For the operation of the supercritical once-through boiler generation units, the control of the temperature at intermediate point (IPT) is highly significant. IPT is the steam temperature at the outlet of the separator. Currently, PID control algorithms are widely adopted for the IPT control. However, PID cannot achieve the optimal performances as the units’ dynamic characteristic changes at different working points due to the severe nonlinearity. To address the problem, a new control algorithm using affine nonlinear system is adopted for a 600 MW unit in this paper. In order to establish the model of IPT via affine nonlinear system, the simplified mechanism equations on the evaporation zone and steam separator of the unit are established. Then, the feedback linearizing control law can be obtained. Full range simulations with the load varying from 100% to 30% are conducted. To verify the effectiveness of the proposed control algorithm, the performance of the new method is compared with the results of the PID control. The feed-water flow disturbances are considered in simulations of both of the two control methods. The comparison shows the new method has a better performance with a quicker response time and a smaller overshoot, which demonstrates the potential improvement for the supercritical once-through boiler generation unit control.
Developing supercritical once-through boiler generation units [
On the one hand, high performance is required for the IPT control, as 1°C variation of IPT could end up with fluctuations of main-steam temperature around 8°C generally. The variation of main-steam temperature has profound effects on the stability, security, and efficiency of supercritical units. Therefore, the IPT control is a key problem to all of the units. On the other hand, more and more distributed energy is integrated into the grid. Renewable energy such as solar and wind power has bad capacity of peak regulation which leads to the increasing requirement of load regulation for the traditional units. To improve the control performance, the nonlinearity must be addressed.
For nonlinear systems [
In 2000, Åström and Bell established a simplified nonlinear model of the drum-boiler unit [
In [
With rapid development of nonlinear control theory and affine nonlinear system [
In this paper, affine nonlinear system based on exact feedback linearization [
In order to simplify boiler model [ medium enthalpy at the outlet of the economizer (kJ/kg); steam pressure at the outlet of the economizer (MPa); feed-water flow at the outlet of the economizer (kg/s); steam pressure at the outlet of the evaporation zone (MPa); steam temperature at the outlet of the evaporation zone (K); steam density at the outlet of the evaporation zone (kg/m3); metal mass of the evaporation zone (kg); steam flow at the outlet of the evaporation zone (kg/s); internal energy of steam at the outlet of the evaporation zone (kJ/kg); metal temperature at the outlet of the evaporation zone (K); specific heat capacity of the metal in evaporation zone (kJ/(kg·K)); steam enthalpy at the outlet of the evaporation zone (kJ/kg); average steam density in evaporation zone (kg/m3); heat which the steam transfers to the metal pipe in evaporation zone (kJ/s); heat which the metal pipe transfers to the steam in evaporation zone (kJ/s); length (m) and volume ( metal mess of the steam separator (kg); inner surface area of the steam separator (m2); steam temperature at the outlet of the separator (K); volume of the separator ( metal temperature at the outlet of the separator (K); steam flow at the outlet of the separator (kg/s); steam density at the outlet of the separator (kg/m3); specific heat capacity of the separator's metal (kJ/(kg·K)); steam enthalpy at the outlet of the separator (kJ/kg); steam pressure at the outlet of the separator (MPa); heat which the steam transfers to the metal pipe in separator (kJ/s); specific heat capacity under constant pressure in pipe (constant); average specific heat capacity of the steam in heat-transfer zone (kJ/(kg·K)); coal-fired value (kg/s); the steam temperature difference between input and output of the economizer (K).
By establishing the differential equations for the supercritical once-through boiler generation units, the model of the evaporation zone and the steam-separator can be acquired [
If there is no other source which transfers heat to the separator, the following equations can be written as
It is assumed that the steam and the liquid medium are thoroughly mixed without any pressure loss. Therefore, the differential equations are presented as
Meanwhile, the steam evaporated equation is given as
The nonlinear system is difficult to solve as the model from (
In order to obtain the relative degree, the LIE derivative should be calculated.
Firstly, the LIE derivative is figured out as
Secondly the coordinate transformation
Finally, a new linear system after coordinate transformation and exact feedback linearization is derived as
Using the optimal control law [
To verify the validation of the law (
The enthalpy formula is difined as
The enthalpy can be obtained by using (
With these parameters at full load, the equations are obtained as
The Lyapunov Law is used to analyze the stability of the systems (
At 100% load,
Coefficient matrix eigenvalues at different loads.
Load proportion | Load |
eigenvalue |
eigenvalue |
---|---|---|---|
100% | 486 |
|
|
90% | 437.4 |
|
|
80% | 388.8 |
|
|
70% | 340.2 |
|
|
60% | 291.6 |
|
|
50% | 243 |
|
|
40% | 194.4 |
|
|
30% | 145.8 |
|
|
From Table
In order to reflect the real dynamic of the practical system, the feed-water flow disturbance is considered in the simulation. The structure diagram of affine nonlinear system is presented in Figure
Structure diagram of affine nonlinear system.
The model in Figure
Performance of affine nonlinear system on IPT at 100% load.
In Figure
Performance with the feed-water flow disturbance at 100% load.
As shown in Figure
To study the affine nonlinear system further, more simulations have been conducted on IPT for the 600 MW supercritical unit at different loads (boiler type: SG1913/25.40-MXXX). While keeping other parameters constant, different loads leads to different
Simulation performances via affine nonlinear system.
Load proportion |
|
With feed-water flow | |||
---|---|---|---|---|---|
|
|
|
|
|
|
100% | 486 | 3.7 | 8 |
|
4 |
90% | 437.4 | 4.1 | 9 |
|
4 |
80% | 388.8 | 1.2 | 11 |
|
5 |
70% | 340.2 | 4.2 | 9 |
|
4 |
60% | 291.6 | 3.9 | 8 |
|
6 |
50% | 243 | 4.3 | 9 |
|
6 |
40% | 194.4 | 3.9 | 10 |
|
7 |
30% | 145.8 | 4.2 | 8 |
|
5 |
Response of affine nonlinear system at different loads.
100%
90%
80%
70%
60%
50%
40%
30%
As shown in Figure
The results such as the overshoot
The results in Table
In engineer application, PID control is used widely. To compare it with the optimal control, the PID control is applied in this paper to control of IPT. As the model via affine nonlinear system is state equation which cannot be simulated with PID controller directly, it is essential that the system transfer function should be calculated by point approximation linearization. The first equation of (
After substituting
The enthalpy can be obtained by using (
The initial feed-water flow at the outlet of the coal economizer is
Therefore, the system structure diagram after PID control of IPT is presented in Figure
System structure diagram of PID control on IPT.
To verify the rationality of (
Response of PID control on IPT at 100% load.
As shown in Figure
Performance of PID control with feed-water flow at 100% load.
As shown in Figure
The PID control of IPT for the 600 MW supercritical unit has been simulated at different loads. For example, at 100% load, the simulation result with the feed-water disturbance is presented in Figure
Parameters
Load proportion |
|
|
---|---|---|
100% | 486 | 485.53 |
90% | 437.4 | 436.977 |
80% | 388.8 | 388.42 |
70% | 340.2 | 339.871 |
60% | 291.6 | 291.318 |
50% | 243 | 242.765 |
40% | 194.4 | 194.212 |
30% | 145.8 | 145.659 |
Then simulations are conducted after using the above parameters into (
Response on system of PID control on at different loads.
100%
90%
80%
70%
60%
50%
40%
30%
As shown in Figure
Traditional PID control performance.
Load proportion |
|
With feed-water flow | |||
---|---|---|---|---|---|
|
|
|
|
|
|
100% | 486 | 19.4 | 40 |
|
20 |
90% | 437.4 | 21.8 | 40 |
|
20 |
80% | 388.8 | 25.3 | 40 |
|
20 |
70% | 340.2 | 29 | 50 |
|
30 |
60% | 291.6 | 32.8 | 55 |
|
30 |
50% | 243 | 39.7 | 76 |
|
35 |
40% | 194.4 | 46.3 | 84 |
|
40 |
30% | 145.8 | 58.7 | 133 |
|
45 |
Two methods include control based on exact feedback linearization via affine nonlinear system and PID control has been adopted to control the IPT of the 600 MW supercritical unit. From Tables
In this paper, the affine nonlinear model of IPT for the supercritical boiler unit has been established. The optimal control method based on exact feedback linearization has been adopted into system with the feed-water flow disturbance at different loads. To verify the validation of the new method, PID control simulation is also conducted for the comparison. The control via affine nonlinear system based on exact feedback linearization can be more effectively on IPT. It is seen that the overshoot is smaller and the regulation time is shorter which shows it can meet the unit's requirements better at different loads.
The future plans for control of IPT have been proposed as follows. More accurate models for the supercritical once-through boiler generation units should be established. Under practical operation, the models must be more complicated and more precise with high nonlinearity. More parameters changes should be considered. In this paper only the relationship between the feed-water flow and the IPT is focused on. More changing parameters should be studied in control of IPT in future. More control methods such as Robust Control [
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work was supported partly by the National Key Technology R&D Program of China 2013BAA01B01, the National Natural Science Foundation of China under Grants nos. 61374064 and 61304152, and the China Postdoctoral Science Foundation Funded Project 2012M511258 and 2013T60738.