with the sound state of reality;

Optimum secondary Gauss controller gain device, for obtaining reactive power compensator optimum secondary Gauss controller gain matrix K=R ^-1b ^tp, and to the reactive power compensator state variable estimate that Kalman filter obtains carry out gain calculating, obtain gain reactive power compensator state variable estimate; Wherein P is positive definite symmetric matrices, by solving Riccati equation A ^tp+PA-PBR ^-1b ^tp+C ^tnC=0 obtains;

The given gain apparatus of reactive power, for obtaining the given gain matrix G=R of reactive power ^-1b ^t[PBR ^-1b ^t-A ^t] ^-1c ^tn, and gain calculating is carried out to given reactive power, obtain gain reactive power;

Subtracter, the gain reactive power for being obtained by given for reactive power gain apparatus deducts the gain reactive power compensator state variable estimate that excellent secondary Gauss controller gain device obtains, and its result is as reactive power compensator thyristor control angle u.