Pressure Equilibrium Control for Boiler-turbine Units

Fang Fang School of Control Science and Engineering

North China Electric Power University Beijing, China

ffang@ncepu.edu.cn

Wei Le School of Control Science and Engineering

North China Electric Power University Hebei Baoding, China weile@ncepu.edu.cn

Abstract—An equilibrium control structure for boiler-turbine units is presented in this paper to restrict the exceeding change of steam pressure. The central component of this structure is named as “Steam Pressure Equilibrium Controller”, which is composed with two parts: the pressure error compensator and the pressure set-point optimizer. The former is designed to regulate the change rate and directions of load demand under certain rules according to the steam pressure error. The latter is designed to change the set-point of steam pressure in a reasonable range if the aberrance of steam pressure is serious. Simulation results show that the proposed control structure has good performance for pressure error control.

Keywords—boiler-turbine unit; steam pressure equilibrium control; set-point optimization; error compensation

I. INTRODUCTION Boiler-turbine unit is the typical and popular configuration

in modern power plants. The principal characteristic of this configuration is that a single boiler generates steam to directly feed a single turbine to generate electricity. The relationship between boiler and turbine can be shown in Fig. 1.

Figure 1. Schematic diagram of a fossil-fired boiler-turbine unit

Although, this configuration has been proved as the most efficient and economical form in fossil fired power plants, there are also some conflicts should be resolved in the generation process of electric power.

Conflict 1: The speed of energy conversion and transfer is much slower in boiler than in turbine. When the megawatt output N has to follow the load demand by the dispatch, the boiler must generate enough steam as fast as possible by adding the fuel input B. But the boiler’s ability is always not equal to its ambition.

Conflict 2: In order to accelerate the response of electric output, throttle valve μT of turbine will always be adjusted before the fuel is added to the boiler. Accordingly, the storage energy of boiler can be released in advance to generate much extra steam fleetly to meet the load demand. After that, the lose energy can be complement gradually by firing the input fuel in furnace. But, an intractable problem appears in this process: with the tuning of throttle valve, the main steam pressure PT is disturbed obviously. As the principal process parameter, the fluctuation of main steam pressure will be a serious threat to the safe and economic operation of boiler-turbine unit.

Summing up the above conflicts, the following capability of the megawatt output N and the stabilization of the main steam pressure PT should be considered synchronously when a control system is designed for a boiler-turbine unit. Coordination and cooperation is the kernel purpose of power generation unit control.

From the control point of view, large time delay exist in boiler, nonlinearity exist in both side of the boiler-turbine unit, and strong coupling relationship exist between boiler and turbine. So various control theories and techniques are used to settle these problems. [1] proposed a designing and tuning method for coal-fired boiler–turbine units based on linear decoupling theory. The controller is of PID type, and thus is easy to be implemented. [2] analyzed the dynamic characters of a 330MW boiler-turbine unit in Inner Mongolia, China, and adopted the method proposed in [1] to construct the field controller. [3] deduced a feedback linearization law via the dynamic extension algorithm of vector relative degree for a typical boiler-turbine unit model to overcome the influence of process nonlinearities and improving the load-following capability. [4] proposed a gain scheduling control strategy to adapt wide-range load variations. [5] used a fuzzy auto-regressive moving average (FARMA) model to design an intelligent control system for the boiler-turbine unit.

These literatures usually paid more attention to the load-following capability but to the stability of main steam pressure. And the fluctuation of steam pressure can always be tolerated when the fast response of load demand is obtained in researches and simulations. But in production field, the boiler-turbine control system is often turned off or interrupted when the steam pressure exceed its safe range (usually a narrow range). So it will be valuable for not only theory but also practice to study the steam pressure error control of boiler-turbine units.

This research is supported by the National Natural Science Foundation of China (NSFC) under grants 60704030.

Feedwater Pump

~ N

PT

PD

B

Coal/Oil

Air

μT Turbine

HP LP

DQ

Boiler

Generator

Condense

CIMSA 2009 - International Conference on Computational Intelligence for Measurement Systems and Applications Hong Kong, China May 11-13, 2009

978-1-4244-3820-4/09/$25.00 ©2009 IEEE

In this paper, an equilibrium control structure is presented to restrict the exceeding change of steam pressure. The central component of the structure is named as “Steam Pressure Equilibrium Controller”, which is composed with two parts: the pressure error compensator and the pressure set-point optimizer. The former is used to regulate the change rate and directions of load demand under certain rules according to the steam pressure error. The latter is used to change the set-point of steam pressure in a reasonable range if the aberrance of steam pressure is serious. Simulation results show that the proposed control structure has good performance for pressure error control.

II. EQUILIBRIUM CONTROL OF STEAM PRESSURE The fossil-fired boiler-turbine unit can be modeled as a 2×2

system [1]. The two inputs are boiler firing rate B and throttle valve position μT. The two outputs are megawatt output N and throttle pressure PT. The qualitative dynamic relationship between inputs and outputs is shown in Fig. 2.

Figure 2. Qualitative dynamic relationship between inputs and outputs of the fossil-fired boiler-turbine unit

This is a typical strong coupling system, so a certain multivariable decoupling controller is often adopted to control it (Fig. 3). The controller can be designed by linear or nonlinear, traditional or modern methods.

Figure 3. Multivariable decoupling control for boiler-turbine unit

The PTsp and Nsp are the target values of main steam pressure PT and megawatt output N (Nsp is also called load demand). And the decoupling controller is composed with four sub controllers: C11, C21, C12, and C22. Just as what were discussed in section I, the decoupling control can coordinate the main steam pressure and megawatt output in certain degree, but the disturbance from μT is sometimes remarkable to steam pressure. The fluctuation of steam pressure has been the inevitable cost of speeding up the following capability of load.

A. Structure of Steam Pressure Equilibrium Control In fact, some additional information in the control system,

like the steam pressure error signal, the target values of main steam pressure, the load demand, etc., should be utilized more effectively to restrain the fluctuation of steam pressure. So a novel control structure which is shown in Fig. 4 is presented. It is named as “Steam Pressure Equilibrium Control Structure”.

Figure 4. Pressure Equilibrium Control Structure for boiler-turbine unit

The key part of the structure, which is different from other control systems, is Steam Pressure Equilibrium Controller. There are two sub-parts in this controller: the Pressure Error Compensator (PEC) and the Pressure Set-point Optimizer (PSO). The common input of the two sub-parts is the error signal of steam pressure PE. The PEC is driven by the load demand Nsp and PE to generate the real load demand NR, and PSO is driven by the target values of main steam pressure PTsp and PE to generate the real target of steam pressure PTR. The idea of target values optimization is contained in this structure.

B. Strategy of Steam Pressure Error Compensator (PEC) PEC is used to regulate the change rate and directions of

load demand under certain rule according to the steam pressure error. The purpose of this regulating is to give an inverted compensation of throttle valve position to restrict the fluctuation of pressure.

The rule of PEC can be designed in a simple way as:

( ) ( ) ( )R sp EN k N k P kα= − (1)

where NR (k) is the current real load demand, and α is a compensating coefficient. Obviously, the real load demand will be influenced by the pressure error, and the intensity will be decided by the compensating coefficient α.

In order to enhance the dynamic effect of compensation, the compensating coefficient α can be replaced with a lead-lag function as:

1

2

1( ) ( ) ( )1R sp E

sN k N k P ks

τβτ

+= −

+ (2)

where β is the compensating coefficient, and τ1, τ2, are the lead and lag time respectively. Usually, the τ1 is chosen bigger than τ2. This kind of compensator will be provided with good dynamic performance [6].

In (1) and (2), the current pressure error PE (k) is the counteractive of the current real load demand NR (k). It can also be considered as a kind of disturbance for the megawatt output. So, the previous step value of load demand is used sometimes to replace the counteractive from PE (k) to care for not only the

N

PTB

μT

Fossil-fired

Boiler-turbine

Unit

C11

N

PTB

μT

C21

C12

C22 Nsp

PTsp

Decoupling Controller

Foss

il-fir

ed

Boi

ler-

turb

ine

Uni

t

N

PTB

μT Nsp

PTsp

Steam Pressure Equilibrium Controller

Dec

oupl

ing

Con

trolle

r

PSO

PEC

PE PTR

NR NE

stability of steam pressure but also the following capability of power output. The change rate is also limited as:

( ) ( ),

( ) ( 1)for 0.05 and

( ) ( 1)( ) [ ( ) ( 1)] ( 1),

( ) ( 1)for 0.05 and

( ) ( 1)( ) [ ( ) ( 1)] ( 1),

( ) ( 1)for 0.05 and

(

R sp

sp RE Tsp N N

R N R

sp RE Tsp N

R N R

sp RE Tsp

N k N k

N k N kP P F R

t k t kN k R t k t k N k

N k N kP P R

t k t kN k F t k t k N k

N k N kP P

t k

=

− −< < <

− −= − − + −

− −< >

− −= − − + −

− −<

) ( 1)( ) ( 1),

for 0.05

N

R R

E Tsp

Ft k

N k N k

P P

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪

<⎪ − −⎪⎪ = −⎪

>⎪⎩

(3)

where t(k) and t(k-1) are the current and previous step time, NR (k-1) is the real load demand at the previous step, RN and FN are the given raising and falling rate of NR respectively. Operators can modify RN and FN online under a certain working condition.

C. Strategy of Steam Pressure Set-point Optimizer (PSO) PSO is used to change the set-point of steam pressure in a

reasonable range and at an appropriate rate to ease up the stress when the error of steam pressure is exacerbating.

As we know, there are two operation mode for boiler-turbine units, fixed pressure mode and sliding pressure mode. The fixed pressure mode means that the target values of main steam pressure is kept to a fixed value. On the contrary, the target values of steam pressure will be varied follow the load demand in sliding mode. Operators of the unit can change the mode from one to the other based on the working statues of the power unit or economical target of the enterprise.

In fixed pressure mode, according to the magnitude of pressure error, the rules of PSO are separated into five segments:

( ) 0.98 ( ), 0.05( ) ( 1), 0.02 0.05( ) ( ), 0.02 0.02( ) ( 1), 0.05 0.02( ) 1.02 ( ), 0.05

TR Tsp E Tsp

TR TR Tsp E Tsp

TR Tsp Tsp E Tsp

TR TR Tsp E Tsp

TR Tsp E Tsp

P k P k P PP k P k P P PP k P k P P PP k P k P P PP k P k P P

= > +⎧⎪ = − + ≤ ≤ +⎪⎪ = − ≤ ≤ +⎨⎪ = − − ≤ ≤ −⎪

= < −⎪⎩

(4)

where PTR (k) is the current real target of steam pressure, and PTR (k-1) is the real target at the previous step. If necessary, the change rate of PTR (k) can be limited, such as 0.002PTsp/second.

In sliding pressure mode, the change rate of PTsp should be limited firstly. And then, the PTR will be holding at the previous value when pressure error PE is paranormal. So the rules of PSO are separated into four cases:

( ) ( ),

( ) ( 1)for 0.06 and

( ) ( 1)( ) [ ( ) ( 1)] ( 1),

( ) ( 1)for 0.06 and

( ) ( 1)( ) [ ( ) ( 1)] ( 1),

( )for 0.06 and

TR Tsp

Tsp TRE Tsp P P

TR P TR

Tsp TRE Tsp P

TR P TR

TspE Tsp

P k P k

P k P kP P F R

t k t kP k R t k t k P k

P k P kP P R

t k t kP k F t k t k P k

P kP P

=

− −< < <

− −= − − + −

− −< >

− −= − − + −

<( 1)

( ) ( 1)( ) ( 1),

for 0.06

TRP

TR TR

E Tsp

P kF

t k t kP k P k

P P

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪

− −⎪<⎪ − −⎪

⎪ = −⎪

>⎪⎩

(5)

where RP and FP are the given raising and falling rate of PTR respectively. Operators can modify RP and FP online under a certain working condition. But the change rate of steam pressure target should be slow especially when the load is low than 30%MCR (Maximal Continuous Rated load) or high than 80%MCR.

In order to distinguish between fixed pressure and sliding pressure mode, the differential coefficient, dPTsp/dt, should be detected online. Sometimes, the rules (4) and (5) can be used together to optimize the real target of pressure synthetically.

III. ILLUSTRATIVE EXAMPLE OF A BOILER-TURBINE UNIT

A. A Boiler-turbine Model and It’s Decoupling Controller A nonlinear boiler-turbine unit model [7], which is shown

in Fig. 5, is adopted in this section to prove the performance of the presented steam pressure equilibrium control. This model was built for a 500MW boiler-turbine unit of ShenTou No.2 Power plant in Sanxi, China based on a set of differential equations from [8].

The boiler firing rate and the throttle valve opening are limited as |dB/dt|≤1.0/s, 0.0≤B≤100.0, and 0.0≤μT≤100.0.

Figure 5. A 500MW nonlinear boiler-turbine unit model

0.04 2.408 0.36

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_ _

_1650.0

1981+s 16

1+s

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×

s1

1101+s

161+s

4.0224

0.303

0.2486

101.98 N

PT B

μT

Just as discussed in Section I, various control theories and techniques can be used to design a decoupling controller for this model. The adopted method which based on linear and multivariable theory is from [2]. After identifying and deducing, the final form of the controller is expressed as:

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡−

++=⎥

⎦

⎤⎢⎣

⎡

E

E

T NP

sssssB

4.0018.00001.0

/001.0/0625.0/001.01298.076091.6

μ (6)

where NE is the error between NR and N. combining the controller with the 500MW model, a multivariable decoupling control system will be established as Fig. 3.

B. Simulation Tests of Pressure Equilibrium Control Case 1. In fixed pressure mode, the expectation load

demand Nsp is step decreased from 500MW to 400MW.

The rule of PEC is selected as (1), and the rules of PSO are selected as (4). The compensating coefficient α in (1) is chosen as 18 after several experiments. The dynamic responses of the process, with and without pressure equilibrium control, are both shown in Fig. 6.

Figure 6. Dynamic responise for Case 1

With the steam pressure equilibrium control structure, the real target values of load demand NR and steam pressure PTR were changed regularly (dash dot line in Fig. 6 (a) and (b)). And then, the fluctuation of steam pressure is decreased accordingly (solid line in Fig. 6 (b)), but the megawatt output has no remarkable change than that without equilibrium control (solid and dash line in Fig. 6 (a)). Under the driven of pressure error PE, the equilibrium control structure can restrain the fluctuation of steam pressure effectively in fixed pressure mode.

Case 2. In sliding pressure mode, the expectation load demand Nsp is raised from 300MW to 400MW.

The sliding pressure curve, which is used to describe the relationship between load and steam pressure of boiler-turbine unit, is shown in Fig. 7. In sliding pressure mode, the target value of steam pressure will move follow the load demand based on this curve. There are four inflexions on the curve: {(500, 16.18)，(475, 15.98)，(250, 10.2)，(75, 6.66)}.

Figure 7. Sliding pressure curve of a 500MW boiler-turbine unit

The rule of PEC is selected as (3), and the rules of PSO are selected as (4). The raising rate RN and falling rate FN of NR are both set as 12MW/min. The dynamic responses of the changing process, with and without pressure equilibrium control, are shown in Fig. 8.

Figure 8. Dynamic responise for Case 2

In Case 2, the load demand Nsp (dot line in Fig. 8 (a)) was changed at certain rate, and the corresponding steam pressure PTsp (dot line in Fig. 8 (b)) was indexed from Fig. 7. Under equilibrium control, the real load demand has no remarkable change (dash dot line in Fig. 8 (a)), but the real target of steam pressure has a notable change from about t=180s to t=590s (dash dot line in Fig. 8 (b)) to restrain the pressure error. It is noticed that the raising process of steam pressure is smoother than that without equilibrium control (solid and dash line in Fig. 8 (b)), and the megawatt output has a little delay (solid and dash line in Fig. 8 (a)).

From the above two simulation tests, we see that the proposed steam pressure equilibrium control structure has a good fluctuation restraining performance, works well under both the sliding pressure mode and the fixed pressure mode, and may work in a wide range of load variations.

IV. CONCLUSION With a Boiler-turbine unit, the following capability of the

megawatt output N and the stability of the main steam pressure PT should be considered synchronously when a control system is designed. But, in majority cases, the latter will be more important than the former not only for safety but also for

0 200 400 600 800 s

400

450

500 N with Equilibrium Control N without Equilibrium Control NR with Equilibrium Control NR without Equilibrium Control

0 200 400 600 800 s15.5

16

16.5

17 PT with Equilibrium Control PT without Equilibrium Control PTR with Equilibrium Control PTR without Equilibrium Control

(a) Load demand and megawatt output (MW)

(b) Target and real value of steam pressure (MPa)

100 200 300 400 0

1816141210

86

500 600

Stea

m P

ress

ure

(MPa

)

megawatt output (MW)

300

350

400

0 200 400 600 800 s

N with Equilibrium Control N without Equilibrium Control NR with Equilibrium Control NR without Equilibrium Control

0 200 400 600 800 s

12

13

14

PT with Equilibrium Control PT without Equilibrium Control PTR with Equilibrium Control PTR without Equilibrium Control

(a) Load demand and megawatt output (MW)

(b) Target and real value of steam pressure (MPa)

economical performance of the power generation process. So a steam pressure equilibrium control structure is proposed in this paper to restrict the exceeding change of steam pressure.

The central component of the structure is “Steam Pressure Equilibrium Controller”, which is composed with two parts: the Pressure Error Compensator (PEC) and the Pressure Set-point Optimizer (PSO). The PEC is used to regulate the change rate and directions of load demand under certain rules according to the steam pressure error. And the PSO is used to change the set-point of steam pressure in a reasonable range if the aberrance of steam pressure is serious. Five rules are designed for the two parts, and the first three rules and the last two rules can be selected respectively and fitted together according to the transformation of working condition.

Simulation tests in two cases (the sliding pressure operation mode and the fixed pressure operation mode) are given based on a 500MW coal-fired boiler-turbine unit model. And the test results show that the proposed control structure has good performance for pressure error control.

For the simple form, the proposed control structure and its rules can be configured in majority of industrial control systems and equipments, such as ABB Symphony, Westinghouse Ovation, Siemens T-XP, etc.

REFERENCES

[1] W. Tan, J. Z. Liu, F. Fang, and Y. Q. Chen, “Tuning of PID controllers for boiler–turbine units,” ISA Transactions, vol. 43, pp. 571–583, August 2004.

[2] W. Tan, F. Fang, L. Tian, C. F. Fu, and J. Z. Liu, “Linear control of a boiler–turbine unit: Analysis and design,” ISA Transactions, vol. 47, pp. 189–197, April 2008.

[3] F. Fang, L. Wei, W. Tan, and J. Z. Liu, “A new nonlinear coordinated control strategy for coal-Fired boiler-turbine units,” 16th IEEE International Conference on Control Applications, Singapore, pp. 712–716, October 2007.

[4] P. C. Chen, J. S. Shamma, “Gain-scheduled l1-optimal control for boiler–turbine dynamics with actuator saturation,” Journal of Process Control, vol. 14, pp. 263–277, 2004.

[5] U-C. Moon, K. Y. Lee. “A boiler–turbine system control using a fuzzy auto-regressive moving average (FARMA) model,” IEEE Transactions on Energy Conversion, vol. 18, pp. 142–148, January 2003.

[6] F. Fang, L. Wei, W. Tan, and J. Z. Liu, “Application of dynamic feed-forward with lead-lag component to thermal processes in power station,” (in Chinese) 6th World Congress on Control and Automation, Dalian, Cniha, pp. 7632–7635, June 2006.

[7] D. L. Zeng, Z. Zhao, Y. Q. Chen, “A practical 500MW boiler dynamic model analysis,” (in Chinese) Proceedings of the CSEE, vol. 23, pp. 149–152, May 2003.

[8] F. P. de Mello, “Boiler models for system performance studies,” IEEE Trans. Power Systems, vol. 6, pp. 66–74, Febryary 1991.