Abstract — This paper presents a coordinated controller

parameter adjusting method for boilers. The method includes constructing a simplified engineering boiler model and adjusting controller parameters with nonlinear constrained optimization. Because many control loops in the generation plants interfere with each other, the improvement in the control ability by the method is remarkable. Simulation results are shown in the paper.

I. INTRODUCTION

ecently, rapid load following capability is increasingly becoming a requirement of electric power generation utilities, due to power market liberalization. Usually in

the liberalized electricity market, the electricity sale price varies depending on the load following capability. Rapid load following capability yields a higher price than that of slow load following machines.

Several methods are available to realize fast load following capability. The most frequently adopted method is adjusting the PI parameter manually and adding some feed forward circuits. This takes considerable time and money, and furthermore, the results differ depending on the adjusting engineer. Another method is to adopt the multivariable control strategy. Another typical scheme is to use a model predictive controller. However, almost all the multivariable controllers assume linearity on the control object. Consequently, the strategy is not practical for a wide range of operation conditions because of the nonlinearity in boiler characteristics. Due to the defect, most control systems still consist of PID single loop controllers.

In this paper, a new adjusting technology for the PID controller is introduced. The main features of the method are as follows.

(1) PID parameters are adjusted so that a coordinated control system is realized. This means that PID control loops help each other to realize fast load following.

(2) PID parameters are calculated by nonlinear optimisation. Consequently, the constant optimal results are always obtained.

(3) The adjusting method is applicable to any type of boiler, because optimisation is performed under presumed control system logics.

Dai Murayama is with Toshiba Corporation, Toshiba-cho, Fuchu-city, 183-8511 Japan (corresponding author dai.murayama@toshiba.co.jp)

Y. Takagi, K. Mitsumoto, H. Oguchi, A. Nakai and S. Hino are also with Toshiba Corporation.

In Section II, a coordinated controller-adjusting method using the MPM (Modal Performance Measure) adjusting method is introduced. In Section III, a simple boiler model for engineering is described. In Section IV, a total thermal power plant system and its control system are presented. And in Section V, a PID adjusting example is shown.

II. COORDINATED CONTROLLER ADJUSTING METHOD

The concept is a type of optimisation-based controller design that is introduced by Simo et al [1]. The concept was firstly invented to design a damping-controller for power systems. The main feature is that the optimising criterion is defined at one’s discretion according to the purpose, and that the optimisation is easily achieved whatever the controller logics are, such as PID elements or lead-lag compensators.

In the paper [2], the modal performance index to be optimised is mentioned. The index assesses the summation of areas that all mode response curves make during unit impulse input. The formulae are given as follows.

State space equation of the closed-loop system nmlnnn RCRBRA ××× ∈∈∈ ,, is given as

)()()( tButAxtx += (1) )()( tCxty = (2)

A modal decomposed expression is given so that A becomes a diagonal matrix consisting of eigenvalues.

),,,,( 21 ndiag λλλ=Λ kkk jωσλ += (3) nk ,,2,1=

Then, the system equations are as follows. )()()( tGutztz +Λ= (4)

)()( tFzty = (5) where Tzx = and T is the corresponding transformation

matrix. Furthermore, the next expression is introduced for the calculation.

TTm

TT fffCTF ][ 21== (6) From the state equation, the unit impulse to the j-th input

yields the following state vector and the i-th output responses.

Tnj

tj

tj

tt gegegejGetz n ][),(;|)( 21j21 λλλ== Λ (7)

=====

n

kikj

n

k

tijkjji yeRtZiFty k

11

~|)();,(|)( λ (8)

lj ,,2,1= , mi ,,2,1=where

kjikijk gfR = is the contribution factor of the k-th mode in the transfer function of j to i while the scalar

Dai MURAYAMA, Yasuo TAKAGI, Kenji MITSUMOTO, Haruo OGUCHI, Akimasa NAKAI and Shiro HINO (non-member)

A new control strategy for coal fired thermal power plants

R

Proceedings of the2005 IEEE Conference on Control ApplicationsToronto, Canada, August 28-31, 2005

WC5.3

0-7803-9354-6/05/$20.00 ©2005 IEEE 1680

ji ty |)( is the i-th output response to the j-th input unit impulse excitation. The envelope of the k-th mode to i-th component of output )(ty is defined as follows.

*~~ikjikjk yya (9)

where tikjikj

jjeRy λε 2~ =and realifa kk λ1= , complexifa kk λ2= .

Furthermore, 22kk

kk ωσ

σε+

−= means the damping

factor of mode k. Thus, MPM is defined as follows with the integral time

TMPM.

==

n

kkMPM JJ

1

(10)

and

= == MPMT l

j

m

iikjikjkk dtyyaJ

01 1

*~~

= =

Ψ=l

j

m

iikjkkk Ra

1 1

2),( ωσ ,

)1(2

),(22

32

3

22

−+=Ψ + kk

kT

k

kkkk e ωσ

σ

σωσωσ (11)

In addition, we can add some modification to the MPM index so that the control performance attains desired characteristics.

III. BOILER MODEL FOR ENGINEERING

The engineering model adopted here is the model developed by Astrom and Bell, which is a simple yet effective mathematical model for drum boilers [3]. Even though the complexity of the model is relatively low and suitable for model-based control design, the model is capable of capturing the many interesting physical behaviors of drum boilers especially the distribution of steam in risers, and the shrink and swell effect–the phenomena that often prevents controllers from compensating an appropriate feed-water flow rate in drum-level control. The development of this drum-boiler model can be traced back to [4], [5], [6]. Therefore, in order to gain more insight into drum-boiler characteristics, this paper aimed to imitate the dynamic model given in [3] by reconstructing a model representing the dynamic equations, and comparing the simulation results.

The manipulated variables of the drum-boiler system are fuel flow rate Q, feed-water flow rate qf, and steam flow rate qs. The measured outputs are the drum pressure p, and water level in the drum. The state variables are the drum pressure p, the total water volume Vwt, the steam mass-fraction r at the riser’s outlets, and the steam volume Vsd under the liquid level. The drum boiler model is of the fourth order, and can be expressed as follows.

sfwt qq

dtdpe

dtdVe −=+ 1211

(13)

ssffwt hqhqQ

dtdpe

dtdV

e −+=+ 2221 (14)

dccrr qhQ

dtd

edtdpe αα

−=+ 3332 (15)

fc

wfsdsd

d

ssdr qh

hhVV

TdtdVe

dtde

dtdpe

−+−=++ )( 0

444342ρα

(16) where the coefficients are given by

swe ρρ −=11 (17)

pV

pVe s

stw

wt ∂∂

+∂

∂=

ρρ12

(18)

ssww hhe ρρ −=21 (19)

pt

CmV

ph

phV

ph

phVe

sptt

ss

ssst

ww

wwwt

∂∂

+−

∂∂

+∂

∂+

∂∂

+∂

∂= ρρρρ

22 (20)

ptCmV

pVh

Vph

ph

Vp

hphe

sprr

vrcrsws

rvs

ss

cr

rvw

crw

w

∂∂+−

∂∂−++

∂∂+

∂∂−+

−∂

∂−∂∂=

ααρρρ

αρρα

αραρ

))((

)1(

)1(32

(21)

r

vrcrsws Vhe

αααρρρ

∂∂

−+= ))((33 (22)

∂∂−+

∂∂−+

∂∂+

∂∂+−−

∂∂+

∂∂+

∂∂=

pppV

ptCmVV

phV

phV

h

pVe

vws

wv

svrr

spdwdsd

wwdw

ssds

c

ssd

αρρραραβα

ρρ

ρ

)()1()1(

1

42

(23)

r

vrwsr Ve

αα

ρρβα∂∂

−+= ))(1(43 (24)

se ρ=44 (25) where

wsc hhh −= (26)

The specific density and enthalpy of the saturated water is wρ , wh , steam sρ , sh , feed water

fρ ,fh . The temperature

of saturated steam is st . β is the empirical parameter. The riser’s mass and volume mr , Vr, total mass and volume mt, Vt,

and downcomer’s mass and volume mdc, Vdc are also parameters. Cp is specific heat of metal. vα is the average volume fraction Astrom and Bell found. The down comer

1681

mass flow rate qdc is important too.

( )

++

−+

+

⋅∂

∂−

∂∂

−=

∂∂

)1ln()1

1(1

12

ηηρ

ρρηρ

ρ

ρρρρρρ

α

s

ws

s

w

ws

sw

sw

v

ppp (27)

+−+=

∂∂

ηη

ηηρρ

αα

11)1ln(1

s

w

r

v (28)

where

s

swr

ρρραη )( −

= (29)

All necessary algebraic relations can be summarized as follows.

−+

−−

−= )

)(1ln(

)(1

s

rsw

rsw

s

sw

wv ρ

αρραρρ

ρρρ

ρα (30)

rvdcwtwd VVVV )1( α−−−= (31)

d

sdwd

AVV

l+

= (32)

sd

sdsd q

VT0ρ= (33)

rvswdcwdc VgAk

q αρρρ )(2 −= (34)

dtd

V

dtdp

pppVqq

r

r

vrsw

vws

wv

svrdcr

ααα

ρρ

αρρ

ρα

ρα

∂∂

−+

∂∂

−+∂

∂−+

∂∂

−=

)(

)()1(

(35) The total condensation rate qct is also caluculated.

tp

ptCmV

phV

phV

hq

hhh

q sptt

wwtw

ssts

cf

c

fwct

∂∂⋅

∂∂+−

∂∂+

∂∂+

−= ρρ1

(36) The parameters required in these interactions are as

follows: drum area Ad, down comer area Adc, friction coefficient in down comer-riser loop k, and residence time Td

of steam in the drum. The total water volume Vwt is also required.

The drum level in Eq.(32) is caused by two contributions: water level contribution dwdw AVl /= , and steam level contribution dsds AVl /= .

IV. THERMAL POWER PLANT AND CONTROL SYSTEM

A. Thermal Power Plant Model In order to realize the optimal control design of a coal fired

thermal power plant, an engineering model of the total power plant is required. The developed thermal power plant model consists of a boiler, economizer, super heater, high and low pressure turbine, reheater, heater and deaerator. The drum boiler model used is described in Section II. The total plant model is shown in Fig.1. The structure of the plant model is based on a 710[MW] coal fired thermal power plant. The parameters such as drum volume, riser and down comer volume, total metal mass, feed water flow, steam flow and pressure of drum are also based on the target plant.

In the boiler, the water in the drum descends in the down comer and is heated by the fuel. Next, the heated water ascends through the riser. And in the drum, heated water is evaporated into saturated steam. The saturated steam is further heated in the super heater and then works at the turbine. After passing through the turbine steam is condensed at the condenser. The feed water is supplied from the condenser, which is heated in the heater by the steam from the turbine. Feed water is heated in the economizer and supplied to the boiler.

Each model considers the enthalpy and flow rate of the steam or water. Set points of the controller corresponding to the MW demand are also calculated in the models and other control logistics are embedded in the model.

Economizer

Super Heater HPT LPT

Reheater

G

RiserDownComer

Drum

P

level

feed water

fuel

Governor

Condenser

boiler

heaterheater deaerator

spray

Fig. 1 Thermal Power Plant Model

B. Control System The thermal power plant model works with the three main

feedback controllers shown in Fig2. The power of the plant is controlled by the main steam valve to follow the MW demand. The rotational power generated by the turbine is converted to electric power.

The other feedback controllers control the boiler drum dynamics. The feed water qf is supplied to the boiler drum and controls the water level in it, and the fuel flow rate Q is

1682

controlled to control the pressure of the drum to control the set point. The set point of the drum pressure is designed corresponding to the output power.

C1 Valve TurbineMW Demand Power

CV

qs

+ -

C2 Drum

drum levelset point drum level

qf

+ -

C3 Drum

drum pressureset point

drum pressure

Q

+ -

+

+

+

+

+

+

Fig. 2 Controllers of Thermal Power Plant Model

Each controller is assumed to be a PI controller (

sIPC i

ii += ) and is manually coordinated to stabilise the

response. The coordination is shown in Table 1.

Table 1 Manually Coordinated Controller C1 C2 C3

Pi 0.5 2160.0 300.0 Ii 0.05 7.71 10.0

The response of the total thermal power plant model is shown in Fig. 3. In Fig. 3 MW demand (dotted line) is changed in the ramp shape and the drum pressure set point (dotted line) is changed corresponding to the MW demand. Then main steam flow (solid line) and fuel flow (solid line) is controlled by the controller C1 and C3. The drum level is regulated at constant value. The behaviour of the model contains the interesting features of a coal fired thermal power plant.

Fig. 3 Model Response with Parameters

V. OPTIMIZATION OF CONTROLLER PARAMETERS

A. Obtaining Linear Model The total thermal power plant model is linearized into state

space model to apply the MPM method. To coordinate the three feedback controllers, the total plant model is linearized into the 3-input-3-output model: inputs are MW demand, drum level set point and drum pressure set point, outputs are power of the plant, drum level and drum pressure. And to confirm the accuracy of the linearized model, a comparison of the simulation of the model (dotted line) and linearized model (solid line) is shown in Fig. 4. There is good agreement between both.

Fig. 4 Linear Model Response

The impulse response of the linear model is shown in Fig.5. The response becomes stable within 10-15 minutes. The optimization with the MPM value should be evaluated by the closed loop model that consists of controllers and the process linear model.

1683

Fig. 5 Linear Model Impulse Response

B. MPM for Step Response Optimization The MPM method obtains the optimized controller for the

impulse response of the system. However, the load following command of the thermal power plant changes the set points of the controllers. Therefore the boiler controllers should be optimized not for the impulse responses but for the step responses. Fig. 6 shows step response of the transfer function

( )sP . The difference between the set point and response is equal to the impulse response of the transfer function

( ) ( ){ }sPPs

−∞1 . Here ( )∞P is the step response value at the

time ∞ .

( ) ( ){ }sPPs

−∞1

( )sP

step

impulse

Fig. 6 System Conversion for MPM

When the transfer function is ( )sP , the state space system is realized in

lmnmlnnn RDRCRBRA ×××× ∈∈∈∈ ,,, .

)()()()()()(tDutCxtytButAxtx

+=+= (37)

The transfer function ( ) ( ){ }sPPs

−∞1 is realized in

DCBA ′′′′ ,,, given by

( )( )[ ]OD

DPCCIO

B

OOBA

A

=′−∞−=′

=′

=′

(38)

Furthermore, step response at the time ∞ : ( )∞P iscalculated by the equation below.

( ) ( )

( )( )BCA

BAsIC

sP

sPs

sP

s

s

s

1

1

0

0

0

lim

lim

1lim

−

−

→

→

→

−=

−=

=

=∞

(39)

Finally, this system is represented in the equation below.

( )[ ]OD

DBCACC

IO

B

OOBA

A

=′+−−=′

=′

=′

−1

(40)

With this system DCBA ′′′′ ,,, , optimal controllers are obtained using the same algorithm of the impulse optimized MPM method. The impulse response of this system

DCBA ′′′′ ,,, is shown in Fig. 7.

Fig. 7 Impulse Response of Converted System

The MPM method optimizes the impulse response generated due to each mode of the system and is mainly applied to the system whose ranges of outputs are the same. However, in the thermal power plant model in this paper, output ranges differ from each other. Thus, when MPM method is applied to the thermal power plant controller optimization, the output of the system should be normalized

1684

by the matrix C. The system’s output equation is shown below.

[ ] xcccc

CxyTT

mTTT321=

= (41)

The size of each vector is 1×∈ ni Rc . To normalize matrixC ,

C is replaced by ^C as shown by

xcc

cc

cc

cc

xCyT

m

Tm

TTT

=

=

3

3

2

2

1

1

^^

(42)

C. Optimization The MPM method is applied to the system mentioned

above. The MPM method’s optimal conditions are shown in Table 2. The index to be minimized is the MPM value calculated in the time TMPM=300[sec] (TMPM: defined in Eq. (11)). Initial parameters are manually coordinated as shown in Table 1. And constraints are closed loop stability and the range of the parameters to be optimized.

This optimization is easily convergent and the result obtained is shown in Table 3. The simulation result along with the optimal parameters is shown in Fig. 8. With optimal parameters, the thermal power plant exhibits good responses. The drum level response is especially improved.

Table 2 Conditions of Optimization Conditions Index MPM Initial parameters manually coordinated

parameters Constraint closed-loop’s stability

22/ ×≤≤ ioi xxx ( ox : optimized parameters,

ix : initial parameters)

Table 3 Optimal Controllers by MPM C1 C2 C3

P 0.774 3674.2 294.4 I 0.1 15.42 5.0

Fig. 8 Model Response with Optimal Controller

As mentioned above, if suitable system and suitable index and constraints are adopted, presumed control system logics can be optimized by the method.

IV. CONCLUSION

This paper described an effective adjusting technology for PID controller and applied it to a coal fired thermal power plant. The thermal power plant model consists of the fourth order boiler model and other apparatus. The control loops of the thermal power plant, which interfere with each other, co-operate efficiently with the MPM method.

REFERENCES

[1] J.B. Simo, I. Kamwa, G. Trudel and S.-A. Tahan. “Validation of a new modal performance measure flexible controller design, ” IEEE Trans., Vol. PWRS-11 No. 2, pp.819-828, May 1996

[2] I. Kamwa, Gilles Trudel and Luc Gerin-Lajoie, “Robust Design and Coordination of Multiple Damping Controllers Using Nonlinear Constrained Optimization” IEEE Trans., Vol PS-15 No. 3, pp 1084-1092, August 2000

[3] K. J. Astrom and R. D. Bell, “Drum-Boiler Dynamics,” Automatica, vol. 36, no. 3, pp. 363-378, 2000.

[4] K. J. Astrom and R. D. Bell, “Simple Drum-Boiler Models,” In IFAC Int. Symposium on Power Systems, Modeling and Control Applications, Brussels, Belgium, 1988.

[5] K. J. Astrom and R. D. Bell, “A Nonlinear Model for Steam Generation Process,” In Preprints IFAC 12th World Congress, Sydney, Australia, Vol. 3, pp. 395-398, July 1993.

[6] R. D. Bell and K. J. Astrom, “A Fourth Order Non-linear Model for Drum-Boiler Dynamics,” In Preprints IFAC 13th World Congress, San Francisco, California, Vol. O, pp. 31-36, July 1996.

1685