CN106842913B - A Turbine Regulation System Based on Stochastic Probability Distribution Control - Google Patents

Abstract

The invention discloses a hydraulic turbine regulating system based on random probability distribution control. Firstly, the hydraulic turbine speed regulating system is directly modeled by a differential equation based on an affine nonlinear system, thereby establishing a simplified dissipation Hamiltonian of the hydraulic turbine system. Model. Then, a control method based on probability distribution is designed by using the technique of obtaining the accurate stationary solution of the dissipative nonintegrable Hamiltonian system, so that a preset steady-state probability density function value of the output of the hydraulic turbine system can be obtained. In addition, the stability analysis of the system is based on the Lyapunov function method to prove that the transition probability density of the controlled system converges to the preset steady-state probability density function value. The system simulation shows that the proposed control strategy can achieve the expected control. Effect.

Description

A Turbine Regulation System Based on Stochastic Probability Distribution Control

technical field

The invention relates to the field of positioning devices, in particular, to a hydraulic turbine regulating system based on random probability distribution control.

Background technique

Turbine regulation and control system is a kind of power generation equipment widely used in hydropower plants to ensure the safe operation of power generation. The control of the hydraulic turbine system plays a very critical role in maintaining the stability of the power system. Most of the early research on turbine control system is based on the assumption of linear model, while the actual turbine control system is a nonlinear system. With the development of nonlinear control theory in recent decades, the research on turbine control system based on nonlinear model has received extensive attention.

Currently, most nonlinear models rely on modern control theory. The main idea is to accurately linearize the nonlinear model without system disturbance through state feedback, so that the traditional linear theory can be used to design the control method to achieve the desired performance index. Although these models have taken into account the nonlinear characteristics existing in the turbine system, these control models have complex structures and parameter estimation procedures. More importantly, few turbine systems can handle random uncertainties in the control process.

In the actual working environment, the hydraulic turbine regulating system will always be disturbed by the complex random uncertainty excitation, which will seriously affect the stability of the system. Therefore, the dynamic and electromechanical system transients should be considered in the process of modeling the hydraulic turbine system. and other random disturbances. In particular, there is no stochastic control method for the speed regulation of the hydraulic turbine, which is more in line with the actual operation process of the hydraulic turbine.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a new control design process based on probability distribution in view of the deficiencies in the prior art. The design utilizes the technique of obtaining the exact stationary solution of the dissipative nonintegrable Hamiltonian system to make the control objective of the stochastic nonlinear system reach the preset static probability distribution function (SPDF) value. In this method, the turbine speed governing system is directly modeled by the differential equation based on the affine nonlinear system, and a simplified dissipative Hamiltonian model of the turbine system is established. Then, a control method based on probability distribution is designed by using the technology of obtaining the accurate stationary solution of the dissipative nonintegrable Hamiltonian system, so that a preset steady-state probability density function value of the output of the hydraulic turbine system can be obtained. In addition, the stability analysis of the system is carried out through the Lyapunov function method to prove that the transition probability density of the controlled system converges to the preset steady-state probability density function value.

The technical problem solved by the present invention can be realized by the following technical solutions:

A hydraulic turbine regulation system based on random probability distribution control, comprising the following steps:

1) Consider the dynamic system between the output of the speed controller and the turbine output as a nonlinear turbine system, and fuse the surge transfer function between the initial speed and the flow velocity;

2) The generalized Hamiltonian system is directly modeled by the differential equation based on the affine nonlinear system. The simplified Hamiltonian model of the turbine is as follows:

3) In order to deal with various random disturbances of the turbine, a random variable w is introduced into the nonlinear turbine model under elastic water hammer, and a Hamiltonian model of the turbine based on random excitation and elastic water hammer is established:

Among them, W=[w ₁ ,...w _k ] ^T is a Gaussian white noise vector in the Stratonovich sense, and its correlation function is E[W _k (t)W _l (t+τ)]=2D _kl δ(τ), f(x) is the noise intensity coefficient function;

4) By tracking the predetermined steady-state probability density, a controlled nonlinear stochastic hydraulic turbine system model is obtained:

u′＝[u′₁，…，u′₄]^T＝g(x)u_p；in,

u' ₌ [ _u'1 ,..., _u'4 ] ^T =g(x)up;

The purpose of control design is to enable the controlled system to achieve the target SPDF:

ρ(H)=c exp[-φ(H)]

u′_i可结合由此得到u′_i为：at this time

u' _i can be combined Thus, _u'i is obtained as:

Therefore, up ₌ g(x) ^Tu ';

5) The convergence of the probability density of the controlled system is proved by the Lyapunov function, that is, the transition probability density of the controlled system will gradually approach the target steady-state probability density with time, and the process is as follows:

随机微分方程组如下：controlled system

The system of stochastic differential equations is as follows:

x is a process vector with the following elliptic differential operator:

in,

Let the Lyapunov function be

Its derivative is

Obviously V(X)≥0, V(X)→∞ when |X|→∞ and L ^* V＜0 in the interval R ⁴ -Ω,

in

It can be seen that the transition probability density of the controlled system will gradually approach the target steady state probability density with time.

Compared with the prior art, the beneficial effects of the present invention are as follows:

1. The host and receiver are encapsulated in a small volume shell, which is convenient for portability, installation and maintenance.

2. Adopting modular structure design, it can be installed in various production sites, and has strong versatility.

3. There are functional units for alarm prompting on both the host and the receiver. When the distance from the receiver exceeds the preset range, or the host detects that people or objects are approaching, it can send an alarm through sound, light or vibration.

Description of drawings

FIG. 1 is a structural block diagram of the UWB security positioning alarm system according to the present invention.

FIG. 2 is a schematic diagram of the evolution of the transition probability density of the controlled system according to the present invention.

FIG. 3 is a schematic diagram of the output power response curve of the hydraulic turbine according to the present invention.

Detailed ways

In order to make the technical means, creative features, achievement goals and effects realized by the present invention easy to understand, the present invention will be further described below with reference to the specific embodiments.

The invention firstly directly models the water turbine speed control system through the differential equation based on the affine nonlinear system, so as to establish a simplified dissipation Hamiltonian model of the water turbine system. Then, a control method based on probability distribution is designed by using the technique of obtaining the exact stationary solution of the dissipative nonintegrable Hamiltonian system, and the Lyapunov function method is used to prove that the transition probability density of the controlled system converges to the preset stability. State probability density function value. The specific implementation steps are described as follows in conjunction with the accompanying drawings:

Step 1: The model treats the dynamic system between the output of the speed controller and the turbine output as a nonlinear turbine system and incorporates the surge transfer function between the initial speed and the flow rate.

Step 2: Direct modeling of the generalized Hamiltonian system by differential equations based on affine nonlinear systems. The simplified method of the turbine model is also applicable to higher-order complex systems. The simplified Hamiltonian model of the turbine is as follows:

Step 3: As shown in the model diagram of elastic water hammer turbine under random excitation in Fig. 1, the nonlinear hydraulic turbine system under elastic water hammer is inevitably subject to various disturbances, including random and external disturbances, such as Circuit failure, load disturbance, surge current, etc. These random disturbances can seriously disturb the stability and output power quality of the system. However, most nonlinear turbine models ignore the effects of random disturbances. In order to be able to deal with the nonlinearity of elastic water hammer and the disturbance existing in the system, the present invention proposes a probability density control method for improving the actual performance of the stochastic hydraulic turbine system. A random variable w is introduced in the turbine model under elastic water hammer. A controlled nonlinear stochastic turbine system is modeled as follows:

where W=[w ₁ ,...w _k ] ^T is a Gaussian white noise vector in the Stratonovich sense, and its correlation function is E[W _k (t)W _l (t+τ)]=2D _kl δ(τ), f(x) is the noise intensity coefficient function. This stochastic controlled Hamiltonian system will be used to track the preset SPDF value.

Step 4: Trace the design process of a given steady-state probability density control A controlled nonlinear stochastic turbine system model can be obtained by the above formula:

u′＝[u′₁，…，u′₄]^T＝g(x)u_p；in,

u' ₌ [ _u'1 ,..., _u'4 ] ^T =g(x)up;

The purpose of control design is to enable the controlled system to achieve the target SPDF:

ρ(H)=cexp[−φ(H)].

由此得到u′_i为：at this time u' _i can be combined

Thus, _u'i is obtained as:

Hence up ₌ g(x) ^Tu '.

随机微分方程组如下：Step 5: Convergence of the Controlled System Probability Density of the Controlled System

The system of stochastic differential equations is as follows:

x is a process vector with the following elliptic differential operator:

in,

Let the Lyapunov function be

Its derivative is

由此可见,受控系统的转移概率密度会随着时间逐渐逼近到目标稳态概率密度。Obviously there is V(X)≥0, V(X)→∞ when |X|→∞ and there is L ^* V＜0 in the interval R ⁴ -Ω, where

It can be seen that the transition probability density of the controlled system will gradually approach the target steady state probability density with time.

As shown in Fig. 2, the evolution of the transition probability density of the controlled system can be represented by the change of ρ(H,t) of the controlled system with time t. When t>3, ρ(H,t) reaches the target SPDFρ(H). Therefore, the control design of the present invention can actually make the controlled system track to the given desired SPDF value. Figure 3 shows the output power response curve of the turbine. It can be seen from this that the output p _m of the controlled system can be satisfied within a short period of time, about 2-3 seconds later, after a small oscillation, it can be stabilized in a specific range.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments, and the descriptions in the above-mentioned embodiments and the description are only to illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have Various changes and modifications fall within the scope of the claimed invention. The claimed scope of the present invention is defined by the appended claims and their equivalents.

Claims (1)

1. a water turbine regulating system based on random probability distribution control, is characterized in that, comprises the steps: 1) Consider the dynamic system between the output of the speed controller and the turbine output as a nonlinear turbine system, and fuse the surge transfer function between the initial speed and the flow velocity; 2) The generalized Hamiltonian system is directly modeled by the differential equation based on the affine nonlinear system. The simplified Hamiltonian model of the turbine is as follows:

3) In order to deal with various random disturbances of the turbine, a random variable w is introduced into the nonlinear turbine model under elastic water hammer, and a Hamiltonian model of the turbine based on random excitation and elastic water hammer is established:

Among them, W=[w ₁ ,...w _k ] ^T is a Gaussian white noise vector in the Stratonovich sense, and its correlation function is E[W _k (t)W _l (t+τ)]=2D _kl δ(τ), f(x) is the noise intensity coefficient function; 4) By tracking the predetermined steady-state probability density, a controlled nonlinear stochastic hydraulic turbine system model is obtained:

in,

u' ₌ [ _u'1 ,..., _u'4 ] ^T =g(x)up; The purpose of control design is to enable the controlled system to achieve the target SPDF: ρ(H)=c exp[-φ(H)] at this time

u' _i can be combined Thus, _u'i is obtained as:

Therefore, up ₌ g(x) ^Tu '; 5) The convergence of the probability density of the controlled system is proved by the Lyapunov function, that is, the transition probability density of the controlled system will gradually approach the target steady-state probability density with time, and the process is as follows: controlled system

The system of stochastic differential equations is as follows:

x is a process vector with the following elliptic differential operator:

in,

Let the Lyapunov function be

Its derivative is

Obviously V(X)≥0, V(X)→∞ when |X|→∞ and L ^* V＜0 in the interval R ⁴ -Ω, in

It can be seen that the transition probability density of the controlled system will gradually approach the target steady state probability density with time.

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