CN106842913B - Water turbine adjusting system based on random probability distribution control - Google Patents
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Abstract
The invention discloses a water turbine regulating system based on random probability distribution control, which is characterized in that firstly, a water turbine speed regulating system is directly modeled through a differential equation based on an affine nonlinear system, so that a simplified dissipative Hamilton model of a water turbine system is established. Then, a control method based on probability distribution is designed by utilizing the technology of obtaining the accurate stationary solution of the dissipative non-integrable Hamiltonian system, so that a preset steady-state probability density function value output by the water turbine system can be obtained. In addition, the stability analysis of the system proves that the transition probability density of the controlled system is converged to a preset steady-state probability density function value by a Lyapunov function method, and the system simulation shows that the proposed control strategy can achieve the expected control effect.
Description
Technical Field
The invention relates to the field of positioning devices, in particular to a water turbine adjusting system based on random probability distribution control.
Background
The hydraulic turbine regulation control system is a power generation device widely used by hydroelectric power plants for ensuring safe operation of power generation, and plays a very critical role in maintaining the stability of a power system in controlling the hydraulic turbine system. Most of the early water turbine control system research is based on the assumption of linear model, and the actual water turbine control system is a nonlinear system. With the development of nonlinear control theory in recent decades, the research on the water turbine control system based on the nonlinear model has attracted much attention.
Currently, most non-linear models rely on modern control theory. The main idea is to linearize the nonlinear model without system disturbance accurately through state feedback, so that the control method can be designed by using the traditional linear theory to achieve the expected performance index. Although these models have considered the non-linear characteristics present in turbine systems, these control models have complex structural and parameter estimation processes. More importantly, few turbine systems can handle random uncertainties in the control process.
The turbine regulating system always suffers from the interference of complex random uncertainty excitation in the actual working environment, so that the stability of the system is seriously affected, and therefore random disturbance such as transient of a power system and an electromechanical system and the like should be considered in the process of modeling the turbine system. Particularly, a random control method for regulating the speed of the water turbine by elastic water hammer which is more consistent with the operation process of the actual water turbine does not exist.
Disclosure of Invention
The invention aims to provide a new design process based on probability distribution control, aiming at the defects in the prior art. The design utilizes a technology of obtaining an accurate stationary solution of a dissipative non-integrable Hamiltonian system to enable a control target of a random nonlinear system to reach a preset Static Probability Distribution Function (SPDF) value. According to the method, firstly, a differential equation based on an affine nonlinear system is used for directly modeling a water turbine speed regulating system, so that a simplified dissipative Hamilton model of the water turbine system is established. Then, a control method based on probability distribution is designed by utilizing the technology of obtaining the accurate stationary solution of the dissipative non-integrable Hamiltonian system, so that a preset steady-state probability density function value output by the water turbine system can be obtained. In addition, the stability analysis of the system proves that the transition probability density of the controlled system converges to the preset steady-state probability density function value by the Lyapunov function method.
The technical problem solved by the invention can be realized by adopting the following technical scheme:
a water turbine regulating system based on random probability distribution control comprises the following steps:
1) regarding a dynamic system between the output of the speed controller and the output of the water turbine as a nonlinear water turbine system, and fusing a surge transfer function between the initial speed and the flow speed;
2) the generalized Hamiltonian system is directly modeled through a differential equation based on an affine nonlinear system, and a simplified hydraulic turbine Hamiltonian model is as follows:
3) in order to process various random interferences of the water turbine, a random variable w is introduced into a nonlinear water turbine model under elastic water attack, and a water turbine Hamilton model based on random excitation and elastic water attack is established:
wherein W ═ W1,…wk]TIs a white Gaussian noise vector in the sense of Stelatongoriqi, and has a correlation function of E [ W ]k(t)Wl(t+τ)]＝2Dklδ (τ), f (x) is a noise intensity coefficient function;
4) obtaining a controlled nonlinear stochastic turbine system model by tracking a predetermined steady state probability density:
wherein,
u′＝[u′1，…，u′4]T＝g(x)up；
the purpose of the control design is to bring the controlled system to the target SPDF:
ρ(H)＝c exp[-φ(H)]
at this time
u′iCan be combined withThus obtaining u'iComprises the following steps:
therefore, up＝g(x)Tu′；
5) The controlled system probability density convergence is proved through the Lyapunov function, namely the transition probability density of the controlled system gradually approaches to the target steady-state probability density along with time, and the process is as follows:
of controlled systems
The system of random differential equations is as follows:
x is a process vector with the following elliptical differential operator:
wherein,
let the Lyapunov function be
The derivative of which is
It is obvious that there are V (X) ≧ 0, V (X) → infinity | → and L*V < 0 in the interval R4Within-omega of the time of the start of the operation,
wherein
It can be seen that the transition probability density of the controlled system gradually approaches the target steady-state probability density over time.
Compared with the prior art, the invention has the following beneficial effects:
1. the host and the receiver are packaged in the shell with small volume, and the portable electronic device is convenient to carry, install and maintain.
2. The modular structure design is adopted, the device can be installed in various production places, and the universality is strong.
3. The host machine and the receiver are both provided with functional units for alarm prompt, and when the distance away from the receiver exceeds a preset range or the host machine monitors that people or objects around the receiver approach the receiver, the alarm can be given out through sound, light or vibration.
Drawings
Fig. 1 is a block diagram of a UWB 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 water turbine according to the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
According to the method, firstly, a differential equation based on an affine nonlinear system is used for directly modeling a water turbine speed regulating system, so that a simplified dissipative Hamilton model of the water turbine system is established. Then, a control method based on probability distribution is designed by utilizing the technology of obtaining the accurate stationary solution of the dissipative non-integrable Hamiltonian system, and the transition probability density of the controlled system is proved to be converged to a preset steady-state probability density function value by a Lyapunov function method. The specific implementation steps are described in the following with reference to the attached drawings:
step 1: the model treats the dynamic system between the output of the speed controller and the output of the turbine as a nonlinear turbine system and fuses the surge transfer function between the initial speed and the flow rate.
Step 2: the generalized Hamiltonian system is directly modeled by differential equations based on an affine nonlinear system. The simplification method of the water turbine model is also suitable for high-order complex systems. The simplified Hamiltonian model of the turbine is as follows:
and step 3: as shown in a model diagram of an elastic surge turbine under random excitation in fig. 1, a nonlinear turbine system under elastic surge is inevitably subjected to various disturbances including random and external disturbances such as circuit faults, load disturbance, surge current and the like. These random disturbances can severely disturb the stability and output power quality of the system. However, most non-linear turbine models ignore the effects of random disturbances. In order to be able to cope with the non-linearity of the elastic water hammer and the disturbances present in the system, the present invention proposes a probability density control method for improving the practical performance of a random turbine system. A random variable w is introduced into the model of the water turbine under elastic water hammer. A model of a controlled nonlinear stochastic turbine system is as follows:
wherein W ═ W1,…wk]TIs a white Gaussian noise vector in the sense of Stelatongoriqi, and has a correlation function of E [ W ]k(t)Wl(t+τ)]＝2Dklδ (τ), f (x) is a noise intensity coefficient function. The stochastic controlled Hamiltonian system will be used to track the preset SPDF value.
And 4, step 4: tracking the design process of the control of the predetermined steady state probability density a controlled nonlinear stochastic turbine system model is obtained from the equation:
wherein,
u′＝[u′1，…，u′4]T＝g(x)up；
the purpose of the control design is to bring the controlled system to the target SPDF:
ρ(H)＝cexp[-φ(H)]。
at this timeu′iCan be combined with
Thus obtaining u'iComprises the following steps:
therefore up＝g(x)Tu′。
And 5: controlled system of convergence of probability density of controlled system
The system of random differential equations is as follows:
x is a process vector with the following elliptical differential operator:
wherein,
let the Lyapunov function be
The derivative of which is
It is obvious that there are V (X) ≧ 0, V (X) → infinity | → and L*V < 0 in the interval R4Within- Ω of wherein
It can be seen that the transition probability density of the controlled system gradually approaches the target steady-state probability density over 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 over time t. When t is>3, ρ (H, t) reaches the target SPDF ρ (H). Thus, the control design of the present invention can truly track the controlled system to a given periodThe SPDF value is expected. Fig. 3 shows the output power response curve of a water turbine. It can be seen therefrom that the output p of the controlled systemmCan meet the requirement that the liquid is stabilized in a specific interval after small oscillation within a short time, about 2-3 seconds.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (1)
1. A water turbine regulating system based on random probability distribution control is characterized by comprising the following steps:
1) regarding a dynamic system between the output of the speed controller and the output of the water turbine as a nonlinear water turbine system, and fusing a surge transfer function between the initial speed and the flow speed;
2) the generalized Hamiltonian system is directly modeled through a differential equation based on an affine nonlinear system, and a simplified hydraulic turbine Hamiltonian model is as follows:
3) in order to process various random interferences of the water turbine, a random variable w is introduced into a nonlinear water turbine model under elastic water attack, and a water turbine Hamilton model based on random excitation and elastic water attack is established:
wherein W ═ W1,…wk]TIs a white Gaussian noise vector in the sense of Stelatongoriqi, and has a correlation function of E [ W ]k(t)Wl(t+τ)]＝2Dklδ (τ), f (x) is a noise intensity coefficient function;
4) obtaining a controlled nonlinear stochastic turbine system model by tracking a predetermined steady state probability density:
wherein,
u′＝[u′1，…，u′4]T＝g(x)up；
the purpose of the control design is to bring the controlled system to the target SPDF:
ρ(H)＝c exp[-φ(H)]
at this time
u′iCan be combined withThus obtaining u'iComprises the following steps:
therefore, up＝g(x)Tu′；
5) The controlled system probability density convergence is proved through the Lyapunov function, namely the transition probability density of the controlled system gradually approaches to the target steady-state probability density along with time, and the process is as follows:
of controlled systems
The system of random differential equations is as follows:
x is a process vector with the following elliptical differential operator:
wherein,
let the Lyapunov function be
The derivative of which is
It is obvious that there are V (X) ≧ 0, V (X) → infinity | → and L*V < 0 in the interval R4Within-omega of the time of the start of the operation,
wherein
It can be seen that the transition probability density of the controlled system gradually approaches the target steady-state probability density over time.
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| CN112234609B (en) * | 2020-09-30 | 2023-07-25 | 云南电网有限责任公司 | Nonlinear excitation control method based on power system random dynamics model |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101404043A (en) * | 2008-09-10 | 2009-04-08 | 陕西电力科学研究院 | Hydraulic turbine and its pressure discharge system simulation method |
| CN104503228A (en) * | 2014-11-19 | 2015-04-08 | 国家电网公司 | Primary frequency modulation stability domain determination method of water turbine speed regulator under power mode |
| CN104533701A (en) * | 2014-12-23 | 2015-04-22 | 华中科技大学 | Automatic setting method for control parameters of water turbine speed regulating system |
| CN105068424A (en) * | 2015-08-05 | 2015-11-18 | 武汉大学 | Kaplan turbine adjusting system dynamic model suitable for electric power system analysis |
| CN105114242A (en) * | 2015-07-22 | 2015-12-02 | 重庆邮电大学 | Hydro governor parameter optimization method based on fuzzy self-adaptive DFPSO algorithm |
| CN105868497A (en) * | 2016-04-19 | 2016-08-17 | 国家电网公司 | Method for simulation modeling of variable crown elevation tailwater tunnel water turbine regulating system and model |
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| US20160123175A1 (en) * | 2014-11-05 | 2016-05-05 | General Electric Company | Hybrid model based detection of compressor stall |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101404043A (en) * | 2008-09-10 | 2009-04-08 | 陕西电力科学研究院 | Hydraulic turbine and its pressure discharge system simulation method |
| CN104503228A (en) * | 2014-11-19 | 2015-04-08 | 国家电网公司 | Primary frequency modulation stability domain determination method of water turbine speed regulator under power mode |
| CN104533701A (en) * | 2014-12-23 | 2015-04-22 | 华中科技大学 | Automatic setting method for control parameters of water turbine speed regulating system |
| CN105114242A (en) * | 2015-07-22 | 2015-12-02 | 重庆邮电大学 | Hydro governor parameter optimization method based on fuzzy self-adaptive DFPSO algorithm |
| CN105068424A (en) * | 2015-08-05 | 2015-11-18 | 武汉大学 | Kaplan turbine adjusting system dynamic model suitable for electric power system analysis |
| CN105868497A (en) * | 2016-04-19 | 2016-08-17 | 国家电网公司 | Method for simulation modeling of variable crown elevation tailwater tunnel water turbine regulating system and model |
Non-Patent Citations (2)
| Title |
|---|
| Direct modeling method of generalized Hamiltonian system and simulation simplified;TianmaoXu;《Procedia Engineering》;20121231;第902-907页 * |
| 水轮发电机的非线性随机系统研究;丁云飞;《第十届动力学与控制学术会议摘要集》;20160506;第179-180页 * |
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