CN107450325B - A multi-model predictive control method for post-combustion CO2 capture system - Google Patents

Abstract

The invention discloses a multi-model predictive control method for a post-combustion _CO2 capture system. The predictive control method takes the post-combustion _CO2 capture system based on chemical adsorption as the controlled object, and the opening of the lean liquid valve and the low-pressure cylinder of the steam turbine The extraction valve opening is the system control input, and the _CO2 capture rate and reboiler temperature are the system output; firstly, based on the subspace identification method, using the data generated by the system operation, the local State space model; then use the gap metric method to investigate the nonlinear distribution of the controlled object; then establish a predictive controller at a suitable local operating point, and design a membership function to combine them weightedly to establish post-combustion CO ₂ capture System Multi-Model Predictive Control System. The method of the present invention has good global non-linear control capability, can effectively adapt to the needs of the system in a wide range of variable working conditions, quickly track the set value of the _CO2 capture rate, and improve the level of deep, fast and flexible operation of the _CO2 capture system.

Description

A multi-model predictive control method for post-combustion CO2 capture system

technical field

The invention relates to the technical field of predictive control methods, in particular to a multi-model predictive control method for a post-combustion _CO2 capture system.

Background technique

With the increasing severity of the greenhouse effect and related climate and ecological problems, reducing _CO2 emissions has become a key measure for the international community to deal with climate change. As the main equipment for power supply, thermal power units are the most stable and concentrated source of CO ₂ emissions. 30%-40% of the world's CO 2 emissions and 40%-50% of China's CO ₂ emissions come from thermal power units. While actively developing new energy technologies and striving to improve the power generation efficiency of thermal power units, CO ₂ capture by thermal power units has been recognized by many authoritative organizations as the most direct and effective technical means to achieve large-scale CO ₂ emission reductions in the next 30 years.

Among the existing CO 2 capture technologies for thermal power units, the post-combustion CO ₂ capture technology based on chemical absorption method directly separates _{CO 2 from} the flue gas after combustion in power plants, which has excellent inheritance and good influence on existing units. Technical applicability is the mainstream technology adopted by current _CO2 capture power plants. Since _CO2 capture needs to extract a large amount of steam from the middle and low pressure cylinders of thermal power units for lean liquid regeneration, its implementation has a great impact on the power generation efficiency of thermal power units. For this reason, the CO ₂ capture system must achieve a wide range of flexible operation, for example, reduce the CO ₂ capture rate during the period of urgent power supply demand or high electricity price, and increase the capture rate during the period of high environmental protection pressure or high carbon price . However, as the _CO2 capture equipment operates under a wide range of variable operating conditions, its system exhibits strong nonlinear characteristics, which leads to a decrease in the control performance and stability of the traditional predictive controller based on linear model design. Therefore, the development of a predictive control algorithm that incorporates the utilization of flue gas signals in post-combustion _CO2 capture systems is necessary.

Contents of the invention

The technical problem to be solved by the present invention is to provide a multi-model predictive control method for the post-combustion CO ₂ capture system, which can improve the adjustment quality of the CO ₂ capture system in a wide range of variable working conditions, and improve its fast, deep and flexible operation. ability.

In order to solve the above-mentioned technical problems, the present invention provides a multi-model predictive control method for a post-combustion _CO capture system, comprising the following steps:

(1) Switch the post-combustion _CO2 capture system to the manual state, and take the lean liquid flow valve opening u _a and the steam turbine low-pressure cylinder extraction valve opening signal u _b as inputs near the operating points of different capture rates, Energize the _CO2 capture system to obtain open-loop response data for _CO2 capture rate y _a and reboiler temperature y _b ;

(2) Select the sampling period Ts to for input, As the output, the local state space model of the CO ₂ capture system at different capture rate operating points is constructed by using the subspace identification method;

(3) Use the method of gap measurement to analyze the difference between adjacent local models and investigate the nonlinear distribution of _CO2 capture system;

(4) Establish a model predictive controller at a suitable local operating point; at each sampling time, use each sub-model to predict the CO ₂ capture rate of the system in a certain period of time in the future and reboiler temperature The local optimal lean liquid flow valve opening u ⁱ _a-op and steam turbine low pressure cylinder extraction valve opening signal u ⁱ _b-op are obtained through optimization calculation;

(5) Design the final appropriate membership function, and combine the weighted outputs of each controller to obtain the final lean liquid flow valve opening u _a-op and steam turbine low-pressure cylinder extraction valve opening signal u _b-op , and act on the CO ₂ capture system; where ω _i is the membership function corresponding to the i-th controller, which is a function of the scheduling variable and the capture rate CR, u ⁱ _a-op and u ⁱ _b-op are the optimal control signals calculated by the i-th controller ;

(6) Fix the prediction matrices ψ _x , ψ _u , ψ _y output from each local controller, and repeat steps (3)-(4) to realize continuous control.

Preferably, in step (2), T95/T _s =5-15, wherein T95 is the adjustment time for the transition process to rise to 95%.

Preferably, in step (2), a _CO2 capture system local state space model is constructed at different capture rate working conditions, and the specific steps are:

(21) Arrange the output data y and input data u obtained continuously from the 0th moment to the 2N+j-2 moment near a given operating point in the form of Hankel matrix:

Among them, N is the number of rows of the matrix, N is greater than the order of the _CO2 capture system, j is the number of columns of the matrix, Y and U represent the Hankel matrix composed of output and input data, respectively, Y ^f and Y ^p represent the future data of the output data and past data, U ^f and U ^p represent the future data and past data of the input data respectively, y _j represents the jth output data, u _j represents the jth input data;

(22) Let W ^p ＝[(Y ^p ) ^T (U ^p ) ^T ] ^T , perform QR decomposition on the following matrix:

Obtain the matrix L:

(23) To obtain the matrix L _w =L(:,1:N(m+l)), L _u =L(:,N(m+l)+1:end), m is the dimension of the input variable, l is the output variable dimension, L(:,1:N(m+l)) represents the first N(m+l) columns of the matrix L, L(:,N(m+l)+1:end) represents the matrix L All columns after column N(m+l)+1;

(24) Perform singular value decomposition on the L _w matrix:

Obtain the matrix Γ _N ＝U ₁ (S ₁ ) ^1/2 , and then get: model parameters in means to remove the Γ _N of the first row, and Γ _N means to remove the Γ _N of the last row, Indicates the Moore-Penrose pseudo-inverse; the model parameter C=Γ _N (1:l,:) can be obtained directly from the first l rows of Γ _N ;

(25) Solving linear equations:

Obtain model parameters B and D.

Preferably, in step (3), the gap metric value between adjacent local models is calculated, and the specific steps are:

(31) Do orthogonal right coprime decomposition on two adjacent local models P ₁ and P ₂ , get:

(32) Calculate the distance between models P ₁ and P ₂ :

Among them, H _∞ is a special Hardy normed space: σ _max (G(jω)) means the maximum singular value of G(jω); Q is any function in H _∞ space;

(33) Gap measure between two systems

Preferably, in step (4), use formula (1) to predict the _CO capture rate and reboiler temperature of the system within a certain period of time in the future

Among them, the prediction matrices ψ _x , ψ _u , ψ _y are respectively:

are the estimated state, input and output of the _CO2 capture system at time k, respectively, F is the observer gain, u _f is the input data at Nu time in the future, is the estimated output of the system at time N _y in the future,

Use the following formula to calculate the performance index function J:

Among them, Q _f and R _f are the weight matrix for adjusting the quality of input and output control, r _f is the sequence _of system _CO2 capture rate and reboiler temperature setpoint at time N in the future,

Respectively represent the system CO ₂ capture rate r _a and reboiler temperature r _b set values from time k+1 to time k+N ₁ , is the estimated value sequence of _CO2 capture rate and reboiler temperature of the system at time N _y in the future,

Respectively represent the estimated value of system CO ₂ capture rate y _a and reboiler temperature y _b from time k+1 to time k+N _y ,

Δu _f is the sequence of lean liquid flow valve opening signal u _a and low pressure cylinder extraction valve opening signal _{u b} at time Nu in the future increment;

in

The amplitude constraints (u _min , u _max ) and increment constraints (Δu _min , Δu _max ) of the opening signal u of the lean liquid flow valve and the extraction valve of the low-pressure cylinder in the CO ₂ capture system are:

Among them, u _min and u _max represent the minimum value and maximum value of the opening signal u of the lean liquid flow valve and the extraction valve of the low-pressure cylinder respectively, and Δu _min and Δu _max represent the opening signals of the lean liquid flow valve and the extraction valve of the low-pressure cylinder respectively The minimum increment and maximum increment of u;

At each sampling moment, formula (1) is substituted into formula (2), and the performance index function J is minimized under the condition of satisfying formulas (3) and (4), to obtain the optimal control increment sequence u _f :

Extract the first block u _k+1 in the optimal control increment sequence u _f as the optimal lean liquid flow valve and low pressure cylinder extraction valve opening signal

The beneficial effect of the present invention is that: the multi-model predictive control method of the present invention has good global nonlinear control ability, can effectively adapt to the needs of the system in a wide range of variable working conditions when applied to the post-combustion _CO2 capture system of thermal power plants, and quickly track CO ₂ capture rate setting value, improve the level of CO ₂ capture system depth fast and flexible operation.

Description of drawings

Fig. 1 is a schematic diagram of the method principle of the present invention.

Fig. 2 is a schematic diagram of the non-linear research results of the present invention.

Fig. 3 is a schematic diagram of the membership function designed in the present invention.

Fig. 4 is a schematic diagram of the control effect comparison between the multi-model predictive control (solid line) of the present invention and the conventional proportional integral differential control (dashed line) under the small range change of the set value of the _CO2 capture rate (the dotted line is the set value).

Fig. 5 is a schematic diagram of the control effect comparison between the multi-model predictive control (solid line) of the present invention and the conventional linear predictive control (dotted line) when the set value of _CO2 capture rate varies in a wide range (the dotted line is the set value).

Detailed ways

The multi-model predictive control method of the present invention is applied to the simulation model of the post-combustion _CO2 capture system of a 1MW thermal power unit. The control goal is to make the _CO2 capture rate and reboiler temperature Track the set value to realize the operation of the _CO2 capture system in a wide range of variable working conditions.

The post-combustion _CO2 capture system multi-model predictive control method of the present invention, the predictive control method takes the post-combustion _CO2 capture system based on chemical adsorption as the controlled object, the lean liquid valve opening and the steam turbine low-pressure cylinder extraction valve opening The degree is the system control input, and the CO ₂ capture rate and reboiler temperature are the system output. First, based on the subspace identification method, using the data generated by the system operation, the local state space model of the system is established at different operating points; Then use the gap measurement method to investigate the nonlinear distribution of the controlled object, and then establish a predictive controller at a suitable local operating point, and design a membership function to combine them weightedly to establish a multi-model prediction of the post-combustion CO ₂ capture system Control System. Compared with the traditional predictive control, the invention improves the control quality of the CO ₂ capture system in a wide range of variable working conditions, and enhances its flexible operation capability.

As shown in Figure 1, the multi-model predictive control method of the post-combustion _CO capture system of the present invention specifically includes the following steps:

Step 1, in the vicinity of a given capture rate operating point, design the lean liquid flow valve opening signal u _a and the turbine low-pressure cylinder extraction valve opening signal u _b to change once every 30 seconds and last for 30,000 seconds. Stimulate and acquire open-loop response data for a range of _CO2 capture rates y _a and reboiler temperatures y _b ;

Step 2, select sampling period T _s =30s, with for input, As the output, the subspace identification method is used to construct the local state space model of the _CO2 capture system at different capture rate operating points, and the specific steps are as follows:

A: Arrange 1000 sets of output data Y and amplified input data U obtained continuously into Hankel matrix form (2N+j-2=1000):

Among them, N is the number of matrix rows, and N=10; N is greater than the order of the CO ₂ capture system, j is the number of matrix columns, the larger the better if the hardware conditions allow, Y and U represent the composition of output and input data respectively The Hankel matrix of , Y ^f and Y ^p represent the future data and past data of the output data respectively, U ^f and U ^p represent the future data and past data of the input data respectively, y _j represents the jth output data, u _j represents the jth input data;

B: Let W ^p ＝[(Y ^p ) ^T (U ^p ) ^T ] ^T , perform QR decomposition on the following matrix:

Obtain the matrix L:

C: Obtain the matrix L _w ＝L(:,1:N(m+l)), L _u ＝L(:,N(m+l)+1:end), m=2, m is the input variable dimension , l=2, l is the dimension of input and output variables, L(:,1:N(m+l)) means the first N(m+l) columns of L, L(:,N(m+l)+1 :end) indicates all the columns of L after the N(m+l)+1 column;

D: Do a singular value decomposition of the L _w matrix:

Obtain the matrix Γ _N ＝U ₁ (S ₁ ) ^1/2 , and then get: model parameters in means to remove the Γ _N of the first row, and Γ _N means to remove the Γ _N of the last row, Indicates the Moore-Penrose pseudo-inverse; the model parameters C = Γ _N (1:l,:) can be obtained directly from the first l rows of Γ _N.

Subspace matrix l _w =L _w (1:l,:), l _u =L _u (1:l,1:m);

E: Solve a system of linear equations:

Obtain model parameters B and D.

Step 3, using the method of gap measurement, analyze the difference between adjacent local models, and investigate the nonlinear distribution of the _CO2 capture system, the specific steps are:

A: Perform orthogonal right coprime decomposition on two adjacent local models P ₁ and P ₂ to get:

B: Calculate the distance between models P ₁ and P ₂ :

Among them, H _∞ is a special Hardy normed space: σ _max (G(jω)) represents the maximum singular value of G(jω); Q is any function in H _∞ space, and Q=1.

C: Gap measure between two systems

D: According to the results of the gap measurement, select the local working point and design the membership function. In this example, the investigation results of the gap degree are shown in Figure 2. It can be seen that the nonlinearity of the system is strong in the range of low capture rate and high capture rate, and the membership function designed for this is shown in Figure 3.

Step 4: Build a model predictive controller at a suitable local operating point. At each sampling moment, use formula (1) to estimate the _CO2 capture rate and reboiler temperature of the system in the future

Among them, the prediction matrices ψ _x , ψ _u , ψ _y are respectively:

are the estimated state, input and output of the _CO2 capture system at time k, respectively, and F is the observer gain. u _f is the input data of N _u moments in the future, is the estimated output of the system at time N _y in the future, In this example, N _u =2, N _y =100.

Take formula (2) as the performance index function formula:

in, is the weight matrix for adjusting the quality of input and output control, r _f is the sequence of system _CO2 capture rate and reboiler temperature setpoint at time N _y in the future, Respectively represent the system CO ₂ capture rate r _a and reboiler temperature r _b set values from time k+1 to time k+N _y ,

is the estimated value sequence of _CO2 capture rate and reboiler temperature of the system at time Ny in the future,

Respectively represent the estimated value of system CO ₂ capture rate y _a and reboiler temperature y _b from time k+1 to time k+N _y , It can be described by formula (1), taking N _y =10; Δu _f is the lean liquid flow valve opening signal and low _- pressure cylinder extraction valve opening signal sequence at Nu moment in the future increment, of which N _u =2.

Consider the amplitude constraints (u _min ＝[0.4 0.02] ^T ,u _max ＝[ ₁ 0.075] ^T ) and increment constraints (Δu _min ＝[-0.007 -0.001] ^T ,Δu _max = [0.007 0.001] ^T ):

At each sampling moment, substituting (1) into performance index formula (2), and minimizing (2) under the condition of satisfying constraints (3) and (4), to obtain the local control increment sequence u _f : Extract the first block u _k+1 in the local control incremental sequence u _f as the local lean liquid flow valve and low pressure cylinder extraction valve opening signal

Step 5: Use the membership function to combine the weighted outputs of each controller to obtain the final lean liquid flow valve opening u _a-op and steam turbine low-pressure cylinder extraction valve opening signal u _b-op and act on CO ₂ capture system. in ω _i is the membership function corresponding to the i-th controller, which is a function of the scheduling variable and the capture rate CR, u ⁱ _a-op and u ⁱ _b-op are the optimal control signals calculated by the i-th controller .

Step 6, fix the prediction matrices ψ _x , ψ _u , ψ _y output from each local controller, and repeat steps 3-4 to realize continuous control.

In this embodiment, in order to compare the control effects of the post-combustion _CO2 capture system multi-model predictive control method, conventional proportional-integral-derivative control method and general predictive control method in the present invention, two sets of simulation experiments were done: simulation experiment 1, _CO2 The initial capture rate of the capture system was stable at 80%. At t=15min and 115min, the set value of _CO2 capture rate was slowly changed from 80% to 70% and 75%, respectively, and the set value of reboiler temperature was maintained at 383K In simulation experiment 2, the initial capture rate of the CO ₂ capture system is stable at 80%, t=15min and 115min, the set value of CO ₂ capture rate changes slowly from 80% to 90% and 55% respectively, and the reboil The temperature set point of the device remains unchanged at 383K.

As shown in Figure 4, when the set value of the _CO2 capture rate increases or decreases, the optimal control effect curve of the present invention for the post-combustion _CO2 capture system is obviously better than that of the conventional proportional plus integral controller, and has satisfactory Setpoint tracking and adjustment capability. As shown in Figure 5, under the condition that the set value of the _CO2 capture rate varies in a wide range, the optimal control method of the present invention can better coordinate the use of reboiler extraction and lean liquid flow, and realize the control of the capture rate. Fast tracking control can effectively avoid the controller oscillation caused by the mismatch of the linear model under large-scale variable working conditions, and has a more stable control effect, improving the operation quality of the CO ₂ capture system.

The multi-model predictive control method of the post-combustion _CO2 capture system of the present invention uses the subspace identification method to establish the model of the _CO2 capture system at different operating points, and selects the local model on the basis of the nonlinear investigation of the capture system , Establish a predictive controller and design a membership function to greatly improve the system's wide-ranging and variable operating conditions while maintaining all the advantages of conventional linear predictive control, thereby further improving the ability of the CO ₂ capture system to operate quickly, deeply and flexibly.

Although the present invention has been illustrated and described in terms of preferred embodiments, those skilled in the art should understand that various changes and modifications can be made to the present invention without departing from the scope defined by the claims of the present invention.

Claims (4)

1. Post combustion CO₂A multi-model predictive control method for an entrapment system, comprising the steps of:

(1) CO after combustion₂The trap system switches toManually operating at the operating points with different capture rates and with the opening u of the lean flow valve_aAnd the opening signal u of the steam extraction valve of the low-pressure cylinder of the steam turbine_bFor input, to CO₂The capture system is excited to obtain CO₂Trapping rate y_aAnd reboiler temperature y_bOpen loop response data of (a);

(2) the sampling period Ts is selected so as toIn order to be an input, the user can select,for output, a subspace identification method is utilized to construct CO at working condition points with different capture rates₂Capturing a system local state space model;

(3) analyzing the difference between adjacent local models by using a gap measurement method, and investigating CO₂A non-linear profile of the trapping system;

(4) establishing a model predictive controller at a proper local working point; at each sampling moment, CO of the system is estimated in a certain time in the future by utilizing each sub-model respectively₂Trapping rateAnd reboiler temperatureObtaining the local optimal lean solution flow valve opening u through optimization calculationⁱ _a-opAnd the opening signal u of the steam extraction valve of the low-pressure cylinder of the steam turbineⁱ _b-op(ii) a Predicting CO of a system in a future period of time by using formula (1)₂Capture rate and reboiler temperature

Wherein the prediction matrix psi_x、ψ_u、ψ_yRespectively as follows:

u_k,y_krespectively at time k CO₂The estimated state, input and output of the trapping system, F is the observer gain, u_fFor the input data at Nu time instants in the future, is the future N_yThe estimated output of the time of day system,

the performance indicator function J is calculated using the following formula:

wherein Q is_fAnd R_fIs a weight matrix for adjusting the quality of input/output control,r_fis the future N_yTime system CO₂A sequence of capture rates and reboiler temperature setpoints,

respectively representing the time k +1 to k + N_yTime system CO₂Trapping rate r_aAnd reboiler temperature r_bThe setting value is set, is the future N_yTime system CO₂A capture rate and reboiler temperature predictive value sequence,

respectively representing the time k +1 to k + N_yTime system CO₂Trapping rate y_aAnd reboiler temperature y_bThe value to be estimated is estimated in advance,

Δu_fis the future N_uOpening signal u of time lean flow valve_aAnd the opening signal u of the steam extraction valve of the low-pressure cylinder_bSequence ofAn increment of (d);

wherein

CO₂Amplitude constraints (u) of lean liquid flow valve and low-pressure cylinder steam extraction valve opening signals u of capture system_min,u_max) And an incremental constraint (Δ u)_min,Δu_max) Comprises the following steps:

wherein u is_min,u_maxRespectively representing the minimum value and the maximum value, delta u, of the opening signals u of the lean liquid flow valve and the low-pressure cylinder steam extraction valve_min,Δu_maxRespectively representing the minimum increment and the maximum increment of the lean solution flow valve and the low-pressure cylinder steam extraction valve opening signals u;

substituting the formula (1) into the formula (2) at each sampling moment, and minimizing the performance index function J under the condition of satisfying the formulas (3) and (4) to obtain an optimal control increment sequence u_f：

Extracting optimal control increment sequence u_fThe first block u in_k+1As optimal lean liquid flow valve and low-pressure cylinder extraction valve opening degree signals

(5) Designing a final appropriate membership function, and carrying out weighted combination on the outputs of all the controllers to obtain the final opening u of the lean flow valve_a-opAnd the opening signal u of the steam extraction valve of the low-pressure cylinder of the steam turbine_b-opAnd act on CO₂A capture system; whereinω_iIs the membership function corresponding to the ith controller, which is a function of the scheduling variable, the trapping rate CR, uⁱ _a-opAnd uⁱ _b-opCalculating an optimal control signal for the ith controller;

(6) fixing the prediction matrix psi output from each local controller_x、ψ_u、ψ_yAnd (5) repeating the steps (3) to (4) to realize continuous control.

2. Post combustion CO according to claim 1₂The multi-model predictive control method for a trapping system, characterized in that, in the step (2), T95/T_s5-15, wherein T95 is the adjustment time of the transition process rising to 95%.

3. Post combustion CO according to claim 1₂The multi-model predictive control method of the trapping system is characterized in that in the step (2), CO at working condition points with different trapping rates are constructed₂The method comprises the following steps of collecting a system local state space model:

(21) output data y and input data u from 0 th time to 2N + j-2 th time continuously obtained near a given working condition point are respectively arranged in a Hankel matrix form:

wherein N is the number of rows in the matrix, and N is greater than CO₂Capturing the system order, j is the number of matrix columns, Y and U respectively represent Hankel matrix formed by output data and input data, and Y^fAnd Y^pFuture data and past data, U, representing output data, respectively^fAnd U^pFuture data and past data, y, representing input data, respectively_jDenotes the jth output data, u_jRepresents the jth input data;

(22) let W^p＝[(Y^p)^T (U^p)^T]^TThe following matrix is subjected to QR decomposition:

obtaining a matrix L:

(23) thereby obtaining a matrix L_w＝L(:,1:N(m+l))，L_uL (: N (m + L) +1: end), m being the input variable dimension, L being the output variable dimension, L (: 1: N (m + L)) representing the first N (m + L) columns of the matrix L, L (: N (m + L) +1: end) representing all columns of the matrix L following the N (m + L) +1 columns;

(24) to L_wPerforming singular value decomposition on the matrix:

obtaining a matrix gamma_N＝U₁(S₁)^1/2And further obtaining: model parametersWhereinShowing the deletion of the preceding l rows_N，Γ _NRepresenting Γ for the removed l rows_N，Represents Moore-Penrose pseudo-inverse; model parameter C ═ Γ_N(1: l:) may be selected from gamma_NDirectly obtaining in the first line l;

(25) solving a system of linear equations:

model parameters B and D are obtained.

4. Post combustion CO according to claim 1₂The multi-model predictive control method of the trapping system is characterized in that in the step (3), a gap metric value between adjacent local models is calculated, and the specific steps are as follows:

(31) for two adjacent local models P₁、P₂Performing orthogonal right co-prime decomposition to obtain:

(32) calculation model P₁、P₂Distance between:

wherein H_∞A special Hardy canonical space:σ_max(G (j ω)) represents the maximum singular value of G (j ω); q is H_∞An arbitrary function in space;

(33) measurement of the gap between two systems