Data-driven Predictive Control of Micro Gas Turbine Combined Cooling Heating and Power system

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Data-driven Predictive Control of Micro Gas Turbine Combined Cooling Data-driven Predictive Control of Micro Gas Turbine Combined Cooling Data-driven Predictive Heating Control and of Micro Gas Turbine Combined Cooling Power system Heating and Power system Heating and Power system Xiao Wu*, Jiong Shen*, Yiguo Li*, Junli Zhang*, Kwang Y. Lee** Xiao Wu*, Jiong Shen*, Yiguo Li*, Junli Zhang*, Kwang Y. Lee** Xiao Wu*, Jiong Shen*, Yiguo Li*, Junli Zhang*, Kwang Y. Lee** 

* Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, Southeast University, Nanjing, * Key Laboratory of Energy Thermal Conversion [email protected]; and Control of Ministry of Education,[email protected]). Southeast University, Nanjing, 210096, China (e-mail: [email protected]; [email protected]; * Key Laboratory of Energy Thermal Conversion [email protected]; and Control of Ministry of Education,[email protected]). Southeast University, Nanjing, 210096, China (e-mail: [email protected]; [email protected]; ** Department of Electrical and Computer Engineering, Baylor University, 210096, China** (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Department of Waco, Electrical and Computer Engineering, Baylor University, One Bear #97356, TX 76798-7356, USA (e-mail: [email protected]) ** Place Department of Waco, Electrical and Computer Engineering, Baylor University, One Bear Place #97356, TX 76798-7356, USA (e-mail: [email protected]) One Bear Place #97356, Waco, TX 76798-7356, USA (e-mail: [email protected]) Abstract: Micro gas turbine-based combined cooling, heating and power (MGT-CCHP) system is in an Abstract: gastoward turbine-based combined cooling, and power (MGT-CCHP) system iswhich in an important Micro direction the development of smartheating buildings and district energy systems, Abstract: Micro gastoward turbine-based combined cooling, heating and power (MGT-CCHP) system iswhich in an important direction the development of smart buildings and district energy systems, provides a direction clean, highly efficient and reliable means of producing energy for multiple use. However, the important toward the development of smart buildings and district energy systems, which provides aMGT-CCHP clean, highlysystem efficient and reliable due means of behavior producingsuch energy for multiple use. However, the control of is a challenge, to its as large thermal inertia, and strong providesofaMGT-CCHP clean, highlysystem efficient reliable due means of behavior producingsuch energy for multiple use. However, the control is For aand challenge, to as large thermal inertia, and strong couplingofamong multi-variables. this reasons, thisits paper develops a data-driven predictive controller control MGT-CCHP system is a challenge, due to its behavior such as large thermal inertia, and strong coupling among multi-variables. this reasons, this paper performance. develops a data-driven predictive for the MGT-CCHP system toFor improve its operating The technique of controller subspace coupling among multi-variables. this reasons, this paper performance. develops a data-driven predictive controller for the MGT-CCHP system toForimprove its operating The data, technique ofcan subspace identification is utilized to construct the predictor directly from the input-output which be used for the MGT-CCHP system to improve its operating performance. The technique of subspace identification is future utilizedbehavior to construct thesystem. predictor directly fromcontroller the input-output data, which can be used to estimate the of the The predictive is then designed to regulate the identification utilizedbehavior to construct thesystem. predictor fromcontroller the input-output data, which can be used to estimate theisMGT-CCHP future of the Thedirectly predictive is then designed to regulate the multi-variable system under the input-constraints. The effectiveness of the proposed control to estimate theMGT-CCHP future behavior of the system. The predictive controller is then designed to regulate the multi-variable system under the results input-constraints. effectiveness of the proposed control approach is demonstrated through simulation on an 80kwThe MGT-CCHP simulator. multi-variable MGT-CCHP system under the input-constraints. The effectiveness of the proposed control approach is demonstrated through simulation results on an 80kw MGT-CCHP simulator. approach demonstrated through simulation results onand an 80kw MGT-CCHP simulator. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keyword s:isMicro gas turbine-based cooling, heating power system, predictive control, data-driven s: Micro gas turbine-based cooling, heating and power system, predictive control, data-driven Keyword predictive control, subspace identification. Keywords: control, Micro gas turbine-based cooling, heating and power system, predictive control, data-driven predictive subspace identification. predictive control, subspace identification.  

 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION Micro gas turbine-based cooling, heating and power (MGTMicro gas turbine-based cooling, heating and power CCHP) system is a promising energy generating unit,(MGTwhich Micro gas turbine-based cooling, heating and power CCHP) system is a promising energy generating unit,(MGTwhich has the ability to provide hot water, absorbing cooling and CCHP) system is aprovide promising energy generating cooling unit, which has the ability to hot water, absorbing and electricity simultaneously. Because the thermal energy stored has the ability to provide Because hot water, absorbing cooling and electricity simultaneously. the thermal energy stored in the exhaust gas of gas turbine can be continually used as electricity simultaneously. Because the thermal energy stored in thesource exhaust gas ofheater gas turbine canthe be energy continually used of as heat of water or chiller, efficiency in the exhaust gas of gas turbine can be continually used as heat source of water heater orsystem chiller,isthe energy efficiency of the integrated MGT-CCHP up to 80% (Colombo, heat source of water heater or chiller, the energy efficiency of the integrated&MGT-CCHP system up to 80% (Colombo, Armanasco, Perego, 2007), and is although the the integrated&MGT-CCHP system ismoreover, up to 80% (Colombo, Armanasco, Perego, 2007), and moreover, although the investment and maintenance cost of MGT-CCHP unit is Armanasco, & Perego, 2007),cost and of moreover, although the investment and maintenance MGT-CCHP unit is higher compared with conventional internal combustion investment and maintenance cost of MGT-CCHP unit is higher compared with conventional internal combustion engine, compared the MGT-CCHP system is much small combustion in size and higher with conventional internal engine, theflexibly MGT-CCHP system in is much small in size and thus can be installed a small residential or engine, theflexibly MGT-CCHP system in is much small in size and thus can be installed a small residential or commercial district. Therefore, for the purpose of energy thus can flexibly installed for in athesmall residential or commercial district.bereduction Therefore, purpose of energy saving, consumption and environmental protection, commercial district. reduction Therefore,and forenvironmental the purpose protection, of energy saving, consumption employing the MGT-CCHP devices has been promoted as the saving, consumption reduction and environmental protection, employing the MGT-CCHP devices has been promoted as primary direction of leading energy developments (Xu et the al., employing the MGT-CCHP devices has been promoted as primary direction of leading energy developments (Xu et the al., 2010, Wu, & Wang, 2006). primary direction of 2006). leading energy developments (Xu et al., 2010, Wu, & Wang, Current studies of the MGT-CCHP unit mainly focus on the 2010, Wu, & Wang, 2006). Currentsystem studiesconfiguration of the MGT-CCHP unit mainly focus on the static and operation optimization, in Currentsystem studiesconfiguration of the MGT-CCHP unit mainly focus on the static and operation optimization, in which, the capital cost, operation profit, energy consumption static system configuration and profit, operation optimization, in which, the capital cost, operation energy consumption and environmental protection indices areenergy taken consumption into account which, the capital cost, operation profit, and environmental protection indices are2009). taken Although into account (Savola, & Fogelholm, 2007, Shin et al., the and environmental protection indices are2009). taken Although into account (Savola, & Fogelholm, 2007, Shin et al., the dynamic characteristics and modeling of MGT-CCHP system (Savola, & Fogelholm, 2007, Shin et al., 2009). Although the dynamic characteristics and modeling of MGT-CCHP system have beencharacteristics studied in theand pastmodeling few years (Anvari et al.,system 2015, dynamic of MGT-CCHP have been studiedthe in the pastapproaches few years (Anvari et al., 2015, Rey al., 2015), control for the MGT-CCHP haveet studiedthe in the pastapproaches few years (Anvari et al., 2015, Rey etbeen al., 2015), control forconventional the MGT-CCHP system are still staying in the stage of PID Rey et al., 2015), the control approaches forconventional the MGT-CCHP system are still staying in the stage of PID control. system are still staying in the stage of conventional PID control. control.

In Yang (2009), PID control loops are designed for an MGTIn Yangunit, (2009), PID control loops designed for is anused MGTCCHP in which the "trial and are error" approach to In Yangunit, (2009), PID control loops are designed for is anused MGTCCHP in which the "trial and error" approach to tune the controller parameters at the given operating point. CCHP unit, in which the "trial and error" approach is used to tune the controller parameters atchanges, the givenstrong operating point. However, when the set-point oscillation tune the controller parameters at the given operating point. However, the set-point changes, oscillation occurs in when the output-variables, which strong may reduce the However, when the set-point changes, strong oscillation occurs in the output-variables, which may reduce the efficiency of the plant and threat the safety of many devices. occurs in ofthe output-variables, which may reduce the efficiency the plant and threat the safety of many devices. As a direct approach to improve the conventional PI/PID efficiency of the plant and threat the safety of many devices. As a direct aapproach to improve the conventional controller, frequency-domain design method PI/PID based As a direct aapproach to improve the conventional PI/PID controller, frequency-domain design method based decoupling PI algorithm is proposed in Zhang (2015), which controller, PI a algorithm frequency-domain design method based decoupling is proposed in Zhang (2015), which can achieve PI smaller overshoots and faster responses. decoupling algorithm is proposed in Zhang (2015), which can achieve smaller overshoots and faster responses. can achievesince smaller overshootsofand responses. However, the dynamics thefaster MGT-CCHP system has However, since the dynamics of the MGT-CCHP system has complex properties such as large thermal inertia, strong However, since the dynamics of the MGT-CCHP system has complex properties such as large thermal inertia, strong coupling among multi-variables and thermal unknowninertia, disturbances, complex properties such as large strong coupling multi-variables unknown disturbances, the PID among approaches which areand devised on the basis of coupling among multi-variables and unknown disturbances, the PID approaches which are devised on the basis of separate single-input, single-output (SISO) loops are no the PID single-input, approaches which are devised on loops the basis of separate single-output (SISO) are no longer sufficient in meeting performance specifications. separate single-input, single-output (SISO) loops are no longer sufficient in meetingareperformance Advanced control techniques called for tospecifications. improve the longer sufficient in meetingareperformance Advanced control techniques called for tospecifications. improve the operation of MGT-CCHP system. Advancedofcontrol techniques are called for to improve the operation MGT-CCHP system. operation MGT-CCHP system. Predictiveofcontrol has been extensively used in the area of Predictive control has been extensively usedhasinshown the area of power generating unit control recently, and to be Predictive control unit has control been extensively usedhasinshown the area of power generating recently, and to be effective in overcoming the problems ofand multi-variable, large power generating unit control recently, has shown to be effective in constrained overcoming system the problems multi-variable, inertia and (Wu etof 2015). Underlarge the effective in constrained overcoming system the problems ofal., multi-variable, large inertia and (Wu et al., 2015). Under the traditional design framework, modeling is the first and inertia and constrained system (Wu et al., 2015). Under the traditional design framework, modeling is the first and foremost step in predictive controller design. Because the traditional design framework, modeling is the first and foremost stepdata in of predictive design. Because the input-output a systemcontroller can be easily acquired during foremost stepdata in of predictive controller design. Because the input-output a system can be easily acquired during the operation,data data-driven models are employed for most of input-output of a system can be easily acquired during the operation, controllers. data-driven However, models arethe employed most of the predictive modelingfor procedure the operation, data-driven models are employed for most of thestill predictive However, the modeling procedure is complexcontrollers. and the modeling mismatch that will greatly the predictive controllers. However, the modeling procedure is still complex and the modeling mismatch that will greatly is still complex and the modeling mismatch that will greatly

Copyright © 2016 IFAC 419 Copyright 419 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016 2016, IFAC IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 419Control. Peer review©under responsibility of International Federation of Automatic 10.1016/j.ifacol.2016.10.769

2016 IFAC CTDSG 420 October 11-13, 2016. Prague, Czech RepublicXiao Wu et al. / IFAC-PapersOnLine 49-27 (2016) 419–424

Hot Water

Waste Gas Cryogen Steam Valve

Air Flow

Combustor

Gas

Exhaust Gas

Recuperator

HighTemp Heater

Regenerative Heat Valve

—

Fuel Flow

Condensor

Fan Cooling Water

Generator

~

Electricity

HighTemp Heat Exchange

Compressor Turbine

———

LowTemp Heat Exchange

Evaporator

Micro Gas Turbine Absorption Refrigerating Machine Fig. 1. Schematic diagram of the MGT-CCHP process.

the high temperature heater for hot water supply and then is chilled in the condenser. After leaving the condenser, the condensed cryogen absorbs the heat from the water in the evaporator for refrigeration and is fed into the high temperature heater for another cycle. Following this way, besides generating the electricity, the MGT-CCHP system is also capable of producing 60℃-80℃ hot water and 7℃12℃ cooling water from the exhaust gas of micro gas turbine.

degrade the control performance is unavoidable. On the other hand, since the models are developed from the data, data itself contains more information than the model developed, which implies that data can be directly used to build the controller. For these reasons, this paper proposes to develop a predictive controller for the MGT-CCHP system directly from the input-output data. The subspace identification (SID) approach is utilized to construct the predictor from the data without developing the plant model (Kadali, Huang, & Rossiter, 2003, Wu et al., 2013, 2014). Therefore, the modeling effort for the conventional model predictive control (MPC) and resulting model mismatches can be avoided.

The model of this MGT-CCHP unit is developed from the lumped parameters modular modeling approach based on the first principles. It is then simplified and used as a simulator validated in the MATLAB environment. The output variables of the system are: power output y1 (kw), cold water temperature y2 ( ℃ ), and hot water temperature y3 ( ℃ ), control inputs into the system are valve actuator positions that control the flow rate of fuel, represented as u1; regenerative heat load, represented as u2; and flow rate of cryogen steam, represented as u3.

The proposed data-driven predictive controller (DDPC) is implemented in an 80kw MGT-CCHP simulator. The remainder of this paper is organized as follows: Section II introduces the MGT-CCHP system and its dynamics. The DDPC is presented in Section III. Simulation results are given in Section IV and conclusions are drawn in Section V.

The behavior of the MGT-CCHP system is complex due to the strong couplings among the multi-variables and the relatively large thermal inertia property of the absorption refrigerating machine, which is demonstrated in Fig. 2 for a step response test when the three inputs are applied sequentially. Therefore, advanced control techniques are needed in place of the conventional PI/PID controllers.

2. SYSTEM DESCRIPTION The MGT-CCHP system under consideration is composed of an 80kw regenerative micro gas turbine and a 425 kw doubleeffect lithium bromide absorption refrigerating machine. The compressed air is preheated in the recuperator with the exhaust gas from gas turbine and then piped into the combustor, where the mixed fuel gas and air is burned, producing flue gas in high pressure and temperature. The flue gas is expanded to drive a micro gas turbine to produce electrical energy and then sent into the absorption refrigerating machine as the heat source of cryogen after heating the compressed air. The cryogen heats the water in

3. DATA-DRIVEN PREDICTIVE CONTROL OF THE MGT-CCHP SYSTEM Consider the objective function: T

T

J  ( yˆ f  r f ) Q f ( yˆ f  r f )   u f R f  u f

420

(1)

2016 IFAC CTDSG October 11-13, 2016. Prague, Czech RepublicXiao Wu et al. / IFAC-PapersOnLine 49-27 (2016) 419–424

Detailed procedure for identifying the subspace matrices Lw and Lu using the SID can be found in the Appendix.

where Q f  Q Tf  0, R f  R Tf  0 are weighting matrices of future

output

rf   r 

T k 1

and

T k 2

input,

T kNy

r

r

 

respectively,

and

Since the subspace matrices Lw and Lu are constructed directly from the input-output data, prediction of the output can be simply achieved by the predictor (2) without further developing the plant model, therefore the remaining modeling procedure for the MPC and resulting model mismatch can be avoided.

T

is

the

desired

output

trajectory. Using wp   y 

the

past

T k  N 1

T k

y ;

output yˆ f   yˆ kT 1

u

data

T

u  , the predictive  T k

To achieve an offset-free tracking performance of the datadriven predictive controller, an integral action can be included by using a difference operator   1  z  1 in the output prediction (2):

T

T yˆ k  N  can be estimated by y 

T yˆ k  2



output-input

T k  N 1

Kadali, Huang, & Rossiter (2003): yˆ f  l w w p  lu u f

following

the

basic

where u f   u kT  1

uk 2

input.

predictor

In

the

T uk  N  u 

T

(2)

idea

(2),

T

of

 yˆ f  l w  w p  lu  u f

(3)

yˆ f  y k   l w  w p   lu  u f

(4)

SID, Thus, we can have:

is the future control

l w  L w (1 : lN y ,:)

421

and

l u  L u (1 : lN y ,1 : m N u ) are prediction matrices in MATLAB

expression (i.e., lw is the first lNy rows of Lw and lu is the first lNy rows and first mNu columns of Lu), where Lw and Lu are matrices constructed through SID, Ny and Nu, Ny ≥ Nu are, respectively, the prediction horizon and the control horizon, m and l, are the dimensions of the output and input, and N is the number of row blocks in the data Hankel matrix wp .

where y k   y kT

Power Output (kw) Cold Water Temperature (℃ )

T

I

I

0  0 .   I

input rate constraint (  u min ,  u max ) can be imposed as:

75

70

Hot Water Temperature (℃ )

T yk  

0

The input magnitude constraint ( u m in , u m ax ) as well as the

80

7.3

7.2

I  I      I I   (u   (u      uk ) )  u u m in k f m ax         I  I 

(5)

I  I      I I   u   u f     u m ax m in         I  I 

(6)

Substituting (4) into the objective function (1), and at every sampling time, by minimizing (1) subject to (5) and (6),  u f can be calculated, and the value of u k 1 can be obtained

7.1

7

and applied to the plant. The minimization of the objective function can be solved efficiently through the computational tools such as quadratic programming (QP).

80

Remark 3.1: As a finite horizon predictive controller, the DDPC proposed in this paper cannot guarantee the stability even for the un-constrained linear time invariant (LTI) system and the stability depends on a good tuning of controller parameters, such as the weighting matrices Qf and Rf and predictive and control horizons Ny and Nu.

79

78 0

T

yk

I  I and      I

500

1000

1500 2000 Time (Second)

2500

3000

3500

However, considering the advantages of the DDPC, it is still a competitive controller for the boiler–turbine unit. How to develop a stable data-driven predictive controller for the MGT-CCHP system will be the future research.

Fig. 2. Step response of the MGT-CCHP system. Three outputs show strong coupling when three inputs (fuel flow, regenerative heat load, and cryogen steam flow valves) are decreased by 10% sequentially at 100, 1300, and 2500 second, respectively.

4. SIMULATION RESULTS 421

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This section demonstrates the data-driven predictive controller design for the MGT-CCHP system using SID. The proposed controller is tested and compared with the regular MPC and conventional PID controller.

separate SISO loops still cannot consider the interactions of the different variables in the system very well. Therefore, it is difficult to attain a desired control for all the output variables.

0

0

Q2

0

0 0

0

0   R1   0 0 ,R   f 0 0    QN   0 y 

0

0

R2

0

0 0

0

0   0  0   RN  u 

Cold Water Temperature (℃ )

Qf

 Q1  0    0  0 

Power Output (kw)

For the proposed predictive controller, the sampling time is set as 2s, and a prediction horizon Ny =40s and control horizon Nu=40s are adopted. The weighting diagonal matrices Q f , R f for all four controllers are given as:

with diagonal blocks: 0 50 0

0  1   0 , Rj  0    0 50 

0 1 0

0  0 ,  1 

in which i=1, 2,..., Ny, j=1,2,...,Nu. The input constraints are u1,2,3,max=1; u1,2,3,min=0 due to the physical limitations of valves. Considering the fast dynamics of the valve, the rate limitations of control input are ignored. The simulation is devised to show the overall performance of the controllers for the load tracking. At t=50s, the set-points of power output, cold water temperature, and hot water temperature are changed from (80kw, 7℃, 80℃) to (70kw, 8℃, 70℃) simultaneously, which reflects the most stressed operation.

RM

1   1

0.05  1 1  s   1  

    0.3  0.05   1 s 

Fuel Flow Valve

   0.5 

Regenerative Heat Load Valve

K

 0.93     2.48

6.5

80

75

70

40

80

120 160 Time (Second)

200

240

280

0.4 0.3 0.2

  5

Cryogen Steam Flow Valve

GT

7

0.5

(2) Decoupling PI controller (Zhang, 2015), with parameters:

K

7.5

Fig. 3. Performance of the MGT-CCHP system: Output Variables (solid red: DDPC; dotted black: decoupling PI; dashed blue: MPC; dotted-dashed green: reference).

(1) Regular MPC with the same parameters (the model is developed using SID with the same input-output data);

  5  0.1   1 s 

70

0

Two other controllers are used for comparison:

0.03  1   0.84  s   7.85   

75

8

Hot Water Temperature (℃ )

 30  Qi  0   0

80

for the gas turbine and refrigerating machine controllers, respectively. The simulation results in Figs. 3 and 4 show that both predictive controllers (DDPC and MPC) have satisfactory control performance, which can track the power output and temperature set-points quickly. For the PI controller, although the frequency-domain based decoupling approach is utilized in the controller design, the

1

0.8

0.6

0.4 0.56

0.52

0.48

0.44 0

422

40

80

120 160 Time (Second)

200

240

280

2016 IFAC CTDSG October 11-13, 2016. Prague, Czech RepublicXiao Wu et al. / IFAC-PapersOnLine 49-27 (2016) 419–424

Fig. 4. Performance of the MGT-CCHP system: Manipulated Variables (solid red: DDPC; dotted black: decoupling PI; dashed blue: MPC).

( y 0 , y1 ,

423

y 2 N  j  2 ) , where N and j are respectively the row

and column

p

block numbers of Y

f

and Y

. We should

choose N larger than the order of the system n , and number of column blocks j should be sufficiently large (typically j  m ax( m N , lN ) ) to reduce noise sensitivity. The input and noise data Hankel matrices, U and E, can be constructed in the similar format.

The two predictive controllers have almost the same performance. However, for the regular MPC, additional computation for model parameter estimation is needed and, because the state variables in the model do not have physical meanings and is thus unmeasurable, additional observer must be designed to estimate the state values.

Assume that the data is generated by an innovation form of the state-space model given by:

The simulation clearly demonstrate the effectiveness of the proposed DDPC which can enhance the operating level of the MGT-CCHP system.

x k 1  A x k  B u k  K e k

(A1)

y k  C xk  D u k  ek

5. CONCLUSIONS where the innovation term e k is assumed to be zero-mean white noise, and we also assume that the system is observable.

As an important direction towards the development of smart buildings and district energy systems, the MPT-CCHP system provides a clean, highly efficient and reliable way to produce heating and cooling and electrical power simultaneously. In order to overcome the control issues of the MPT-CCHP system and improve its operation performance, a data-driven predictive control strategy is proposed in this paper. The technique of SID is utilized to construct the predictor from the input-output data, thus modeling procedure for the conventional model predictive control (MPC) can be avoided. The advantages and effectiveness of the proposed controller design are demonstrated through the simulations of an 80kw MGT-CCHP system.

Then by stacking up the model (A1) with input-output data for a number of steps, these Hankel matrices can be used to develop the following subspace matrix equations (Favoreel et al., 2000; Overschee & Moor , 1995; Qin, 2006):

The authors acknowledge the National Natural Science Foundation of China (NSFC) under Grant 51506029, Grant 51576041 and Grant 51576042, and the Natural Science Foundation of Jiangsu Province, China under Grant BK20150631 and Grant BK20141119 for funding this work.

H Nd

APPENDIX: IDENTIFYING THE SUBSPACE MATRICES The first step of the SID is to build the following data Hankel matrices using the consequent input and output measurements of the system:

Y Y   Y

p f

y j 1 yj yN  j2 y N  j 1 yN  j y2 N  j2

H Ns

      .      

f

Y

p

X

f

 N X

f

 N X

p

 YY

p

D   CB    CAB   C A N 2 B 

f

 H Nd U

p

p

 UU

(C A )

T

0

0 0

CB

D

N 3

B

CA

0

I

0

CK

I

N 3

K

N 1 K  Y  ( A) 

( A)

N 1 B  U  ( A) 

( A)

f

 H Ns E

p

N

 ( A) X

N 4

0

CA

 H Ns E

(C A

D

CA

I   CK    CAK   C A N 2 K 

 H Nd U

CA N 2

N 2

N 1 T

(A3)

p

(A4)

T

)  , 

0  0  0 ,   D 

B

N 4

(A2)

0  0  0,   I 

K

K

AK

K , 

B

AB

B 

in which A  ( A  K C ) , B  ( B  K D ) . The state matrix X are defined as:

Here, the output data Hankel matrices Y is partitioned into the past (upper-half block Y p ) and the future (lower-half block Y

f

where  N   ( C ) T

ACKNOWLEGEMENT

y0 y1   y1 y2      y N 1 y N   y y N 1   N y y  N 1 N 2   y2 N  y 2 N  1

Y

X X   X

) block matrices and is composed of all the sampled data

423

p f

  x0     x N

x1 x N 1

 . x N  j  1  x j 1

2016 IFAC CTDSG October 11-13, 2016. Prague, Czech RepublicXiao Wu et al. / IFAC-PapersOnLine 49-27 (2016) 419–424 424

Owing

to

the

stability of the Kalman filter, ( A )  ( A  K C )  0 as N   ; thus for a large N , (A4) converges to: N

f

X

 LN W

p

(A5)

where subspace matrices L N and past data matrices W defined as: L N    Y W

p

p T   (Y ) 

Colombo, L. P. M., Armanasco, F., & Perego, O. (2007). Experimentation on a co-generative system based on a micro turbine. Applied Thermal Engineering, 27(4), 705711. Favoreel, W., Moor, B.D., & Overschee, P.V. (2000), Subspace state space system identification for industrial processes. Journal of Process Control, 10(2-3), 149–155. Kadali, R., Huang, B., & Rossiter A. (2003). A data driven subspace approach to predictive controller design. Control Engineering Practice, 11, 261-278. Liu, X. J., & Kong, X. B. (2013). Nonlinear fuzzy model predictive iterative learning control for drum-type boiler–turbine system. Journal of process control, 23(8), 1023-1040. Moon, U., & Lee, K. Y. (2009). Step-response model development for dynamic matrix control of a drumtype boiler–turbine system. IEEE Trans. on Energy Conversion, 24(2), 423-430. Overschee, P.V., & Moor, B.D. (1995), A unifying theorem for three subspace system identification algorithms. Automotica, 31(12), 1853–1861. Qin, S. J. (2006). An overview of subspace identification. Computers and Chemical Engineering, 30 (10-12), 1502–1513. Rey, G., Ulloa, C., Cacabelos A., & Barragáns B. (2015). Performance analysis, model development and validation with experimental data of an ICE-based micro-CCHP system. Applied Thermal Engineering, 76, 233-244. Savola, T., & Fogelholm, C. (2007). MINLP optimization model for increased power production in small-scale CHP plants. Applied Thermal Engineering, 27(4), 89-99. Shin, Y., Seo, J. A., Cho, H. W., Nam, S. C., & Jin, H. J. (2009). Simulation of dynamics and control of a doubleeffect LiBr-H2O absorption chiller. Applied Thermal Engineering, 29(13), 2718-2725. Wu, D. W., & Wang R. Z. (2006). Combined cooling, heating and power: A review. Progress in Energy and Combustion Science, 32, 459-495. Wu, X., Shen, J., Li, Y., & Lee, K. Y. (2013). Data-driven modeling and predictive control for boiler-turbine unit. IEEE Trans. on Energy Conversion, 28(3), 470-481. Wu, X., Shen, J., Li, Y., & Lee, K. Y. (2014). Hierarchical Optimization of Boiler-Turbine Unit Using Fuzzy Stable Model Predictive Control. Control Engineering Practice, 30, 112-123. Wu, X., Shen, J., Li, Y., & Lee, K. Y. (2015). Steam power plant configuration, design and control. WIREs Energy Environ, 4(6), 537-563. Xu, J., Sui, J., Li, B., & Yang M. (2010). Research, development and the prospect of combined cooling, heating, and power systems. Energy, 35(11), 4361-4367. Yang, J. (2009). Integration and performance simulation study of combined cooling heating and power system based on micro turbine. Ph.D. dissertation, Shanghai Jiao Tong University, Shanghai, China. (in Chinese) Zhang, J. (2015). Integrated Optimization and dynamic characteristic research on micro-turbine-based Cooling, Heating and Power System. Ph.D. dissertation, School of Energy and Environment, Southeast University, Nanjing, Jiangsu, China. (in Chinese)

N

p

are

 U  and 

p T (U )  

T

.

Substituting (A5) into (A2), we have: Y

f

 L wW

p

 Lu U

f

 Le E

f

(A6)

with the subspace matrices defined by L w   N L N , L u  H N d and L e  H N s .

With the conditions that (i) u k is uncorrelated with e k , (ii) u k is persistently exciting in the order of 2 N , and (iii) the number of measurements is sufficiently large, i.e., j   , the data Hankel matrices developed can be decomposed by the QR-decomposition as follows : W  U Y 

p f f

  R11      R 21  R   31

0 R 22 R 32

0   Q1  0  Q2 R 33   Q 3 

    

(A7)

By expanding this equation and comparing it with (A6), the subspace matrices L   L w L   R 31 

L u  can be calculated as: 

R R 32   11  R  21

0   R 22 

†

(A8)

where † represents the Moore-Penrose pseudo-inverse. The block matrices are identified as L w  L (:,1 : N ( m  l )) and L u  L (:, N ( m  l )  1 : end )

in

MATLAB

expression,

representing the first N ( m  l ) columns and the remaining columns in L, respectively. Note that (A6) has a potential to be used as a predictor in designing a predictive controller, because the future output is expressed as a function of future input. Furthermore, with the three conditions aforementioned, a predictive expression can be written as: f Yˆ  L wW

p

 Lu U

f

(A9)

REFERENCES Anvari, S., Taghavifar, H., Saray, R. K., Khalilarya, S., & Jafarmadar S. (2015). Implementation of ANN on CCHP system to predict trigeneration performance with consideration of various operative factors. Energy Conversion and Management, 101, 503-514. 424