Introduction The new distributed simulator uses advanced design concepts that are fully integrated with DCS in hardware and software. The virtual DCS system running on the simulator runs on the simulation model except that the operating parameters of the control object are taken from the simulation mathematical model instead of the terminal board. The hardware and software are consistent with the on-site DCS. This excellent feature makes all the screens and configurations running on the simulator are taken from the on-site DCS, which ensures the synchronization of the simulator and the on-site DCS; on the other hand, it also makes it possible to completely download the reasonable screen and configuration on the simulator. The use of DCS in the field, which objectively guarantees the possibility of various thermal debugging and optimization tests on the simulator. Thermal workers can perform various optimization tests on the simulator to eliminate the risk of operating on the DCS in the field, and can also directly apply the optimization strategy for successful testing to the site.
The control accuracy of boiler main steam temperature in thermal power generating units directly affects the thermal efficiency of the whole unit, and it also affects the safe operation of superheater pipes, steam turbines and even the entire unit. From the actual operating experience, the main factors affecting the main steam temperature are: 1) the steam flow, that is, the load level directly affects the main steam temperature; 2) the main steam pressure; 3) the combustion status, including the total coal amount, the upper grinding force, Burner elevation angle, combustion air, etc., these changes in the factors, will directly lead to changes in the combustion center, thus affecting the superheater heat absorption capacity, change the main steam temperature; 4) desuperheating water valve opening. Changes in any one of the above factors will lead to varying degrees of changes in the main steam temperature, thus affecting the economy and safety of the unit. Therefore, in the simulation of the power station, the main steam temperature is a very important parameter, and its simulation accuracy and stability must be guaranteed.
First, the theoretical derivation can be seen from the above, in the main steam temperature regulation system input is not a single. For multiple input and output systems, as well as nonlinear systems, classical control theory is no longer adequate. In order to simplify the mathematical expressions of the system, it is very advantageous to apply matrix operations, and the state space analysis method expresses the system in the form of a matrix of state space equations and then analyzes them. This method is a time-domain method. This method can be used to analyze and design a system with multiple feedbacks and multiple control variables so as to meet a predetermined performance index.
In modern control theory, the state equation is often used to describe the object properties of a multivariate system. More precisely, the state equation is an equation describing the interaction or intrinsic motion law of state variables [1].
The general form of the equation of state is:
![]()
Where X is an n-dimensional state vector![]()
,u is the r-dimensional control input vector ![]()
,Y is the m-dimensional output vector ![]()
. A is the n*n state coefficient matrix, B is the n*r control coefficient matrix, and C is the m*n observation coefficient matrix, ie:
![]()
and so![]()
![]()
At present, although there are many good ways to find continuous solutions to this equation of state, in the computer simulation process, what is needed is its numerical solution. Therefore, this continuous state equation must be discretized first. The Euler method is now commonly used in computer simulations. Euler's method has many advantages. For example, when the calculation step size is relatively small, the required accuracy can be achieved. However, when the calculation requires a relatively large step size, but the accuracy is guaranteed, Euler's law seems to be powerless. A method to solve this kind of problem will be introduced below. It is a dynamic factor method to solve the system state equation. Through the introduction of dynamic factors, this method makes up for the shortcomings of Euler's method.
From the general system state equation, which can be obtained from (1):
![]()
Where i=1.2.3.....n.
There are many ways to solve (1) numerical solutions, such as Euler's method and Runge-Kutta method.
The mathematical model of simulation is generally represented by a variety of differential equations. These differential equations are mostly manifestations or transformations of mass conservation, momentum conservation, and energy conservation equations. In many cases, the simulation mathematical model can be reduced to the following form of differential equation [2]:
![]()
Discretization by dynamic factor method is available:
![]()
Among them, DF is called a dynamic factor (variable factor), X is a value at time t, and x` is a value at time t+Δt.
In this paper, this dynamic factor method is used to solve the numerical solution of the system state equation, and it is called the dynamic factor method of solving the system state equation. Let (3) be the term on the right side of the equal sign. Using this method to discretize (3) yields:
![]()
Among them, A=1 in (4), dynamic factor![]()
It can be seen that when Aii=0, Dfi->1.
From (4) available:
![]()
The written form is as follows:
![]()
![]()
It can be obtained from (5),
![]()
Then get it from (6),
![]()
Then, (7) is the discrete equation obtained by discretization of the system state equation (1) by the dynamic factor method, and Q-1+I=P is made. Since Q contains the dynamic factor Dfi, P is called a dynamic matrix.
Second, the calculation of examples In order to effectively explain this method, the dynamic matrix is ​​now used in the literature [3] in the example of page 26.
2.1 Example The effect of desuperheating water valve opening in the main steam temperature system of a 300MW thermal power generating unit on the main steam temperature can be used as transfer function.![]()
To represent.
Convert (8) to the state-space equation as follows:
![]()
![]()
2.2 Simulation results In the program design, the calculation step length is T=0.6s and T=6s respectively, and the simulation time is ST=600s. Through the loop iteration, the simulation results shown in Figure 1 and Figure 2 are obtained:
![]()
![]()
Third, the conclusion:
(1) From Fig. 1 and Fig. 2, we can see that when the step size is relatively small, the dynamic factor method can achieve almost the same accuracy as the Euler method and the second-order Runge-Kutta method; when the step size is relatively large, The accuracy of the dynamic factor method is much higher than that of Euler's method, and it is also close to that of the second-order Runge-Kutta method. However, the required computation time is shorter than that of the second-order Runge-Kutta method.
(2) In the power plant simulation, some important parameters (such as the main steam temperature described in this article) require relatively high precision, but due to the special requirements of dynamic simulation, sometimes the whole system needs to be quickly brought to a certain operating state. One of the methods is to accelerate the calculation. One of them is to increase the calculation step size. Euler's method may not achieve the required accuracy in this case, but the Longer-Kutta method requires a long calculation time. Therefore, a dynamic factor method between the two can be used at this time. This method can not only meet the requirements for the accuracy of specific parameters, but also satisfy the requirements for rapidity of calculation. It is very valuable for engineering numerical calculations.
(3) Although the example used in this paper is just the effect of the opening of desuperheating water valve on main steam temperature, that is, the problem of single input, it can be seen through theoretical derivation that: through the introduction of dynamic factors and dynamic matrix The discretized state space equation is a very versatile method that applies both to single-input single-output (SISO) systems and to multiple-input multiple-output (MIMO) systems.
The control accuracy of boiler main steam temperature in thermal power generating units directly affects the thermal efficiency of the whole unit, and it also affects the safe operation of superheater pipes, steam turbines and even the entire unit. From the actual operating experience, the main factors affecting the main steam temperature are: 1) the steam flow, that is, the load level directly affects the main steam temperature; 2) the main steam pressure; 3) the combustion status, including the total coal amount, the upper grinding force, Burner elevation angle, combustion air, etc., these changes in the factors, will directly lead to changes in the combustion center, thus affecting the superheater heat absorption capacity, change the main steam temperature; 4) desuperheating water valve opening. Changes in any one of the above factors will lead to varying degrees of changes in the main steam temperature, thus affecting the economy and safety of the unit. Therefore, in the simulation of the power station, the main steam temperature is a very important parameter, and its simulation accuracy and stability must be guaranteed.
First, the theoretical derivation can be seen from the above, in the main steam temperature regulation system input is not a single. For multiple input and output systems, as well as nonlinear systems, classical control theory is no longer adequate. In order to simplify the mathematical expressions of the system, it is very advantageous to apply matrix operations, and the state space analysis method expresses the system in the form of a matrix of state space equations and then analyzes them. This method is a time-domain method. This method can be used to analyze and design a system with multiple feedbacks and multiple control variables so as to meet a predetermined performance index.
In modern control theory, the state equation is often used to describe the object properties of a multivariate system. More precisely, the state equation is an equation describing the interaction or intrinsic motion law of state variables [1].
The general form of the equation of state is:
Where X is an n-dimensional state vector
and so
At present, although there are many good ways to find continuous solutions to this equation of state, in the computer simulation process, what is needed is its numerical solution. Therefore, this continuous state equation must be discretized first. The Euler method is now commonly used in computer simulations. Euler's method has many advantages. For example, when the calculation step size is relatively small, the required accuracy can be achieved. However, when the calculation requires a relatively large step size, but the accuracy is guaranteed, Euler's law seems to be powerless. A method to solve this kind of problem will be introduced below. It is a dynamic factor method to solve the system state equation. Through the introduction of dynamic factors, this method makes up for the shortcomings of Euler's method.
From the general system state equation, which can be obtained from (1):
Where i=1.2.3.....n.
There are many ways to solve (1) numerical solutions, such as Euler's method and Runge-Kutta method.
The mathematical model of simulation is generally represented by a variety of differential equations. These differential equations are mostly manifestations or transformations of mass conservation, momentum conservation, and energy conservation equations. In many cases, the simulation mathematical model can be reduced to the following form of differential equation [2]:
Discretization by dynamic factor method is available:
Among them, DF is called a dynamic factor (variable factor), X is a value at time t, and x` is a value at time t+Δt.
In this paper, this dynamic factor method is used to solve the numerical solution of the system state equation, and it is called the dynamic factor method of solving the system state equation. Let (3) be the term on the right side of the equal sign. Using this method to discretize (3) yields:
Among them, A=1 in (4), dynamic factor
From (4) available:
The written form is as follows:
It can be obtained from (5),
Then get it from (6),
Then, (7) is the discrete equation obtained by discretization of the system state equation (1) by the dynamic factor method, and Q-1+I=P is made. Since Q contains the dynamic factor Dfi, P is called a dynamic matrix.
Second, the calculation of examples In order to effectively explain this method, the dynamic matrix is ​​now used in the literature [3] in the example of page 26.
2.1 Example The effect of desuperheating water valve opening in the main steam temperature system of a 300MW thermal power generating unit on the main steam temperature can be used as transfer function.
To represent.
Convert (8) to the state-space equation as follows:
2.2 Simulation results In the program design, the calculation step length is T=0.6s and T=6s respectively, and the simulation time is ST=600s. Through the loop iteration, the simulation results shown in Figure 1 and Figure 2 are obtained:
Third, the conclusion:
(1) From Fig. 1 and Fig. 2, we can see that when the step size is relatively small, the dynamic factor method can achieve almost the same accuracy as the Euler method and the second-order Runge-Kutta method; when the step size is relatively large, The accuracy of the dynamic factor method is much higher than that of Euler's method, and it is also close to that of the second-order Runge-Kutta method. However, the required computation time is shorter than that of the second-order Runge-Kutta method.
(2) In the power plant simulation, some important parameters (such as the main steam temperature described in this article) require relatively high precision, but due to the special requirements of dynamic simulation, sometimes the whole system needs to be quickly brought to a certain operating state. One of the methods is to accelerate the calculation. One of them is to increase the calculation step size. Euler's method may not achieve the required accuracy in this case, but the Longer-Kutta method requires a long calculation time. Therefore, a dynamic factor method between the two can be used at this time. This method can not only meet the requirements for the accuracy of specific parameters, but also satisfy the requirements for rapidity of calculation. It is very valuable for engineering numerical calculations.
(3) Although the example used in this paper is just the effect of the opening of desuperheating water valve on main steam temperature, that is, the problem of single input, it can be seen through theoretical derivation that: through the introduction of dynamic factors and dynamic matrix The discretized state space equation is a very versatile method that applies both to single-input single-output (SISO) systems and to multiple-input multiple-output (MIMO) systems.
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