Modeling and model predictive control of the BioPower combined heat and power (CHP) plant

Electrical Power and Energy Systems 65 (2015) 453–462

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Modeling and model predictive control of the BioPower combined heat and power (CHP) plant J. Kortela ⇑, S-L. Jämsä-Jounela Aalto University School of Chemical Technology, P.O. Box 16100, FI-00076 Aalto, Finland

a r t i c l e

i n f o

Article history: Received 25 October 2013 Received in revised form 1 July 2014 Accepted 12 October 2014

Keywords: Combustion Biomass Fuel quality MPC Moisture Advanced control

a b s t r a c t This paper presents a model predictive control (MPC) strategy for BioGrate boiler, compensating the main disturbances caused by variations in fuel quality such as the moisture content of fuel, and variations in fuel flow. The MPC utilizes models, the fuel moisture soft-sensor to estimate water evaporation, and the fuel flow calculations to estimate the thermal decomposition of dry fuel, to handle these variations, the inherent large time constants, and long time delays of the boiler. The MPC strategy is compared with the method currently used in the BioPower 5 CHP plant. Finally, the results are presented, analyzed and discussed. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction The utilization of renewable energy sources is increasing due to demand to replace fossil energy sources with more ecological ones. The biomass is one of these renewable energy sources [1,2]. BioGrate burns this fuel with a moisture content as high as 65% [3]. However, a varying moisture content and varying fuel flow of the biomass results in uncertainty about its energy content and complicates operation of BioGrate process. Kortela and Lautala [4] developed a method in order to estimate how much fuel is burning at the time moment and combustion power based on the flue gas oxygen and the air measurements, and the fuel composition. It was reported that the amplitude and the settling time of the response of the boiler power decreased to about one-third-of the original. Havlena and Findejs [5] employed model-based predictive control strategy to enable dynamical coordination between fuel and air flows. This enabled the boiler to permanently operate with the optimum excess air, and resulted in reduced NOx production. Prasad et al. [6] tested the application of a multivariable long-range predictive control (LRPC) with global linear models and local model networks in the simulation of a 200 MW oil-fired drumboiler thermal plant. They reported extremely small variations of ⇑ Corresponding author. Tel.: +358 9 4702 2647; fax: +358 9 4702 3854. E-mail addresses: jukka.kortela@aalto.fi (J. Kortela), sirkka-liisa.jamsa-jounela@ aalto.fi (S-L. Jämsä-Jounela). http://dx.doi.org/10.1016/j.ijepes.2014.10.043 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.

±0.5 bar, ±1.0 °C, and ±1.5 °C for steam pressure, steam temperature, and reheat steam temperature, respectively. Swarnakar et al. [7] presented a scheme for robust stabilization of a boiler, based on linear matrix inequalities (LMIs). The simulation results showed that the proposed control is effective against sudden load changes. However, BioGrate process needs a special consideration in its control strategy development due to its long time delay of min seconds and moisture variations in fuel feed. Bauer et al. [8] derived a simple model for the grate combustion of biomass based on two mass balances for dry fuel and water. The model was verified by experiments at a pilot scale furnace with a horizontally moving grate. The test results showed that the overall effect of the primary air flow rate on the thermal decomposition of dry fuel is multiplicative. This is also shown in the results of Yang et al. [9] when the air factor is not much larger than stoichiometric air, staying in a typical optimal level from around 1.2 to 1.7. Higher air flows begin to cool the bed, decreasing the propagation rates [10]. In addition, the test results of Bauer et al. [8] showed that the water evaporation rate is mainly independent of the primary air flow. For fuel moisture measurement, Kortela and Jämsä-Jounela [11] developed a fuel moisture soft sensor that is based on a dynamic model that makes use of combustion power estimates and that makes use of the model of the secondary superheater. This paper presents a model predictive control (MPC) strategy for a BioGrate boiler. The paper is organized as follows: Section ‘‘Description of the process and its control strategy’’ presents The BioPower 5 CHP plant process and its control strategy. Section

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J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

‘‘Model predictive control for the BioPower 5 CHP plant’’ presents the MPC strategy, and dynamic models, and fuel-moisture softsensors of a boiler. The identifications of the models of BioPower 5 CHP plant are presented in Section ‘‘Test results of system identification of model parameters of BioGrate boiler’’. The simulation results of the MPC strategy are presented in Section ‘‘Test results of the MPC control strategy of BioGrate boiler’’, followed by the conclusions in Section ‘‘Conclusions’’.

Description of the process and its control strategy In the BioPower 5 CHP plant, the heat used for steam generation is obtained by burning solid biomass fuel: bark, sawdust and pellets, which are fed to the steam boiler together with combustion air. As a result, combustion heat and flue gases are generated. The heat is then used in the steam-water circulation process. The fuel is fed onto the center of a grate from below by a stoker screw. The grate is divided into concentric rings with alternate rotating rings and the rings between remaining stationary. Alternate rotating rings are pushed hydraulically clockwise or counterclockwise respectively. This design distributes the fuel evenly over the entire grate with the burning fuel forming an even layer of the required thickness [3]. The water content of the wet fuel in the center of the grate evaporates rapidly due to the heat of the surrounding burning fuel and thermal radiation from the brick walls. The gasification and visible combustion of the gases and solid carbon take place as the fuel moves to the periphery of the circular grate. Finally, at the edge of the grate, ash falls into a water-filled ash basin underneath the grate [3]. The primary air for combustion, and the recirculation flue gas, are fed from underneath the grate and penetrate the fuel through slots in the concentric rings. Secondary air is fed above the grate directly into the flame. Air distribution is controlled by dampers and speed-controlled fans [3] (see Fig. 1). Fig. 2 shows the boiler part of the BioPower 5 CHP plant. The essential components of the water-steam circuit are an economizer, a drum, an evaporator and superheaters. Feed water is pumped from a feed water tank to the boiler. First the water is led to the economizer (4) that is heated by flue gases. The temperature of flue gases is decreased by the economizer, and the efficiency of the boiler is improved. From the economizer, heated feed water is led to the drum (5) and along downcomers into the bottom of the evaporator (6) tubes that surround the boiler. From the evaporator tubes the heated water and steam return back to the steam drum, where steam

and water are separated. Steam rises to the top of the steam drum and flows to the superheaters (7). Steam heats up further so that it superheats. The superheated high-pressure steam (8) is led to a steam turbine, where electricity is generated. Current control strategy of the BioPower plant The main objective of the BioPower plant is to produce a desired amount of energy by keeping the drum pressure constant. The necessary boiler power is produced by manipulating primary air, secondary air, and stoker speed as illustrated in Fig. 3. The fuel feed is controlled by manipulating the motor speed of the stoker screw to track the primary air flow measurement. The necessary amount of primary air and secondary air for diverse power levels are specified by air curves. The set point of the secondary air controller is adjusted by the flue gas oxygen controller to provide excess air for combustion and enable the complete combustion of fuel. Model predictive control for the BioPower 5 CHP plant The improvised MPC strategy over the current control strategy is illustrated in Fig. 4. The proposed strategy utilizes fuel and moisture soft-sensors to estimate the burned fuel and the water evaporation respectively. Subsequently, the combustion power is estimated based on these fuel-moisture soft sensors. As a result, the required amount of combustion power from the boiler can be produced, which is done by manipulating the primary air and the stoker speed. In addition, this combustion power can be accurately predicted. MPC for BioGrate boiler The primary air and the stoker speed are the input variables (u); the fuel moisture content in the fuel feed and the power demand are the measured disturbances (d); and the estimated amount of fuel, the combustion power and the drum pressure are the controlled variables (z), as illustrated in Fig. 5. The developed MPC utilizes the linear state space system as follows [12]:

xkþ1 ¼ Axk þ Buk þ Edk z k ¼ C z xk

ð1Þ

Regulator The process is described by linear time invariant (LTI) state space model

zk ¼ C z Ak x0 þ

k1 X Hkj uj

ð2Þ

j¼0

where Hkj are impulse response coefficients. Using Eq. (2), the MPC with input, the input rate of movement, and output constraints is formulated as

min / ¼

N 1X 1 kzk  r k k2Q z þ kDuk k2S 2 k¼1 2

s:t: xkþ1 ¼ Axk þ Buk þ Edk ; k ¼ 0; 1; . . . ; N  1 zk ¼ C z xk ; k ¼ 0; 1; . . . ; N umin 6 uk 6 umax ; k ¼ 0; 1; . . . ; N  1

Dumin 6 Duk 6 Dumax ; k ¼ 0; 1; . . . ; N  1 zmin 6 zk 6 zmax ; k ¼ 1; 2; . . . ; N Fig. 1. BioGrate including the stoker screw and a water-filled ash basin underneath the grate.

where Duk ¼ uk  uk1 . The vectors Z; R, and U are defined as

ð3Þ

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J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

8.

7.

5.

4.

6. 3.

2.

1.

BioGrate

Feed water tank

Fuel storage

Fig. 2. (1) Fuel; (2) Primary air; (3) Secondary air; (4) Economizer; (5) Drum; (6) Evaporator; (7) Superheaters; (8) Superheated steam.

and the predictions by Eq. (2) are expressed as

Power demand

Z ¼ Uxo þ CU þ Cd D:

ð5Þ

U; C and Cd are assembled as 3 2 Cz A H1 6 6 2 7 6 CzA 7 6 H2 7 6 6 3 7 6 U¼6 6 C z A 7; C ¼ 6 H 3 6 . 7 6 . 6 . 7 6 . 4 . 5 4 . 2

Drum pressure control

C z AN

Oxygen correction control

Total air/Primary air control

HN

0

0

H1

0

H2 .. .

H1 .. .

HN1

HN2

...

0

3

7 0 7 7 0 7 7; .. 7 7 . 5 . . . H1

...

ð6Þ

and

2

H1;d 6H 6 2;d 6 Cd ¼ 6 6 H3;d 6 . 6 . 4 .

Primary air fan

HN;d

0

0

H1;d H2;d .. . HN1;d

0 H1;d .. . HN2;d

...

0

3

0 7 7 7 0 7 7: .. 7 7 . 5 . . . H1;d ...

ð7Þ

For the case N ¼ 6, the matrices

Total air/Stoker speed control

Total air/Secondary air control

Stoker motor speed

2

Secondary air fan

I

0

0

0

I

I

0

0

I

I

07 7 7; 05

0

0

0

I

2

Boiler power

Qz 6Q 6 z Qz ¼ 6 6 4 0

0 Qz

Fig. 3. Current control strategy of the biograte process.

2

z1

3

2

r1

3

2

u0

6z 7 6r 7 6 u 6 27 6 27 6 1 7 7 6 6 . Z¼6 ; R ¼ ; U ¼ 6 .. 7 6 .. 7 6 . 4 . 5 4 . 5 4 . zN

rN

uN1

3

2

d0

3

7 6 7 6 7; D ¼ 6 7 6 5 4

d1 .. .

7 7 7 7 5

dN1

2

ð4Þ

3

I 6 0 6 K¼6 4 0

ð8Þ

I 3

0

0 0 .. .

0 0 7 7 7; 7 0 5

0

0

0

Qz

2S

S

0

0

ð9Þ

0

3

7 6 0 7 6 S 2S S 0 7 6 6 HS ¼ 6 0 S 2S S 0 7 7 7 6 0 S 2S S 5 4 0 0

0

0

S

2S

ð10Þ

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J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

Power demand

Drum pressure control

Combustion power control

Flue gas oxygen content

Oxygen correction control

Total air/Stoker speed control Stoker motor speed

Combustion power estimation

Moisture evaporation

Total air/Primary air control

Total air/Secondary air control

Primary air fan

Secondary air fan

thermal decomposition of fuel

Boiler power

Fig. 4. Model predictive control (MPC) strategy of BioGrate boiler.

u1 Primary air SP

u2 Stoker speed SP

d1 Moisture in fuel

z1 Estimated amount of fuel Combustion power estimation

Thermaldecomposition of dry fuel

z2 Combustion power

-

Drum pressure

z3 Drum pressure

d2 Power demand

Water evaporation

Fig. 5. Configuration of the boiler model of MPC strategy for BioPower 5 CHP plant.

and

where

M u1

2 3 S 6 7 0 6 7 6 7 7 ¼ 6 6 0 7: 6 7 405 0

ð11Þ

Q z are tuned so that drum pressure has more importance than combustion power. S for primary air and stoker speed can be tuned separately from each other. Then the objective function is expressed as

w¼

N 1X 1 kzk  r k k2Q z þ kDuk k2S 2 k¼1 2

1 ¼ U 0 HU þ g 0 U þ q 2

g ¼ C0 Qz Ux0  C0Qz R þ Mu1 u1 þ C0 Qz Cd D

ð14Þ

The MPC regulator problem Eq. (3) can be solved by the solution of the following convex quadratic program

minw ¼

DU min 6 KU 6 DU max Z min 6 CU 6 Z max

ð17Þ

In order to achieve offset-free performance, the state of the system is augmented with an integrating disturbance vector [13]. The designed system uses an input disturbance model where Bd ¼ B; Ad is the unit matrix and C g is the zero matrix.



xkþ1



 ¼

ð15Þ

A

Bd



xk



0 Ad g k    xk Cg þ vk

þ

      B E wk uk þ dk þ 0 0 nk

ð18Þ ð19Þ

gk

ð12Þ

ð13Þ

U min

Z max ¼ Z max  Uxo  Cd D

 yk ¼ C

H ¼ C0 Qz C þ HS

U

ð16Þ

gkþ1

where

1 0 U HU þ g 0 U 2 6 U 6 U max

Z min ¼ Z min  Uxo  Cd D

where xk are the states and gk the integrating disturbance states. The state and the additional integrating disturbance are estimated from the plant measurement by using a Kalman filter designed for the augmented system. The vectors wk and v k are white-noise disturbances with zero-mean for the augmented state equation and the output equation, respectively. Thus, the state and the disturbance of the system are estimated as follows:

"

^xkjk g^ kjk

#

" ¼

^xkjk1 g^ kjk1

#

 þ

Lx Lg



^ kjk1 Þ ðyk  C ^xkjk1  C g g

ð20Þ

^ k disturbance estimawhere ^ xk are the state estimations, and the g tions. The prediction of the state of the augmented system is obtained by

J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

"

^xkþ1jk g^ kþ1jk

#



A Bd 0 Ad

¼

"

^xkjk g^ kjk

# þ

    B E uk þ dk 0 0

ð21Þ

Additional disturbances, gk , are not controllable by the inputs u. However, since they are observable, their estimates are used to remove their influence from the controlled variables. The disturbance model is defined by choosing the matrices Bd and C g . Since the additional disturbance modes introduced by disturbance are unstable, it is necessary to check the detectability of the augmented system. The augmented system in Eq. (18) is detectable if and only if the nonaugmented system in Eq. (1) is detectable, and the following condition holds:

  I  A Bd ¼ n þ ng rank C Cg

ð22Þ

In addition if the system is augmented with a number of integrating disturbances ng equal to the number of the measurements p (ng ¼ p) and if the closed-loop system is stable and constraints are not active at steady state, there is zero offset in controlled variables

457

where cds is the fuel bed height coefficient, and cpa the primary air flow coefficient. Drum model The drum level is kept at a constant level by its controller, and therefore the variations in the steam volume are small. Thus, the drum model is [14]

dp 1 _ f ðhw  hf Þ  m _ s ðhs  hw ÞÞ ¼ ðQ  m dt e e  .w V w

@hw @T s þ mt C p @p @p

ð29Þ

ð30Þ

_ f is the feed water flow where Q is the combustion power (MJ=s), m (kg=s), hw is the specific enthalpy of the water (MJ=kg), hf is the _ s is the steam flow specific enthalpy of the feed water (MJ=kg), m rate (kg=s), hs is the specific enthalpy of the steam (MJ=kg), .w is the specific density of the water (kg=m3 ), V w is the volume of the water (m3 ), mt is the total mass of the metal tubes and the drum (kg), and C p is specific heat of the metal (MJ=kgK).

Modeling of BioGrate boiler for MPC An unknown flue flow and the water evaporation rate results in uncertainty in the combustion power. Therefore, the models of the boiler include, model for water evaporation, the model for themal decomposition of fuel, and the drum model. The model of water evaporation The model of water evaporation is [8]

dmw ðtÞ dmw;in ðt  T d ðtÞÞ ¼ cwev mw ðtÞawev ðtÞ þ ½kg=s dt dt

qwf ¼ 0:348  wC þ 0:938  wH þ 0:105  wS þ 0:063  wN ð23Þ

where cwev is the correction coefficient, awev is the coefficient for a dependence on the position of the moving grate, and mw;in the moisture in the fuel feed (kg=s).

T d ðtÞ ¼ cd

mw ðtÞ

ads;in mds;in ðtÞ

½s

ð24Þ

where cd is the delay coefficient, ads;in is the stoker speed correction coefficient (kg=s=%), and mds;in ðtÞ is the stoker speed (%).

mw;in ðtÞ ¼

Z

t

_ w;in ðsÞ ds ½kg m

ð25Þ

0

ð26Þ

where cthd is the thermal decomposition rate coefficient, athd ðtÞ is the coefficient for a dependence on the position of the moving grate, _ pa ðtÞ is the primary air flow rate bias (kg=s), and m _ pa;0 ðtÞ the prim mary air flow rate in (kg=s).

mds;in ðtÞ ¼

Z

 0:108  wO ½MJ=kg

ð31Þ

where wC is the carbon in the fuel (%), wH is the hydrogen in the fuel (%), wS is the sulfur in the fuel (%), wN is the nitrogen in the fuel (%), and wO the oxygen in the fuel (%). The effective heat value of a wet fuel is obtained using the equation

qf ¼ qwf  ð1  w=100Þ  0:0244  w ½MJ=kg

ð32Þ

where w is the moisture content of the wet fuel (%). In order to use Eqs. (31) and (32), the composition of the fuel has to be known. Oxygen consumption signals how much fuel is burning at the time moment. This information can be used to calculate the combustion power of the burned fuel. The amount of oxygen needed to burn one kilogram of the fuel is

NgO2 ¼ nC þ 0:5  nH2 þ nS  nO2 ½mol=kg

The model of thermal decomposition of dry fuel The model of thermal decomposition of dry fuel is [8]

dmds ðtÞ _ pa ðtÞ þ m _ pa;0  ¼ cthd mds ðtÞathd ðtÞ½m dt dads;in mds;in ðt  T d ðtÞÞ ½kg=s þ dt

Fuel flow soft-sensor The elemental composition, and moisture content of a fuel have a strong effect on its heat value. If fuel contains moisture, this evaporates when the fuel is burned, but this evaporation requires energy, which is absorbed from the heat of the fuels combustion and decreases its heat value. The effective heat value of a dry fuel is

ð33Þ

where nC is the carbon (mol/kg), nH2 is the hydrogen (mol/kg), nS is the sulfur (mol/kg), and nO2 the oxygen (mol/kg). Combustion air includes 3.76 times more nitrogen than oxygen. The flue gas flow to burn one kilogram of fuel is thus

Nfg ¼ nC þ nH2 þ nS þ 3:76  NgO2 þ nN2 þ nH2 O ½mol=kg

ð34Þ

where nH2 O is the water (mol/kg). Similarly, the flue gas losses per kilogram of fuel are determined by:

qgfg ¼ ðnC C CO2 þ nS C SO2 þ ðnH2 O þ nH2 ÞC H2 O þ ð3:76  NgO2

t

_ ds;in ðsÞ ds ½kg m

ð27Þ

0

For the linear state space model of Eqs. (1) and (26) is linearized as

dmds ðtÞ _ pa ðtÞ ¼ cds mds ðtÞ  cpa m dt dads;in mds;in ðt  T d ðtÞÞ ½kg=s þ dt

ð28Þ

_ thd ðwÞÞ  4:76 þ nN2 ÞC N þ ðF Air =ð22:41  103  m  NgO2 ÞC Air Þ  ðT fo  T 0 Þ ½J=kg

ð35Þ

where C i is the specific heat capacity of the component i (J=molT), _ thd is the themal decomposition of fuel F Air is total air flow (m3 =s), m (kg=s), T fo is the flue gas temperature after the economizer (°C), and T 0 the reference temperature (°C). The thermal decomposition of fuel is calculated as follows [11], that is estimated amount fuel burning at the time moment:

458

J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

 _ thd ðwÞ ¼ m

 XO 0:21  1002 nAir

XO

NgO2 þ 1002 ðNfg  4:76  NgO2 Þ

½kg=s

ð36Þ

where X O2 ðt þ sÞ is the flue gas oxygen content ð%Þ, and nAir the sum of the primary and secondary air flows (total air) (mol=sÞ. The net combustion power for the given thermal decomposition of fuel is

_ thd ðwÞðqf  qgfg  qcr Þ ½MJ Q ¼m

ð37Þ

where qgfg is the flue gas loss ðMJ=kgÞ, and qcr the convection and radiation losses (MJ=kg), which are typically 1.5% of the effective heat value qf . Flue gas flow for fuel flow in Eq. (36) is given by:

_ fg ¼ F Air þ m _ thd ðwÞðNfg  4:76  NgO Þ  22:41  103 ½m3 =s m 2

ð38Þ

where as the temperature before the secondary superheater is calculated using: 3

T fg ¼ ðqf þ 0:21ðF Air =ð22:41  10 3

þ 0:79ðF Air =ð22:41  10

Compression factor (s)

Pressure Steam temperature Steam flow Feed water pressure Feed water temperature Feed water flow Primary air flow Secondary air flow Flue gas oxygen content Flue gas moisture content Stoker speed

182 395 10 320 5082 6 4 6 75 25 367

_ 0:8 Q t ¼ ac m 2 ðT w  TÞ ½MJ=s

ð44Þ

T ¼ ðT 1 þ T 2 Þ=2 ½ C

_ thd ðwÞÞC N2 Þ=ðnC C CO2 m

þ nS C SO2 þ ðnH2 O þ nH2 ÞC H2 O þ ð3:76 

Measurement

where ac is the convection heat transfer coefficient.

_ thd ðwÞÞC O2 m NgO2

Table 1 The compression factors of the measurements.

þ nN2 ÞC N2



þ 0:21  NExAir C O2 þ 0:79  NExAir C N2 Þ ½ C

ð39Þ

ð45Þ

where T 1 is the steam temperature before the secondary superheater (°C) and T 2 the steam temperature after the secondary superheater (°C).

where the N EAir excess air ðmol=kgÞ. Fuel moisture soft-sensor The fuel moisture soft-sensor assumes that a change in the water evaporation rate affects the enthalpy of the secondary superheater; The effective value of the fuel qgf changes linearly when the water evaporation rate changes [15]. The water evaporation rate w is obtained by minimizing N X ^2 j jh2  h

ð40Þ

i¼0

where N is the prediction horizon, h2 is the specific enthalpy after ^ 2 is the estimated specific the secondary superheater ðMJ=kgÞ, and h enthalpy after the secondary superheater ðMJ=kgÞ. The prediction model for the specific enthalpy after the secondary superheater is

DðDÞi ¼

dh2 1 _ 1 h1  m _ 2 h2 Þ ½MJ=ðs kgÞ ¼ ðQ þ m dt .V t

h

_ 0:65 Q w ¼ aw m fg ððT fg  afo  T fo Þ  T w Þ þ kw ððT fg  afo  T fo Þ

4

ð42Þ

where aw is the convection heat transfer coefficient, afo is the correction coefficient, T fo is the flue gas temperature after the economizer ( C), T w is the temperature of the metal tubes of the secondary superheater (°C), and kw is the radiation heat transfer coefficient. The temperature of the tube walls of the secondary superheater is

ð43Þ

60

50

40

30

0

1000

2000

0

1000

2000

3000

4000

5000

3000

4000

5000

60 50 40 30 20

where mt is the mass of the metal tubes of the secondary superheater (kg), and C p is the specific heat capacity of the metal (MJ=kgK). The heat transfer from the metal tubes of the secondary superheater to the steam in the presence of convection heat transfer is

ð46Þ

2

^ is a reconstructed signal and h is the sampling interval. The where y index i ranges from 2 to N  1, where N is the number of samples. If the reconstructed data is differenced twice, there will be n ¼ N  m

Water evaporation (%)

where . is the specific density of the steam (kg=m ), V is the volume _ 1 is the steam of the steam of the secondary superheater (m3 ), m flow before the secondary superheater (kg=sÞ; h1 is the specific _ 2 is the enthalpy before the secondary superheater (MJ=kg), and m steam flow after the secondary superheater (kg=s). The heat transfer from the flue gas to the metal tubes of the secondary superheater in the presence of mixed convection and radiation heat transfer is

dT w 1 ¼ ðQ  Q t Þ ½K=s mt C p w dt

^iþ1  2y ^i þ y ^i1 y

ð41Þ 3

 T 4w Þ ½MJ=s

The identification of models of the water evaporation, the thermal decomposition of dry fuel, and the drum pressure was conducted using the measurements of the BioPower 5 CHP plant. For the fuel feed, the samples were taken every 5 min from fuel dropping from the fuel silo just before the stoker screw and analyzed manually. The Servomex 2500 FT-IR analyzer was used to measure the water evaporation. The flue gas was extracted from the flue gas duct and led into the analyzer. The samples were taken every second. The compression factors for the measurements of the BioPower 5 CHP plant were detected as follows:

Fuel moisture (%)

min JðwÞ ¼

Test results of system identification of model parameters of BioGrate boiler

Time (s) Fig. 6. The measured (dashed line) and estimated (solid line) water evaporation, and input parameter, the moisture content of fuel feed in the identification. The delay between input and output variables is 20 min.

459

40 30 20

0

500

1000

1500

2000

Fuel moisture (%)

80

60

40

20

0

500

1000

1500

2000

Time (s)

Stoker speed (%)

Primary air (m3/s)

Thermal decomposition of biomass fuel (kg/s)

Fig. 7. The measured (dashed line) and estimated (solid line) water evaporation, and the input parameter, the moisture content of fuel feed in the validation. The delay between input and output variables is 20 min.

Stoker speed (%)

50

Primary air (m /s)

Thermal decomposition of biomass fuel (kg/s)

60

4.4 4.2 4 3.8 3.6 3.4

0

500

1000

1500

2000

0

500

1000

1500

2000

0

500

1000

1500

2000

3

Water evaporation (%)

J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

5.4 5.2 5 4.8 4.6

58 56 54 52 50 48

Fig. 9. The measured (dashed line) and estimated (solid line) thermal decomposition of biomass fuel, and the model input parameters, primary air and stoker speed in the validation.

4 3 2 0

1000

2000

3000

4000

5000

6000

7000

8000

0

1000

2000

3000

4000

5000

6000

7000

8000

0

1000

2000

3000

4000

5000

6000

7000

8000

6 4 2

60 40 20

Fig. 8. The measured (dashed line) and estimated (solid line) thermal decomposition of biomass fuel, and the model input parameters, primary air and stoker speed in the identification.

second differences whose values are zero. Therefore, the compression factor is determined from

CF est ¼

N m

ð47Þ

where m ¼ N  n. The compression factor of the measurements are presented in Table 1. Fig. 6 shows the estimated and measured water evaporation based on the measured data. The model performance is illustrated in Fig. 7. Due to the longer sampling time of 5 min of the fuel feed, the estimated values and the measurements are not exactly the same. Fig. 8 shows the estimated and measured thermal decomposition of fuel. The validation of the identified model was performed on another measurement series. The model performance is presented in Fig. 9. The good performance of the model was due to the constant fuel bed height of grate that affects the thermal decomposition of the fuel. Fig. 10 shows the estimated and measured drum pressure based on the measured data. The validation

Fig. 10. The measured (dashed line) and estimated (solid line) drum pressure, and the model input parameters, combustion power estimation, steam temperature, steam flow, feed water pressure, feed water temperature, and feed water flow in the identification.

0 −1 0

Feed water Feed water temperature (°C) pressure (bar)

1000

1500

49.9

0

50

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30 25

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380 370

4.2

Primary air flow (m3/s)

20

4.1 4 3.9

360

0

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1

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108 107 0

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4 3 2 1

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Fig. 12. Drum pressure reaction to a change in the moisture content of flue flow in the MPC strategy.

6.5 6

2

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2

52

106

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5.6 5.4 5.2

49

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Moisture fuel flow (kg/s)

Steam flow (kg/s)

Steam temperature (°C)

Estimated power (MW)

−2

Pressure (bar)

J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

Pressure (bar)

460

0

500

1000

1500

Fig. 11. The measured (dashed line) and estimated (solid line) drum pressure, and the model input parameters, combustion power estimation, steam temperature, steam flow, feed water pressure, feed water temperature, and feed water flow in the validation.

0:0013 0 6 0 0:0028 6 6 2:44 A¼6 6 0:3900  19:3644 6 0 0 4 0

0

0

0

0

3

7 07 7 07 7; 7 0 1 05 0:0020 0:0020 0 0 1

0 0

ð49Þ of the identified model was performed on another measurement series. The model performance is presented in Fig. 11. The measurement data was compressed. Therefore, the estimated values and the measurements are not exactly the same. The compression factor of the pressure measurement was 3 min as shown in Table 1. However, it was small enough to capture the dynamics for the variable e of the drum model in Eq. (29). The inputs, the primary air flow, the secondary air flow, the flue gas oxygen content, and the flue gas moisture content had the small compression factors of 4, 6, 75, 25 s that were needed to accurately estimate the thermal decomposition of the fuel and the combustion power. Furthermore, the feed water temperature had a large compression factor of 85 min as it does not vary greatly.

2 6 6 6 B¼6 6 6 4

0:0033 0 0 0 0

2

0 6 0:0028 6 6 E¼6 6 0 6 4 0 0

0:0015

3

7 0 7 7 19:3644  0:0015 7 7; 7 0 5 0 0

ð50Þ

3

7 07 7 07 7; 7 15 0

ð51Þ

and Test results of the MPC control strategy of BioGrate boiler

2

The performance of the MPC strategy was compared with the currently used control strategy by using the BioPower 5 CHP plant simulator in a MATLAB simulation environment. The following identified model was used for the simulation:

xkþ1 ¼ Axk þ Buk þ Edk z k ¼ C z xk where

ð48Þ

1 0 0 0 0

3

6 7 C ¼ 40 0 1 0 05

ð52Þ

0 0 0 0 1 The first rows of the matrix A and B describe the thermal decomposition of the dry fuel. However, no delay was detected in the system identification, which might be caused by the fact that the stoker screw actively pushes the dry fuel. The second rows of the matrix A and E describe the water evaporation model. The moisture

461

Pressure (bar)

J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

Pressure (bar)

50.5

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Time (second)

2.5

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3

15

Total air flow (kg/s)

5 4 3 2

2

Time (hour)

0

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350

10 5

0

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1

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400

Fuel flow (kg/s)

Time (second)

1.5 1 0.5

3 2

0

0

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350

Fig. 15. Drum pressure reaction to a change in power demand in the currently used control strategy.

16 14 12 50

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55

400

50 45

Steam power (MW)

Fig. 13. Drum pressure reaction to a change in power demand in the MPC strategy.

55 50 45 40

0

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Superheated

15 10

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Time (hour)

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5

Flue gas oxygen content (%)

0

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Time (hour)

5

0

20

4

Time (hour) Fig. 14. Drum pressure reaction to a change in the moisture content of flue flow in the currently used control strategy.

content is calculated as a percentage from the fuel feed and it is delayed with 1200 time samples. Then it takes 6 min water to evaporate. The integrating disturbance states gk were 0.047 and 0.072, 4.8975 for the model of thermal decomposition of fuel, the pressure model, and the water evaporation model, respectively, and were determined by calculating the variance of the prediction errors in the system identification. The measurement disturbances v k were approximated 1%. Furthermore, the rank of the augmented system was 7. Therefore, the closed-loop system is stable. The input limits were u1;min ¼ 0; u1;max ¼ 5; Du1;min ¼ 0:03, and Du1;max ¼ 0:03 [kg/s] for the stoker speed; u2;min ¼ 0; u2;max ¼ 8; Du2;min ¼ 0:03, and Du2;max ¼ 0:03 [kg/s] for the primary air. The output limits were

Primary air flow (m3/s)

Pressure (bar)

1.5

400

Time (second)

Total air flow (kg/s)

1

18

0

Fuel flow (kg/s)

0.5

Time (hour) Time (second)

Steam power (MW)

4

Pressure (bar)

Dry fuel flow (kg/s)

2

4 3

6 4 2

Fig. 16. Drum pressure, steam power, superheated temperature, flue gas oxygen content, and primary air reactions at the plant start-up in the improved control strategy.

y1;min ¼ 0; y1;max ¼ 1 [m] for the estimated amount of fuel; y2;min ¼ 0; y2;max ¼ 35 [MW] for the combustion power; and y3;min ¼ 0; y3;max ¼ 55 [bar] for the drum pressure. The MPC is tuned 2 3   with 0:01 0 0 0:1 0 0:01 0 5 and S ¼ Qz ¼ 4 0 The fast response 0 0:1 0 0 0:1 is achieved by the combustion power control. However, the inaccu-

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J. Kortela, S-L. Jämsä-Jounela / Electrical Power and Energy Systems 65 (2015) 453–462

Pressure (bar)

55 50

Superheated

Steam power (MW)

45

0

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20 15

The simulation results were used to improve the currently used control strategy of the BioPower 5 CHP plant based on the advanced control. Figs. 16 and 17 show the responses of the improved control strategy and the currently used control strategy in the real plant start-up. The drum pressure of the improved control strategy in Fig. 16 stabilizes much faster when compared with the currently used control strategy. In addition, the variation of the flue gas oxygen content was greatly reduced which improves the efficiency of the boiler.

10 5

450 400 350

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6 4

Conclusions This paper presented a model predictive control (MPC) strategy for BioGrate boiler, compensating the main disturbances caused by variations in fuel quality such as the moisture content of fuel, and variations in fuel flow. The performance of the MPC strategy was tested in a simulation environment. The simulation results showed that the settling time of the drum pressure is 2 min with the MPC strategy, whereas it was 1.5 h with the currently used control strategy. In addition, the settling time with the MPC strategy was mainly limited by the drying rate of the fuel. The control strategy has been implemented by using MPC. However, the same models and principles can be used to implement the strategy by using classical control and some compensation methods. References

2

Fig. 17. Drum pressure, steam power, superheated temperature, flue gas oxygen content, and primary air reactions at the plant start-up in the currently used control strategy.

racies are corrected by the pressure control, and therefore, controlling of the pressure has greater the priority. In the first simulation test, the moisture content of the fuel feed was changed from 55% to 65% while the power demand was 17 MW. With the currently used strategy, the power demand was lowered to 14 MW due to the stabilization issues. The settling time of the drum pressure is only 2 min with the MPC control strategy, whereas it was 1.5 h with the currently used control strategy, as shown in Figs. 12 and 14. In the developed MPC strategy, the amount of dry fuel in the furnace is kept at the needed level and the fast response is achieved by manipulating the primary air. Due to the linearized model Eq. (28), the combustion power could be increased by manipulating only the primary air. Therefore, the change rate of both the fuel flow and primary air have been limited to 0.03 kg/s to realistically simulate the limiting drying rate of fuel. In the second simulation test, the power demand was changed from 12 MW to 17 MW while the moisture content of the fuel weed was 57%. With the currently used strategy, the maximum power demand was lowered to 16 MW due to the stabilization issues. The settling time of the drum pressure is only 2 min with the MPC strategy, whereas it was 1.5 h with the currently used control strategy, as shown in Figs. 13 and 15. The settling time with the MPC strategy was again mainly limited by the drying rate of the fuel.

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