1. LADRC-based steam turbine generator control system having a governor dead band, including a governor, a steam turbine, a power system, and a linear extended state observer, characterized in that the control system further comprises: an error compensation module;

and the error compensation module is used for feeding back the error between the theoretical output and the actual output of the speed regulator to the linear extended state observer, and estimating by using the linear extended state observer to enable the LADRC to achieve the purpose of eliminating the dead zone of the speed regulator.

2. The LADRC-based turbine generator control system of claim 1, further comprising: a state feedback gain module; the error compensation module comprises an upper compensation branch and a lower compensation branch; wherein:

the output of the control system being a frequency change Δf(ii) a Taking the output of the control system as a first input signal of the linear extended state observer;

subtracting the output of the linear extended state observer from an original input signal u and then using the subtracted output as the input of a state feedback gain module;

the output of the state feedback gain module is divided into two paths: one way output delta with control systemfWarp beam1/RResult after doubling of gain Δf/RPerforming subtraction operation and outputting intermediate quantity u'; the other path is used as error compensationA first path of input signals of a lower compensation branch of the module;Rthe unit descent characteristic is obtained;

directly taking the intermediate quantity u' as a first path of input signal of an upper compensation branch of the error compensation module, and directly taking the actual output of the speed regulator as a second path of input signal of the upper compensation branch of the error compensation module;

the first path of input signal and the second path of input signal of the upper compensation branch of the error compensation module are subjected to subtraction operation and then subjected to subtraction operationkAfter the gain is multiplied, the second path of input signals is used as the second path of input signals of the lower compensation branch of the error compensation module;kis a static compensation coefficient which can be adjusted manually;

and the first path of input signal and the second path of input signal of the lower compensation branch of the error compensation module are subjected to subtraction operation and then are used as the second path of input signal of the linear extended state observer.

3. The LADRC-based turbine generator control system of claim 2,

the intermediate quantity u' is also used as a first reference quantity for calculating an input signal of the speed regulator after passing through a dead zone of the speed regulator; the actual output of the speed regulator is respectively directly used as a second reference quantity for calculating the input signal of the speed regulator and directly used as a first reference quantity for calculating the input signal of the steam turbine; the first reference quantity and the second reference quantity of the input signal of the speed regulator are subtracted to be used as the input signal of the speed regulator;

the output of the steam turbine is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the steam turbine, and the other path is directly used as a first reference quantity for calculating the input signal of the power system; the method comprises the following steps that a first reference quantity and a second reference quantity of an input signal of the steam turbine are subtracted to be used as the input signal of the steam turbine;

the output of the power system is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the power system, and the other path passes throughK _p After the gain is multiplied, the output delta of the control system is obtainedf(ii) a Perturbing the load byP _d As input signal for calculating power systemThree reference amounts; the first reference quantity of the input signal of the power system is subtracted from the second reference quantity and the third reference quantity in sequence to be used as the input signal of the power system;K _p is the generator gain.

4. The LADRC-based method for determining the static compensation factor of a steam turbine generator control system according to any of claims 1 to 3, comprising:

step 1: obtaining describing function of non-linear elementN(X) And draws a negative countdown function-1-N(X) The curve of (1) specifically includes: describing function with dead zone non-linear characteristicN(X) As in equation (1), where the dead zone width of the dead zone nonlinearity and the slope of the linear output characteristic are 0.1 and 1, respectively:

(1)

and has the following components:

wherein the content of the first and second substances,Xthe amplitude of the non-linearity is represented,Ka slope representing a linear output characteristic, and Δ represents a dead zone width of the dead zone nonlinearity;

step 2: transfer function solvingG(jq) The method specifically comprises the following steps: definition of

Wherein the content of the first and second substances,G _L is the transfer function of the LADRC;jqthe frequency characteristics are represented by a frequency characteristic,g ₁the overall transfer function of the linear element is represented,g ₂which is indicative of the transfer function of the speed regulator,g ₃which represents the transfer function of the steam turbine,g ₄represents the transfer function of the power system and,g ₅the inverse of the droop characteristic of the unit is represented,g ₆representing static compensation coefficientsk，T _G Which is indicative of the time constant of the governor,T _T the time constant of the steam turbine is shown,T _P which is indicative of the time constant of the generator,srepresenting a differential operator;

then, the transfer function shown in the formula (2) can be obtained through the signal flow diagram and the Merson formulaG(jq)：

(2)

And step 3: plotting a transfer functionG(jq) Then, applying a nyquist stability criterion to analyze the nyquist curve, specifically: will be provided withG(jq) And-1-N(X) The curves of (a) are plotted in the same coordinate system,G(jq) The intersection point of the Nyquist curve and the negative real axis isIf, ifG(jq) The Nyquist curve of does not enclose-1-N(X) Curve of (i), i.e.The system is stable; if it isG(jq) The Nyquist curve of encloses-1-N(X) Curve of (i), i.e.The system is not stable.

5. LADRC-based steam turbine generator control system, the control system has steam turbine generation rate constraint, including speed regulator, steam turbine, electric power system and linear expansion state observer, characterized in that, the control system still includes: an error compensation module;

and the error compensation module is used for feeding back an error between theoretical output and actual output of the steam turbine as external disturbance to the linear extended state observer, and estimating by using the linear extended state observer to enable the LADRC to eliminate the influence of power generation rate constraint of the steam turbine.

6. The LADRC-based turbine generator control system of claim 5, further comprising: a state feedback gain module; the error compensation module comprises an upper compensation branch and a lower compensation branch; wherein:

the output of the control system being a frequency change Δf(ii) a Taking the output of the control system as a first input signal of the linear extended state observer;

subtracting the output of the linear extended state observer from an original input signal u and then using the subtracted output as the input of a state feedback gain module;

the output of the state feedback gain module is divided into two paths: one way output delta with control systemfIs based on 1RResult after doubling of gain Δf/RPerforming subtraction operation and outputting intermediate quantity u'; the other path is used as a first path of input signal of a lower compensation branch of the error compensation module;Rthe unit descent characteristic is obtained;

passing the intermediate quantity u' in sequenceAndafter the gain is multiplied, the first path of input signal of the upper compensation branch of the error compensation module is used, and the actual output of the steam turbine is directly used as the second path of input signal of the upper compensation branch of the error compensation module; wherein the content of the first and second substances,T _G which is indicative of the time constant of the governor,T _T representing the turbine time constant;

the first path of input signal and the second path of input signal of the upper compensation branch of the error compensation module are subjected to subtraction operation and then subjected to subtraction operationk ₁After the gain is multiplied, the second compensation branch of the error compensation moduleTwo paths of input signals;k ₁is a static compensation coefficient which can be adjusted manually;

and the first path of input signal and the second path of input signal of the lower compensation branch of the error compensation module are subjected to subtraction operation and then are used as the second path of input signal of the linear extended state observer.

7. The LADRC-based turbine generator control system of claim 6,

the intermediate quantity u' is also directly used as a first reference quantity for calculating the input signal of the speed regulator;

the output of the speed regulator is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the speed regulator, and the other path is directly used as a first reference quantity for calculating the input signal of the steam turbine; the first reference quantity and the second reference quantity of the input signal of the speed regulator are subtracted to be used as the input signal of the speed regulator;

the actual output of the steam turbine is respectively directly used as a second reference quantity for calculating the input signal of the steam turbine and a first reference quantity for calculating the input signal of the power system; the method comprises the following steps that a first reference quantity and a second reference quantity of an input signal of the steam turbine are subtracted to be used as the input signal of the steam turbine;

the output of the power system is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the power system, and the other path passes throughK _p After the gain is multiplied, the output delta of the control system is obtainedf(ii) a Perturbing the load byP _d As a third reference for calculating the input signal of the power system; the first reference quantity of the input signal of the power system is subtracted from the second reference quantity and the third reference quantity in sequence to be used as the input signal of the power system;K _p is the generator gain.

8. The LADRC based steam turbine generator control system static compensation system determination method of any of claims 5 to 7, comprising:

step 1: obtaining non-linear elementsDescription function of an articleN ₁(X) And draws a negative countdown function-1-N ₁(X) The curve of (1), specifically comprising; describing function with saturated non-linear characteristicN ₁(X) As in equation (3), where the linear region width of the saturation nonlinearity and the slope of the linear region characteristic are 0.0017 and 1, respectively:

(3)

and has the following components:

wherein the content of the first and second substances,Xthe amplitude of the non-linearity is represented,Ka slope representing a characteristic of the linear region,aa linear region width representing saturation nonlinearity;

step 2: transfer function solvingG ₁(jq) The method specifically comprises the following steps: definition of

Wherein is the transfer function of LADRC;jqrepresenting the frequency characteristic, representing the overall transfer function of the linear element,which is indicative of the transfer function of the speed regulator,andboth represent the transfer function of the steam turbine,represents the transfer function of the power system and,represents the inverse of the transfer function of the power system,representing the product of the transfer function of the governor and the transfer function of the turbine,the inverse of the droop characteristic of the unit is represented,representing static compensation coefficientsk ₁，Which represents a constant value of 1 and,T _G which is indicative of the time constant of the governor,T _T the time constant of the steam turbine is shown, T _P which is indicative of the time constant of the generator,srepresenting a differential operator;

then, the transfer function shown in the formula (4) can be obtained through the signal flow diagram and the Merson formulaG ₁(jq)：

(4)

And step 3: plotting a transfer functionG ₁(jq) Then, applying a nyquist stability criterion to analyze the nyquist curve, specifically: will be provided withG ₁(jq) And-1-N ₁(X) The curves of (a) are plotted in the same coordinate system,G ₁(jq) The intersection point of the Nyquist curve and the negative real axis isIf, ifG ₁(jq) The Nyquist curve of does not enclose-1-N ₁(X) Curve of (i), i.e.The system is stable; if it isG ₁(jq) The Nyquist curve of encloses-1-N ₁(X) Curve of (i), i.e.The system is not stable.

Background

With the ever-increasing size and complexity of modern power systems, the risk of wide area blackouts caused by system oscillations is increasing. Therefore, many advanced control methods have been used to solve the load frequency control problem, such as an inertia control and descent rate control strategy, an adaptive fuzzy gain scheduling, a Sliding Mode Control (SMC) method, and a PID (proportional-integral-derivative) Tuning method of 2-degree-of-freedom (TDF) Internal Mode Control (IMC) (refer to Tan w. Unified Tuning of PID load frequency controller for Power Systems components IMC [ J ]. IEEE Transactions on powers, 2010, V25(1):341 system 350). However, these documents ignore the fact that the system has non-linear characteristics. In a turbonator control system, there are a number of typical non-linear characteristics, such as: governor dead band and Generation Rate Constraints (GRCs), which can degrade the dynamic performance of the system and even be unstable. The literature has also been studied to address these problems. Such as fuzzy C-means clustering techniques (FCM), Bacterial Foraging Optimization Algorithms (BFOA), Gravity Search Algorithms (GSA) and pattern search methods (PS) and multivariate Model Predictive Control (MPC) methods (references Mojtaba S, Mohammad R, Ali M. Robust multivariable predicted located parameter control [ J ]. Electrofocal Power and Energy Systems, 2013, 46: 405). In the above documents, various control strategies are proposed to solve the nonlinear problem existing in the control system of the steam turbine generator, and parameter optimization and setting are performed. However, the designed controller has a relatively complex structure, large calculation amount and difficult industrial application.

Disclosure of Invention

Aiming at the problems of relatively complex structure and large calculation amount of the existing controller, the invention provides a steam turbine generator control system based on LADRC and a static compensation coefficient determining method thereof.

In a first aspect, the present invention provides a larcd ac based steam turbine generator control system, the control system having a governor dead band, including a governor, a steam turbine, a power system, and a linear extended state observer, the control system further comprising: an error compensation module;

and the error compensation module is used for feeding back the error between the theoretical output and the actual output of the speed regulator to the linear extended state observer, and estimating by using the linear extended state observer to enable the LADRC to achieve the purpose of eliminating the dead zone of the speed regulator.

Further, the control system further includes: a state feedback gain module; the error compensation module comprises an upper compensation branch and a lower compensation branch; wherein:

the output of the control system being a frequency change Δf(ii) a Taking the output of the control system as a first input signal of the linear extended state observer;

subtracting the output of the linear extended state observer from an original input signal u and then using the subtracted output as the input of a state feedback gain module;

the output of the state feedback gain module is divided into two paths: one way output delta with control systemfWarp beam1/RResult after doubling of gain Δf/RPerforming subtraction operation and outputting intermediate quantity u'; the other path is used as a first path of input signal of a lower compensation branch of the error compensation module;Rthe unit descent characteristic is obtained;

directly taking the intermediate quantity u' as a first path of input signal of an upper compensation branch of the error compensation module, and directly taking the actual output of the speed regulator as a second path of input signal of the upper compensation branch of the error compensation module;

the first path of input signal and the second path of input signal of the upper compensation branch of the error compensation module are subjected to subtraction operation and then subjected to subtraction operationkAfter the gain is multiplied, the second path of input signals is used as the second path of input signals of the lower compensation branch of the error compensation module;kis a static compensation coefficient which can be adjusted manually;

and the first path of input signal and the second path of input signal of the lower compensation branch of the error compensation module are subjected to subtraction operation and then are used as the second path of input signal of the linear extended state observer.

Further, the intermediate quantity u' is also used as a first reference quantity for calculating an input signal of the speed regulator after passing through a dead zone of the speed regulator; the actual output of the speed regulator is respectively directly used as a second reference quantity for calculating the input signal of the speed regulator and directly used as a first reference quantity for calculating the input signal of the steam turbine; the first reference quantity and the second reference quantity of the input signal of the speed regulator are subtracted to be used as the input signal of the speed regulator;

the output of the steam turbine is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the steam turbine, and the other path is directly used as a first reference quantity for calculating the input signal of the power system; the method comprises the following steps that a first reference quantity and a second reference quantity of an input signal of the steam turbine are subtracted to be used as the input signal of the steam turbine;

the output of the power system is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the power system, and the other path passes throughK _p After the gain is multiplied, the output delta of the control system is obtainedf(ii) a Perturbing the load byP _d As a third reference for calculating the input signal of the power system; the first reference quantity of the input signal of the power system is subtracted from the second reference quantity and the third reference quantity in sequence to be used as the input signal of the power system;K _p is the generator gain.

In a second aspect, the present invention further provides a method for determining a static compensation coefficient of a LADRC-based steam turbine generator control system, including:

step 1: obtaining describing function of non-linear elementN(X) And draws a negative countdown function-1-N(X) The curve of (1) specifically includes: describing function with dead zone non-linear characteristicN(X) As in equation (1), where the dead zone width of the dead zone nonlinearity and the slope of the linear output characteristic are 0.1 and 1, respectively:

(1)

and has the following components:

wherein the content of the first and second substances,Xthe amplitude of the non-linearity is represented,Ka slope representing a linear output characteristic, and Δ represents a dead zone width of the dead zone nonlinearity;

step 2: transfer function solvingG(jq) The method specifically comprises the following steps: definition of

Wherein the content of the first and second substances,G _L is the transfer function of the LADRC;jqthe frequency characteristics are represented by a frequency characteristic,g ₁the overall transfer function of the linear element is represented,g ₂which is indicative of the transfer function of the speed regulator,g ₃which represents the transfer function of the steam turbine,g ₄represents the transfer function of the power system and,g ₅the inverse of the droop characteristic of the unit is represented,g ₆representing static compensation coefficientsk，T _G Which is indicative of the time constant of the governor,T _T the time constant of the steam turbine is shown, T _P which is indicative of the time constant of the generator,srepresenting a differential operator;

then, the transfer function shown in the formula (2) can be obtained through the signal flow diagram and the Merson formulaG(jq)：

(2)

And step 3: plotting a transfer functionG(jq) Then, applying a nyquist stability criterion to analyze the nyquist curve, specifically: will be provided withG(jq) And-1-N(X) The curves of (a) are plotted in the same coordinate system,G(jq) The intersection point of the Nyquist curve and the negative real axis isIf, ifG(jq) The Nyquist curve of does not enclose-1-N(X) Curve of (i), i.e.The system is stable; if it isG(jq) The Nyquist curve of encloses-1-N(X) Curve of (i), i.e.The system is not stable.

In a third aspect, the present invention provides a larcd ac based steam turbine generator control system having steam turbine generation rate constraints including a governor, a steam turbine, a power system, and a linear extended state observer, the control system further comprising: an error compensation module;

and the error compensation module is used for feeding back an error between theoretical output and actual output of the steam turbine as external disturbance to the linear extended state observer, and estimating by using the linear extended state observer to enable the LADRC to eliminate the influence of power generation rate constraint of the steam turbine.

Further, the control system further includes: a state feedback gain module; the error compensation module comprises an upper compensation branch and a lower compensation branch; wherein:

the output of the control system being a frequency change Δf(ii) a Taking the output of the control system as a first input signal of the linear extended state observer;

subtracting the output of the linear extended state observer from an original input signal u and then using the subtracted output as the input of a state feedback gain module;

the output of the state feedback gain module is divided into two paths: one way output delta with control systemfIs based on 1RResult after doubling of gain Δf/RPerforming subtraction operation and outputting intermediate quantity u'; the other path is used as a first path of input signal of a lower compensation branch of the error compensation module;Rthe unit descent characteristic is obtained;

passing the intermediate quantity u' in sequenceAndafter the gain is multiplied, the first path of input signal of the upper compensation branch of the error compensation module is used, and the actual output of the steam turbine is directly used as the second path of input signal of the upper compensation branch of the error compensation module; wherein the content of the first and second substances,T _G which is indicative of the time constant of the governor,T _T representing the turbine time constant;

the first path of input signal and the second path of input signal of the upper compensation branch of the error compensation module are subjected to subtraction operation and then subjected to subtraction operationk ₁After the gain is multiplied, the second path of input signals is used as the second path of input signals of the lower compensation branch of the error compensation module;k ₁is a static compensation coefficient which can be adjusted manually;

and the first path of input signal and the second path of input signal of the lower compensation branch of the error compensation module are subjected to subtraction operation and then are used as the second path of input signal of the linear extended state observer.

Further, the intermediate quantity u' is also directly used as a first reference quantity for calculating the input signal of the speed regulator;

the output of the speed regulator is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the speed regulator, and the other path is directly used as a first reference quantity for calculating the input signal of the steam turbine; the first reference quantity and the second reference quantity of the input signal of the speed regulator are subtracted to be used as the input signal of the speed regulator;

the actual output of the steam turbine is respectively directly used as a second reference quantity for calculating the input signal of the steam turbine and a first reference quantity for calculating the input signal of the power system; the method comprises the following steps that a first reference quantity and a second reference quantity of an input signal of the steam turbine are subtracted to be used as the input signal of the steam turbine;

the output of the power system is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the power system, and the other path passes throughK _p After the gain is multiplied, the output delta of the control system is obtainedf(ii) a Perturbing the load byP _d As a third reference for calculating the input signal of the power system; the first reference quantity of the input signal of the power system is subtracted from the second reference quantity and the third reference quantity in sequence to be used as the input signal of the power system;K _p is the generator gain.

In a fourth aspect, the present invention further provides a method for determining a static compensation system of a LADRC-based steam turbine generator control system, including:

step 1: obtaining describing function of non-linear elementN ₁(X) And draws a negative countdown function-1-N ₁(X) The curve of (1), specifically comprising; describing function with saturated non-linear characteristicN ₁(X) As in equation (3), where the linear region width of the saturation nonlinearity and the slope of the linear region characteristic are 0.0017 and 1, respectively:

(3)

and has the following components:

wherein the content of the first and second substances,Xthe amplitude of the non-linearity is represented,Ka slope representing a characteristic of the linear region,aa linear region width representing saturation nonlinearity;

step 2: transfer function solvingG ₁(jq) The method specifically comprises the following steps: definition of

Wherein the content of the first and second substances,is the transfer function of the LADRC;jqthe frequency characteristics are represented by a frequency characteristic,the overall transfer function of the linear element is represented,which is indicative of the transfer function of the speed regulator,andboth represent the transfer function of the steam turbine,represents the transfer function of the power system and,represents the inverse of the transfer function of the power system,representing transfer function of speed regulatorThe product of the transfer function of the turbine,the inverse of the droop characteristic of the unit is represented,representing static compensation coefficientsk ₁，Which represents a constant value of 1 and,T _G which is indicative of the time constant of the governor,T _T the time constant of the steam turbine is shown, T _P which is indicative of the time constant of the generator,srepresenting a differential operator;

then, the transfer function shown in the formula (4) can be obtained through the signal flow diagram and the Merson formulaG ₁(jq)：

(4)

And step 3: plotting a transfer functionG ₁(jq) Then, applying a nyquist stability criterion to analyze the nyquist curve, specifically: will be provided withG ₁(jq) And-1-N ₁(X) The curves of (a) are plotted in the same coordinate system,G ₁(jq) The intersection point of the Nyquist curve and the negative real axis isIf, ifG ₁(jq) The Nyquist curve of does not enclose-1-N ₁(X) Curve of (i), i.e.The system is stable; if it isG ₁(jq) The Nyquist curve of encloses-1-N ₁(X) Curve of (i), i.e.The system is not stable.

The invention has the beneficial effects that:

compared with other control algorithms, the Linear Active Disturbance Rejection Control (LADRC) is a universal control structure independent of a controlled object model, has a simpler structure, is suitable for various nonlinear systems, and particularly only needs to set 2 parameters, so the LADRC is easily understood by a control engineer. Therefore, aiming at the control system of the steam turbine generator with a dead zone of a speed regulator or a GRC of a steam turbine, the invention adopts a linear active disturbance rejection control algorithm.

However, as a general control structure, when the system has non-linear characteristics, the linear active disturbance rejection control algorithm needs to convert the lardc into a high-order controller, but this destroys its inherent control structure, and may make it lose the active disturbance rejection characteristics. Therefore, aiming at the control system of the steam turbine generator with a dead zone of a speed regulator or a GRC of a steam turbine, the invention provides a novel steam turbine generator control system adopting an error compensation strategy based on a linear active disturbance rejection control algorithm, so that the linear active disturbance rejection control algorithm can quickly eliminate the influence of the dead zone of the speed regulator or the GRC of the steam turbine. In addition, the compensation strategy has a static compensation coefficient which can be adjusted manuallykOrk ₁However, as the compensation coefficient increases, the control performance of the system is also affected, and therefore, it is necessary to check the value range of the compensation coefficient. Therefore, the method for stably verifying and obtaining the value range of the static compensation coefficient in the compensation strategy by adopting the description function method is correspondingly and respectively provided. Simulation results show that the error compensation strategy provided by the invention has good performance for improving the control performance of the system, and the value range of the compensation coefficient is obtained by adopting a description function method, so that the method is feasible for providing reference for the selection of the coefficient.

Drawings

FIG. 1 is a schematic structural diagram of a LADRC-based steam turbine generator control system according to an embodiment of the present invention;

fig. 2 is a schematic diagram of a step response of an electrical power system of a LADRC using an error compensation strategy according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of an embodiment of the present inventionG(jq) And-1-N(X) A schematic diagram of a curve of (a);

FIG. 4 shows a second step response of the power system in LADRC using an error compensation strategy according to an embodiment of the present invention;

fig. 5 shows a third step response of the power system of the LADRC using the error compensation strategy according to the embodiment of the present invention;

FIG. 6 is a second schematic structural diagram of a LADRC-based steam turbine generator control system according to an embodiment of the present invention;

fig. 7 is a fourth schematic diagram of the step response of the power system of the LADRC using the error compensation strategy according to the embodiment of the present invention;

FIG. 8 is a schematic diagram of an embodiment of the present inventionG ₁(jq) And-1-N ₁(X) A schematic diagram of a curve of (a);

fig. 9 is a fifth schematic diagram of a step response of an electrical power system of a LADRC using an error compensation strategy according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Example 1

In a steam turbine generator control system, governor dead band nonlinearity is ubiquitous and therefore affects the control performance of the system. The embodiment of the invention aims at a turbine generator control system with a speed regulator dead zone nonlinearity, and the LADRC is used in the system. Next, based on the LADRC, an error compensation strategy is proposed, which is shown in fig. 1. The idea is to feed back the error between the theoretical output and the actual output of the speed regulator to the LESO, and estimate by using the LESO, so that LADRC achieves the purpose of eliminating dead zones, thereby quickly recovering and improving the control performance of the system.

As shown in fig. 1, an embodiment of the present invention provides a larcd ac-based steam turbine generator control system having a governor dead band, including a governor, a steam turbine, a power system, and a linear extended state observer, the control system further including: an error compensation module;

the error compensation module is used for feeding back the error between the theoretical output and the actual output of the speed regulator to the linear extended state observer, and estimating by using the linear extended state observer to enable the LADRC to achieve the purpose of eliminating the dead zone of the speed regulator, so that the control performance of the control system is rapidly recovered and improved.

As an implementation, the control system further comprises a state feedback gain module; the error compensation module comprises an upper compensation branch and a lower compensation branch; wherein:

the output of the control system being a frequency change Δf(ii) a Taking the output of the control system as a first input signal of the linear extended state observer;

subtracting the output of the linear extended state observer from an original input signal u and then using the subtracted output as the input of a state feedback gain module;

the output of the state feedback gain module is divided into two paths: one way output delta with control systemfIs based on 1RResult after doubling of gain Δf/RPerforming subtraction operation and outputting intermediate quantity u'; the other path is used as a first path of input signal of a lower compensation branch of the error compensation module; the unit descent characteristic is obtained;

directly taking the intermediate quantity u' as a first path of input signal of an upper compensation branch of the error compensation module, and directly taking the actual output of the speed regulator as a second path of input signal of the upper compensation branch of the error compensation module;

the first path of input signal and the second path of input signal of the upper compensation branch of the error compensation module are subjected to subtraction operation and then subjected to subtraction operationkAfter multiplying the gain, asThe second path of input signals of the lower compensation branch of the error compensation module;kis a static compensation coefficient which can be adjusted manually;

and the first path of input signal and the second path of input signal of the lower compensation branch of the error compensation module are subjected to subtraction operation and then are used as the second path of input signal of the linear extended state observer.

As an implementation mode, the intermediate quantity u' is also used as a first reference quantity for calculating an input signal of the speed regulator after passing through the dead zone of the speed regulator; the actual output of the speed regulator is respectively directly used as a second reference quantity for calculating the input signal of the speed regulator and directly used as a first reference quantity for calculating the input signal of the steam turbine; the first reference quantity and the second reference quantity of the input signal of the speed regulator are subtracted to be used as the input signal of the speed regulator;

the output of the steam turbine is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the steam turbine, and the other path is directly used as a first reference quantity for calculating the input signal of the power system; the method comprises the following steps that a first reference quantity and a second reference quantity of an input signal of the steam turbine are subtracted to be used as the input signal of the steam turbine;

the output of the power system is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the power system, and the other path passes throughK _p After the gain is multiplied, the output delta of the control system is obtainedf(ii) a Perturbing the load byP _d As a third reference for calculating the input signal of the power system; the first reference quantity of the input signal of the power system is subtracted from the second reference quantity and the third reference quantity in sequence to be used as the input signal of the power system;K _p is the generator gain.

Example 2

In the LADRC-based steam turbine generator control system in the above embodiment, there is a static compensation coefficient that can be manually adjustedkHowever, as the compensation coefficient increases, the control performance of the system is also affected, and therefore, it is necessary to check the value range of the compensation coefficient. Therefore, corresponding to the LADRC-based steam turbine generator control system in the above-described embodiment,the embodiment of the invention also provides a method for determining the static compensation coefficient of the steam turbine generator control system based on LADRC, which is called as a description function method and comprises the following steps:

s101: obtaining describing function of non-linear elementN(X) And draws a negative countdown function-1-N(X) The curve of (1) specifically includes: describing function with dead zone non-linear characteristicN(X) As in equation (1), where the dead zone width of the dead zone nonlinearity and the slope of the linear output characteristic are 0.1 and 1, respectively:

(1)

and has the following components:

wherein the content of the first and second substances,Xthe amplitude of the non-linearity is represented,Krepresents the slope of the linear output characteristic and Δ represents the dead zone width of the dead zone nonlinearity.

S102: transfer function solvingG(jq) The method specifically comprises the following steps: for the single-zone steam turbine generator control system shown in FIG. 1, definitions are provided

Wherein the content of the first and second substances,G _L is the transfer function of the LADRC;jqthe frequency characteristics are represented by a frequency characteristic,g ₁the overall transfer function of the linear element is represented,g ₂which is indicative of the transfer function of the speed regulator,g ₃which represents the transfer function of the steam turbine,g ₄represents the transfer function of the power system and,g ₅the inverse of the droop characteristic of the unit is represented,g ₆representing static compensation coefficientsk，T _G Which is indicative of the time constant of the governor,T _T the time constant of the steam turbine is shown, T _P representing generator time constant，sRepresenting a differential operator.

Then, the transfer function shown in the formula (2) can be obtained through the signal flow diagram and the Merson formulaG(jq)：

(2)

S103: plotting a transfer functionG(jq) Then, applying a nyquist stability criterion to analyze the nyquist curve, specifically: can be prepared by MATLABG(jq) And-1-N(X) The curves of (a) are plotted in the same coordinate system,G(jq) The intersection point of the Nyquist curve and the negative real axis isIf, ifG(jq) The Nyquist curve of does not enclose-1-N(X) Curve of (i), i.e.The system is stable; if it isG(jq) The Nyquist curve of encloses-1-N(X) Curve of (i), i.e.The system is not stable.

In order to verify the feasibility and accuracy of the control system and the compensation coefficient determination method thereof, the invention considers a single-region power system with the following model parameters:

adopting LADRC for control, wherein the parameters are selected as follows:

wherein the content of the first and second substances,w _c is the bandwidth of the controller(s),w _o is the observer bandwidth, the compensation coefficient is taken ask=0.7, for displaying the control effect of LADRC under the compensation strategytStep signal delta is added when the time is 1 secondP _d =0.01, and the dead zone value is 0.1, the response curve of the system is shown in fig. 2. The black dotted line represents the condition when the system has a dead zone of the speed regulator, the black solid line represents the condition when the system has no dead zone of the speed regulator, and the black dotted line represents the condition after the system adopts an error compensation strategy. It can be seen that when the error compensation strategy is not adopted, the control performance of the system is deteriorated due to the existence of the dead zone nonlinearity, and when the error compensation strategy is adopted, the control performance of the system is better improved. Therefore, the compensation strategy is effective in eliminating the dead zone non-linearity.

In order to determine the value range of the compensation coefficient, stability analysis is performed by using a description function method, and the requirement for stabilizing the system is metAnd the available value range 0<k<0.91. When inkWhen the value of the chemical oxygen demand is not less than 0.91,G(jq) The Nyquist curve of encloses-1-N(X) The curve (2) shows that the system is unstable, and the result is shown in FIG. 3. Next, we adjust the compensation coefficient manuallykThe value range is confirmed, and the simulation results are shown in fig. 4 and 5. Obviously, whenkAs it becomes larger, the compensation effect becomes higher, but when it increases to 0.91, the system becomes unstable. Simulation results prove that the stability analysis is carried out on the control system of the steam turbine generator with the dead zone of the speed regulator by adopting a description function method to obtain a static compensation coefficientkA range of values of (c) is feasible.

Example 3

In a steam turbine generator control system, a steam turbine GRC may affect the control performance of the system and cause instability. Therefore, the embodiment of the present invention proposes an error compensation strategy based on the LADRC, and the compensation strategy is shown in fig. 6. The idea is that the error between the theoretical output and the actual output of the turbine is used as external disturbance, and LESO is added for estimation, so that LADRC eliminates the influence of GRC, and the control performance of the system can be quickly recovered and improved.

As shown in fig. 6, an embodiment of the present invention provides a larcd ac-based steam turbine generator control system, the control system having steam turbine generation rate constraints, including a governor, a steam turbine, an electric power system, and a linear extended state observer, the control system further including: an error compensation module;

and the error compensation module is used for feeding back an error between theoretical output and actual output of the steam turbine as external disturbance to the linear extended state observer, and estimating by using the linear extended state observer to enable the LADRC to eliminate the influence of power generation rate constraint of the steam turbine.

As an implementable embodiment, the control system further comprises: a state feedback gain module; the error compensation module comprises an upper compensation branch and a lower compensation branch; wherein:

the output of the control system being a frequency change Δf(ii) a Taking the output of the control system as a first input signal of the linear extended state observer;

subtracting the output of the linear extended state observer from an original input signal u and then using the subtracted output as the input of a state feedback gain module;

the output of the state feedback gain module is divided into two paths: one way output delta with control systemfIs based on 1RResult after doubling of gain Δf/RPerforming subtraction operation and outputting intermediate quantity u'; the other path is used as a first path of input signal of a lower compensation branch of the error compensation module;Rthe unit descent characteristic is obtained;

passing the intermediate quantity u' in sequenceAndthe multiplied gain is used as the first input signal of the upper compensation branch of the error compensation module, and the actual output of the steam turbine is directly used as the upper compensation branch of the error compensation moduleA second path of input signals; wherein the content of the first and second substances,T _G which is indicative of the time constant of the governor,T _T representing the turbine time constant;

the first path of input signal and the second path of input signal of the upper compensation branch of the error compensation module are subjected to subtraction operation and then subjected to subtraction operationk ₁After the gain is multiplied, the second path of input signals is used as the second path of input signals of the lower compensation branch of the error compensation module;k ₁is a static compensation coefficient which can be adjusted manually;

and the first path of input signal and the second path of input signal of the lower compensation branch of the error compensation module are subjected to subtraction operation and then are used as the second path of input signal of the linear extended state observer.

As an embodiment, the intermediate quantity u' is also directly used as a first reference quantity for calculating the input signal of the speed regulator;

the output of the speed regulator is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the speed regulator, and the other path is directly used as a first reference quantity for calculating the input signal of the steam turbine; the first reference quantity and the second reference quantity of the input signal of the speed regulator are subtracted to be used as the input signal of the speed regulator;

the actual output of the steam turbine is respectively directly used as a second reference quantity for calculating the input signal of the steam turbine and a first reference quantity for calculating the input signal of the power system; the method comprises the following steps that a first reference quantity and a second reference quantity of an input signal of the steam turbine are subtracted to be used as the input signal of the steam turbine;

the output of the power system is divided into two paths, one path is directly used as a second reference quantity for calculating the input signal of the power system, and the other path passes throughK _p After the gain is multiplied, the output delta of the control system is obtainedf(ii) a Perturbing the load byP _d As a third reference for calculating the input signal of the power system; the first reference quantity of the input signal of the power system is subtracted from the second reference quantity and the third reference quantity in sequence to be used as the input signal of the power system;K _p is the generator gain.

Example 4

In the LADRC-based steam turbine generator control system in the above embodiment, there is a static compensation coefficient that can be manually adjustedk ₁However, as the compensation coefficient increases, the control performance of the system is also affected, and therefore, it is necessary to check the value range of the compensation coefficient. Therefore, corresponding to the steam turbine generator control system based on the LADRC in the foregoing embodiment, an embodiment of the present invention further provides a method for determining a static compensation system of a steam turbine generator control system based on the LADRC, including the following steps:

s201: obtaining describing function of non-linear elementN ₁(X) And draws a negative countdown function-1-N ₁(X) The curve of (1), specifically comprising; describing function with saturated non-linear characteristicN ₁(X) As in equation (3), where the linear region width of the saturation nonlinearity and the slope of the linear region characteristic are 0.0017 and 1, respectively:

(3)

and has the following components:

wherein the content of the first and second substances,Xthe amplitude of the non-linearity is represented,Ka slope representing a characteristic of the linear region,aindicating the linear region width of the saturation nonlinearity.

S202: transfer function solvingG ₁(jq) The method specifically comprises the following steps: for the single-zone steam turbine generator control system shown in FIG. 6, definitions are provided

Wherein the content of the first and second substances,is the transfer function of the LADRC;jqthe frequency characteristics are represented by a frequency characteristic,the overall transfer function of the linear element is represented,which is indicative of the transfer function of the speed regulator,andboth represent the transfer function of the steam turbine,represents the transfer function of the power system and,represents the inverse of the transfer function of the power system,representing the product of the transfer function of the governor and the transfer function of the turbine,the inverse of the droop characteristic of the unit is represented,representing static compensation coefficientsk ₁，Which represents a constant value of 1 and,T _G which is indicative of the time constant of the governor,T _T the time constant of the steam turbine is shown, T _P which is indicative of the time constant of the generator,srepresenting a differential operator.

Then, the transfer function shown in the formula (4) can be obtained through the signal flow diagram and the Merson formulaG ₁(jq)：

(4)

S203: plotting a transfer functionG ₁(jq) Then, applying a nyquist stability criterion to analyze the nyquist curve, specifically: can be prepared by MATLABG ₁(jq) And-1-N ₁(X) The curves of (a) are plotted in the same coordinate system,G ₁(jq) The intersection point of the Nyquist curve and the negative real axis isIf, ifG ₁(jq) The Nyquist curve of does not enclose-1-N ₁(X) Curve of (i), i.e.The system is stable; if it isG ₁(jq) The Nyquist curve of encloses-1-N ₁(X) Curve of (i), i.e.The system is not stable.

In order to verify the feasibility and accuracy of the control system and the compensation coefficient determination method thereof provided by the invention, the single-region power system with the following model parameters is considered:

the LADRC parameters were selected as follows:

wherein the content of the first and second substances,w _c is the bandwidth of the controller(s),w _o is the observer bandwidth, the compensation coefficient is taken ask ₁=1.14, in order toShows the control effect of LADRC under the compensation strategy, when GRC =0.0017MW/stStep signal delta is added when the time is 1 secondP _d =0.01, the response curve of the system is shown in fig. 7. The black dotted line represents the case where the error compensation strategy is adopted by the system, and the black solid line represents the case where the error compensation strategy is not adopted by the system. It can be seen that when the error compensation strategy is not adopted, the control performance of the system is deteriorated and becomes unstable due to the influence of the turbine GRC, and after the error compensation strategy is adopted, the control performance of the system is well improved and restored. Therefore, the compensation strategy is effective.

In order to determine the value range of the compensation coefficient, stability analysis is performed by using a description function method, and the requirement for stabilizing the system is metAnd further can obtaink ₁Value range of (1)< k ₁<1.24. When ink ₁When the molar ratio is not less than 1.24,G ₁(jq) The Nyquist curve of encloses-1-N ₁(X) The system was unstable, and the results are shown in fig. 8. We adjust the compensation coefficient manuallyk ₁The value range is confirmed, and the simulation result is shown in fig. 9. It can be seen that whenk ₁Gradually getting larger to 1.24, the system becomes unstable. Simulation results prove that the stability analysis is carried out on the control system of the steam turbine generator with the steam turbine GRC by adopting a description function method, so that the value range of the static compensation coefficient is feasible.

The invention respectively provides an error compensation strategy based on a linear active disturbance rejection control algorithm aiming at a steam turbine generator control system with a speed regulator dead zone or a steam turbine GRC, so that the linear active disturbance rejection control algorithm can rapidly eliminate the influence of the speed regulator dead zone or the steam turbine GRC. Meanwhile, the method for verifying and acquiring the value range of the static compensation coefficient in the compensation strategy by adopting a description function method is correspondingly provided. Simulation results show that the error compensation strategy provided by the invention has good performance for improving the control performance of the system, and the value range of the compensation coefficient is obtained by adopting a description function method, so that the method is feasible for providing reference for the selection of the coefficient.

Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.